complex nanophotonics · complex and non-linear optical systems •laser theory and complex...
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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)
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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
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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)