Complex Nanophotonics Hui Cao Department of Applied Physics Department of Electrical Engineering Department of Physics Yale University
Complex Nanophotonics
Hui CaoDepartment of Applied Physics
Department of Electrical EngineeringDepartment of Physics
Yale University
Complex Nanophotonics
Light transport, absorp/on, amplifica/on, lasing in
• Disordered or par/ally disordered nanostructures
• Wave-chao/c microcavi/es
• Mul/mode fiber with random mode mixing
2
3
Light Scattering
Fog
Paint
Tissue
Coherent Control of Light Transport
Phys. Rev. Le+. 112, 023904 (2014)
Objective
Camera
100x
100x
Objective
Spatial light modulator
Laser
Maximizing Transmission
5
0 0.5 10
50
100
150
200
z/L
I(z)
0 0.5 10
20
40
60
80
z/L
I(z)
Arbitrary Input
Optimized Input
Phys. Rev. Le+. 117, 086803 (2016)
T = 4.7% T = 48%
Chaotic ray dynamics
Wave-Chaotic Microcavity
Rev. Mod. Phys. 87, 61 (2015)
R
R/2
x
Fighting Laser Chaos with Wave Chaos
50 ns50 ns
Regular cavity
Chaotic cavity
8
Multimode Optical Fiber
Short-haul communication Biomedical imaging
Multimode Fiber
Spectrum
Time
Space
• Compressive sensing
• Machine Learning
Multifunctional Sensor
A. Douglas StoneComplex and non-linear optical systems• Laser theory and complex micro/nano lasers• Quantum/wave chaos, random matrix theory• Linear and non-linear optics in complex media• Predicting and controlling NL instabilities• Control of light propagation in random media• Longstanding collaboration with Cao group
Spatial light modulator (SLM)
Sca4ering medium
Question: can we focus to a larger spot (many speckles)?
12
Challenge: Global control at scales R >> 𝜆
q Motivation: imaging, energy delivery, phototherapy...
q Existing theory suggested this was impossible – assumed uncorrelated speckle pattern
13
Polarizer
Laser
Typical input Maximization Minimization10
1
0.1Increased 5 times Reduced 3 times
Output on CCD: 1700 target channels
ZnO particles
𝐿 ≈ 60𝜇m ≫ 𝑙!
)𝑇 ≈ 3%(phaseonly)
Hsu et al, 2017
But it is possible!
Theory: “Filtered” random matrix theory predicts focusing enhancement to high accuracy
r=0.15λ,ε=1.28 + 1.75i
r=λ,ε=2.25
New Topic: perfect absorption in nanophotonic structuresCan I find a steady-state input wave at some 𝜔which will be perfectly absorbed by the “buried” absorber?
Yes!
Also: know the nec. and suff. conditions for this soln to exist.
Example of coherent perfect absorption(Chong et al, PRL 2010, Wan et al. Scence 2011)
Also with Cao group
Resonances/Lasing and CPA
15
𝜔-./01213.Im{𝜔}
Re{𝜔}
𝐇 𝐫 𝑒4567
add gain
decay in time
lase
𝛻×1𝜀 𝐫 𝛻× 𝐇 𝐫 =
𝜔𝑐
"𝐇 𝐫
= 𝐇 𝐫 𝑒456!786"7
Outgoing only(no input)
magnetic field
Can solve by matching at a boundary surface or by using a perfectly matched layer (PML) to find complex {𝜔"}
Solve Maxwell wave eq. with purely outgoing BC
Coherent perfect absorption (CPA)
16
Im{𝜔}
Re{𝜔}
𝐇 𝐫 𝑒4567
add absorption
growth in time
CPA
𝛻×1𝜀 𝐫 𝛻× 𝐇 𝐫 =
𝜔𝑐
"𝐇 𝐫
= 𝐇 𝐫 𝑒456!786"7
Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, Phys. Rev. Le+. 105, 053901 (2010) D.G. Baranov, A. Krasnok, T. Shegai, A. Alù, and Y. Chong, NRM 2, 17064 (2017)
Incoming only(no output)
magnePc field
General concept of reflectionless scattering modes
17
𝜀 𝐫
𝟎𝟎𝟎𝛽!⋮𝛽"
=
𝑆#,# 𝑆#,% 𝑆#,& ⋯ 𝑆#,"𝑆%,#𝑆&,#⋮
𝑆%,% 𝑆%,&𝑆&,% 𝑆&,& ⋮⋮ ⋮
⋮
𝑆",# 𝑆",% 𝑆",& ⋯ 𝑆","
𝛼#𝛼%𝛼&𝟎⋮𝟎
scattering matrix 𝑆
inputoutput
Generalized reflec:on matrix
𝑅#$
𝛼#$
Can prove gives the same mathematical structure as resonance or CPA=> ∃ countably infinite discrete solutions in the complex 𝜔 plane=> tunable to real frequency with a single parameter=> Don’t need to add gain or loss (tune geometry)
𝛼#
𝛼$
𝛼%
No back reflec`on
CPA and Reflectionless Scattering Modes (RSMs)
Im{𝜔}) 𝑅/𝑐
Vision: solve complex optimization problems in nanophotonics using this as a starting pointNew : Exceptional points for RSMs provide structures which may be used for sensitive detectors and to illustrate topological photonics
Reflectionless despite wave chaos
Nanophotonics by design: Reaching the Limits of Light-Matter Interactions
Owen Miller, Yale Applied Physics
& Energy Sciences Institutemillergroup.yale.edu/{people,publications,talks}
Industrial VR/ARfunding + collaboration
Postdoc Phys, Yr. 5 AP, Yr. 3 AP, Yr. 2 EE, Yr. 2 AP, Yr. 2 UndergradHKU
UndergradYale
The Photonics Design Challenge• Nanophotonics is the study of light interacting with
materials patterned at the scale of the wavelength• Nanolithography and chemical-synthesis techniques
are enabling control over thousands -> billions of structural degrees of freedom
à What should we make?
à What performance / functionality / phenomena are possible?
Design and Optimization with WavesTwo thrusts:
• Fast and efficient large-scale (nonconvex) computational optimization techniques
• Inverse design• Machine learning
• Analytical and computational approaches to identify global bounds to what is possible (“fundamental physical limits”)
In a feedback loop with experimental capabilities and industrial applications
Near-field OpticsFor spontaneous emission, radiative heat transfer, Raman scattering, quantum entanglement between qubits, etc., near-field coupling can lead to dramatic rate enhancements.
Physical insight + convex optimization + contour integration
High-efficiency plasmonic resonators
Nano Lett. 17, 3238 (2017)
Power-bandwidth limits for near-field RHT
Phys. Rev. X 9, 011043 (2019)
Photovoltaics, Brightness TheoremExploit complex designs to circumvent classical “brightness-theorem” constraints on multijunction photovoltaics
Generalize brightness-theorem constraints to wave physics
1-junction: 33.5%2-junction design: 36.6%3-junction design: 37.1%
in preparation
Thin, High-Functionality MetasurfacesHigh-numerical-aperture, broad-bandwidth metalenses
Tunable liquid-crystal-based metasurfaces
Opt. Express 28, 6945 (2020)
arXiv: 1910.03132
Ongoing Collaborations w/ Experimental Groups
• Nanoparticle scatterers (Vaia, AFRL)• Near-field RHT (Reddy/Meyhofer/Forrest, U. Mich)• Lenses for maskless lithography (Smith, MIT)• Ideal mode-couplers (Rakich, Yale & Tang, Yale)• Topological slow-light devices (Rechtsman, Penn St.)• Low-loss, high-index materials at optical frequencies (Haglund,
Vanderbilt)• VR/AR optics (industrial collaborator)