Photoluminescence control by hyperbolic ... - DTU Orbit

General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

Users may download and print one copy of any publication from the public portal for the purpose of private study or research.

You may not further distribute the material or use it for any profit-making activity or commercial gain

You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Downloaded from orbit.dtu.dk on: Jul 05, 2022

Photoluminescence control by hyperbolic metamaterials and metasurfaces: a review

Beliaev, Leonid Yu; Takayama, Osamu; Melentiev, Pavel N.; V. Lavrinenko, Andrei

Published in:Opto-electronic Advances

Link to article, DOI:10.29026/oea.2021.210031

Publication date:2021

Document VersionPublisher's PDF, also known as Version of record

Link back to DTU Orbit

Citation (APA):Beliaev, L. Y., Takayama, O., Melentiev, P. N., & V. Lavrinenko, A. (2021). Photoluminescence control byhyperbolic metamaterials and metasurfaces: a review. Opto-electronic Advances, 4(8), [210031].https://doi.org/10.29026/oea.2021.210031

https://doi.org/10.29026/oea.2021.210031

https://orbit.dtu.dk/en/publications/711fc701-5675-4e54-a623-f8a0b17a0fcb

https://doi.org/10.29026/oea.2021.210031

DOI: 10.29026/oea.2021.210031

Photoluminescence control by hyperbolicmetamaterials and metasurfaces: a reviewLeonid Yu. Beliaev1, Osamu Takayama1, Pavel N. Melentiev2,3 andAndrei V. Lavrinenko1*

Photoluminescence including fluorescence plays a great role in a wide variety of applications from biomedical sensingand imaging to optoelectronics. Therefore, the enhancement and control of photoluminescence has immense impact onboth fundamental scientific research and aforementioned applications. Among various nanophotonic schemes and nano-structures to enhance the photoluminescence, we focus on a certain type of nanostructures, hyperbolic metamaterials(HMMs). HMMs are highly anisotropic metamaterials, which produce intense localized electric fields. Therefore, HMMsnaturally boost photoluminescence from dye molecules, quantum dots, nitrogen-vacancy centers in diamonds, per-ovskites and transition metal dichalcogenides. We provide an overview of various configurations of HMMs, including met-al-dielectric multilayers, trenches, metallic nanowires, and cavity structures fabricated with the use of noble metals, trans-parent conductive oxides, and refractory metals as plasmonic elements. We also discuss lasing action realized withHMMs.

Keywords: fluorescence; metamaterials; metasurfaces; Purcell effect; nanophotonics; hyperbolic metamaterials

Beliaev LY, Takayama O, Melentiev PN, Lavrinenko AV. Photoluminescence control by hyperbolic metamaterials and metasurfaces:a review. Opto-Electron Adv 4, 210031 (2021).

IntroductionPhotoluminescence (PL), emission of light from materi-als, have been widely used for numerous applicationsranging from imaging of biological specimen to lasers.Light emitters can take various forms in different materi-al, e.g., fluorescent molecules, quantum dots (QDs), ornitrogen-vacancy centers in diamond1 (NVC). The ap-plications include single molecular detection2, bio-sensing3−7 and imaging8−10, where a fluorophore as a la-bel is attached to analyte molecules in order to imagethem or detect their concentration linked with the in-tensity of emitted fluorescence signals. Detectionschemes with fluorescence markers attached to analytesare routinely used in clinical diagnosis. Moreover, for

optoelectronic emitting devices it is desirable to enhancetheir PL emission to improve efficiency of light sources,such as LEDs, lasers, and single-photon sources, since PLis the essential part of their emitting schemes11,12. This isthe main motivation behind many of the recent develop-ments in engineering spontaneous emission using nano-scale structures. Up to present, there have been numer-ous studies to boost PL by plasmonic, e.g. metal, nano-structures3. For instance, a silver thin film on a glass sub-strate supports highly localized electric field by mean of asurface plasmon polariton, which strengthens the fluor-escence signals of the fluorophores by more than 300%13.Plasmonic nanoantennas tightly focus light withinthe structure, and thus are routinely used for the

1DTU Fotonik-Department of Photonics Engineering, Technical University of Denmark, Ørsteds Plads 343, DK-2800 Kgs. Lyngby, Denmark;2Institute of Spectroscopy RAS, Moscow 108840, Russia; 3Higher School of Economics, National Research University, Moscow 101000, Russia.*Correspondence: Lavrinenko AV, E-mail: [email protected]: 5 March 2021; Accepted: 29 May 2021; Published: 25 August 2021

Opto-Electronic Advances

Review2021, Vol. 4, No. 8

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License.To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

© The Author(s) 2021. Published by Institute of Optics and Electronics, Chinese Academy of Sciences.

210031-1

https://doi.org/10.29026/oea.2021.210031

https://doi.org/10.29026/oea.2021.210031

http://creativecommons.org/licenses/by/4.0/.

enhancement of fluorescent signals2,14,15. Interested read-ers may find review articles on plasmonic nanostruc-tures including plasmonic nanoparticles and gratings forfluorescence enhancement elsewhere16,17. Another cur-rent tendency is to localize fields by Mie-resonances inhigh-index dielectric nanostructures, such as multilayerstacks18−20, 1D gratings21−27, 2D photonic crystal struc-tures28, as well as, metasurfaces made of dielectricparticles29−31.

In this review, we focus on the enhancement of PL bya class of metamaterials, named hyperbolic metamateri-als (HMMs), which are also referred to as an indefinitemedia, and hyperbolic metasurfaces (HMSs)32−42. Hyper-bolic materials are known for the extreme anisotropyand unique dispersion bands in the wavevector space (k-space) generated by the principal permittivity tensorcomponents being of opposite signs. These bands takethe shape of a hyperboloid as opposed to spherical or el-lipsoid shapes of dispersion contours of dielectric mater-ials. HMMs feature highly localized bulk waves thatpropagate within the structures which can be used, forexample, for sensing43−45, sub-diffraction imaging46, anddirectional emission of light by quantum emitters47,48.The underlying features used for the control of PL byHMMs are large accepted wavevectors (high-k case),highly localized fields and large optical density of states,leading to enhanced light-matter interactions (increasein the Purcell factor) and control of emissiondirectivity49,50. High-k modes wavevectors values ofHMM can reach infinity for semi-infinitely thick HMMsalthough in reality the numbers are limited by finitethickness of HMM slabs51 and inapplicability of effectivemedia approximation to HMMs52,53. Apart from high-kmodes supported by HMMs, they offer the followingthree unique features indispensable for PL enhancementand control:

A. Broadband hyperbolic region.B. Tunability of hyperbolic region.C. Directionality by highly anisotropic nature of

HMM.Regarding (A) point above, the hyperbolic region is

extremely broad and extends from certain cut-offwavelength and beyond, starting from visiblewavelengths to near-infrared54 or even to mid-infraredwavelengths55, which contrasts with dielectric structureswith Mie resonances and plasmonic nanostructureswhose resonance is usually confined to certain band ofwavelengths. This is the unique feature and clear advant-

age of HMMs in order to enhance whole emission band-width of emitters. The cut-off wavelength of HMM as isstated in the listed advantage (B) can be tailored for de-sired wavelength regions by the design of HMMs, such aschoice of materials, more specifically the permittivity ofmetal and dielectric elements and their volume fraction.Regarding the feature (C), the directionality of emissionon HMM can also be exploited to create directionalemitter in-plane47,48 and out of plane of HMM surfaces56.These (A) to (C) features are combined to make HMMsan attractive platform for enhancement and control ofPL.

Apart from the underlined unique nature of HMMs,we discuss the control of PL in terms of (1) intensity en-hancement, (2) lifetime reduction, (3) spectral region, (4)directivity, and (5) lasing. Different configurations ofHMMs have been studied for the enhancement of photo-luminescence from fluorescence dyes, quantum dots,perovskites and nitrogen-vacancy centers in diamond. Inorder to describe these features, this review is organizedas in the following. We start with introduction of hyper-bolic metamaterials and describe their dispersion inwavevector space, which can be categorized as type I andII hyperbolic regions or HMMs. We also overview eachtype of HMM structures, such as metal-dielectric mul-tilayers, trenches which is the vertical version of metal-dielectric multilayers, and nanowires. These are the ba-sic building blocks of HMMs. Out-coupling of enhancedPL emission from metal-dielectric multilayer type HMMis difficult since emitted light is trapped within HMM.Therefore, often, grating out-couplers are integrated in-to HMM structures and we cover various types of grat-ing out-couplers built on HMMs. As a special case ofHMMs, we show PL enhancement by epsilon-near-zero(ENZ) materials. Finally, we discuss the active HMMswith gain media to compensate the absorptive loss of thestructures. Throughout the article, we confine ourselvesto the light wavelengths ranging from UV to near-in-frared, λ = 290 – 1000 nm.

Hyperbolic metamaterialsIn the case of uniaxial anisotropic medium, a relativepermittivity tensor [ε] is expressed by

[ε] =

( εx 0 00 εy 00 0 εz

), (1)

where εx = εy = εo, and εz = εe, εo and εe are ordinary andextraordinary permittivities, respectively. When εo = εe >0, the medium is an isotropic dielectric, while when

Opto-Electron Adv 4, 210031 (2021) https://doi.org/10.29026/oea.2021.210031

210031-2

εo = εe < 0 – it is an isotropic plasmonic material, for ex-ample metal. A HMM or hyperbolic material is a medi-um when the permittivity components along the prin-ciple axes have opposite signs, namely εoεe < 0, and theiso-frequency surface of extraordinary waves given byequation

(kx2 + ky2)/εo + kz2/εe = ω2/c2 , (2)

becomes a hyperboloid, where kx, ky, kz are thewavevector components, ω is the angular frequency andc is the speed of light in vacuum. There are two types ofhyperboloid as shown in Fig. 1, which are convention-ally classified as: 1) type I HMM: εo > 0 and εe < 0, and 2)type II HMM: εo < 0 and εe > 0.

In the case of type I HMM, the dispersion band formsa two-fold hyperboloid in the wavevector space (k-space)42, as illustrated in Fig 1. Typically, a type I HMMcan be realized by a metallic nanowire structure43,57,while type II HMM - by a metal-dielectric multilayerstack with deeply subwavelength layers44,58,59. Note that inthe case of most of naturally occurring materials, bothordinary (εo) and extraordinary (εe) permittivity com-ponents are of the same sign, resulting in either spheric-al (εo = εe, isotropic materials) or elliptical iso-frequencysurfaces when εo ≠ εe. However, there are some naturalmaterials that exhibit hyperbolic dispersion for certainwavelength ranges35,36.

Materials with hyperbolic iso-frequency contours sup-

port propagation of lightwaves with large wavevectors(high-k waves) and correspondingly short effectivewavelengths. However, for certain directions in the k-space, there are no any wavevectors available, and, there-fore, propagation of light in such direction is prohibited.The high-k lightwaves within HMMs are called bulkplasmon polaritons, BPPs (sometimes also called asvolume plasmon-polaritons), as well as hyperbolic sur-face waves (sometimes referred to as Dyakonov plas-mons) that are supported on the top surface ofHMMs47,48,60. BPPs propagate and are tightly confinedwithin HMM structures55,57,61. Such high-k waves in met-al-dielectric multilayer systems are known to originatefrom the hybridization of short-ranged surface plasmonpolaritons supported in each of the dielectric-metal-dielectric set61,62. Usually, BPPs exhibit highly localizedintense electric fields, which together with a non-reson-ant (broadband) spectral range of their existence, makesthem rather convenient tools for the enhancement of PL.A single emitter as a source of PL can be considered as apoint dipole that emits light in the form of bothpropagating (far-field) and evanescent (near-field)waves. In free space, emitted light transfers into far-fieldpropagating waves, and the emitter relaxes by losing en-ergy. However, in the vicinity of a HMM, the near-fieldcomponents of emitted light are more efficiently coupledto the evanescent (near-field) components of BPPs with

EmissionEmission

EmissionEmission

EmissionEmitter

Emitter

High-k

wave

High-k

wave

High-k

wave

High-k

wave

No wave

propagation

No wave

propagation

No wavevector

No

wavevector

Emitter

Emitter

Emission

z

y

x

εe

OA

εo

εo

y

o < 0, εe > 0a bType l: εo > 0, εe < Type ll: ε

kz

kx

kz

kx

Fig. 1 | Schematic illustration of hyperbolic metamaterials and metasurfaces. (a) Type I hyperbolic metamaterials (εo > 0 and εe < 0) in

metallic nanorod or nanowire configuration and their representative dispersion in the wavevector space (k-space). (b) Type II hyperbolic metama-

terials (εo < 0 and εe > 0) in metal-dielectric multilayer configuration and their dispersion in the wavevector space.


210031-3

wavenumbers higher than those of the far-fieldpropagating waves, creating a new decay mechanism forthe emitter, since the emitted energy is directly sucked bythe BPP modes. This results in the reduced lifetime ofemitters in comparison with the free space situation. Atypically large number of BPP modes supported byHMMs produces an increased photonic density of states(PDOS), leading to a broadband enhancement of thespontaneous emission, referred to as Purcell’seffect49,50,63,64. In order to characterize the PL enhance-ment, either the PL intensity or the emission life time (orboth) measurement as opposed to the reference emittersamples on a glass substrate or on metal films are typic-ally employed.

Metal-dielectric multilayersMetal-dielectric multilayer HMMs have been studiedand realized extensively due to the relative ease of fabric-ation. Their layer thicknesses should be sufficiently smal-ler than the wavelength of light that they can be charac-terized by effective parameters, i.e. effective permittivitytensor. By design of a metamaterial (i.e. choosing mater-ials, thicknesses of each layer, filling fraction), the effect-ive dielectric functions or permittivities can be tuned tohyperbolic iso-frequency surface in the wavelength re-gion of interest (see Fig. 1). So, to characterize the optic-al properties of a HMM, the first step is to find its effect-ive permittivities, and the simplest approach is based onthe effective medium approximation (EMA)38,65,66. In thecase of metal-dielectric multilayers, the effective ordinaryand extraordinary permittivities, εo, εe are expressed by

εo = fm · εm + fd · εd, (3)

εe = (εm · εd)/(fd · εm + fm · εd), (4)

where εm, εd, fm, and fd are the permittivities of the metaland dielectric, and filling factors of metal, and dielectriclayers in the multilayer structure, respectively. The lightemitters placed into the near-field of optical modes sup-ported by HMMs release their energy predominantly viaradiative emission and excitation of plasmonic modesand other non-radiative channels, where usually plas-monic modes dominate as the decay channel.

The first experimental evidence of fluorescence en-hancement was demonstrated on a multilayer HMM thatconsist of 16 stacked layers of gold (Au, 19 nm) and alu-mina (Al2O3, 19 nm) with a 21-nm thick epoxy with dis-persed rhodamine 800 (Rh800)67, where 1.8-fold reduc-tion of the lifetime was reported. The control of spontan-

eous emission with multilayer HMMs with alternatingmetal and dielectric layers was described in ref.68. Severaldifferent samples were fabricated for the sake of compar-ison, such as Ag(25 nm, 11 layers)/PMMA(30 nm, 10layers), Ag(30 nm, 5 layers)/LiF(40 nm, 4 layers), Ag(30nm)/LiF(40 nm) with 8 periods, Ag(20 nm)/MgF2(30nm) with 8 periods. Two types of dyes were exploited forPL study: IR-140 dye, whose emission peak lies at λ ≈ 850nm, as well as rhodamine G6 (R6G). Compared with thereference glass substrate, shortening of the luminescencelife-times was observed for all samples. For the Ag/MgF2,the best result was 1.4-times shortening, for Ag/LiF - 1.5-times, and for Ag/PMMA - 5.7-times.

Apart from Ag layers, Au has been extensively used asthe constituent of multilayer HMM structures. HMMsthat consist of 16 stacked layers of gold (Au) and alu-mina (Al2O3) on a glass substrate with a 21-nm dye thinfilm of epoxy mixed with rhodamine 800 (Rh800) at a100 μM concentration spin coated on top of the spacerlayer were realized for fluorescence enhancement69. Forcomparison purposes, two control samples with singlethick (300 nm) and thin (20 nm) gold layers were alsofabricated. In addition, a reference dye thin film was pre-pared on a bare glass substrate. The dye concentration inthe thin film affects the dye parameters. At high concen-trations, above 100 M, the fluorescence lifetime in dye-epoxy solution is rapidly reduced due to quenching pro-cesses, while at low concentrations the fluorescence life-time is independent of concentration. In thin films ofrhodamine 800 embedded in an epoxy matrix, thequantum yield of the dye gradually increases with de-creasing concentration. In the experiments, a 100 μMconcentration was chosen to avoid concentrationquenching and to obtain better performance with a high-er quantum yield. The PL signal for the 89-nm spacerlayer is about 9.3 times stronger for both the HMM andthe thick gold substrates (compared with the bare glasssubstrate), while the thin gold film provides about 6.4times enhancement.

Enhancement of photoluminescence from colloidalcore-shell QDs of cadmium selenide and zinc sulfide(CdSe/ZnS) in proximity with a multilayer HMM wasdemonstrated54. Quantum dots were placed on top of thestructure, consisting of alternating layers of silver (Ag, 9nm thick) and titanium dioxide (TiO2, 22 nm) as shownin Fig. 2. Time-resolved PL measurements were carriedout on the metamaterial sample, the control sample, andthe glass substrate (Fig. 2(c, d)) at the anticipated


210031-4

transition wavelength (elliptic-to-hyperbolic regime, at621 nm) and on both sides from it (605 and 635 nm).When compared with the control sample, the metama-terial enhanced the spontaneous emission rate by a factorof 3 at the transition wavelength and by a factor of 4.3deeper in the hyperbolic regime (635 nm). The overallreduction in the lifetime of the QDs when comparedwith those on a glass substrate is 11 ns. The lifetime ofthe QDs increases as a function of wavelength on boththe glass substrate and the control sample [Fig. 2(d)].This is due to the size distribution of QDs and the de-pendence of the oscillator strength on energy. Themetamaterial sample exhibits a decrease in the lifetime asa function of wavelength in the hyperbolic regime, whilesuch variation is very small in the elliptical spectral re-gion. The lifetimes of QDs on both structures with 1 and

10 bilayers are almost the same in the elliptical spectralregion, but significantly differ above the criticalwavelength. The large change in the spontaneous emis-sion lifetime of the QDs on the metamaterial comparedwith the glass substrate and 1 bilayer case is explained byexcitation of the high-k BPPs in the metamaterial, as wellas by the nonradiative contribution of the surface plas-mon polariton (SPP) modes at the metamaterialinterface.

Directional PL enhancement of dyes on multilayerHMMs was studied for the sample consisting of 20 al-ternating layers (10 periods) of Au (15 nm thick) andAl2O3 (28 nm thick)70. A dye-dissolved PMMA layer wasdeposited on top of the HMM, separated by an Al2O3

spacer layer of thickness 12 nm from the HMM interface.Coumarin 500 was selected as the organic dye that emit

a b

c

d

CdSe/ZnS QDs

TiO2 spacer layer ~ 10 nm

TiO2 ~ 22 nm

Ag ~ 9 nm

Glass substrate

z

y

x

10

9

8

7

6

5

4

3

2

1

0

−1−2−3

400 450 500

605 610 615 620 625 630 635

550 600 650 700 750 800

ε II, ε ⊥

Wavelength (nm)

Wavelength (nm)

Elliptical

dispersion

Elliptical

dispersion

Hyperbolic

dispersion

Hyperbolic

dispersion

εII

ε⊥

0

5

10

15

20 630620

610

Tim

e (n

s)

Metamaterial

Wavelength (nm)

Control

Counts

Glass

MetamaterialControlGlass

22

20

18

16

14

12

10

8

6

4

2

0

Life

tim

e (

ns)

Fig. 2 | Photoluminescence enhancement by metal-dielectric multilayer HMMs. (a) Schematic illustration of Ag-TiO2 multilayer HMM struc-

tures. (b) The real part of effective ordinary and extraordinary permittivities. (c) Time-resolved photoluminescence from QDs deposited on the

HMM, control sample, and glass substrate at 605, 621, and 635 nm. (d) Lifetime of the QDs as a function of wavelength on the HMM, control

sample, and glass substrate. Figure reproduced with permission from ref.54. American Association for the Advancement of Science (AAAS).


210031-5

light at wavelength 480 nm. The structure showed a 2-fold enhancement of spontaneous emission during time-resolved photoluminescence measurements. A similarexperiment was conducted on Au-Al2O3 multilayerHMMs with 19 nm thick metal and dielectric layers,where 3 times reduction in emission lifetime of nitrogenvacancy centers (NVCs) in nanodiamonds was demon-strated71. The enhancement of single –photon emissionfrom NVCs in nanodiamonds was also observed for aplanar multilayer metamaterial that consisted of CMOS-compatible ceramics: titanium nitride (TiN) and alumin-um scandium nitride (AlxSc1-xN)72. Such structure im-proved the emission properties of a single NVC nanodia-mond placed on top. Lifetime reduction was from 17 nson a reference sample to 4.3 ns on the HMM on average.The Purcell factor corresponded to the value 4.Moreover, it was found that the collected emission powerfor NVCs near the HMM was increased by a factor of 1.8on average, although a quite remarkable enhancement of4.7 was detected in one particular case. A TiN-basedmultilayer HMM with 10 alternating layers (5 periods) ofTiN and SiO2 deposited on a glass substrate was used forthe enhancement of QD emission73. A 20 nm thick SiQDs layer was deposited on the top of the HMM and upto 1.6-times enhanced emission decay rate was observedin respect with identical QDs deposited on silica glass.Up to the 4.4-fold fluorescence enhancement from thenanocomposites made of CdTe QDs monolayers placedbetween layers of gold nanoparticles was demonstrated74.Later on, it was theoretically demonstrated that suchstructures represents itself a hyperbolic metamaterial andthus is able of increasing the radiative decay rate of emis-sion centers placed inside the structures75. Depending onthe geometric parameters, such as thickness of the spacerlayer, the number of quantum dots and nanoparticle lay-ers, effective permittivity tensor of the entire nanocom-posite may become indefinite or hyperbolic. This factleads to the rise in the photonic density of states, in turnresulting in strong enhancement and pronounced polar-ization anisotropy of QDs luminescence. Enhancementof UV emission from semiconductor nanoparticles76 andmultiple quantum wells (MQWs)77,78 deposited onHMMs was also demonstrated.

Upper-excited state emission from molecules is notusually observed owing to strong competition with muchfaster nonradiative relaxation pathways. However, theradiative decay rate can be increased by modifying thePDOS. Zinc tetraphenylporphyrin (ZnTPP) molecules as

emitters embedded in a HMM were shown to enable a18-fold increase in fluorescence intensity from thesecond singlet excited state relative to that from the low-est singlet excited state79. Varying the number of periodsof the HMM stack enables systematical tuning of theZnTPP fluorescence spectrum from red (dominated byemission from lowest singlet excited state) to blue (dom-inated by emission from the second singlet excited state).

Spin-coated organic thin films based on the quinoidaloligothiophene derivative (QQT(CN)4) were demon-strated to exhibit hyperbolic dispersion over a wide spec-tral range from 670 to 920 nm80. To study the influenceof QQT(CN)4 dispersion on the Styryl 9M light-emit-ting dye molecules, blend films containing apolyvinylpyrrolidone (PVP) host doped with dye mo-lecules were deposited on top of three different sub-strates: (1) fused silica (FS), (2) 80 nm thick dielectric-metal HMMs containing 4 Ag/Al2O3 pairs and (3) or-ganic monolithic natural hyperbolic materials based on a60 nm thick QQT(CN)4 film. To gain further insights,polyvinyl alcohol (PVA) layers (spin-coated from water)with thicknesses of 25 and 100 nm were also insertedbetween the three types of substrates and the PVPblends. The photoluminescence exhibited slower dynam-ics at longer wavelengths. The fluorescence decays weredescribed by the sum of two exponential functions. Thepresence of the two fluorescence lifetimes were attrib-uted to the presence of Styryl 9M monomers and higheraggregates in the PVP blends. The Purcell factor wasmeasured to be around 1.3 and 1.4 on top of theQQT(CN)4 and HMM substrates correspondingly.

It is well-known that the effective medium theory ap-plied for characterization of dielectric multilayer systemand HMMs can experience a breakdown, depending onthe thickness of each layer, number of periods, etc.53,81.Recently the optimum number of periods of a multilayerHMM for the enhancement of PL from a quantum emit-ter was theoretically analyzed82. In practical system, thenumber of periods is finite and it is essential to design amultilayer HMM with the optimum number of periodsto enhance PL by achieving the highest PDOS. In thiswork, HMMs consisting of 3, 5, and 8 periods of Au (15nm)/SiO2 (25 nm) pairs with a quantum emitter, placedinside and in near vicinity of the HMM surface werestudied. Modeling confirmed that multilayer HMM slabswith lower number of periods, 3 periods in this study,provide higher total PDOS, giving rise to larger trans-ition rate enhancement. The unit cell thickness can also


210031-6

affect enhancement of quantum dots emission83. Thetotal thickness of Ag/ITO HMMs was kept 320 nm, whilethe unit cell thickness ranges from 20 to 80 nm. Thestudy suggested that the Purcell factor increases as theunit cell thickness decreases, exhibiting the maximumenhancement factor of about 40. Related analysis wasdone in work84, where the number of layers and theirthickness were varied to study changes of the Purcellfactor. The HMM was composed of alternate silver andsilicon layers with a dipolar emitter on top of it. It wasshown that the multilayer structures with a few layers ofsmall thickness outperform those with many layers oflarge thickness in terms of the Purcell effect. Such effectwas attributed to the larger wavevectors and localizationof modes due to the stronger coupling between shortrange SPPs on thinner metal layers.

Unlike conventional planar multilayer HMMs, HMMswith a curved surface demonstrated an efficient out-coupling of nonradiative modes due to the gradual taper-ing of HMMs thickness down to few nm. Such outcoup-ling leads to enhanced spontaneous emission85. High-kplasmonic modes propagate along the curved surfacesare then outcoupled into radiative modes and emitted in-to the far field, realizing a directional light emission withthe maximal fluorescent intensity. Detailed simulationsrevealed a high Purcell factor and a spatial power distri-bution in the curved HMM, which agreed with the ex-perimental result. The HMMs consist of 20 stacked lay-ers (10 periods) of Ag and TiO2 deposited on top of atapered glass capillary. On top of the uppermost Ag lay-er, an extra 10-nm-thick TiO2 spacer was deposited todecrease the dye absorption. The fabricated HMM has agradient in its thickness due to the directional depos-ition. Subsequently, the HMM-capped tapered glass ca-pillary was dipped into the solution of R6G with a con-centration of 100 μM. The PL-intensity distribution in-dicates enhancement of both its directionality and effi-ciency. Such curved HMMs, maintaining excellent prop-erty in the Purcell effect, can achieve an 80-fold maxim-um intensity enhancement for directional emission com-pared with planar HMMs. Another flexible HMM thatcan be folded was realized by Au and polymer (PVA)layers, with water-soluble characteristics86. These transi-ent HMMs devices can be easily washed away, disappear-ing with just few drops of deionized water at room tem-perature. Two samples were made with different fill-frac-tions of Au: 37.31% (marked as the HMM1) and 26.87%(marked as the HMM2), and various dye molecules em-

bedded inside PMMA. The photoluminescence kineticswas measured to explore the spontaneous emission ef-fect. The best enhancement of 5.55 (3.80) times for theHMM1 (HMM2) was achieved for the R6G dyemolecules.

In order to enhance emission to far-field, metallic cyl-inder patch antennas can be integrated with HMM struc-tures87,88. As an example, a 5-layered planar HMM struc-ture consisting of Au and zinc sulfide (ZnS) layers with acylindrical Au patch antenna on the top was modeled87.Silicon carbide (SiC)-based emitters with emission peaksaround 900 nm were placed inside the HMM. For dipoleorientation perpendicular to the interface, the HMM-coupled antenna leads to a spontaneous emission en-hancement with a Purcell factor on the order of 400 at850 nm and 300 at 680 nm. A similar order of enhance-ment was actually reported throughout the broad spec-tral range of 650−1000 nm. Similarly, a cylindrical Agpatch antenna on top of HMM structures with 5, 9, 13,and 17 periods of Ag (24 nm) and TiO2 (30 nm) layerswas optimized for dipole emission at 660 nm88. Aftercharacterization, the best 200-fold emission enhance-ment of CdSeS/ZnS core-shell QDs embedded inside theHMM was achieved for the 5-layered structure. Thistendency of better enhancement by fewer periods ofHMMs confirms conclusions stemmed from the theoret-ical analysis82.

Optical cavities or resonators made of dielectric ma-terials can trap photons and support strong electricfields, however, the smallest size of such cavities is lim-ited to the order of effective wavelengths of light, λ/n,where n is the refractive index of the dielectric. In case ofHMMs with high-k (large mode refractive index) BPPs,the effective wavelength can be small and hence the sizeof cavities made of HMMs can be deeply subwavelength,much smaller than conventional dielectric cavities. Suchconfinement leads to smaller mode volumes and, hence,more intense electric fields in the nanocavities, resultingin the enhancement of the emission rate. An HMMnanocavity was initially demonstrated for 2 to 4 periodsmultilayers HMMs curved into pyramid shape89. Re-cently, HMM resonators were used for the enhancementof emission from a transition metal dichalcogenide (TM-DC) monolayers, WS2, in order to boost light-matter in-teractions with an atomically thin TMDC film as illus-trated in Fig. 390. The authors demonstrated about 30-fold enhancement of the overall photoluminescenceemission intensity from a WS2 monolayer that is placed


210031-7

on top of the HMM resonators. Remarkably, the struc-ture enhances both the excitation (absorption) at 514 nmand radiative decay rate at 620 nm.

Förster resonance energy transfer (FRET) is the non-radiative transfer of excited state energy from one fluoro-phore (donor) to another fluorophore (acceptor) via adipole−dipole coupling process91,92. FRET for donor-ac-ceptor pairs located on top of a HMM was experiment-ally studied for the environments with high local densit-ies of photonic states93. Authors observed strong collect-ive interactions of the dye molecules and surface plas-mon polaritons, which can affect the absorption andemission spectra and, correspondingly, influence the rateof the Förster energy transfer.

Apart from fluorescence dye, quantum dots, andNVCs, nanocrystals of lead halide perovskite, namelyCsPbI3, were used as emitters placed on top of HMMs tostudy the enhancement of the Purcell factor94. The mul-tilayer HMM contained 6 or 8 periods of Ag (25 nm or40 nm) and LiF (35 nm or 40 nm) with CsPbI3 placed ona 10−50 nm thick spacer on top of the HMMs. CsPbI3

nanocrystals with size distribution of 11−16 nm emitslight at around 520 nm when excited by 405 nm laser ra-diation, 3-fold reduction of emission lifetime was ob-

served when the nanocrystals were placed on top of theHMMs. Interestingly, very similar enhancement of radi-ative rate recombination, by almost 3 times, in quasi-2Dperovskite thin films of BA2Cs3MA3Pb7Br2I20 composi-tion deposited on top of gold-alumina HMMs of differ-ent thicknesses (from 2 to 7 periods) was reported95. ThePurcell factor was demonstrated to grow almost linearlywith the number of periods in contrary to ref.75,81. Itmeans that it is necessary to take into account propertiesof active material since it has significant influence onspontaneous emission process. The Purcell factor alsodepends on the pump power. For the pump intensityabout 0.2 pJ, there are no any difference in the rate en-hancement produced by 2- and 7-period HMMs.However, with the increase in pumping to 20 pJ, there isa significant difference in the Purcell factor: 1.62 versus3.1.

Most of multilayer HMMs are fabricated on a rigidplanar substrate which cannot be bent. However, re-cently multilayer HMMs on flexible rollable paper sub-strate have been demonstrated96. The fabricated struc-tures consisted of four periods of Au(25 nm) and PMMApolymer (30 or 40 nm) multilayers deposited on aflexible PDMS intermediate layer and rollable paper

P=380 nm

a b c

d e f

Kx/K0

Kz/K0

20 nm

K

1.0

0.8

0.6

0.4

0.2

500 600 700 800 9000

Arb

.U.

Wavelength (nm)

Scattering (radiative)Absorption

(nonradiative)

KHMM

Fig. 3 | Photoluminescence enhancement by metal-dielectric multilayer HMM cavities. (a) Schematic illustration of the WS2 monolayer on

the HMM cavities. (b) Type I hyperbolic iso-frequency contour of the HMM. (c) Scanning transmission electron microscopy (STEM) image of the

cross section of a WS2 monolayer on a HMM cavity with chemical composition analysis. (d,e) Scanning electron microscopy (SEM) images of

HMM cavities with pseudo colors. (f) Normalized calculated scattering and absorption at cross sections of the HMM cavities with a diameter of

160 nm and a pitch of 380 nm at the bottom. Figure reproduced with permission from ref.90, American Chemical Society.


210031-8

substrate. The structures can be rolled up to thecurvature radius of 1 mm without performance degrada-tion. The emitter is an organic –inorganic perovskitenanocrystal, CH3NH3PBr3, which emits light in the vis-ible wavelengths of 520−550 nm. In the paper, 3.5 timesenhancement of emission intensity was reported. Thisnew type of HMMs was used to demonstrate enhance-ment of stimulated emission, as well as laser action.

Emission of quantum dots can be strongly enhancedvia coupling to aperiodic metal-dielectric multilayers.Two such cases are reported in literature97,98. In bothcases, colloidal CdSe/ZnS quantum dots were placed ontop of aperiodic sequences of metal and dielectric thinfilms. The decay rate of quantum emitters was character-ized by standard lifetime measurements of fluorescence.For comparison characterization was also conductedwith HMM structures composed of Ag and SiO2 layerswith the same metal filling ratio as in the aperiodic stackand thicknesses of 20 nm each. The sample with aperiod-ic structure was based on the use of Fibonacci sequence(FS)97. The fluorescence decay curves showed a biexpo-nential behavior. The contribution of the faster decaycomponents was dependent on the density of QDs, and itwas minimized by reducing their concentration. First,the lifetime of quantum dots near the uniform silver filmand HMM samples was checked giving shorter life timefor the latter case. This result indicates that the reduc-tion of lifetime for the HMM is not simply the extinc-tion effect (quenching) due to presence of silver, but re-gards to the presence of high-k modes. Next, the lifetimeon the HMM and FS samples was compared, showingstronger reduction of lifetime by the FS sample. Thiscomparison indicates that the combined contribution oflarger PDOS for FS is higher than that of the HMM. Theexperimental results were consistent with simulationsshowing a 1.35 fold Purcell factor enhancement on theFibonacci sequence multilayer than on the HMM and260-nm-thick silver film (control sample) on one partic-ular wavelength.

Another periodic multilayer arranged in a Tue-Morse(TM) sequence (8 layers ABBABAAB, where A and Brepresent Au and SiO2 layers with thicknesses of 20 and80 nm, respectively) was compared with a periodicHMM (4 periods, 8 layers) with the same fillingfraction98. The photoluminescence measurements wereperformed for the QDs on the two multilayer stacks andthe glass substrate at the emission wavelength of 580 nm.The most substantial reduction occurred on the

wavelength 640 nm with quantified lifetime reduction in1.45 and 1.33 times for TM multilayer stacks and period-ic HMMs respectively.

The summary of the following chapter is presented inTable 1. From the table, one can see materials used forboth metal and dielectric layers, emitters, and enhance-ment factors. The metallic layers are mostly made ofeither Ag or Au and a wide variety of materials are usedfor the dielectric layers, such as silica (SiO2), alumina(Al2O3), titania (TiO2), polymers. The number of peri-ods is in the range of 4 to 10. From the data presented inthe table it follows that depending on the structure thefluorescence can be enhance from 1.3 to 200-fold.

Plasmonic trench structuresApart from a conventional configuration of horizontalmetal and dielectric layers, a HMM can be realized withvertically standing layers (Fig. 4). Such deep subwave-length plasmonic gratings can be characterized as hyper-bolic metasurfaces (HMS)99 or so-called trench struc-tures (HMMs)55,100. The HMS exhibits in-plane aniso-tropy, which leads to hyperbolic dispersion and supportsboth directional surface waves and bulk plasmon modespropagating inside of the trenches. An emitter placed onthe surface will show emission in specific directionsonly47,48. Ag-based trenches with semiconductor In-GaAsP quantum walls as emitters embedded in thetrenches were realized as the HMS as shown in Fig. 456.The trench HMS displayed extreme absorption andemission polarization anisotropy. Hyperbolic dispersionwas verified by finite difference time domain (FDTD)simulations and > 350% emission intensity enhance-ment was experimentally observed relative to the baresemiconductor quantum wells.

Recently, a hyperbolic metasurface made of a metal-halide perovskite gain medium infiltrated between Autrenches was realized101. The Au trenches with pitch ofeither 80 nm or 120 nm function as a type-II HMM inthe wavelength range of 740−780 nm were realized.Strong photoluminescence from MAPbI3 perovskitepeaking around 770 nm was observed. Furthermore, thephotoluminescence measurements demonstrated highlyanisotropic emission from the HMSs with strong polariz-ation dependence in both the emission and absorptiondue to the highly anisotropic nature of the trench HMS.Perovskites simultaneously function as PL material andas constituent dielectric, hence, a luminescent hyperbol-ic metasurface could be utilized as a light source with atailorable emission polarization. Using another


210031-9

perovskite material instead of MAPbI3 could allow fortuning of emission wavelengths.

Nanorod and nanowire structuresIn the case of HMMs consisting of metal nanorods ornanowires with diameters and periods sufficiently smal-

ler than that of operating wavelengths, the effective or-dinary and extraordinary permittivities of themetamaterial are expressed by

εo = [(1+ fm) εmεd + (1− fm) εd]/ (1+ fm) εd+ (1− fm) εm , (5)

Table 1 | Summary of photoluminescence enhancement by multilayer HMM structures. Unless noted, emitters are located on the top sur-

face of HMM structures and the works are experimental.

HMM structures and materialsEmitters (emission peak

wavelength)Enhancement factor

References(year)

Au(19 nm)/Al2O3(19 nm), 8 periods Rhodamine 800 (715 nm) 1.8-fold reduction of lifetime ref.67 (2010)Ag(25 nm, 11 layers)/PMMA(30 nm, 10 layers); Ag(30

nm, 5 layers)/LiF(40 nm, 4 layers); Ag(30 nm)/LiF(40 nm)8 periods, and Ag(20 nm)/MgF2(30 nm) 8 periods

IR-140 dye (850 nm) 1.4 for Ag/LiF; 5.7 for Ag/PMMA ref.68 (2011)

Au(19 nm)/Al2O3(19 nm), 8 periods Rhodamine 800 (720 nm) 9.3 ref.69 (2012)

Ag(9 nm)/TiO2(22 nm), 10 periods CdSe/ZnS colloidal QDs (630 nm) 3 ref.54 (2012)

Au(15 nm)/Al2O3(28 nm), 10 periods Coumarin 500 (480 nm) 2 ref.70 (2013)

Au(19 nm)/Al2O3(19 nm), 8 periods NVC (637 nm) 2.57 ref.71 (2013)

Au nanoparticles (15 nm)/CdTe QDs (5.5 nm), separatedby dielectric (PDDA/PPS) spacers with varied thickness

(0–10 nm), 2–5 periodsCdTe QDs (590 nm) 4.4

ref.74,75 (2011,2014)

TiN(8.5 nm)/Al0.7Sc0.3N(6.3 nm),10 periods NVC (600–800 nm) 4.7 max Purcell factor ref.72 (2015)

TiN(15 nm)/SiO2(15 nm), 5 periods 20 nm thick Si QDs (720 nm) 1.6 ref.73 (2015)

Ag(25 nm) 7 layers /MgF2(35 nm) 6 layersHITC dye-doped polymeric film

(860 nm)7 ref.78 (2015)

Ag(10 nm)/TiO2(30 nm), 10 periods Rhodamine 6G (R6G, 540–600 nm) 80-fold intensity enhancement ref.85 (2018)

Au(26.87–37.31%)/poly(vinyl alcohol) (PVA), 4 periods R6G dye (540–600 nm) 1.55 for HMM1, 1.18 for HMM2 ref.86 (2018)

Ag(22 nm)/MoO3(10 nm) 6 periods, HMM;Ag(12 nm)/MoO3(20 nm) 6 periods, elliptic

ZnO nanoparticles (395 nm)Lasing threshold 20% less and 6

times emission intensityref.76 (2018)

Al(20 nm)/MgF2(20 nm), 4 periods 15-nm thick AlGaN MQWs (318 nm) 160-fold emission rate ref.77 (2018)

Au(30 nm)/ZnS(30 nm) 5 periods, with cylindrical goldpatch antenna

SiC (900 nm)Purcell factor of 400 at 850 nm.

(Theory)ref.87 (2018)

Ag(25 nm)/PMMA(30 nm), 5 periodsZinc tetraphenylporphyrin (ZnTPP),S1 (580–670 nm), S2 (400–460 nm)

18-fold increase in fluorescenceintensity from S2 state to S1.

ref.79 (2018)

320 nm thick HMM of Ag/ITO with unit cell thickness from20 to 80 nm

CdSe/ZnS QDs (550 nm) 40-fold intensity enhancement ref.83 (2018)

Quinoidal oligothiophene derivativeQQT(CN)4 (60 nm thick), 670 to 920 nm

Styryl9M dye (680–850 nm) 1.3-1.4 Purcell factor ref.80 (2019)

Ag(24 nm)/TiO2(30 nm) 5, 9, 13, and 17 layers withcylindrical Ag antenna

CdSeS/ZnS QDs (660 nm)200-fold enhancement for 5-layered

HMMref.88 (2020)

Au(15 nm)/SiO2(25 nm) 3, 5, and 8 periods Emitter (600–1600 nm) 60–85 (Theory) ref.82 (2020)

Ag(16 nm)/Al2O3(24 nm), 3 periods WS2 monolayer (615 nm)30-fold enhancement of the overall

PL intensityref.90 (2020)

Ag(25 nm)/LiF(35 nm) and Ag(40 nm)/LiF(40 nm), 6 or 8periods

CsPbI3 Perovskite nanocrystals(520 nm)

3-fold Purcell enhancement ref.94 (2020)

Au(10 nm)/ Al2O3(10 nm), 2–7 periodsBA2Cs3MA3Pb7Br2I20 Perovskite

film (700 nm)1.6-3-fold Purcell enhancementdepending on number of periods

ref.95(2021)

Ag(25 nm)/PMMA(40 nm) and Ag(25 nm)/PMMA(30 nm),4 periods on paper

MAPbBr3 perovskite nanocrystals(520–550 nm)

3.5-fold intensity enhancement ref.96 (2021)

Aperiodic Ag (20 nm, 6 layers)/SiO2(20 nm, 6 layers) inFibonacci sequence

Colloidal CdSe/ZnS QDs (640 nm)1.6 than Ag layer, 1.35 than

periodic materialref.97 (2014)

Aperiodic Ag(20 nm, 8 layers)/SiO2(80 nm, 8 layers) inTue-Morse (TM) sequence

Colloidal CdSe/ZnS QDs (640 nm) 1.45 than glass substrate ref.98 (2019)


210031-10

εe = fm · εm + fd · εd , (6)

where εm, εd and fm, fd are the permittivities and volumefractions of metal nanowires and dielectric matrix, re-spectively.

One of the earliest works on PL enhancement by aHMM was conducted with an array of Ag nanowires inAl2O3 matrix102, where Ag nanowires with 35 nm dia-meter occupied 15% of volume fraction. The emitter wasIR-140 laser dye with the maximum radiation at 892 nm.Dye was dispersed in an 80 nm thick PMMA film depos-ited on the nanowire HMM structure. A 6-fold reduc-tion of the emission lifetime of the dye was reported.Later, an array of gold nanorods or nanowires with type Ihyperbolic dispersion for bulk plasmon modes thatpropagate inside the metamaterial was used for enhance-ment of fluorescence, as shown in Fig. 5103. The structureconsisted of Au nanorods with dimensions: approxim-ately 38 nm diameter, 150 nm height, and approximately80 nm pitch. Almost 50-fold reduction of the fluores-cence lifetime for the emitters placed inside the HMMwas observed in comparison with a 2-3-fold reductionfor emitters placed on top of the metamaterial. This workdemonstrated that the BPP modes play a significant rolein determining the spontaneous emission propertieswithin plasmonic nanorod HMMs. The spectrum andlifetime of the emission can be controlled separately forTM and TE polarizations by coupling to different BPPssupported in the metamaterial slab. Similar spontaneousradiation of an emitter inside nanorod-based metamater-ials was studied by the same group104. It was not possibleto accomplish direct measurement of the specific life-

time reduction. A broadband macroscopically averagedlifetime measurements were conducted instead. The av-eraged lifetime reduction over the sample was of the or-der of 30, showing that the real numbers are orders ofmagnitude higher. Furthermore, the Au nanorod array isemployed to increase the FRET rate for donor-acceptorpairs separated by fixed distances (3.4, 6.8, and 10.2 nm)embedded inside the HMM structure105. It was shownthat donor-acceptor pairs placed inside the gold nanor-od-based metamaterial exhibited a 12-fold increase ofthe PDOS and a 13-fold increase of the FRET rate com-pared to those located on bare glass.

Another approach to fabricate nanorod based HMMswas realized with using ion-etching of electrochemicallygrown Au nanorods, which provides closely packedstructures with well-defined and smooth nanocones(cone base 40−60 nm, cone apex 2 nm, nanocone dens-ity 1010 cm−2)106. For the nanorod and nanopencil (nanor-od with tapered end) metamaterials, the strongest fieldenhancement occurs at the wavelength of 596 nm withthe corresponding intensity enhanced by a factor of ap-proximately 40 and 60, respectively. For the nanoconemetamaterials, this occurs at 660 nm with a 105-fold in-tensity enhancement. For both nanopencil and nano-cone metamaterials, the maximum field enhancement isobserved at the apex.

In the specific case of phosphorescence, which is asecond-order quantum process, emitters typically exhib-it lifetimes in the range of milliseconds to seconds, or-ders of magnitude longer than the common nanosecondlifetimes of fluorescent dyes. This comes from the

a

b

c⊥

KB

ll

100 nm

100 nm

Ag

Pump Emission

QWAg

InGaAsP

QWs

εll

k⊥, ε⊥

ε⊥

kll, εll

pTE⊥

TMpll

TMEll

KB

TMEll

Fig. 4 | Photoluminescence enhancement on trench hyperbolic metasurface. (a,b) SEM images of InGaAsP MQW trenches of 100 nm

height and 40 nm width, separated by 40 nm trenches. Ag is deposited by sputtering, partially filling the trenches to create a HMS with 80 nm

period. (c) Illustration of optical pumping with different polarizations (TMP‖ or TEP⊥ of the HMS results in collected emission polarized predomin-

antly parallel (TME||) to the metasurface. KB is the Bloch wavevector. Figure reproduced from ref.56, under a Creative Commons Attribution 4.0

International License.


210031-11

forbidden nature of the transitions involved in the emis-sion process, including transitions between states of dif-ferent spin multiplicities such as singlet−triplet trans-itions. The decay rate enhancement of a singlet−triplettransition was investigated for a long lifetime phosphor-escent ruthenium-based complex (Ru(dpp)) inside agold-nanorod-based hyperbolic metamaterial107. Typic-ally, the decay rate enhancement in fluorescence pro-cesses follows theoretical predictions by the PDOS the-ory. However, in the case of singlet–triplet transitions thestrong local gradients of the electro-magnetic field in theplasmonic nanostructures need to be taken into account.For example, a 2750-fold decay rate enhancement

demonstrated in this publication cannot be explainedonly by the standard PDOS approach.

The summary of plasmonic nanowire-based HMMstructures is given in Table 2. It has been demonstratedthat these structures can be used to enhance photolumin-escence by more than 30 times. Nanowires are made ofeither gold or silver with diameters of 38 to 60 nm,periods of 100 to 250 nm, and heights of 150 nm to 250nm. The enhancement factors range from 40 to 105. Inaddition, nanorods HMMs improve the FRET effective-ness and allow forbidden transitions such as asinglet–triplet transitions in a long lifetime phosphores-cent ruthenium-based complex.

1.9

1.8

1.7

1.6

7 9 11 13 15

En

erg

y (

eV

)

Kx (μm−1)

Emission

a b

Fig. 5 | Plasmonic nanowire-based HMMs. (a) An array of Au nanorods with approximately 38 nm diameter, 150 nm height and 80 nm spacing

embedded in a dye-doped PMMA matrix. (b) Emission in waveguided modes. Experimental dispersions of the photoluminescence (PL) enhance-

ment measured for TM-polarized emission whose position reproduced from the reflection dispersion is shown as shaded area. Gray dotted line is

the light line in air, bulk greyed region is the emission band of LD700 dye. Figure reproduced with permission from: ref.103, American Chemical Society.

Table 2 | Summary of photoluminescence enhancement by plasmonic nanowire HMM structures. Unless noted, emitters are located on

the top surface of HMM structures and the works are experimental.



References(year)

Ag nanowires, 35 nm diameter, 15% volume fraction in Al2O3

hostIR-140 laser dye (892 nm) 6-fold reduction of lifetime ref.102 (2010)

Au nanorods, 38 nm diameter, 150 nm height, and 80 nm pitch. LD700 dye (700 nm) 50 ref.103 (2017)

Au nanorods, 40 and 25 nm diameter, 250 nm height, andsurface densities of 35% and 14%

PVA embedded with R101 dye(606 nm)

4.6 ref.108 (2017)

Silver nanowire-alumina HMM (filling fractions f=0.15 and 0.2)CdSe QDs of diameters 5 nm and

6.5 nm (580 and 670 nm)2−3 for the f = 0.15 against

f = 0.2ref.109 (2017)

Au nanorod, 50 nm diameter, 100 nm pitch, and 250 nm heightD1 (fluorescein, 514 nm), D2 (Alexa514, 550 nm), D3 (ATTO 550, 575nm) and D4 (ATTO 647N, 670 nm)

30 ref.104 (2017)

Au nanorod, 50 nm diameter, 260 nm height, 100 nm inter-rodspacing

ATTO 550 and ATTO 647N dyes(554 nm)

13 FRET rate ref.105 (2018)

Au nanorod, 50 nm diameter, 250 nm height, 100 nm inter-rodspacing

Ruthnium-based phosphorescentcomplex (Ru(dpp), 620 nm)

2750 (Theory) ref.107 (2019)

Au nanorod (60 nm diameter and 110, 160, and 240 nm lengths),nanocone (cone base ~40–60 nm, cone apex < 2 nm),

nanopenscil (60 nm base diameter and 10 nm at the top)None

40, 60 at 596 nm, and 105 at660 nm of the field

enhancementref.106 (2019)


210031-12

Grating out-coupler on HMMThere are various works on combining a grating on topor inside multilayer and nanowire HMMs. The role ofthe grating is to out-couple photoluminescence en-hanced inside of HMM to far-field since there is a pro-nounced momentum mismatch between the HMMmodes and lightwaves in ambient space, i.e. air super-strate and substrate. A line (1D) grating with pitch Pprovides the parallel wave vector of

Ng = n sinφ−mλ/P (m = 1, 2, 3 · · ·) , (7)

where n is the refractive index of the ambient medium,usually air (n = 1) and φ is the incident angle. When Ng

equals the effective mode index of BPP modes, emissionis straightforwardly out-coupled from the HMMs. Thegratings couplers studied here are 1D line grating, 2Dgratings made of square lattice or hexagonal lattice of airhole arrays, and circular grating, also known as “ bull-seye” gratings.

1D (line) grating out-couplerThe spontaneous emission rate of a dye molecule embed-ded in a polymeric matrix can be greatly enhanced by ananostructured HMM composed of alternating multilay-ers of Ag and Si110. To demonstrate this, four samples(Fig. 6) were used: bulk silver slab, Ag grating, Ag/SiHMM, and Ag/Si HMM with grating. By adjusting thefilling ratio of Ag in HMMs, the Purcell enhancementcan be tuned to achieve better control of emission pro-cesses at desired wavelengths, demonstrating the versatil-ity of plasmonic PDOS engineering in multilayer HMMs.The lifetime of R6G dye molecules on various sampleswas characterized using resolved luminescence time. Asa reference, the lifetime in a methanol solution wasmeasured to be 3.8 ns with a mono-exponential fit. Forthe Ag/Si HMM with 200 nm period grating, the lifetimeis reduced by almost one order of magnitude comparedto the bare silver grating. In total, there is an increase indecay rate by 54 times compared with the dye on a Si

film. The increase in the decay rate is observed in thecase of Ag/Si HMM with grating compared with the sig-nal from the dye in PMMA on the surface of a bulk sil-ver slab or Ag/Si HMM. The decay rate and lumines-cence intensity are growing with shortening the latticeperiod. The lifetime is minimal for the period of 80 nm(in 76 times). A luminescence enhancement coefficientclose to 80-fold was achieved for HMM with a period of80 nm. Shorter lattice periods are better suited to excitehigh-k bulk plasmon modes, what leads to a simultan-eous increase in both the Purcell factor and fluorescenceintensity. For the 1D grating with the period of 200 nm,the averaged 120-fold intensity enhancement and localenhancement up to 1000-fold at some positions was ob-served. Later, in a theoretical work on the systematic op-timization conducted by the same group111, they studiedthe multilayer HMMs that consisted of 10 layers of Agand 11 layers of Si with a period of 20 nm on a glass sub-strate to find optimal material combinations for Purcellenhancement. Large emission intensity with up to 120-fold enhancement was shown by comparing differentgeometry parameters, the emitter distance and theirwavelengths.

To demonstrate the Purcell effect of a pristine and pat-terned HMMs, Fig. 7(a, b), time-resolved photolumines-cence decay measurements of QDs on a Ag-SiO2 mul-tilayer stack and glass substrate (control case) were con-ducted. Characterization of CdSe/ZnS QDs spontaneousemission rate was performed in a broad wavelengthrange from 570 to 680 nm. Such broad band was used toensure probing the Purcell effect of QD emission inelliptical, ENZ, and hyperbolic regions of the multilayermetamaterial nanostructures112. A large PDOS in theENZ and hyperbolic regions results in a higher Purcellfactor and QD emission rate enhancement compared tothe elliptical region. The measured photoluminescencedecay data from QDs on the multilayer at emissionwavelengths of 570 (ENZ region), 600, and 650 nm (hy-perbolic region) show faster decay than that on the glass

a b c d

Ag Ag Ag

R6G/PMMA

Ag/Si HMM

Glass substrate

Fig. 6 | 1D grating out-couplers on multilayer HMMs. Schematic illustration of (a) Ag slab, (b) Ag grating, (c) Ag/Si HMM, and (d) Ag/Si HMM

with grating. R6G fluorescence dye is in PMMA layers. Gratings period is 200 nm.


210031-13

substrate. To further enhance the interactions, the mul-tilayer HMMs was patterned as a grating with a pitch ofP = 300 nm (see Fig. 7(a, b)). Such subwavelength grat-ing provided larger spatial overlap and enabled strongercoupling between QDs inside the grating grooves and thehigh-k BPPs of the multilayer structure. A 6-fold emis-sion rate enhancement by the multilayer grating struc-ture was demonstrated in comparison with the referencecase.

In addition, one-dimensional HMMs lattices were act-ively used for so-called “trapped rainbow” as a storage ofelectromagnetic waves. By changing the parameters ofthe plasmonic grating, trapping could be achieved fordifferent wavelengths in a wide spectral range115,116. Forexample, in the 2014 work of the group F. J. Bartoli, thefabricated series of 1D nanopatterned gratings with dif-ferent groove depths on a 300-nm-thick layer of Ag ex-perimentally shows "trapped rainbow" effect in the500–700-nm region115. This effect is possible due to theaccumulation of modes due to the rapid reduction of theSPP group velocity at specific position along the gratingsurface115. HMMs support high-k modes with largermode refractive index than plasmonic slabs for broader

wavelength region, which propagate slower117 and thetapered HMM lattices or cavities were shown to trapelectromagnetic modes and enhance light absorption formid-infrared wavelengths118.

Square or hexagonal lattice grating out-couplerBy using a square lattice of air holes as a grating coupleron multilayer HMMs, the large spontaneous emissionrate enhancement of an organic dye was demonstrated asillustrated in Fig. 7(c, d)113. The metamaterial contains 12alternating layers of Al2O3 and Ag (6 periods) with 23nm and 12 nm thicknesses, respectively. To investigatethe influence of the designed HMM on spontaneousemission enhancement, a dye doped PMMA layer (thick-ness around 100 nm) was spin coated over a pre-depositedAl2O3 spacer (12 nm) on the HMM structure. Then the2D grating with 500 nm period and 160 nm diameter airholes array was patterned above the dye mixed PMMAlayer over the HMM, followed by the deposition of an Aglayer of thickness 20 nm. The fluorescence time decay inspectral regions with different dispersion, such as ellipt-ical dispersion of the HMM (λ = 420 nm), the criticalwavelength with the epsilon-near-zero regime for

a

c d e f

b

QD/PMMA

PAg substrate

SiO2 Agy

z

x

12 nm83 nm

200 nm 500 nm1 μm

2 μm 10 μm

300 μm

50 nm

y

x

z

r :

52 nm

71 nm

75 nm

80 nm

370 335 305 280 255

aa

a:

Fig. 7 | 1D and 2D grating out-couplers on multilayer HMMs. (a) Schematic illustration and (b) SEM images of HMM with 1D gratings. HMM is

composed of four periods of Ag (12 nm thick) and SiO2 (83 nm) layers on top of 100 nm thick Ag substrate as a reflector. The pitch of grating is P =

300 nm. A thin layer of QDs in PMMA is spin-coated on top of the HMM structures. (c) Schematic of 2D grating in Ag film on HMM with 6 periods

of Ag (12 nm) and Al2O3 (23 nm) layers. (d) SEM image of 2D Ag on top of the PMMA layer with an average period of 500 nm and hole size of

160 nm (top view). (e) Cross-section view of transmission electron microscope (TEM) image of HMM made of Ag (dark color, 15 nm), Al2O3

(bright color, 15 nm), and embedded QD layer (false color). The bottom and top layers are glass substrate (false yellow) and Pt protection (false

violet) layer, respectively (shown in false color). (f) SEM image of the top view of 2D gratings on HMMs with lattice constant of 255−370 nm with

air hole radius of 52−80 nm. Figure reproduced with permission from: (a, b) ref.112, American Chemical Society; (c, d) ref.113, under a Creative

Commons Attribution-NonCommercial- ShareAlike 4.0 International License; (e, f) ref.114, PNAS.


210031-14

ordinary permittivity (λ = 430 nm), and type II hyperbol-ic dispersion (λ = 450 nm) were compared. Four differ-ent samples such as a reference (pink curve), HMM (redcurve), HMM with Ag film on top (black curve) andHMM with a 2D grating (blue curve) were investigatedfor comparison. Among these configurations, a maxim-um of 18-fold decay rate enhancement is obtained for thegrating coupled HMM structures at 510 nm emissionwavelength (in the hyperbolic region), while the life timevalue is larger in the elliptical region.

As a follow-up work to further enhance emission, dyemolecules were not deposited on top of the HMM, butdirectly embedded inside its volume, so that the emitterscan interact more effectively with the BPP modes119. Inorder to compare the decay rate enhancement, threestructures were investigated: a reference sample that is aspin coated DCM dye-dissolved 100 nm thick PMMAlayer on a 5 nm thick SiO2 spacer on a glass substrate, thesame thickness PMMA layer with dye on top of theHMM, and a 15 nm thick PMM layer with dye embed-ded inside the HMM. The dye molecules embedded inthe HMM exhibit about a 35-fold decay rate enhance-ment with respect to those in the reference sample. Inaddition, a 17-fold decay rate enhancement was ob-tained for the dye-dissolved PMMA layer on top of theHMM. This large spontaneous emission rate enhance-ment of the grating coupled HMM is attributed to theout-coupling of non-radiative plasmonic modes, as wellas strong plasmon-exciton coupling in HMM via diffrac-tion grating.

Broadband enhancement of spontaneous emissionfrom two-dimensional semiconductors was demon-strated for molybdenum disulfide (MoS2) and tungstendisulfide (WS2) by placing the monolayers on a multilay-er HMM with a grating coupler in hexagonal arrange-ment120. Great advantage of using 2D materials is that themonolayer can be positioned at a very precise distance tothe substrate to achieve the maximal enhancement effectof the PDOS. The HMM consisted of alternating layersof Al2O3 of about 20 nm thickness and Ag of about 10nm thickness. For each Ag layer, an ultrathin germani-um seed layer (~2 nm) is first deposited that allows thesilver to form optically smooth, high quality films. Pho-toluminescence measurements showed 56 times and 60times intensity enhancement for the WS2 and MoS2, re-spectively, in comparison with the reference sample.

A multilayer HMM with a hexagonal array of built-inair holes was realized in order to extract enhanced emis-

sion from quantum dots embedded in the HMM asshown in Fig. 7(e, f)114. The HMM consists of 7 periodsof Ag and Al2O3 with approximately 15 nm for both lay-ers with 1 nm Ge adhesion layers at each interface of Agand Al2O3. Quantum dots are colloidal CdSe/ZnSparticles embedded inside the fifth from the substrateAl2O3 layer with the emission peak around 630 nm. Thegrating is made of 120−160 nm diameter air holes ar-ranged in a hexagonal lattice with period of 280−300 nm.Twenty times enhanced spontaneous emission rate andone hundred times improved out-coupling efficiency ofemission from quantum dots embedded in the structurewas reported.

Circular (bullseye) grating out-couplerA circular or bullseye grating is composed of concentriccircular gratings with certain periods, so that the out-coupling of optical modes is achieved for every directionin the plane, where the grating is placed. The circulargratings have been employed for efficient out-couplingof enhanced photoluminescence from HMM structurestoo. The multilayer Ag/TiO2 structure with a bullseyegrating on top was theoretically studied121. The grating-HMM configuration exhibited 6-fold far-field Purcellfactor. The spectral location of the out-coupled peak canbe tuned by varying the bullseye grating period.

In another study, bullseye gratings with variouspitches were created on top of a multilayer HMM madeof Al2O3 (20 nm) and Ag (12 nm) layers with a thin (1−2nm) germanium (Ge) adhesion layer between them122.Bullseye gratings with various half-periods, ∆ = 125, 150,170, 200, 250, 265, and 300 nm were patterned onPMMA placed on top of the HMM. In order to enhancespontaneous emission from QDs by high-k BPP modes,QDs were embedded in the middle of HMMs by spin-coating, for instance, in the 3rd period out of 7 periods.The photoluminescence and lifetime of the patternedHMM were measured simultaneously using a confocalmicroscope. Measurements revealed that lifetime of QDsis decreased with increasing number of periods,indicating the presence of high-k modes and their contri-bution to the spontaneous emission enhancement. Ob-served lifetime for QDs located under the bullseye grat-ing (≈ 1.9 ns) was less than lifetime of QDs located awayfrom the bullseye (≈ 2.6 ns).

A bullseye grating on a metal nanowire HMM was alsostudied theoretically123. A dipole emitter is placed on topof the Au nanowire HMM and a Si circular grating


210031-15

out-coupler is placed below the HMM structure. The en-hanced emission is coupled to high-k BPP waveguide inthe HMM slab and emitted to far-field via the bullseyegrating. By optimizing the HMM slab thickness and fillratio of metal nanowires, 18-fold far-field emission en-hancement was predicted.

The summary of grating out-couplers performance isgiven in Table 3.

Epsilon-near-zero (ENZ) materialsAn epsilon-near-zero (ENZ) material is an optical mater-ial whose relative permittivity (dielectric function) be-comes near zero (ε ~ 0) for a certain wavelength range124.Nanostructures, whose effective refractive index ap-proaches the near zero regime are often referred to asnear-zero-index (NZI) materials125. A thin slab of ENZmaterial (thickness < λ/50, one fiftieth of the wavelength)supports a highly localized within-the-slab optical mode,sometimes referred to as an ENZ mode, enabling to con-centrate light energy at nanoscale126,127. Recently, ENZmodes have been observed in a thin film of doped semi-conductor, aluminum nitride (AlN)127 and siliconcarbide (SiC) grating structures128 for mid-infraredwavelengths. Near the ENZ regimes, the hyperbolic (orindefinite) iso-frequency surfaces of HMMs changes itsdispersion shape and allow wavevectors of BPPs up to

infinitely high values (high-k modes regime)129−131. Thus,a high value of the PDOS in the vicinity of the ENZwavelength can occur33,54,113,132,133. Consequently, if afluorophore is placed near the ENZ medium, it experi-ences the enhanced Purcell effect32,33,132,134.

Planar plasmonic multilayers as illustrated in Fig. 8(a,b) were designed to exhibit single ENZ (permittivity be-comes near zero) and double ENZ behavior (both per-mittivity and permeability simultaneously become nearzero)135. The single ENZ structures consist of metal-insu-lator (dielectric)-metal (MIM) layers with 20 nm thickAg layers and 80 nm thick Al2O3 layers. The first ENZcondition, which occurs at shorter wavelengths, is tunedto match the absorbance band of the fluorophore placedon the top of MIM structures with Al2O3 spacer separa-tion. Cesium lead halide perovskite (CsPbBr3) nanocrys-tals are used as a fluorophore that emits in the greenspectral region. The double ENZ structures are com-posed of MIMIM configuration with the same metal anddielectric layers, such that ENZ wavelengths are alsotuned to the emission peak of the fluorophore. The max-imum PL enhancement occurs for a space layer thick-ness of 50 nm [see the inset of Fig. 8(c)]. In order tohighlight the contribution of both ENZ conditions, acomparison between the single ENZ regime in the ab-sorption band of the fluorophore and double ENZ case

Table 3 | Summary of photoluminescence enhancement by grating out-coupler on HMM structures. Unless noted, emitters are located on

the top surface of HMM structures and the works are experimental. Here P is the pitch or lattice constant of the grating out-coupler.



References(year)

1D grating (P=200 nm) on Ag(9 nm)/Si (10 nm), 15 period R6G dye (600 nm) 80 ref.110 (2014)

1D grating (P=300 nm) on Ag(12 nm)/SiO2(83 nm), 4 periodCdSe/ZnS QDs(570–680 nm)

6 ref.112 (2017)

1D grating (P=200 nm) on Ag(10 nm, 10 layer)/Si(10 nm, 11 layers)

Dipole emitters (582 nm) 120 (Theory) ref.111 (2018)

Square lattice grating (P=500 nm) on Ag(12 nm)/Al2O3(23 nm),6 period

Coumarin 500 (510 nm) 18 ref.113 (2014)

Dye molecules embedded grating-coupled HMM (GC-DEHMM)(P=500 nm and hole radius 100 nm) on

Ag(12 nm)/SiO2(5 nm)/dye-dissolved PMMA(15 nm)DCM dye (580 nm)

35 for the GC-DEHMM, 17 GC-DEHMM with respect to the

DEHMMref.119 (2016)

Hypercrystal, hexagonal lattice grating (P=280 nm and holeradius 100 nm) on Ag(20 nm)/Al2O3(20 nm)

MoS2 (660 nm) WS2

(620 nm)56 times enhancement for WS2, 60

times for MoS2ref.120 (2016)

Hypercrystal, hexagonal lattice grating (P=280–300 nm) onAg(15 nm)/Al2O3(15 nm) multilayer, 7 period

CdSe/ZnS QDs (630 nm) 20 times ref.114 (2017)

Bullseye grating (P=400 nm) on multilayer HMM Ag(10 nm)/TiO2(30 nm), 4.5 period

Emitter (800 nm) 6 far-field Purcel factor (Theory) ref.121 (2013)

Bullseye grating (P=250–600 nm) on Ag(12 nm)/Al2O3(20 nm)multilayer

CdSe/ZnS quantum dots(630 nm)

20 ref.122 (2015)

Si bullseye grating (P=600 nm) on Au nanowire (44 nm pitch) inPMMA HMM (100 nm thickness)

Dye (850 nm) 18 (Theory) ref.123 (2019)


210031-16

was presented. In the case of the single ENZ, small in-crease in the emission (by about a factor of 1.5 com-pared with a bare Al2O3 layer) and a slightly reduced de-cay time was observed, while a 4-fold enhancement ofthe emission, accompanied by a significantly shorteneddecay time, was observed for the double ENZ case asshown in Fig. 8(c, d). In addition, double ENZwavelengths for both near zero permittivity and per-meability wavelengths can be tuned within the whole vis-ible range by adjusting the thickness of each singledielectric layer in order to use a wide variety offluorophores.

Active HMMsAs shown above, layered metal-dielectric HMMs sup-port a wide variety of surface and BPP modes with highmodal confinement inside the multilayer. Far-field radi-ation can excite only a subset of these polaritonic modes,typically with a limited energy and momentum range inrespect to the wide set of large wave vectors (high-kmodes) of BPP modes supported by hyperbolic disper-sion media. Localization of light emitters (dye molecules,quantum dots, and nanodiamonds with color centers) inthe HMMs’ bulk makes it possible to excite many BPPmodes directly. The relaxation of the excitation of thesemodes, accompanied by radiation, provides tools for cre-ating light sources with a controlled spectral composi-

tion determined by the resonance properties of theHMMs.

Of particular practical interest is the creation of lightsources characterized by a spectrally narrow emission,since the high spectral brightness realized in suchsources is fundamentally important in molecular spec-troscopy and related sensing with a sensitivity at the levelof single molecules136,137, and future electronics operat-ing at optical frequencies.138,139 However, optical losses inmetals do not allow achieving high-Q resonance proper-ties of existing metamaterials and plasmonic devices.Thus, the characteristic values of the spectral width ofthe corresponding resonances are at the level of 30−50nm in the visible spectral range. Loss compensation(transition from passive to active systems) can overcomethis limitation. The inclusion of gain media offers a path-way to mitigate these losses, and gives rise to the newclass of active HMMs, where light strongly interacts withquantum transitions of the active medium140−142. In act-ive HMMs the simultaneous interaction of light with anabsorption and emission lines of optically pumped gainmedia can take place. The use of stimulated emission andloss compensation are necessary ingredients for achiev-ing the lasing regime and have been known in laser phys-ics since the invention of the first laser. However, the useof small optical cavities significantly complicates the

a

c d

bMIM single εNZ

CsPbBr3 NCs

Ag (20 nm)

Ag (20 nm)

Al2O3 (50 nm) (Spacer)

Al2O3 (80 nm)

CsPbBr3 NCs

Ag (20 nm)

Ag (20 nm)

Ag (20 nm)

Al2O3 (50 nm) (Spacer)

Al2O3 (80 nm)

Al2O3 (80 nm)

MIMIM double εNZ

4550

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

2.50

490 525 560 595 630 665 700 735Wavelength (nm)

PL c

oun

ts (

×10

5)

0

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

10 20 30 40 50 60 70 80

0

100

1000

10000

1010 20 30 40 50 60 70 80

90100

Normalized simulated

El.field (spacer)Normalized experimental PL

Dielectric spacer thickness (nm)MIMIM

MIM

Al2O3

MIMIM

MIM

fit

Time (ns)

Coun

ts

Al2O3

Fig. 8 | Epsilon-near-zero (ENZ) materials. Sketches of the (a) single ENZ (MIM) and (b) double ENZ (MIMIM) structures. A 50 nm thin Al2O3

layer has been deposited on top of each structure as a spacer between the dye (CsPbBr3 nanocrystals) and the Ag layer. (c) Spontaneous emis-

sion and decay times of CsPbBr3 nanocubes deposited on a bare Al2O3 substrate (black), a MIM (red), and a MIMIM (blue) structure 1D grating.

(d) PL enhancement by plasmonic nanostructures. Figure reproduced with permission from ref.135, American Chemical Society.


210031-17

physical picture of lasing. Indeed, to achieve losscompensation for a HMM cavity, it is necessary to have alarge number of emitters in the high-intensity region ofthe respective mode143. However, the small mode volumeof such resonators containing a high number of emittersleads to hybridization of quantum emitters with theHMM cavity-an effect very difficult to achieve inphotonic lasers due to the significantly large dimensionsof such resonators, in comparison with the opticalwavelength144.

Figure 9 shows two typical schemes for creating anactive HMM: with dye molecules located on top of theHMM (Fig. 9(a)) and dye molecules located in eachdielectric layer of the HMM (Fig. 9(b)). The first schemeis simpler in experimental implementation, while thesecond one provides the highest saturation of the BPPmodes volume by dye molecules. The energy levels of thedye molecules that provide gain can be approximated bya four-level model as sketched in Fig. 9(c). Pumping ofthe dye and population inversion involves the excitationof electrons from the fundamental level to the excitedstate (blue arrow in Fig. 9(c)). The electrons relaxthrough fast non-radiative processes (green arrows inFig. 9(c)) and spontaneous and stimulated light emis-sion occurs via the optically active transition from E3 toE4 providing gain (red arrow in Fig. 9(b)). The choice ofthe four-level system for active layer is important to getgreat population inversion (population of E3 energy levelcompared to E4 level) and hence high gain. To obtain aphysical pattern of a system presented in Fig. 9, fullquantum analysis of coupled electronic-vibronic systemis required, involving understanding of the absorption,emission, and plasmon tunings, together with phononand relaxation pathways, while also exploring the effectof the tight plasmonic confinement on the molecular re-laxation. Although there have been some recent progressin developing models145−147, a full theory accounting for

how different phonon subsystem interact with the optic-al cavity is currently missing for purely dielectric cavities,plasmonic cavities formed by nanostructures and forHMMs, as well.

Arrangement of emitters in the field of an optical cav-ity can modify the spontaneous emission rate leading tothe reduced lifetime and altered far-field emission pat-tern150. Two regimes of emitter-optical cavity interac-tions are known: (i) weak-coupling151−153 and (ii) strong-coupling regime154−156. Strong coupling, unlike the weak-coupling regime, relies on the back action between theemitter and metamaterial to create coherent statesbetween light and matter. In the weak coupling regimeconsidered in the previous sections, only a small perturb-ation of the band takes place. In the strong coupling re-gime, both emission and absorption lines produce ex-treme distortions of the plasmonic band due to Rabisplitting and a parity-time (PT) symmetry broken phasewith generation of exceptional points at the loss-gaincompensation frequencies147,149. It is important to pointout that in the strong coupling regime the photonic andexcitonic components of the system cannot be treated asseparate entities, as they form new polaritonic eigen-states (exciton-polaritons) having both light and mattercharacteristics.

To commit optical pumping and light-injection intohyperbolic modes the dye-molecules energy levels shouldmatch BPP bands. HMMs have distinct plasmonicbands, the lower ones providing the propagation of ex-tremely high momentum waves and the upper ones ly-ing partially inside the light cone. The absorption line ofthe dye should fall within the upper bands inside thelight cone, while the emission line should reside in thelower bands. This particular arrangement allows for lightemission into the hyperbolic modes, benefiting simultan-eously from both strong field enhancement and largewavevectors. To describe weak and strong coupling scen-

a b cDye molecules in PMMA

HMM

Z

Y

X

xy

z

h

Dye-infiltrated epoxy

Ag D

1

Optical

pumping

Fast non-radiative

decay

Fast non-radiative

decay

Light emission

E2

E

E3

E4

ћωa ћωe

Fig. 9 | Active HMM structure: (a) dye molecules mixed in PMMA located on top of HMM; (b) dye molecules arranged in dielectric layers of

HMM; (c) energy diagram of a four-level dye molecule, with an absorption (blue) and emission line (red). Figure reproduced with permission from:

(a) ref.148, American Physical Society; (b) ref.149, American Chemical Society.


210031-18

arios in active HMMs, we will follow in the followingdiscussion an analytical approach developed in an art-icle149. A simplified analysis of active HMMs considerscoupling with only one excitonic line (either the emis-sion or absorption line). In this case a semi-classicalmodel for this system can be found from the Maxwell-Bloch equations. The result can be written in the form ofthe coupled oscillator equations for the modal field amp-litude E and the polarization of the respective transition P:

∂t

(E

P/ε0

)= − iΩ±

(E

P/ε0

)=

(−iΩm iAm

iK12 −iΩ12

)(E

P/ε0

), (8)

where Ωm and Ω12 are the complex frequencies of the se-lected optical mode and the excitonic transition (absorp-tion or emission), whose negative imaginary parts are themodal damping rate γm and the linewidth of the trans-ition (γa or γe), respectively. The off-diagonal couplingterms are determined as Am = ΩmΓ/2 and K12 = σ12/ε0,introducing the spatial overlap factor Γ of the plasmonicmode with the dielectric medium, and the cross-sectionσ12 of the excitonic transition under consideration.

Solving for the eigenfrequencies Ω± of the coupled sys-tem (8) defines the mode splitting within the semi-clas-sical coupling model for two oscillators:

Ω± =12(Ωm + Ω12)±

12

√4K12Am + (Ωm − Ω12)

2. (9)

It is important to note that, with all other parametersdetermined, the only remaining parameters to fit are thefrequency of the selected optical mode Ωm, and its spa-tial overlap factor Γ with the gain layers. Both paramet-ers depend only on properties of the passive structureand are independent of the dye characteristics. Thecross-section σ12 is related to the population levels via

σ12 = −μ212

3ℏ(N2 − N1), (10)

where μ12 is the dipole matrix element, N1 and N2 are thedensity of atoms in the ground and excited states, re-spectively. For absorption transitions (where N2 < N1),Eq. (9) describes the usual transition from weak coup-ling to strong coupling, manifesting itself as vacuumRabi splitting within the semi-classical framework. Asthe cross-section becomes negative for emission pro-cesses (N2 > N1), the term 4K12Am in the discriminant ofEq. (9) becomes negative, as well. For sufficiently largecoupling, the sign flips, and the emission line produces asplitting behavior similar to the fork observed in PT -

symmetry breaking scenarios. In the complete case offour-level dyes, coupling occurs simultaneously to bothemission and absorption lines. Each line provides its ownpolarization that interacts with the amplitude of the op-tical mode. This results in a modified coupling model.

It is possible to distinguish two considered regimes (aweak coupling regime characterized by small distortionsof the dispersion, and a strong coupling regime leadingto Rabi splitting of modes) in light reflectance from aHMM sample. Note the weak or strong coupling re-gimes can be realized through the dye molecules – HMMmodes overlapping factor Γ. Figure 10(a) shows the re-flectance map of a finite structure presented at Fig. 9(b)formed by 10-unit cells (a single unit cell is marked bythe orange dashed lines in the figure) via transfer-matrixcalculations, with each reflectance maximum indicating adiscrete plasmonic mode. For a small value of coupling aslight perturbation and smearing of the optical modes isobserved around ωa = 0.313ωp (an indication of a weakcoupling regime) when compared with the passive case.

ℏΩRabi =√2KaAm ℏωp

The dispersion is qualitatively changed in the strongcoupling regime (Fig. 10(b)). In this case anti-crossingsappear, and a gap opens in the reflectance map. This ef-fect is particularly visible for the discrete system ofmodes in finite structures. In the figure, two such modesobtained with the use of the semiclassical model Eq. (9)are marked with the green and magenta curves. FromFig. 10(b) it is obvious that close to the crossing point ofthe optical mode and the excitonic line (ωm = ωa) thefirst term in the square root of Eq. (9) dominates. In thestrong coupling regime the resonance linewidth of theoptical mode and the exciton are smaller than the expec-ted splitting, the square root becomes real and a gapopens. The width of this gap is the Rabi splitting energy

equals about 0.02 . Figure 10(c)shows the dispersion of the polaritons calculated withuse of Eq. (9) (green curves) using parameters of the ex-citonic line (blue dashed curve) and the unperturbed op-tical mode (black dashed curve). Away from the crossing,the polaritons simply follow the two components, withone polariton being dominantly plasmonic (polariton 1)while the other is dominantly excitonic (polariton 2) forsmall wavevector kx (and vice versa for large kx). At thecrossing point the gap opens, and the two polaritonsform a mixed state between the excitonic and plasmonicmodes.

The full system presented by four-level dye moleculesembedded in the dielectric medium of multilayer HMMs


210031-19

with impact of coupling on both absorption andemission was further studied in paper149. It was shownthat introduction of gain in HMMs provides a tool forloss-compensation and opens a convenient route facilit-ating injection of light into hyperbolic modes. At theloss-gain compensation conditions both emission andabsorption lines produce extreme distortions of the plas-monic band due to Rabi splitting and a PT-symmetrybroken phase with generation of exceptional points. Thepresence of exceptional points has significant implica-tions on the group index (along z direction) ng,z, Figure11(a, b, c) show zoom-ins on two exceptional points,providing evidence that ng,z diverges, which is a signa-ture of the existence of exceptional points, connectingwith recent results157,158.

Recent studies show that the equal-frequency surfacemodel suffers to describe the topology of entire bands for

continuous HMMs. Better description can be found withuse of a non-Hermitian Hamiltonian formed from Max-well’s equations. Successful implementation of this ap-proach helped to find two types of three-dimensionalnon-Hermitian triply degenerate points with complexlinear dispersions and topological charges ±2 and 0 in-duced by chiral and gyromagnetic effects, paving the wayfor exploring topological phases in photonic continuaand device implementations of topological HMMs159.The effect of strong coupling on laser emission genera-tion was further studied in many details, including ef-fects of exceptional points and search for lowering downlasing threshold as well as narrowing corresponding ra-diation linewidth160.

Only few experimental works are known in this field.The first observation of strong coupling of emitters withHMM was reported by Indukuri et al109. A monolayer of

cb

0.35

0.30

0.25

0 2 4 6 8 10 0 2 4 6 8 1012

−2 0 2−2 0 2

a

0.35

0.30

0.25

0 2 4 6 8 10 12

−2 0 2

0.25

0.30

0.35

0.40

2

2

1

1

kx/k0 kx/k0 kx/k0

ω/ω

p

ω/ω

p

Re

(ω)/ω

p

Fig. 10 | FDTD simulations and analytical calculations of emitter-HMM coupling in light reflectance: (a) reflectance with an absorption line

in the weak coupling regime, (b) strong coupling regime for the finite structure of HMM Fig. 9(b) (logarithmic scale), (c) real and imaginary parts

of the complex eigenfrequencies Ω± obtained with the model (green curves) in the strong coupling regime. The green and magenta curves are

obtained via semi-classical model for two different modes (Eq. (9)). The blue dashed curve is the excitonic absorption line and black dashed

curve is the unperturbed optical mode. The two polaritons resulting from the coupling of the optical mode with the excitonic line are identified by

numbers 1 and 2 (Ω− and Ω+, respectively). Figure reproduced with permission from ref.149, American Chemical Society.

a

0.34

0.30

0.32

0.28

0.26

0 2 4 6 8 10 1412

−100 0 100

EP4

EP3

EP1

EP5

EP2

b

0.2720

0.2716

0.2718

0.2714

0.2712

0.27109.25 9.26 9.27 9.28 9.29 9.30

−400 0 400 −400 0 400

Re [ng, z] Re [ng, z]

EP1

c

0.29800

0.29790

0.29795

0.29785

0.29780

5.720 5.725 5.730 5.735 5.740

EP3

kx/k0 kx/k0 kx/k0

ω/ω

p

ω/ω

p

Re [ng, z]

ω/ω

p

Fig. 11 | Exceptional points (EP) in the system formed by four-level dye molecules embedded in the dielectric medium of multilayerHMMs: (a) group index in z direction ng,z of the dye infiltrated multilayer, (b) zoom on EP1, (c) zoom on EP3. Orange curves correspond to the

band edges at the Brillouin zone center kzD = 0, magenta curves correspond to the band edges at the Brillouin zone edge kzD = π, and cyan

curves correspond to the gain-loss compensation line where Im(cos(kzD)) = 0. Figure reproduced with permission from: ref.149, American Chemic-

al Society.


210031-20

quantum dots was arranged on top of HMM formed byAg nanowires, Fig. 12(a), with a number of CdSe QDsper HMM unit cell equals about 350. Figure 12(b) showsphotoluminescence spectra of the CdSe QD monolayerfor various polymer spacer layer thickness h. Splitting ofthe photoluminescence peaks are clearly seen at small hvalues only. This splitting corresponds to coupling en-ergy of about 120 meV and fits theoretical expectations.For large h, these peaks disappear due to reduced coup-ling of QDs to HMM modes. Note the ambiguities in thestrong coupling evidence interpretation161. The demon-strated splitting in photoluminescence spectrum was notverified in scattering and can be related to excitation ofdark modes of HMMs leading to a dip in the QDs photo-luminescence, rather than associated with a strong coup-ling regime.

Stimulated emission of surface plasmons on top ofmetamaterials with hyperbolic dispersion as well aslosses compensation were realized in a number of works.The very first experimental verification of stimulatedemission of surface plasmons propagating on top of met-al-dielectric multilayered HMMs coated with opticallypumped dye-doped polymer for the wavelengths around860 nm, as well as loss compensation was reported inref.81. The HMMs were composed of Ag/MgF2 alternat-ing layers. In the realized experimental conditions, thestimulated emission of propagating plasmons on top ofthe metamaterial was enhanced by the nonlocal dielec-tric environment and high local PDOS.

The loss compensation and lasing action in metama-terials based on gold nanorod arrays coated with thinfilms of PVA embedded with R101 dye was demon-strated108. Depending on the chosen parameters (metal

fill ratio), the sample under study can exhibit hyperbolicor elliptic dispersion. With both types of metamaterials,a lasing action was demonstrated with the emission linewidth as narrow as 6 nm when the samples were pumpedabove respective thresholds compared to more than 60nm wide pristine spectrum of dye molecules.

The first successful attempt to demonstrate the integ-ration of the HMM with random laser systems for en-hancing stimulated emission and reducing lasingthreshold was reported in ref.79. The sample design in-cluded ZnO nanoparticles as the active material ar-ranged in a random order on top of HMM samples. Thetwo kinds of Ag/MoO3 multilayers with hyperbolic andelliptic dispersion, respectively, were fabricated. The firstHMM sample exhibiting hyperbolic dispersion con-tained 6 pairs of Ag (22 nm) and MoO3 (10 nm) layerswith the Ag fill-fraction of 68.75%. As for the secondsample with elliptic dispersion, the structure was com-posed of Ag (12 nm) and MoO3 (20 nm) layers with theAg fill-fraction of 37.5%. The random laser action wasrealized with ZnO nanoparticles on 8 nm thick MoO3

deposited as a capping spacer layer to prevent unwantedoxidation and quenching of the emission from ZnO nan-oparticles. The first HMM structure showed about 20%reduction of lasing threshold and about 6 times higheremission intensity. The rough interface between ZnOnanoparticles and the HMM assisted the out-coupling ofthe high-k modes to the far-field rather than letting theemitted light get trapped inside the multilayer structure.The Purcell factor for the HMM sample at thewavelength of 395 nm, which corresponds to the spon-taneous emission of ZnO nanoparticles, is larger thanthat of the second sample with elliptic dispersion. Fur-

a b

CdSe QD monolayer

h

Polymer

Alumina Ag NW

HMM

80

0 n

m

Coupled QD

emission

k

ω

1800 1900 2000 2100 2200 2300 2400 2500

5 nm

10 nm

15 nm

20 nm

45 nm

0

65

130

195

260

Energy (meV)

h

PL inte

nsity

Fig. 12 | Coherent interaction between HMM and multiple emitters leading to strong coupling: (a) schematic diagram of HMM with QDs on

top of the polymer spacer, (b) PL measurement on QD monolayer. The magnitude of the splitting of the various PL peaks are indicated by the

quantity ΔEexp. Figure reproduced with permission from ref.109, The Royal Society of Chemistry.


210031-21

thermore, deep-UV LED on a HMM system wasrealized77. The LED was made with three pairs of AlGaNMQWs with a 318-nm emission wavelength and a 15-nmthick AlGaN cap layer grown on sapphire. The HMMconsisted of four pairs of Al (20 nm) and MgF2 (20 nm)layers deposited on the LED surface. A 160-fold increasein the radiative emission rate and a 3.5-fold increase inthe quantum efficiency were achieved. Moreover, thecapability of metacavity in tailoring the direction of lightemission led to a 520% increase in total emission intens-ity and 148% increase in emission extraction.

In recent paper162, deep-ultraviolet lasing at room tem-perature using a hyperbolic meta-cavity and multiplequantum-well sample was demonstrated. The meta-cav-ity was formed by nanoscale HMM cubes with four pairsof Al and MgF2 alternating layers with 20 nm thicknesseach, dimensions of 200 × 200 nm2, and a spacingbetween cubes of 200 nm. The plasmon resonance modemerges within the cube and provides a resonant radi-ation feedback to the multiple quantum-well as activemedium. The latter consists of AlGaN semiconductorwith a wide bandgap (3.4−6.2 eV) in the UV range. TheHMM high-k modes allow the dipoles with various ori-entations to contribute to radiative emission, achievingenhancement of spontaneous emission rate by a factor of33 and quantum efficiency by a factor of 2.5. Withpumping above a threshold, the sample shows a clearnarrowing of emission line spectral width down to 0.8nm at 289 nm emission wavelength.

This young direction of research is still in a rapid de-velopment. A number of successful results has beenshown, however more research is anticipated in theory aswell as in experiment. Deeper understanding the effect oflight matter strong coupling for the case of HMMs cavit-ies is of high demand, including the Raman scattering aswell as statistics of corresponding emission163. Recentstudies with other types of cavities show possibility of vi-brational strong coupling in Raman scattering164. Get-ting any type of statistics of emitted photons165 suggestsnew areas for HMMs applications.

ConclusionIn this review, we have provided an overview of currentprogress in photoluminescence control on various typesof HMMs and metasurfaces. Highly localized electricfields of high-k bulk plasmon polaritons enable large op-tical density of states and extreme anisotropy. The band-width of the hyperbolic region where high-k modes are

supported is extremely broad for HMM, spreading fromcertain cut-off wavelength and beyond in contrast withMie-resonance based dielectric nanostructures andmetallic nanostructures whose resonance bandwidth isnarrower. By the combination of constituent materialsand structural parameters, HMMs can be designed tocontrol PL in terms of enhancement, emission directiv-ity, and statistics (single-photon emission, classical light,lasing) at any desired wavelength range in visible andnear-infrared wavelength regions. Major building blocksof HMMs are metal-dielectric multilayer and metalnanowire structures that give two different types of hy-perbolic region. Apart from these, more advanced struc-tures with grating out-coupler embedded in HMM andcavity structures made out of HMM have been de-veloped. While fabrication of HMM structures for vis-ible to near-infrared wavelengths have been well-estab-lished, the control of light emission by HMMs can alsobe extended for other wavelength regime since HMMcan be tailored for such longer wavelength region asmid-infrared wavelengths45,55,100,166. Moreover, 2D materi-als with hyperbolic dispersion for certain mid-infraredwavelengths are also shown to support directional high-ksurface waves, including patterned hexagonal boron ni-tride (h-BN)167, α-molybdenum trioxide (α-MoO3)168,169.Moreover, recently numerous natural hyperbolic materi-als have been proposed35−37 and discovered170,171. Espe-cially, some of these natural materials exhibit hyperbolicdispersion from ultraviolet to near-infrared wavelengthswhere demand for PL control is enormous. Althoughtheir hyperbolic regions are fixed to certain bandwidthdefined by materials, they do not require advanced nan-ofabrication technology and therefore such natural ma-terial facilitate the exploitation of hyperbolic dispersion.In this regards, two potential direction can be envisaged:exploration and characterization of such new natural hy-perbolic materials and the demonstration of PL enhance-ment and control, as well as their applications. We be-lieve that HMM-based systems can serve as a robust plat-form for PL controls in vast wavelengths regions, thusleading to numerous applications, from light sources tobioimaging and sensing. Note another important field ofactive HMMs application in the on-chip quantum tech-nologies which is currently underway172.

References Schirhagl R, Chang K, Loretz M, Degen CL. Nitrogen-vacancycenters in diamond: nanoscale sensors for physics and bio-

1.


210031-22

logy. Annu Rev Phys Chem 65, 83–105 (2014). Kinkhabwala A, Yu ZF, Fan SH, Avlasevich Y, Müllen K et al.Large single-molecule fluorescence enhancements producedby a bowtie nanoantenna. Nat Photonics 3, 654–657 (2009).

2.

Bauch M, Toma K, Toma M, Zhang QW, Dostalek J. Plasmon-enhanced fluorescence biosensors: a review. Plasmonics 9,781–799 (2014).

3.

Li JF, Li CY, Aroca RF. Plasmon-enhanced fluorescence spec-troscopy. Chem Soc Rev 46, 3962–3979 (2017).

4.

Jeong Y, Kook YM, Lee K, Koh WG. Metal enhanced fluores-cence (MEF) for biosensors: general approaches and a re-view of recent developments. Biosens Bioelectron 111,102–116 (2018).

5.

Zhang SL, Liu LW, Ren S, Li ZL, Zhao YH et al. Recent ad-vances in nonlinear optics for bio-imaging applications. Opto-Electron Adv 3, 200003 (2020).

6.

Sultangaziyev A, Bukasov R. Review: applications of surface-enhanced fluorescence (SEF) spectroscopy in bio-detectionand biosensing. Sens Bio-Sens Res 30, 100382 (2020).

7.

Joyce C, Fothergill SM, Xie F. Recent advances in gold-basedmetal enhanced fluorescence platforms for diagnosis and ima-ging in the near-infrared. Mater Today Adv 7, 100073 (2020).

8.

Zhang CJ, Zhang CY, Zhang ZL, He T, Mi XH et al. Self-sus-pended rare-earth doped up-conversion luminescent wave-guide: propa-gating and directional radiation. Opto-ElectronAdv 3, 190045 (2020).

9.

Ui Lee Y, Posner C, Zhao JX, Zhang J, Liu ZW. Imaging of cellmorphology changes via metamaterial-assisted photobleach-ing microscopy. Nano Lett 21, 1716–1721 (2021).

10.

Heo M, Cho H, Jung JW, Jeong JR, Park S et al. High-per-formance organic optoelectronic devices enhanced by surfaceplasmon resonance. Adv Mater 23, 5689–5693 (2011).

11.

Kochuveedu ST, Kim DH. Surface plasmon resonance medi-ated photoluminescence properties of nanostructured mul-ticomponent fluorophore systems. Nanoscale 6, 4966–4984(2014).

12.

Chien FC, Lin CY, Abrigo G. Enhancing the blinking fluores-cence of single-molecule localization imaging by using a sur-face-plasmon-polariton-enhanced substrate. Phys ChemChem Phys 20, 27245–27255 (2018).

13.

Curto AG, Volpe G, Taminiau TH, Kreuzer MP, Quidant R etal. Unidirectional emission of a quantum dot coupled to ananoantenna. Science 329, 930–933 (2010).

14.

Taminiau TH, Stefani FD, van Hulst NF. Enhanced directionalexcitation and emission of single emitters by a nano-opticalYagi-Uda antenna. Opt Express 6, 10858–10866 (2008).

15.

Badshah MA, Koh NY, Zia AW, Abbas N, Zahra Z et al. Re-cent developments in plasmonic nanostructures for metal en-hanced fluorescence-based biosensing. Nanomaterials 10,1749 (2020).

16.

Miranda B, Chu KY, Maffettone PL, Shen AQ, Funari R. Metal-enhanced fluorescence immunosensor based on plasmonic ar-rays of gold nanoislands on an etched glass substrate. ACSAppl Nano Mater 3, 10470–10478 (2020).

17.

Stella U, Boarino L, De Leo N, Munzert P, Descrovi E. En-hanced directional light emission assisted by resonant blochsurface waves in circular cavities. ACS Photonics 6,2073–2082 (2019).

18.

Toma K, Descrovi E, Toma M, Ballarini M, Mandracci P et al.Bloch surface wave-enhanced fluorescence biosensor. Bio-

19.

sens Bioelectron 43, 108–114 (2013). Prusakov KA, Bagrov DV, Basmanov DV, Romanov SA, KlinovDV. Fluorescence imaging of cells using long-range electro-magnetic surface waves for excitation. Appl Opt 59,4833–4838 (2020).

20.

Pokhriyal A, Lu M, Huang CS, Schulz S, Cunningham BT. Mul-ticolor fluorescence enhancement from a photonics crystal sur-face. Appl Phys Lett 97, 121108 (2010).

21.

Pokhriyal A, Lu M, Chaudhery V, George S, Cunningham BT.Enhanced fluorescence emission using a photonic crystalcoupled to an optical cavity. Appl Phys Lett 102, 221114(2013).

22.

Pokhriyal A, Lu M, Chaudhery V, Huang CS, Schulz S et al.Photonic crystal enhanced fluorescence using a quartz sub-strate to reduce limits of detection. In CLEO: 2011 - Laser Ap-plications to Photonic Applications CThQ1 (Optical Society ofAmerica, 2011); http://doi.org/10.1364/cleo_si.2011.cthq1.

23.

Chen W, Long KD, Yu H, Tan YF, Choi JS et al. Enhanced livecell imaging via photonic crystal enhanced fluorescence micro-scopy. Analyst 139, 5954–5963 (2014).

24.

Menon SHG, Lal Krishna AS, Raghunathan V. Silicon nitridebased medium contrast gratings for doubly resonant fluores-cence enhancement. IEEE Photonics J 11, 4500711 (2019).

25.

Boonruang S, Srisuai N, Charlermroj R, Makornwattana M,Somboonkaew A et al. Excitation of multi-order guided moderesonance for multiple color fluorescence enhancement. OptLaser Technol 106, 410–416 (2018).

26.

Lin JH, Liou HY, Wang CD, Tseng CY, Lee CT et al. Giant en-hancement of upconversion fluorescence of NaYF4:Yb3+,Tm3+

nanocrystals with resonant waveguide grating substrate. ACSPhotonics 2, 530–536 (2015).

27.

Hoang NV, Pereira A, Nguyen HS, Drouard E, Moine B et al.Giant enhancement of luminescence down-shifting by a doublyresonant rare-earth-doped photonic metastructure. ACSPhotonics 4, 1705–1712 (2017).

28.

Sun S, Wu L, Bai P, Png CE. Fluorescence enhancement invisible light: dielectric or noble metal? Phys Chem Chem Phys18, 19324–19335 (2016).

29.

Bucher T, Vaskin A, Mupparapu R, Löchner FJF; George A etal. Tailoring photoluminescence from MoS2 monolayers bymie-resonant metasurfaces. ACS Photonics 6, 1002–1009(2019).

30.

Lin HJ, de Oliveira Lima K, Gredin P, Mortier M, Billot L et al.Fluorescence enhancement near single TiO2 nanodisks. ApplPhys Lett 111, 251109 (2017).

31.

Cortes CL, Newman W, Molesky S, Jacob Z. Quantum nano-photonics using hyperbolic metamaterials. J Opt 14, 063001(2012).

32.

Shekhar P, Atkinson J, Jacob Z. Hyperbolic metamaterials:fundamentals and applications. Nano Converg 1, 14 (2014).

33.

Takayama O, Lavrinenko AV. Optics with hyperbolic materials[Invited]. J Opt Soc Am B 36, F38–F48 (2019).

34.

Sun JB, Litchinitser NM, Zhou J. Indefinite by nature: from ul-traviolet to terahertz. ACS Photonics 1, 293–303 (2014).

35.

Korzeb K, Gajc M, Pawlak DA. Compendium of natural hyper-bolic materials. Opt Express 23, 25406–25424 (2015).

36.

Narimanov EE, Kildishev AV. Naturally hyperbolic. Nat Photon-ics 9, 214–216 (2015).

37.

Ferrari L, Wu C, Lepage D, Zhang X, Liu ZW. Hyperbolicmetamaterials and their applications. Prog Quantum Electron

38.


210031-23

https://doi.org/10.1146/annurev-physchem-040513-103659

https://doi.org/10.1038/nphoton.2009.187

https://doi.org/10.1007/s11468-013-9660-5

https://doi.org/10.1039/c7cs00169j

https://doi.org/10.1016/j.bios.2018.04.007

https://doi.org/10.29026/oea.2020.200003

https://doi.org/10.29026/oea.2020.200003

https://doi.org/10.1016/j.sbsr.2020.100382

https://doi.org/10.1016/j.mtadv.2020.100073

https://doi.org/10.29026/oea.2020.190045

https://doi.org/10.29026/oea.2020.190045

https://doi.org/10.1021/acs.nanolett.0c04529

https://doi.org/10.1002/adma.201103753

https://doi.org/10.1039/c4nr00241e

https://doi.org/10.1039/c8cp02942c


https://doi.org/10.1126/science.1191922

https://doi.org/10.1364/oe.16.010858

https://doi.org/10.3390/nano10091749

https://doi.org/10.1021/acsanm.0c02388


https://doi.org/10.1021/acsphotonics.9b00570



https://doi.org/10.1364/ao.389120

https://doi.org/10.1063/1.3485672

https://doi.org/10.1063/1.4809513

http://doi.org/10.1364/cleo_si.2011.cthq1

https://doi.org/10.1039/c4an01508h

https://doi.org/10.1109/JPHOT.2019.2909794

https://doi.org/10.1016/j.optlastec.2018.04.029


https://doi.org/10.1021/ph500427k




https://doi.org/10.1039/c6cp03303b


https://doi.org/10.1063/1.4994311

https://doi.org/10.1063/1.4994311

https://doi.org/10.1088/2040-8978/14/6/063001

https://doi.org/10.1186/s40580-014-0014-6

https://doi.org/10.1364/josab.36.000f38

https://doi.org/10.1021/ph4000983

https://doi.org/10.1364/oe.23.025406




https://doi.org/10.1016/j.pquantelec.2014.10.001

https://doi.org/10.1146/annurev-physchem-040513-103659


https://doi.org/10.1007/s11468-013-9660-5

https://doi.org/10.1039/c7cs00169j


https://doi.org/10.29026/oea.2020.200003

https://doi.org/10.29026/oea.2020.200003

https://doi.org/10.1016/j.sbsr.2020.100382

https://doi.org/10.1016/j.mtadv.2020.100073

https://doi.org/10.29026/oea.2020.190045

https://doi.org/10.29026/oea.2020.190045

https://doi.org/10.1021/acs.nanolett.0c04529


https://doi.org/10.1039/c4nr00241e




https://doi.org/10.1364/oe.16.010858

https://doi.org/10.3390/nano10091749






https://doi.org/10.1364/ao.389120

https://doi.org/10.1063/1.3485672

https://doi.org/10.1063/1.4809513

http://doi.org/10.1364/cleo_si.2011.cthq1

https://doi.org/10.1039/c4an01508h

https://doi.org/10.1109/JPHOT.2019.2909794







https://doi.org/10.1039/c6cp03303b


https://doi.org/10.1063/1.4994311

https://doi.org/10.1063/1.4994311

https://doi.org/10.1088/2040-8978/14/6/063001

https://doi.org/10.1186/s40580-014-0014-6

https://doi.org/10.1364/josab.36.000f38

https://doi.org/10.1021/ph4000983

https://doi.org/10.1364/oe.23.025406




https://doi.org/10.1016/j.pquantelec.2014.10.001

40, 1–40 (2015). Lu L, Simpson RE, Valiyaveedu SK. Active hyperbolicmetamaterials: progress, materials and design. J Opt 20,103001 (2018).

39.

Smalley JST, Vallini F, Zhang X, Fainman Y. Dynamically tun-able and active hyperbolic metamaterials. Adv Opt Photonics10, 354–408 (2018).

40.

Adams DC, Inampudi S, Ribaudo T, Slocum D, Vangala S etal. Funneling light through a subwavelength aperture with epsi-lon-near-zero materials. Phys Rev Lett 107, 133901 (2011).

41.

Poddubny A, Iorsh I, Belov P, Kivshar Y. Hyperbolic metama-terials. Nat Photonics 7, 948–957 (2013).

42.

Kabashin AV, Evans P, Pastkovsky S, Hendren W, Wurtz GAet al. Plasmonic nanorod metamaterials for biosensing. NatMater 8, 867–871 (2009).

43.

Sreekanth KV, Alapan Y, Elkabbash M, Ilker E, Hinczewski Met al. Extreme sensitivity biosensing platform based on hyper-bolic metamaterials. Nat Mater 15, 621–627 (2016).

44.

Shkondin E, Repän T, Panah MEA, Lavrinenko AV, TakayamaO. High aspect ratio plasmonic nanotrench structures withlarge active surface area for label-free mid-infrared molecularabsorption sensing. ACS Appl Nano Mater 1, 1212–1218(2018).

45.

Lu D, Liu ZW. Hyperlenses and metalenses for far-field super-resolution imaging. Nat Commun 3, 1205 (2012).

46.

Jacob Z, Narimanov EE. Optical hyperspace for plasmons:dyakonov states in metamaterials. Appl Phys Lett 93, 221109(2008).

47.

Kildishev AV, Boltasseva A, Shalaev VM. Planar photonicswith metasurfaces. Science 339, 1232009 (2013).

48.

Poddubny AN, Belov PA, Kivshar YS. Spontaneous radiationof a finite-size dipole emitter in hyperbolic media. Phys Rev A84, 023807 (2011).

49.

Kidwai O, Zhukovsky SV, Sipe JE. Dipole radiation near hyper-bolic metamaterials: applicability of effective-medium approx-imation. Opt Lett 36, 2530–2532 (2011).

50.

Mahmoodi M, Tavassoli SH, Takayama O, Sukham J, Malur-eanu R et al. Existence conditions of high-k modes in finite hy-perbolic metamaterials. Laser Photonics Rev 13, 1800253(2019).

51.

Kidwai O, Zhukovsky SV, Sipe JE. Effective-medium ap-proach to planar multilayer hyperbolic metamaterials: strengthsand limitations. Phys Rev A 85, 053842 (2012).

52.

Sukham J, Takayama O, Mahmoodi M, Sychev S, Bogdanov Aet al. Investigation of effective media applicability for ultrathinmultilayer structures. Nanoscale 11, 12582–12588 (2019).

53.

Krishnamoorthy HNS, Jacob Z, Narimanov E, Kretzschmar I,Menon VM. Topological transitions in metamaterials. Science336, 205–209 (2012).

54.

Takayama O, Shkondin E, Bodganov A, Panah MEA, Golenit-skii K et al. Midinfrared surface waves on a high aspect rationanotrench platform. ACS Photonics 4, 2899–2907 (2017).

55.

Smalley JST, Vallini F, Montoya SA, Ferrari L, Shahin S et al.Luminescent hyperbolic metasurfaces. Nat Commun 8, 13793(2017).

56.

Vasilantonakis N, Nasir ME, Dickson W, Wurtz GA, Zayats AV.Bulk plasmon-polaritons in hyperbolic nanorod metamaterialwaveguides. Laser Photonics Rev 9, 345–353 (2015).

57.

Avrutsky I, Salakhutdinov I, Elser J, Podolskiy V. Highly con-fined optical modes in nanoscale metal-dielectric multilayers.

58.

Phys Rev B 75, 241402 (2007). Zhukovsky SV, Orlov AA, Babicheva VE, Lavrinenko AV, SipeJE. Photonic-band-gap engineering for volume plasmon polari-tons in multiscale multilayer hyperbolic metamaterials. PhysRev A 90, 013801 (2014).

59.

Takayama O, Bogdanov AA, Lavrinenko AV. Photonic surfacewaves on metamaterial interfaces. J Phys Condens Matter 29,463001 (2017).

60.

Higuchi M, Takahara J. Plasmonic interpretation of bulkpropagating waves in hyperbolic metamaterial optical wave-guides. Opt Express 26, 1918–1929 (2018).

61.

Zhukovsky SV, Kidwai O, Sipe JE. Physical nature of volumeplasmon polaritons in hyperbolic metamaterials. Opt Express21, 14982–14987 (2013).

62.

Poddubny AN, Belov PA, Ginzburg P, Zayats AV, Kivshar YS.Microscopic model of purcell enhancement in hyperbolicmetamaterials. Phys Rev B 86, 035148 (2012).

63.

Slobozhanyuk AP, Ginzburg P, Powell DA, Iorsh I, Shalin ASet al. Purcell effect in hyperbolic metamaterial resonators.Phys Rev B 92, 195127 (2015).

64.

Rytov SM. Electromagnetic properties of a finely stratified me-dium. Sov Phys JETP 2, 466–475 (1956).

65.

Agranovich VM. Dielectric permeability and influence of extern-al fields on optical properties of superlattices. Solid State Com-mun 78, 747–750 (1991).

66.

Jacob Z, Kim JY, Naik GV, Boltasseva A, Narimanov EE et al.Engineering photonic density of states using metamaterials.Appl Phys B 100, 215–218 (2010).

67.

Tumkur T, Zhu G, Black P, Barnakov YA, Bonner CE et al.Control of spontaneous emission in a volume of functionalizedhyperbolic metamaterial. Appl Phys Lett 99, 151115 (2011).

68.

Kim J, Drachev VP, Jacob Z, Naik GV, Boltasseva A et al. Im-proving the radiative decay rate for dye molecules with hyper-bolic metamaterials. Opt Express 20, 8100–8116 (2012).

69.

Sreekanth KV, Biaglow T, Strangi G. Directional spontaneousemission enhancement in hyperbolic metamaterials. J ApplPhys 114, 134306 (2013).

70.

Shalaginov MY, Ishii S, Liu J, Liu J, Irudayaraj J et al. Broad-band enhancement of spontaneous emission from nitrogen-va-cancy centers in nanodiamonds by hyperbolic metamaterials.Appl Phys Lett 102, 173114 (2013).

71.

Shalaginov MY, Vorobyov VV, Liu J, Ferrera M, Akimov AV etal. Enhancement of single-photon emission from nitrogen-va-cancy centers with TiN/(Al,Sc)N hyperbolic metamaterial.Laser Photonics Rev 9, 120–127 (2015).

72.

Wang Y, Sugimoto H, Inampudi S, Capretti A, Fujii M et al.Broadband enhancement of local density of states using silic-on-compatible hyperbolic metamaterials. Appl Phys Lett 106,241105 (2015).

73.

Ozel T, Nizamoglu S, Sefunc MA, Samarskaya O, Ozel IO etal. Anisotropic emission from multilayered plasmon resonatornanocomposites of isotropic semiconductor quantum dots.ACS Nano 5, 1328–1334 (2011).

74.

Zhukovsky SV, Ozel T, Mutlugun E, Gaponik N, Eychmuller Aet al. Hyperbolic metamaterials based on quantum-dot plas-mon-resonator nanocomposites. Opt Express 22,18290–18298 (2014).

75.

Lin HI, Shen KC, Liao YM, Li YH, Perumal P et al. Integrationof nanoscale light emitters and hyperbolic metamaterials: anefficient platform for the enhancement of random laser action.

76.


210031-24

https://doi.org/10.1088/2040-8986/aade68

https://doi.org/10.1364/aop.10.000354

https://doi.org/10.1103/PhysRevLett.107.133901


https://doi.org/10.1038/nmat2546



https://doi.org/10.1021/acsanm.7b00381

https://doi.org/10.1038/ncomms2176

https://doi.org/10.1063/1.3037208


https://doi.org/10.1103/PhysRevA.84.023807

https://doi.org/10.1364/ol.36.002530

https://doi.org/10.1002/lpor.201800253


https://doi.org/10.1039/c9nr02471a





https://doi.org/10.1103/PhysRevB.75.241402



https://doi.org/10.1088/1361-648X/aa8bdd

https://doi.org/10.1364/oe.26.001918

https://doi.org/10.1364/oe.21.014982



https://doi.org/10.1016/0038-1098(91)90856-Q

https://doi.org/10.1016/0038-1098(91)90856-Q

https://doi.org/10.1016/0038-1098(91)90856-Q

https://doi.org/10.1007/s00340-010-4096-5

https://doi.org/10.1063/1.3631723

https://doi.org/10.1364/oe.20.008100

https://doi.org/10.1063/1.4824287

https://doi.org/10.1063/1.4824287

https://doi.org/10.1063/1.4804262


https://doi.org/10.1063/1.4922874

https://doi.org/10.1021/nn1030324

https://doi.org/10.1364/oe.22.018290

https://doi.org/10.1088/2040-8986/aade68

https://doi.org/10.1364/aop.10.000354






https://doi.org/10.1021/acsanm.7b00381


https://doi.org/10.1063/1.3037208



https://doi.org/10.1364/ol.36.002530



https://doi.org/10.1039/c9nr02471a








https://doi.org/10.1088/1361-648X/aa8bdd

https://doi.org/10.1364/oe.26.001918

https://doi.org/10.1364/oe.21.014982



https://doi.org/10.1016/0038-1098(91)90856-Q

https://doi.org/10.1016/0038-1098(91)90856-Q

https://doi.org/10.1016/0038-1098(91)90856-Q

https://doi.org/10.1007/s00340-010-4096-5

https://doi.org/10.1063/1.3631723

https://doi.org/10.1364/oe.20.008100

https://doi.org/10.1063/1.4824287

https://doi.org/10.1063/1.4824287

https://doi.org/10.1063/1.4804262


https://doi.org/10.1063/1.4922874

https://doi.org/10.1021/nn1030324

https://doi.org/10.1364/oe.22.018290

ACS Photonics 5, 718–727 (2018). Shen KC, Hsieh C, Cheng YJ, Tsai DP. Giant enhancement ofemission efficiency and light directivity by using hyperbolicmetacavity on deep-ultraviolet AlGaN emitter. Nano Energy45, 353–358 (2018).

77.

Kitur JK, Gu L, Tumkur T, Bonner C, Noginov MA. Stimulatedemission of surface plasmons on top of metamaterials with hy-perbolic dispersion. ACS Photonics 2, 1019–1024 (2015).

78.

Shen YF, Yan YX, Brigeman AN, Kim H, Giebink NC. Efficientupper-excited state fluorescence in an organic hyperbolicmetamaterial. Nano Lett 18, 1693–1698 (2018).

79.

Ui Lee Y, Gaudin OPM, Lee KJ, Choi E, Placide V et al. Or-ganic monolithic natural hyperbolic material. ACS Photonics 6,1681–1689 (2019).

80.

Zhukovsky SV, Andryieuski A, Takayama O, Shkondin E,Malureanu R et al. Experimental demonstration of effectivemedium approximation breakdown in deeply subwavelengthall-dielectric multilayers. Phys Rev Lett 115, 177402 (2015).

81.

Mahmoodi M, Tavassoli SH, Lavrinenko AV. Mode-resolveddirectional enhancement of spontaneous emission inside/out-side finite multilayer hyperbolic metamaterials. Mater TodayCommun 23, 100859 (2020).

82.

Kannegulla A, Wang YC, Liu Y, Wu B, Cheng LJ. Large-areaoutcoupling of quantum dot emission on multilayer hyperbolicmetamaterials. In Proceedings of SPIE 10719, Metamaterials,Metadevices, and Metasystems 2018 107192K (SPIE, 2018);http://doi.org/10.1117/12.2322085.

83.

Li L, Zhou ZY, Min CJ, Yuan XC. Few-layer metamaterials forspontaneous emission enhancement. Opt Lett 46, 190–193(2021).

84.

Wang L, Li SL, Zhang BR, Qin YZ, Tian Z et al. Asymmetric-ally curved hyperbolic metamaterial structure with gradientthicknesses for enhanced directional spontaneous emission.ACS Appl Mater Interfaces 10, 7704–7708 (2018).

85.

Lin HI, Shen KC, Lin SY, Haider G, Li YH et al. Transient andflexible hyperbolic metamaterials on freeform surfaces. SciRep 8, 9469 (2018).

86.

Inam FA, Ahmed N, Steel MJ, Castelletto S. Hyperbolicmetamaterial resonator-antenna scheme for large, broadbandemission enhancement and single-photon collection. J OptSoc Am B 35, 2153–2162 (2018).

87.

Kala A, Inam FA, Biehs SA, Vaity P, Achanta VG. Hyperbolicmetamaterial with quantum dots for enhanced emission andcollection efficiencies. Adv Opt Mater 8, 2000368 (2020).

88.

Yang XD, Yao J, Rho J, Yin XB, Zhang X. Experimental realiz-ation of three-dimensional indefinite cavities at the nanoscalewith anomalous scaling laws. Nat Photonics 6, 450–454(2012).

89.

Indukuri SRKC, Frydendahl C, Bar-David J, Mazurski N, LevyU. WS2 monolayers coupled to hyperbolic metamaterialnanoantennas: broad implications for light –matter-interactionapplications. ACS Appl Nano Mater 3, 10226–10233 (2020).

90.

Forster T. Energiewanderung und fluoreszenz. Naturwis-senschaften 33, 166–175 (1946).

91.

Förster T. Zwischenmolekulare energiewanderung undfluoreszenz. Ann Phys 437, 55–75 (1948).

92.

Tumkur TU, Kitur JK, Bonner CE, Poddubny AN, NarimanovEE et al. Control of Förster energy transfer in the vicinity ofmetallic surfaces and hyperbolic metamaterials. Faraday Dis-cuss 178, 395–412 (2015).

93.

Adl HP, Gorji S, Habil MK, Suárez I, Chirvony VS et al. Purcellenhancement and wavelength shift of emitted light by CsPbI3perovskite nanocrystals coupled to hyperbolic metamaterials.ACS Photonics 7, 3152–3160 (2020).

94.

Tonkaev P, Anoshkin S, Pushkarev A, Malureanu R, MasharinM et al. Acceleration of radiative recombination in quasi-2Dperovskite films on hyperbolic metamaterials. Appl Phys Lett118, 091104 (2021).

95.

Lin HI, Wang CC, Shen KC, Shalaginov MY, Roy PK et al. En-hanced laser action from smart fabrics made with rollable hy-perbolic metamaterials. npj Flex Electron 4, 20 (2020).

96.

Moritake Y, Nakayama K, Suzuki T, Kurosawa H, Kodama T etal. Lifetime reduction of a quantum emitter with quasiperiodicmetamaterials. Phys Rev B 90, 075146 (2014).

97.

Li L, Mathai CJ, Gangopadhyay S, Yang XD, Gao J. Spontan-eous emission rate enhancement with aperiodic Thue-Morsemultilayer. Sci Rep 9, 8473 (2019).

98.

High AA, Devlin RC, Dibos A, Polking M, Wild DS et al. Visible-frequency hyperbolic metasurface. Nature 522, 192–196(2015).

99.

Takayama O, Dmitriev P, Shkondin E, Yermakov O, Panah Met al. Experimental observation of dyakonov plasmons in themid-infrared. Semiconductors 52, 442–446 (2018).

100.

Li ZT, Smalley JST, Haroldson R, Lin DY, Hawkins R et al.Active perovskite hyperbolic metasurface. ACS Photonics 7,1754–1761 (2020).

101.

Noginov MA, Li H, Barnakov YA, Dryden D, Nataraj G et al.Controlling spontaneous emission with metamaterials. Opt Lett35, 1863–1865 (2010).

102.

Roth DJ, Krasavin AV, Wade A, Dickson W, Murphy A et al.Spontaneous emission inside a hyperbolic metamaterial wave-guide. ACS Photonics 4, 2513–2521 (2017).

103.

Ginzburg P, Roth DJ, Nasir ME, Segovia P, Krasavin AV et al.Spontaneous emission in non-local materials. Light: Sci Appl6, e16273 (2017).

104.

Roth DJ, Nasir ME, Ginzburg P, Wang P, Le Marois A et al.Förster resonance energy transfer inside hyperbolic metama-terials. ACS Photonics 5, 4594–4603 (2018).

105.

Córdova-Castro RM, Krasavin AV, Nasir ME, Zayats AV, Dick-son W. Nanocone-based plasmonic metamaterials. Nanotech-nology 30, 055301 (2019).

106.

Roth DJ, Ginzburg P, Hirvonen LM, Levitt JA, Nasir ME et al.Singlet –triplet transition rate enhancement inside hyperbolicmetamaterials. Laser Photonics Rev 13, 1900101 (2019).

107.

Chandrasekar R, Wang ZX, Meng XG, Azzam SI, ShalaginovMY et al. Lasing action with gold nanorod hyperbolic metama-terials. ACS Photonics 4, 674–680 (2017).

108.

Indukuri C, Yadav RK, Basu JK. Broadband room temperaturestrong coupling between quantum dots and metamaterials.Nanoscale 9, 11418–11423 (2017).

109.

Lu D, Kan JJ, Fullerton EE, Liu ZW. Enhancing spontaneousemission rates of molecules using nanopatterned multilayerhyperbolic metamaterials. Nat Nanotechnol 9, 48–53 (2014).

110.

Lu D, Ferrari L, Kan JJ, Fullerton EE, Liu ZW. Optimization ofnanopatterned multilayer hyperbolic metamaterials for spon-taneous light emission enhancement. Phys Status Solidi (A)215, 1800263 (2018).

111.

Li L, Wang W, Luk TS, Yang XD, Gao J. Enhanced quantumdot spontaneous emission with multilayer metamaterial nano-structures. ACS Photonics 4, 501–508 (2017).

112.


210031-25


https://doi.org/10.1016/j.nanoen.2018.01.020

https://doi.org/10.1021/ph500475x

https://doi.org/10.1021/acs.nanolett.7b04738



https://doi.org/10.1016/j.mtcomm.2019.100859


http://doi.org/10.1117/12.2322085

https://doi.org/10.1364/ol.413268

https://doi.org/10.1021/acsami.7b19721

https://doi.org/10.1038/s41598-018-27812-4

https://doi.org/10.1038/s41598-018-27812-4

https://doi.org/10.1364/josab.35.002153


https://doi.org/10.1002/adom.202000368



https://doi.org/10.1007/BF00585226

https://doi.org/10.1007/BF00585226

https://doi.org/10.1002/andp.19484370105

https://doi.org/10.1039/c4fd00184b



https://doi.org/10.1021/acsphotonics.0c01219

https://doi.org/10.1063/5.0042557

https://doi.org/10.1038/s41528-020-00085-6


https://doi.org/10.1038/s41598-019-44901-0

https://doi.org/10.1038/nature14477

https://doi.org/10.1134/S1063782618040279


https://doi.org/10.1364/ol.35.001863


https://doi.org/10.1038/lsa.2016.273


https://doi.org/10.1088/1361-6528/aaea39




https://doi.org/10.1039/c7nr03008h

https://doi.org/10.1038/nnano.2013.276

https://doi.org/10.1002/pssa.201800263



https://doi.org/10.1016/j.nanoen.2018.01.020

https://doi.org/10.1021/ph500475x






http://doi.org/10.1117/12.2322085

https://doi.org/10.1364/ol.413268

https://doi.org/10.1021/acsami.7b19721

https://doi.org/10.1038/s41598-018-27812-4

https://doi.org/10.1038/s41598-018-27812-4






https://doi.org/10.1007/BF00585226

https://doi.org/10.1007/BF00585226

https://doi.org/10.1002/andp.19484370105





https://doi.org/10.1063/5.0042557

https://doi.org/10.1038/s41528-020-00085-6


https://doi.org/10.1038/s41598-019-44901-0


https://doi.org/10.1134/S1063782618040279


https://doi.org/10.1364/ol.35.001863


https://doi.org/10.1038/lsa.2016.273






https://doi.org/10.1039/c7nr03008h

https://doi.org/10.1038/nnano.2013.276

https://doi.org/10.1002/pssa.201800263


Sreekanth KV, Krishna KH, De Luca A, Strangi G. Largespontaneous emission rate enhancement in grating coupledhyperbolic metamaterials. Sci Rep 4, 6340 (2014).

113.

Galfsky T, Gu J, Narimanov EE, Menon VM. Photonichypercrystals for control of light-matter interactions. Proc NatlAcad Sci USA 114, 5125–5129 (2017).

114.

Gan QQ, Gao YK, Wagner K, Vezenov D, Ding YJ et al. Ex-perimental verification of the rainbow trapping effect in adiabat-ic plasmonic gratings. Proc Natl Acad Sci USA 108,5169–5173 (2011).

115.

Ni X, Wu Y, Chen ZG, Zheng LY, Xu YL et al. Acoustic rain-bow trapping by coiling up space. Sci Rep 4, 7038 (2014).

116.

Hu HF, Ji DX, Zeng X, Liu K, Gan QQ. Rainbow trapping in hy-perbolic metamaterial waveguide. Sci Rep 3, 1249 (2013).

117.

Zhou J, Kaplan AF, Chen L, Guo LJ. Experiment and theory ofthe broadband absorption by a tapered hyperbolic metamateri-al array. ACS Photonics 1, 618–624 (2014).

118.

Krishna KH, Sreekanth KV, Strangi G. Dye-embedded andnanopatterned hyperbolic metamaterials for spontaneousemission rate enhancement. J Opt Soc Am B 33, 1038–1043(2016).

119.

Galfsky T, Sun Z, Considine CR, Chou CT, Ko WC et al.Broadband enhancement of spontaneous emission in two-di-mensional semiconductors using photonic hypercrystals. NanoLett 16, 4940–4945 (2016).

120.

Newman WD, Cortes CL, Jacob Z. Enhanced and directionalsingle-photon emission in hyperbolic metamaterials. J Opt SocAm B 30, 766–775 (2013).

121.

Galfsky T, Krishnamoorthy HNS, Newman W, Narimanov EE,Jacob Z et al. Active hyperbolic metamaterials: enhancedspontaneous emission and light extraction. Optica 2, 62–65(2015).

122.

Cheng Y, Liao CT, Xie ZH, Hung YC, Lee MC. Study of cavity-enhanced dipole emission on a hyperbolic metamaterial slab. JOpt Soc Am B 36, 426–434 (2019).

123.

Niu XX, Hu XY, Chu SS, Gong QH. Epsilon-near-zero photon-ics: a new platform for integrated devices. Adv Opt Mater 6,1701292 (2018).

124.

Vulis DI, Reshef O, Camayd-Muñoz P, Mazur E. Manipulatingthe flow of light using Dirac-cone zero-index metamaterials.Rep Prog Phys 82, 012001 (2019).

125.

Campione S, Brener I, Marquier F. Theory of epsilon-near-zeromodes in ultrathin films. Phys Rev B 91, 121408 (2015).

126.

Nordin L, Dominguez O, Roberts CM, Streyer W, Feng K et al.Mid-infrared epsilon-near-zero modes in ultra-thin phononicfilms. Appl Phys Lett 111, 091105 (2017).

127.

Folland TG, Lu GY, Bruncz A, Nolen JR, Tadjer M et al. Vibra-tional coupling to epsilon-near-zero waveguide modes. ACSPhotonics 7, 614–621 (2020).

128.

Engheta N. Pursuing near-zero response. Science 340,286–287 (2013).

129.

Javani MH, Stockman MI. Real and imaginary properties of ep-silon-near-zero materials. Phys Rev Lett 117, 107404 (2106).

130.

Fleury R, Alù A. Enhanced superradiance in epsilon-near-zeroplasmonic channels. Phys Rev B 87, 201101 (2013).

131.

Sreekanth KV, De Luca A, Strangi G. Experimental demon-stration of surface and bulk plasmon polaritons in hypergrat-ings. Sci Rep 3, 3291 (2013).

132.

Caligiuri V, Dhama R, Sreekanth KV, Strangi G, De Luca A.Dielectric singularity in hyperbolic metamaterials: the inversion

133.

point of coexisting anisotropies. Sci Rep 6, 20002 (2016). Drachev VP, Podolskiy VA, Kildishev AV. Hyperbolic metama-terials: new physics behind a classical problem. Opt Express21, 15048–15064 (2013).

134.

Caligiuri V, Palei M, Imran M, Manna L, Krahne R. Planardouble-epsilon-near-zero cavities for spontaneous emissionand purcell effect enhancement. ACS Photonics 5, 2287–2294(2018).

135.

Walt DR. Optical methods for single molecule detection andanalysis. Anal Chem 85, 1258–1263 (2013).

136.

Melentiev PN, Son LV, Kudryavtsev DS, Kasheverov IE, Tset-lin VI et al. Ultrafast, ultrasensitive detection and imaging ofsingle cardiac troponin-T molecules. ACS Sens 5, 3576–3583(2020).

137.

Engheta N. Circuits with light at nanoscales: optical nanocir-cuits inspired by metamaterials. Science 317, 1698–1702(2007).

138.

Melentiev PN, Kalmykov A, Kuzin A, Negrov D, Klimov V et al.Open-type SPP waveguide with ultrahigh bandwidth up to 3.5THz. ACS Photonics 6, 1425–1433 (2019).

139.

Argyropoulos C, Estakhri NM, Monticone F, Alù A. Negativerefraction, gain and nonlinear effects in hyperbolic metamateri-als. Opt Express 21, 15037–15047 (2013).

140.

Wan MJ, Gu P, Liu WY, Chen Z, Wang ZL. Low thresholdspaser based on deep-subwavelength spherical hyperbolicmetamaterial cavities. Appl Phys Lett 110, 031103 (2017).

141.

Janaszek B, Tyszka-Zawadzka A, Szczepański P. Control ofgain/absorption in tunable hyperbolic metamaterials. Opt Ex-press 25, 13153–13162 (2017).

142.

Bergman DJ, Stockman MI. Surface plasmon amplification bystimulated emission of radiation: quantum generation of coher-ent surface plasmons in nanosystems. Phys Rev Lett 90,027402 (2003).

143.

Bozhevolnyi SI, Khurgin JB. The case for quantum plasmon-ics. Nat Photonics 11, 398–400 (2017).

144.

del Valle E, Laussy FP, Tejedor C. Luminescence spectra ofquantum dots in microcavities. Phys Rev B, 79, 235326(2009).

145.

Shahbazyan TV. Exciton-plasmon energy exchange drives thetransition to a strong coupling regime. Nano Lett 19,3273–3279 (2019).

146.

Khurgin JB. Exceptional points in polaritonic cavities and sub-threshold fabry–perot lasers. Optica 7, 1015–1023 (2020).

147.

Pustovit VN, Urbas AM, Zelmon DE. Surface plasmon amplific-ation by stimulated emission of radiation in hyperbolicmetamaterials. Phys Rev B 94, 235445 (2016).

148.

Vaianella F, Hamm JM, Hess O, Maes B. Strong coupling andexceptional points in optically pumped active hyperbolicmetamaterials. ACS Photonics 5, 2486–2495 (2018).

149.

Ni X, Naik GV, Kildishev AV, Barnakov Y, Boltasseva A et al.Effect of metallic and hyperbolic metamaterial surfaces onelectric and magnetic dipole emission transitions. Appl Phys B103, 553–558 (2011).

150.

Michler P, Kiraz A, Becher C, Schoenfeld WV, Petroff PM et al.A quantum dot single-photon turnstile device. Science 290,2282–2285 (2000).

151.

Pelton M, Santori C, Vučković J, Zhang BY, Solomon GS et al.Efficient source of single photons: a single quantum dot in amicropost microcavity. Phys Rev Lett 89, 233602 (2002).

152.

Lodahl P, van Driel AF, Nikolaev IS, Irman A, Overgaag K et153.


210031-26

https://doi.org/10.1038/srep06340

https://doi.org/10.1073/pnas.1702683114





https://doi.org/10.1021/ph5001007






https://doi.org/10.1364/optica.2.000062




https://doi.org/10.1088/1361-6633/aad3e5


https://doi.org/10.1063/1.4996213








https://doi.org/10.1364/oe.21.015048


https://doi.org/10.1021/ac3027178

https://doi.org/10.1021/acssensors.0c01790



https://doi.org/10.1364/oe.21.015037

https://doi.org/10.1063/1.4974209

https://doi.org/10.1364/oe.25.013153

https://doi.org/10.1364/oe.25.013153

https://doi.org/10.1364/oe.25.013153





https://doi.org/10.1364/optica.397378



https://doi.org/10.1007/s00340-011-4468-5

https://doi.org/10.1126/science.290.5500.2282








https://doi.org/10.1021/ph5001007






https://doi.org/10.1364/optica.2.000062




https://doi.org/10.1088/1361-6633/aad3e5


https://doi.org/10.1063/1.4996213








https://doi.org/10.1364/oe.21.015048


https://doi.org/10.1021/ac3027178

https://doi.org/10.1021/acssensors.0c01790



https://doi.org/10.1364/oe.21.015037

https://doi.org/10.1063/1.4974209

https://doi.org/10.1364/oe.25.013153

https://doi.org/10.1364/oe.25.013153

https://doi.org/10.1364/oe.25.013153





https://doi.org/10.1364/optica.397378



https://doi.org/10.1007/s00340-011-4468-5

https://doi.org/10.1126/science.290.5500.2282


al. Controlling the dynamics of spontaneous emission fromquantum dots by photonic crystals. Nature 430, 654–657(2004). Khitrova G, Gibbs HM, Kira M, Koch SW, Scherer A. VacuumRabi splitting in semiconductors. Nat Phys 2, 81–90 (2006).

154.

Rogacheva AV, Fedotov VA, Schwanecke AS, Zheludev NI.Giant gyrotropy due to electromagnetic-field coupling in abilayered chiral structure. Phys Rev Lett 97, 177401 (2006).

155.

Ameling R, Dregely D, Giessen H. Strong coupling of local-ized and surface plasmons to microcavity modes. Opt Lett 36,2218–2220 (2011).

156.

Goldzak T, Mailybaev AA, Moiseyev N. Light stops at excep-tional points. Phys Rev Lett 120, 013901 (2018).

157.

Pick A, Zhen B, Miller OD, Hsu CW, Hernandez F et al. Gener-al theory of spontaneous emission near exceptional points.Opt Express 25, 12325–12348 (2017).

158.

Hou JP, Li ZT, Luo XW, Gu Q, Zhang CW. Topological bandsand triply degenerate points in non-hermitian hyperbolicmetamaterials. Phys Rev Lett 124, 073603 (2020).

159.

Doronin IV, Zyablovsky AA, Andrianov ES. Strong-coupling-as-sisted formation of coherent radiation below the lasingthreshold. arXiv: 2012.05288 (2020).

160.

Antosiewicz TJ, Apell SP, Shegai T. Plasmon-exciton interac-tions in a core-shell geometry: from enhanced absorption tostrong coupling. ACS Photonics 1, 454–463 (2014).

161.

Shen KC, Ku CT, Hsieh C, Kuo HC, Cheng YJ et al. Deep-ul-traviolet hyperbolic metacavity laser. Adv Mater 30, 1706918(2018).

162.

Shishkov VY, Andrianov ES, Pukhov AA, Vinogradov AP. En-hancement of nonclassical raman light intensity by plasmonicnanoantenna. Phys Rev A 103, 013725 (2021).

163.

del Pino J, Feist J, Garcia-Vidal FJ. Signatures of vibrationalstrong coupling in raman scattering. J. Phys Chem C 119,29132–29137 (2015).

164.

Waks E, Sridharan D. Cavity QED treatment of interactionsbetween a metal nanoparticle and a dipole emitter. Phys RevA 84, 043845 (2010).

165.

Hoffman AJ, Alekseyev L, Howard SS, Franz KJ, WassermanD et al. Negative refraction in semiconductor metamaterials.Nat Mater 6, 946–950 (2007).

166.

Li PN, Dolado I, Alfaro-Mozaz FJ, Casanova F, Hueso LE etal. Infrared hyperbolic metasurface based on nanostructuredvan der Waals materials. Science 359, 892–896 (2018).

167.

Ma WL, Alonso-González P, Li SJ, Nikitin AY, Yuan J et al. In-plane anisotropic and ultra-low-loss polaritons in a natural vander Waals crystal. Nature 562, 557–562 (2018).

168.

Wang C, Huang SY, Xing QX, Xie YG, Song CY et al. Van derWaals thin films of WTe2 for natural hyperbolic plasmonic sur-faces. Nat Commun 11, 1158 (2020).

169.

Gao H, Zhang XM, Li WF, Zhao MW. Tunable broadband hy-perbolic light dispersion in metal diborides. Opt Express 27,36911–36922 (2019).

170.

Gao H, Sun L, Zhao MW. Low-loss hyperbolic dispersion andanisotropic plasmonic excitation in nodal-line semimetallic yttri-um nitride. Opt Express 28, 22076–22087 (2020).

171.

Kan YH, Kumar S, Ding F, Zhao CY, Bozhevolnyi SI. On-chipspin-orbit controlled excitation of quantum emitters coupled tohybrid plasmonic nanocircuits. arXiv: 2004.07483 (2020).

172.

AcknowledgementsL. Y. Beliaev, O. Takayama and A. V. Lavrinenko acknowledge the financialsupport from Independent Research Fund Denmark (DFF) (ResearchProject 2, 8022-00387B), Denmark. P.M. acknowledges that the publicationwas prepared within the framework of Academic Fund Program at the HSEUniversity in 2021 (grant No 21-04-056).

Author contributionsL. Y. Beliaev carried out the literature search. L. Y. Beliaev and O. Takayamaprepared the first draft of the paper except active HMMs section. P. N.Melentiev prepared the first draft of the active HMMs section. All authorsedited the manuscript and participated in discussion of the content.

Competing interestsThe authors declare no competing financial interests.


210031-27


https://doi.org/10.1038/nphys227


https://doi.org/10.1364/ol.36.002218


https://doi.org/10.1364/oe.25.012325


https://doi.org/10.1021/ph500032d



https://doi.org/10.1021/acs.jpcc.5b11654




https://doi.org/10.1126/science.aaq1704

https://doi.org/10.1038/s41586-018-0618-9

https://doi.org/10.1038/s41467-020-15001-9

https://doi.org/10.1364/oe.27.036911

https://doi.org/10.1364/oe.397167




https://doi.org/10.1364/ol.36.002218


https://doi.org/10.1364/oe.25.012325










https://doi.org/10.1038/s41586-018-0618-9

https://doi.org/10.1038/s41467-020-15001-9

https://doi.org/10.1364/oe.27.036911

https://doi.org/10.1364/oe.397167




https://doi.org/10.1364/ol.36.002218


https://doi.org/10.1364/oe.25.012325











https://doi.org/10.1364/ol.36.002218


https://doi.org/10.1364/oe.25.012325










https://doi.org/10.1038/s41586-018-0618-9

https://doi.org/10.1038/s41467-020-15001-9

https://doi.org/10.1364/oe.27.036911

https://doi.org/10.1364/oe.397167



https://doi.org/10.1038/s41586-018-0618-9

https://doi.org/10.1038/s41467-020-15001-9

https://doi.org/10.1364/oe.27.036911

https://doi.org/10.1364/oe.397167

Photoluminescence control by hyperbolic ... - DTU Orbit

Documents