Metamaterial Van Hove Singularity

Metamaterial Van Hove Singularity

C. L. Cortes, Z. Jacob*Department of Electrical and Computer Engineering, University of Alberta,

Edmonton, AB T6G 2V4, Canada

*[email protected]

Abstract

We introduce the photonic analogue of electronic Van Hove singularities (VHS) in artificial media (meta-materials) with hyperbolic dispersion. Unlike photonic and electronic crystals, the VHS in metamaterials isunrelated to the underlying periodicity and occurs due to slow light modes in the structure. We show thatthe VHS characteristics are manifested in the near-field local density of optical states inspite of the losses,dispersion and finite unit cell size of the hyperbolic metamaterial. Finally we show that this work shouldlead to quantum, thermal, nano-lasing and biosensing applications of van hove singularities in hyperbolicmetamaterials achievable by current fabrication technology.

1 Introduction

Periodic electronic and photonic crystals support ahost of phenomena associated with the bloch wavesof the underlying lattice structure. Along with band-gaps which completely forbid propagating waves,there exist critical points where the band structure(dispersion relation of propagating waves) has an ex-tremum. These extrema lead to Van Hove singular-ities (VHS) in the density of states of the mediumsince it is related to the band structure E(k) byρ(E) =

∫dS

|∇E(k)| , where dS is iso-frequency surfaceelement. VHS in the electronic density of states sig-nificantly affects the optical absorption spectra ofsolids[1].

In photonic crystals, this extremum in the bandstructure corresponds to slow light modes of thestructure where the group velocity decreases signif-icantly below c. In the ideal limit, slow light modeshave a zero group velocity leading to Van Hove sin-gularities (VHS) in the photonic density of states(PDOS), the physical quantity govering light mat-ter interaction. Thus slow light can enhance light-matter interactions that are critical for many ap-plications in non-linear optics[2], and quantum op-tics [3]. Demonstrations of slow light and associatedeffects have grown rapidly over the past decade –evolving from low-temperature experiments to room-temperature set-ups that utilize electromagnetically

induced transparency (EIT), coherent population os-cillations and photonic crystals (PhCs)[4, 2, 5].

Here, we show that metamaterials can also sup-port VHS, however their origin is unrelated to theunderlying subwavelength periodicity of the latticeand arises due to the effective medium response. TheVHS in metamaterial waveguide structures is due toa balance of energy flow both inside and outside themetamaterial leading to slow light modes[6, 7]. Weconsider a practical waveguide structure where theproposed enhancement in the density of states canbe experimentally verified at optical frequencies. Wecharacterize light-matter enhancement using the lo-cal density of states (LDOS) in the near-field whichdemonstrate large enhancements at slow-light modewavelengths[8] inspite of material absorption, disper-sion, and finite patterning scale. We emphasize thatour paper presents practical designs for the metama-terial waveguide and also consider applications in dis-tinct areas of quantum optics, thermal engineering,nano-lasing and biosensing.

2 Hyperbolic Metamaterials

Our approach uses a non-magnetic uniaxial metama-terial, with dielectric tensor ε = diag[εxx, εxx, εzz],which exhibits hyperbolic dispersion for the extraor-dinary waves that pass through it. These waves are

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Figure 1: (a) Isofrequency surface of type I HMM (εxx > 0, εzz < 0) with Poynting vectors (orange arrows)shown normal to the surface. Note that the Poynting vector component Sx is negative and points in a directionopposite to the wavevector component. (b) The HMM response is achieved by using a multilayer realization ofalternating subwavelength layers of metal and dielectric (shown above), or by using metal nanowires embeddedin a dielectric host (shown below). (c) Real part of perpendicular and parallel components of dielectricpermittivity predicted by EMT. Type I response occurs below 491nm, while the Type II response (εxx <0, εzz > 0) occurs in the longer wavelength region. We study a Ag/TiO2 multilayer structure with unit cellsize a = 30 nm (15nm/15nm).(d) Real part of perpendicular and parallel components of dielectric permittivitypredicted by EMT for a nanowire system. Type I response occurs for a broader range of wavelengths above522nm, while the Type II response (εxx < 0, εzz > 0) occurs in the short wavelength region. The systemconsists of silver nanowires embedded in an alumina matrix with ρ = 0.22 fill-fraction.

governed by the dispersion relation

(k2x + k2y)/εzz + k2z/εxx = ω2/c2 (1)

where kx, ky, kz are the wavevector components oflight inside the medium. The above equation pro-duces a two-sheeted hyperboloid surface when εxx >0 and εzz < 0, referred to as a type I HMM. Whenεxx < 0 and εzz > 0, a single-sheeted hyperboloid isproduced referred to as a type II HMM[9].

There are two main methods for achieving hy-perbolic dispersion consisting of alternating metal-dielectric multilayers[10] or metal nanowires[11] in adielectric host (see Fig. 1(b)). Effective medium the-ory (EMT) predicts these designs to achieve the de-sired extreme anisotropy in a broadband range pro-vided the unit cells are significantly subwavelength(see Fig.1 (c) & (d)). For a planar multilayer struc-ture, EMT predicts the parallel and perpendicularpermittivity components to be

εxx = ρεm + (1− ρ)εd (2)

andεzz =

εmεdρεd + (1− ρ)εm

, (3)

where εm is the metal permittivity, εd is the dielectricpermittivity, and ρ is the fill-fraction of the metal inthe unit cell. The corresponding EMT parameters fora nanowire structure are

εzz = ρεm + (1− ρ)εd (4)

and

εxx =(1 + ρ)εmεd + (1− ρ)ε2d(1− ρ)εm + (1 + ρ)εd

. (5)

We expect both the designs to support slow lightmodes, however we focus here on the multilayer de-sign. The origin of slow light as well as hyperbolicdispersion are the coupled interface plasmon polari-tons (or interface phonon polaritons) at the bound-aries of the metal and dielectric layers [12]. Note thatthe multilayer design does not support localized plas-mons. This is especially important for active meta-materials where amplification and stimulated emis-sion of localized surface plasmons forms a major al-ternative competing channel to delocalized metama-terial modes[13].

We note that previous studies have focused on anegative index metamaterial realization of slow lightand associated effects[14, 15]. In particular, Yao et.al.[8] have an excellent study on the topic of negativeindex metamaterial waveguides and enhanced PurcellFactors as well as Lamb Shifts. However, we note ma-jor differences of our study that render our realizationconducive to experimental verification. i) Bulk opti-cal magnetism which is required for double-negativemetamaterials (ε < 0 and µ < 0) is a severe challengeleading to low figures of merit and narrowband opera-tion. The multilayer and nanowire designs presentedhere does not use optical magnetism and only uti-lizes routine fabrication approaches leading to meta-materials with significantly better performance. ii)

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A more significant limitation of negative index ap-proaches is near-field non-locality. Any metamaterialresponse is obtained by homogenization over a lengthscale larger than the unit cell size. The large unit cellsize of NIMs makes spatial dispersion a highly detri-mental effect particularly for near-field effects suchas LDOS enhancement[8]. Thus even state of theart NIMs with unit cell sizes of 250 nm will showpoor performance for any near field studies that re-quire proximity less than 250 nm. iii) Artificial mediathat require ε < 0 and µ < 0 as considered in previ-ous works are resonant metamaterials where effectivemedium theory cannot work in a broad bandwidth.The existence of unique modes such as slow light hasto be ascertained through calculations that take intoaccount the unit cell structure and not only effectivemedium approximations. Our non-magnetic (µ = 1)design takes into account not only absorption anddispersion but also the finite patterning scale. Weinclude the role of near-field non locality and obtainexcellent agreement with effective medium theory, acritical step towards experiment.

We emphasize that the HMM is highly tuneable fora wide range of wavelength regions by using differ-ent materials and layer thicknesses. Thus slow lightin HMM waveguides presents a suitable platform fornear-field studies and light matter interaction phe-nomena. Significant gain enhancement proportionalto the enhanced density of states is expected at theslow light mode, making both the multilayer andnanowire design suitable for Van Hove singularitybased metamaterial nano-lasers.

3 Van Hove Singularity

From the k-space topology in Fig. 1(a), it is clearthat the surface is unbounded. This results in ar-bitrarily large spatial frequency wavevector (high-k)modes and a density of states (DOS) that divergesin the effective medium limit[16]. These two fea-tures, along with the optical topological transition[17]that represents a sharp transition in the DOS,have been recently studied for device applicationsin nanophotonics[9, 18, 19]. However, experimentaldemonstrations have only shown a modest increase inthe LDOS by a factor of 2-5.

Our focus in this paper is on a different mechanismfor an order of magnitude larger enhancement in thelocal density of states. The density of states can bewritten as ρ(ω) =

∫dS

|∇ω(k)| in the low loss limit. Notethat in electronic and photonic crystals, the points of

high symmetry in k-space lead to a vanishing groupvelocity and corresponding Van Hove singularities inthe density of states. This leads to observable conse-quences in transport properties and heat conductionin one dimensional electronic systems such as car-bon nanotubes[20]. A similar mechanism is relatedto band edge phenomena in photonic crystals[21]. Inthe low loss limit, the photonic density of states canbe related to the inverse group velocity and henceslow light waveguide modes lead to features similarto Van Hove Singularities.

We consider a multilayer system of silver (Ag) andtitanium dioxide (TiO2). The layer thicknesses are15nm each, with unit cell size a = 30nm which is sig-nificantly subwavelength at optical frequencies buteasily realizable experimentally. The waveguide slabthickness d = 240nm consisting of 8 unit cells. EMTpredicts that this structure will exhibit type I hyper-bolic dispersion below 490.5nm (see Fig. 1(c), onlyreal parts have been shown).

We define the LDOS in the near field normalizedto its free-space value using a Green’s function for-malism [22]

ρ(ro, ωo) =2ωoπc2

Im{Tr[G(ro, ro;ωo)]}. (6)

where ro = (0, 0, zo) represents the position of thedipole located above the HMM waveguide, ωo =2πc/λ is the free-space frequency and c is the speed

of light. The Green’s tensor G is related to the radi-ation field produced by an oscillating electric dipolesource.

Fig. 2 shows the LDOS enhancement in the type IHMM wavelength region at a distance of zo = 15nmaway from the HMM slab. Note the excellent agree-ment between the calculated LDOS for the homoge-nized metamaterial slab and the practical multilayerdesign. A number of recent experiments have focusedon hyperbolic metamaterials and broadband densityof states enhancement by a factor of 2-3. However,these experiments dealt with HMMs in the type IIregime[19, 17] and the epsilon-near-zero regime[23].We see two major differences for the aforementionedtype I regime: i) an order of magnitude larger en-hancements, and ii) discrete wavelengths at which theeffect occurs.

Also, note that the metamaterial LDOS peaks inFig. 2 bear a striking resemblance to the Van Hovesingularities that are often seen in electronic and pho-tonic crystals. However, they are not a result of theperiodicity of the structure, but rather they are pre-

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Figure 2: Local density of states (normalized to free-space) at a distance zo = 15nm away from HMM slabpredicted by EMT. An excellent agreement seen forthe multilayer structure calculated via transfer ma-trix method. We show the type I HMM wavelengthregion only which has not been studied before. Noticehow the LDOS peaks occur at discrete wavelengthsindicating that they must be fundamentally differentfrom the usual broadband high-k modes in HMMs[9].

dicted by the effective medium model of the meta-material based on hyperbolic dispersion. In the nextsection, we will argue that these peaks can be physi-cally attributed to slow light modes that lead to VanHove singularities when vg ≈ 0 (low loss limit).

4 Slow Light

To understand the origin of these anomalous peaks,we define the wavevector-resolved local density ofstates (W-LDOS) as the LDOS distribution acrossthe frequency spectrum and parallel wavevector (kx)spectrum[9], i.e.

ρ(ro, ωo)

ρo= Im

∞∫0

ρ(ro, ωo, kx)

ρodkx, (7)

such that the W-LDOS ρ(ro, ωo, kx) is given by

ρ(ro, ωo, kx)

ρo=

3

2

i

|p|2k31kxkz

{p2⊥(1 + rpei2kzzo)k2x

}(8)

for a perpendicular dipole with dipole moment p andfresnel reflection coefficient rp for p-polarized light.This definition is a result of the Green’s tensor whichcan be expanded as a summation of plane waves byusing the Weyl identity. For simplicity, we use thenotation kx throughout the text however we take into

account the entire radial component kρ for the planewaves emitted by the point dipole.

Fig. 3 shows the log scale W-LDOS, normalized tofree-space, for the homogenized effective medium aswell as the practical multilayer system (zo = 15nm).Note that the bright bands in Fig. 3(a) correspondto metamaterial modes which are bulk propagatingwaves in the effective medium limit. An excellent cor-respondence is seen with Fig. 3(b) where these modesarise due to coupled plasmonic Bloch modes in themultilayer structure[12]. At lower wavelengths andlarge wavevectors there is discrepancy between thetwo plots since effective medium theory is no longervalid for such modes[9].

The brighest regions in Fig. 3 occur when the slopeof the W-LDOS bands is equal to zero. The densityof states is proportional to the inverse of the groupvelocity of light, ρ(λ) ∝ ∂k/∂ω ∝ 1/vg , therefore weattribute the LDOS peaks in Fig. 1(c) to slow-lightmodes with a group velocity nearly equal to zero.This is in accordance with the work of Yao.et.al[8],which predicted LDOS peaks for a (ε < 0 and µ < 0)

Figure 3: Wavevector-resolved local density of states(normalized to free-space) of an emitter 15nm awayfrom HMM predicted by (a) effective medium the-ory. (b) Excellent agreement is seen for the practicalmultilayer structure. The highest LDOS occurs whenthe group velocity(∂ω/∂k), equal to the slope of theyellow regions, is nearly zero. These bright regionsare the slow light modes that supported by the typeI HMM.

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metamaterial as a result of slow light modes as well.As we mentioned earlier, however, optical magnetismis quite difficult to achieve in practive, thus we pro-vide an alternative approach based on metamateri-als with hyperbolic dispersion. Also, notice that inthe ideal case of vg = 0, these modes would corre-spond to Van Hove singularities in the PDOS at dis-crete wavelengths[6] which are fundamentally differ-ent from the broadband singularity in the density ofstates that is a result of the hyperbolic dispersion[16].

We now turn to the physical nature of the slowlight mode supported by the HMM. In the low ab-sorption limit, the Poynting vector is normal to theisofrequency surface (see Fig. 1(a)). From this pictureit is clear that the component of the Poynting vectoralong the x-direction (Sx) can be of opposite sign tothe wavevector component (kx) such that kx ·Sx < 0.This argument also remains true with absorption be-cause the Poynting vector, ~S ∝ kx/εzzx + kz/εxxz,satisfies the relation Re(kx) · Re(Sx) < 0 [24]. Prop-agating modes in the waveguide must have the sameparallel wavevector (kx) component in all three medi-ums in order to satisfy the boundary conditions.We define Re(kx) to be positive which consequentlymakes the energy flow inside the HMM negative. Asa result, it is clear that the slow light waveguidemode is due to a negative energy flow (kx · Sx < 0)inside the HMM which negates the positive energyflow (kx · Sx > 0) of the outer dielectric claddings[7]. This directly contrasts other slow-light effectsseen in PhCs or EIT systems that rely on a standingwave condition or an atomic resonance of the materialrespectively[3, 5].

5 Complex Band Structure

Next, we analyze the effect of losses and dispersionon the slow-light modes by analyzing the complex-kx dispersion relation of the hyperbolic metamaterialwaveguide. The complex-kx picture shows the detri-mental effect of loss and is relevant for applicationsthat utilize a continuous pump source to excite themodes of the system. Note that while the W-LDOSplots in Fig. 3 do take loss into account, the resolu-tion is performed with respect to the real wavevectorkx.

The waveguide modes inside an HMM are de-scribed in general by the transcedental equation:

tan(kz,2d) =εxxkz,2(ε3kz,1 + ε1kz,3)

(ε3ε1k2z,2 − ε2xxkz,1kz,3), (9)

Figure 4: Complex-kx dispersion relation of slow-light modes predicted by EMT, calculated numeri-cally (a) λ vs. Re(kx) and λ vs. Im(kx) (shown ininset). Note that the waveguide mode solutions splitinto two branches: a forward travelling wave (blackbranch) and backward travelling wave (red branch).A negative real part of the wavenumber has to bechosen for this backward branch so that Im(kx) > 0(b) Energy velocity is calculated numerically usingvalues from dispersion relation. The arrows pointtowards slow-light mode region before it becomes ahighly leaky slow light mode.

where kz,i is the perpendicular wavevector componentinside medium εi (i=1,2,3)[7]. Medium 1 (ε1 = 1) isthe half-space of the emitter, medium 2 is the HMMslab, and medium 3 (ε3 = 1) is the substrate half-space.

The solution to the HMM waveguide equation isshown in Fig. 4(a). Note that Fig. 4(a) follows veryclosely with the yellow regions of Fig. 3. However,the key difference lies near the slow light mode wave-lengths (denoted by the black arrows) where it isclear from this plot that the modes split into twobranches: a forward travelling wave (black branch)where the Poynting vector and wavevector point inthe same direction kx · Sx > 0, and a backward trav-elling wave (red branch) where kx · Sx < 0. A neg-ative real part of the wavenumber has to be chosenfor this backward branch so that Im(kx) > 0. These

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Figure 5: Near field variation of the spontaneous emission lifetime of quantum emitters near the slow lightHMM waveguide. The distance of the quantum emitter is varied and normalized to the operating wavelength.(a) Numerical calculation of EMT and (b) practical multilayer system. The dark regions (colorbar < 0.2)corresponding to lower lifetime of the slow-light modes extend much further denoting excellent coupling ofthe emitters to slow light modes as opposed to other radiative and non-radiative channels. (c) The refractiveindex of an 80nm embedded layer between two 240nm HMM slabs (shown in inset) is varied to demonstratesensitivity of slow-light mode, useful for optical biosensing. Inset shows the linear relation of the 450nmslow-light mode as a function of the refractive index n equal to: 1.0, 1.2, 1.3, 1.5 and 1.6 (follows black arrowin main plot).

two branches get closer together near the slow-lightmode wavelength (denoted by the black arrows) andform a leaky slow-light wave that eventually mergesto the bulk plasma oscillation branch of the metal at(ω ≈ ωp and kx ≈ 0). Note that the leaky modes arevery lossy and have short propagation length as seenby the Im(kx) plot (inset Fig. 4(a)). This interestingbehavior of slow light modes has been noted in mediawith ε < 0 and µ < 0[8].

In an absorbing, dispersive medium the group ve-locity loses its true physical meaning and becomes ill-defined[25]. This has been an important issue whileundertanding slow-light modes and so we use energyvelocity vE as the correct physical quantity[26, 27].vE is defined as the ratio of the time-averaged Poynt-ing vector Sx and electromagnetic energy densityuem, where both are integrated along the z-directionto obtain the contribution along the propagation di-rection of the waveguide mode

vE =

∫∞−∞Re(Sx)dz∫∞−∞ uemdz

. (10)

For the calculation of Eqn. (10), we first found theanalytical expressions for the time-averaged Poynt-ing vectors inside the HMM and outer media. Then,we used a well-defined (positive definite) electromag-netic energy density for HMMs taking into accountabsorption and dispersion[28, 29]. In order to use theformalism used in Ref. 38, we require the parallel andperpendicular components of the permittivity to be

defined by either a Drude or Lorentz model. For anHMM based on a planar multilayer structure, εxx canbe modeled by a Drude model with plasma frequencyωP , while εzz can be modeled by a Lorentz model

εxx = εo1 −ω2P

ω2 + iΓω(11)

εzz = εo2 +ω2P

ω21 − ω2 − iΓω

, (12)

where εo1 = 9.7, εo2 = 6, Γ = 6.5 × 1013s−1,ω1 = 3.84 × 1015s−1 and ωP = 1.19 × 1016s−1. Weobtained values for εxx and εzz based on a fitting tothe EMT result in Fig. 1(c). This definition was usedto calculate the results in Fig. 4(a) and (b).

Fig. 4(b) shows the energy velocity for all fourslow-light modes as a function of wavelength. Thewaveguide modes slow down at specific wavelengths(denoted by the black arrows) before becoming leakymodes, showing that stopped-light is not possible inthe complex-kx case. Our result for hyperbolic meta-materials is in agreement with previous results ofε < 0, µ < 0 media[8]. Light reaches an average min-imum velocity of c/100 around the slow-light regionwhile also reaching the global minimum of c/1000 inthe region of highest dispersion, λ ≈ 480nm. It isimportant to note that for time-dependent processeswhere modes are excited by an optical pulse, thecomplex-kx picture is not sufficient. Nevertheless, wehave confirmed that solving the complex-ω dispersionrelation gives similar results.[8, 14]

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6 Applications

We now discuss multiple applications of Van Hovesingularities in multilayer and nanowire hyperbolicmetamaterials.

6.1 Lifetime Engineering

One approach to observing the strong LDOS en-hancement effect and unique spectral signatures ofthe Van Hove singularities is through the sponta-neous emission lifetime of emitters such as quan-tum dots and dye molecules. The scaling depen-dence of the lifetime to the distance (zo) due to near-field coupling with the slow-light modes is markedlydifferent[8] from other photonic channels like quench-ing, non-radiative decay, plasmon modes and conven-tional HMM modes[30].

We compare the scaling dependence between theslow-light modes in the type I region with the high-kmodes in the type II wavelength region (see Fig. 5(a) and (b)). We see that the slow-light modes havelifetimes that remain quite small, denoted as the darkregions (< 0.2 in the colorbar), for much larger dis-tances than the previously studied high-k modes[16].This is due to the fact that slow light modes are muchcloser to the light line (kx/ko = 1) than the high-k modes and so they do not decay as quickly out-side the HMM. This marked difference from previousexperiments[19, 17] should be discernible in near-fieldlifetime studies.

Furthermore, we have calculated that approxi-mately 90% of the total contribution of the LDOSpeaks (in Fig. 2) is due to the slow-light modes of thetype I HMM, i.e τSL/τ ≈ 0.9. However, these modesare lossy and hence would be eventually absorbed inthe metamaterial. Only 10% of the light is reflectedfrom the metamaterial and reaches the far-field. Thefigure of merit for the slow-light mode, considering re-alistic losses and dispersion, is Re(kslx )/Im(kslx ) ≈ 15where kslx is the wavector of the slow light mode. Thisdemonstrates that the majority of the enhancementfactors are a direct result of the metamaterial VHS,and not the high-k modes of the HMM. The VHS con-tribution could be measured by a far-field detector byusing appropriate out-coupling techniques to convertthe confined slow-light mode into propagating waves.

6.2 Optical Sensing

Another potential application is shown in Fig. 5 (c),which shows the sensitivity of slow light modes to re-

fractive index changes – an important feature for theoptical sensing of biological molecules or compact de-vices for gas monitoring[31] . We modeled the LDOSbetween two 240nm EMT HMM slabs, with an em-bedded layer thickness of 80nm (see Fig. 5(c) inset).This can be probed for example by embedded fluo-rescent molecules or absorbed gases.

Fig. 5(c) shows the LDOS enhancement normalizedto free-space for different refractive indices n of theembedded layer. Note that the peaks red shift as therefractive index increases. The sensitivity, given bylarger shifts, also increases in relation to the increas-ing dispersion in the longer wavelength range[5]. Theinset shows a linear variation of 450nm wavelengthpeak within this refractive index regime. The linear-ity is valid in the first order approximation when therefractive index changes are not very large. The effec-tive index of the slow light varies slowly with smallperturbations of the homogenized metamaterial re-sponse.

6.3 Thermal Engineering

We expect a major application of the predicted nar-rowband enhancement in the LDOS to be in near-field thermal emission beyond the black body limit.Recently, it has been shown that hyperbolic metama-terials can provide broadband super-planckian ther-mal emission[18] that is useful for thermal manage-ment and coherent thermal sources. Thermal energytransfer using van hove singularities will be importantfor near-field thermophotovoltaics [32] where narrow-band super-planckian emission matched to a photo-voltaic cell is required. Note that near-field thermalemission spectroscopy can detect the unique spec-tral signatures of these Van Hove Singularities. Ourrecent work shows that the metamaterial Van Hovesingularity presented here leads to narrowband super-planckian thermal emission[33] which can be detectedby near-field thermal emission spectroscopy[34]. Adetailed analysis of near-field thermal engineering us-ing Van Hove singularities will be published else-where.

6.4 Active Devices

A final important application of the metamaterialVHS will be in active plasmonic devices[6, 35, 36].In such devices, large gain becomes necessary tocompensate for metallic losses that hinder the de-vice performance of many plasmonic systems. TheVHS is ideal for these applications because it pro-

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vides a very large group index leading to large gainenhancement factors[37]. Controlling the decay chan-nels of the gain medium can minimize the thresholdfor nano-lasing [38]. Also, the large PDOS of theVHS provides a dominant channel for which the gainmedium emit into, thus achieving optimal control ofgain medium’s emission.We emphasize that both mul-tilayer and nanowire hyperbolic metamaterials can beused for active devices and van hove singularity nano-lasers.

7 Conclusion

To conclude, we have introduced the photonic ana-logue of the electronic Van Hove singularity in meta-materials based on hyperbolic dispersion. We haveshown that they exhibit a very high LDOS despitematerial absorption and dispersion. We also high-lighted some important applications of the metama-terial VHS through lifetime and active devices. TheVHS also showed high sensitivity to refractive in-dex changes opening the possibility of nanowaveg-uide sensors. The multilayer platform that we havepresented is accessible to many experimentalists, andis suitable for future studies focusing on the realiza-tion of stopped-light in active media. This work willalso be important for other applications in non-linearmetamaterials and quantum optics.

8 Acknowledgments

The authors would like thank A. Fedyanin for insight-ful discussions.

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