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Title: Computational inverse design for cascaded systems of metasurface optics

Abstract

Metasurfaces are an emerging technology that may supplant many of the conventional optics found in imaging devices, displays, and precision scientific instruments. Here, we develop a method for designing optical systems composed of multiple unique metasurfaces aligned in sequence and separated by distances much larger than the design wavelengths. Our approach is based on computational inverse design, also known as the adjoint-gradient method. This technique enables thousands or millions of independent design variables (e.g., the shapes of individual meta-atoms) to be optimized in parallel, with little or no intervention required by the user. The assumptions underlying our method are as follows: we use the local periodic approximation to determine the phase-response of a given meta-atom, we use the scalar wave approximation to propagate light fields between metasurface layers, and we do not consider multiple reflections between metasurface layers (analogous to a sequential-optics ray-tracer). To demonstrate the broad applicability of our method, we use it to design an achromatic doublet metasurface lens, a spectrally-multiplexed holographic element, and an ultra-compact optical neural network for classifying handwritten digits.

Authors:
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1569505
Alternate Identifier(s):
OSTI ID: 1574806
Report Number(s):
SAND2019-6842J
Journal ID: ISSN 1094-4087; OPEXFF
Grant/Contract Number:  
NA0003525; AC04-94AL85000
Resource Type:
Published Article
Journal Name:
Optics Express
Additional Journal Information:
Journal Name: Optics Express Journal Volume: 27 Journal Issue: 21; Journal ID: ISSN 1094-4087
Publisher:
Optical Society of America (OSA)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Backer, Adam S. Computational inverse design for cascaded systems of metasurface optics. United States: N. p., 2019. Web. doi:10.1364/OE.27.030308.
Backer, Adam S. Computational inverse design for cascaded systems of metasurface optics. United States. doi:10.1364/OE.27.030308.
Backer, Adam S. Mon . "Computational inverse design for cascaded systems of metasurface optics". United States. doi:10.1364/OE.27.030308.
@article{osti_1569505,
title = {Computational inverse design for cascaded systems of metasurface optics},
author = {Backer, Adam S.},
abstractNote = {Metasurfaces are an emerging technology that may supplant many of the conventional optics found in imaging devices, displays, and precision scientific instruments. Here, we develop a method for designing optical systems composed of multiple unique metasurfaces aligned in sequence and separated by distances much larger than the design wavelengths. Our approach is based on computational inverse design, also known as the adjoint-gradient method. This technique enables thousands or millions of independent design variables (e.g., the shapes of individual meta-atoms) to be optimized in parallel, with little or no intervention required by the user. The assumptions underlying our method are as follows: we use the local periodic approximation to determine the phase-response of a given meta-atom, we use the scalar wave approximation to propagate light fields between metasurface layers, and we do not consider multiple reflections between metasurface layers (analogous to a sequential-optics ray-tracer). To demonstrate the broad applicability of our method, we use it to design an achromatic doublet metasurface lens, a spectrally-multiplexed holographic element, and an ultra-compact optical neural network for classifying handwritten digits.},
doi = {10.1364/OE.27.030308},
journal = {Optics Express},
number = 21,
volume = 27,
place = {United States},
year = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1364/OE.27.030308

Citation Metrics:
Cited by: 4 works
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Works referenced in this record:

Multicolor localization microscopy and point-spread-function engineering by deep learning
journal, January 2019

  • Hershko, Eran; Weiss, Lucien E.; Michaeli, Tomer
  • Optics Express, Vol. 27, Issue 5
  • DOI: 10.1364/OE.27.006158

Inverse design of large-area metasurfaces
journal, January 2018

  • Pestourie, Raphaël; Pérez-Arancibia, Carlos; Lin, Zin
  • Optics Express, Vol. 26, Issue 26
  • DOI: 10.1364/OE.26.033732

Inverse design of optical elements based on arrays of dielectric spheres
journal, January 2018

  • Zhan, Alan; Fryett, Taylor K.; Colburn, Shane
  • Applied Optics, Vol. 57, Issue 6
  • DOI: 10.1364/AO.57.001437

A broadband achromatic metalens in the visible
journal, January 2018


Periodic Dielectric Metasurfaces with High-Efficiency, Multiwavelength Functionalities
journal, October 2017

  • Sell, David; Yang, Jianji; Doshay, Sage
  • Advanced Optical Materials, Vol. 5, Issue 23
  • DOI: 10.1002/adom.201700645

Broadband achromatic optical metasurface devices
journal, August 2017


Flat dielectric grating reflectors with focusing abilities
journal, May 2010


Inverse-Designed Broadband All-Dielectric Electromagnetic Metadevices
journal, January 2018


High-Efficiency Dielectric Huygens’ Surfaces
journal, February 2015

  • Decker, Manuel; Staude, Isabelle; Falkner, Matthias
  • Advanced Optical Materials, Vol. 3, Issue 6, p. 813-820
  • DOI: 10.1002/adom.201400584

Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations
journal, November 2016

  • Arbabi, Amir; Arbabi, Ehsan; Kamali, Seyedeh Mahsa
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms13682

Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces
journal, January 2017


Topology-optimized metasurfaces: impact of initial geometric layout
journal, January 2017


Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission
journal, August 2015

  • Arbabi, Amir; Horie, Yu; Bagheri, Mahmood
  • Nature Nanotechnology, Vol. 10, Issue 11, p. 937-943
  • DOI: 10.1038/nnano.2015.186

Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics
journal, January 2003

  • Hasman, Erez; Kleiner, Vladimir; Biener, Gabriel
  • Applied Physics Letters, Vol. 82, Issue 3
  • DOI: 10.1063/1.1539300

Training of photonic neural networks through in situ backpropagation and gradient measurement
journal, January 2018


Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers, Part 2
journal, January 1999

  • Reuther, James J.; Jameson, Antony; Alonso, Juan J.
  • Journal of Aircraft, Vol. 36, Issue 1
  • DOI: 10.2514/2.2414

Sub-Wavelength Grating Lenses With a Twist
journal, July 2014

  • Vo, Sonny; Fattal, David; Sorin, Wayne V.
  • IEEE Photonics Technology Letters, Vol. 26, Issue 13, p. 1375-1378
  • DOI: 10.1109/LPT.2014.2325947

Multiwavelength metasurfaces through spatial multiplexing
journal, September 2016

  • Arbabi, Ehsan; Arbabi, Amir; Kamali, Seyedeh Mahsa
  • Scientific Reports, Vol. 6, Issue 1
  • DOI: 10.1038/srep32803

Nonlinear total variation based noise removal algorithms
journal, November 1992


A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures
journal, January 2019


Genetically optimized all-dielectric metasurfaces
journal, January 2017

  • Egorov, Victor; Eitan, Michal; Scheuer, Jacob
  • Optics Express, Vol. 25, Issue 3
  • DOI: 10.1364/OE.25.002583

Fully-automated optimization of grating couplers
journal, January 2018

  • Su, Logan; Trivedi, Rahul; Sapra, Neil V.
  • Optics Express, Vol. 26, Issue 4
  • DOI: 10.1364/OE.26.004023

Subwavelength-thick lenses with high numerical apertures and large efficiency based on high-contrast transmitarrays
journal, May 2015

  • Arbabi, Amir; Horie, Yu; Ball, Alexander J.
  • Nature Communications, Vol. 6, Article No. 7069
  • DOI: 10.1038/ncomms8069

Multilayer Noninteracting Dielectric Metasurfaces for Multiwavelength Metaoptics
journal, November 2018


Reconfigurable Imaging Systems Using Elliptical Nanowires
journal, October 2011

  • Schonbrun, Ethan; Seo, Kwanyong; Crozier, Kenneth B.
  • Nano Letters, Vol. 11, Issue 10
  • DOI: 10.1021/nl202324s

Efficient Light Bending with Isotropic Metamaterial Huygens’ Surfaces
journal, April 2014

  • Pfeiffer, Carl; Emani, Naresh K.; Shaltout, Amr M.
  • Nano Letters, Vol. 14, Issue 5
  • DOI: 10.1021/nl5001746

Adjoint Method and Inverse Design for Nonlinear Nanophotonic Devices
journal, November 2018


Chromatic-aberration-corrected diffractive lenses for ultra-broadband focusing
journal, February 2016

  • Wang, Peng; Mohammad, Nabil; Menon, Rajesh
  • Scientific Reports, Vol. 6, Issue 1
  • DOI: 10.1038/srep21545

High efficiency double-wavelength dielectric metasurface lenses with dichroic birefringent meta-atoms
journal, January 2016

  • Arbabi, Ehsan; Arbabi, Amir; Kamali, Seyedeh Mahsa
  • Optics Express, Vol. 24, Issue 16
  • DOI: 10.1364/OE.24.018468

Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer
journal, May 2015

  • Piggott, Alexander Y.; Lu, Jesse; Lagoudakis, Konstantinos G.
  • Nature Photonics, Vol. 9, Issue 6, p. 374-377
  • DOI: 10.1038/nphoton.2015.69

Light Trapping Textures Designed by Electromagnetic Optimization for Subwavelength Thick Solar Cells
journal, January 2014


Nanophotonic computational design
journal, January 2013


Meta-Lens Doublet in the Visible Region
journal, July 2017


Metasurface optics for full-color computational imaging
journal, February 2018


Achromatic combinations of hologram optical elements
journal, January 1976


A broadband achromatic metalens for focusing and imaging in the visible
journal, January 2018


Simultaneous measurement of emission color and 3D position of single molecules
journal, January 2016

  • Smith, Carlas; Huisman, Max; Siemons, Marijn
  • Optics Express, Vol. 24, Issue 5
  • DOI: 10.1364/OE.24.004996

Nano-optic endoscope for high-resolution optical coherence tomography in vivo
journal, July 2018

  • Pahlevaninezhad, Hamid; Khorasaninejad, Mohammadreza; Huang, Yao-Wei
  • Nature Photonics, Vol. 12, Issue 9
  • DOI: 10.1038/s41566-018-0224-2

Achromatic Metalens over 60 nm Bandwidth in the Visible and Metalens with Reverse Chromatic Dispersion
journal, February 2017


Phase-retrieval algorithms for a complicated optical system
journal, January 1993


Deep learning with coherent nanophotonic circuits
journal, June 2017


Achromatic metalens array for full-colour light-field imaging
journal, January 2019


Decoupling optical function and geometrical form using conformal flexible dielectric metasurfaces
journal, May 2016

  • Kamali, Seyedeh Mahsa; Arbabi, Amir; Arbabi, Ehsan
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms11618

Adjoint shape optimization applied to electromagnetic design
journal, January 2013

  • Lalau-Keraly, Christopher M.; Bhargava, Samarth; Miller, Owen D.
  • Optics Express, Vol. 21, Issue 18
  • DOI: 10.1364/OE.21.021693

Large-Angle, Multifunctional Metagratings Based on Freeform Multimode Geometries
journal, May 2017


Low-Contrast Dielectric Metasurface Optics
journal, January 2016


Inverse design in nanophotonics
journal, October 2018


Sensitivity analysis and optimization of sub-wavelength optical gratings using adjoints
journal, January 2014

  • Niederberger, Armand C. R.; Fattal, David A.; Gauger, Nicolas R.
  • Optics Express, Vol. 22, Issue 11
  • DOI: 10.1364/OE.22.012971

Some fundamental limitations of achromatic holographic systems
journal, January 1989

  • Buralli, Dale A.; Rogers, John R.
  • Journal of the Optical Society of America A, Vol. 6, Issue 12, p. 1863-1868
  • DOI: 10.1364/JOSAA.6.001863

Design and fabrication of blazed binary diffractive elements with sampling periods smaller than the structural cutoff
journal, January 1999

  • Lalanne, Philippe; Astilean, Simion; Chavel, Pierre
  • Journal of the Optical Society of America A, Vol. 16, Issue 5, p. 1143-1156
  • DOI: 10.1364/JOSAA.16.001143

Broadband Achromatic Metasurface-Refractive Optics
journal, November 2018


Feasible adjoint sensitivity technique for EM design optimization
journal, December 2002

  • Georgieva, N. K.; Glavic, S.; Bakr, M. H.
  • IEEE Transactions on Microwave Theory and Techniques, Vol. 50, Issue 12
  • DOI: 10.1109/TMTT.2002.805131

Optical metasurfaces for high angle steering at visible wavelengths
journal, May 2017


Composite functional metasurfaces for multispectral achromatic optics
journal, April 2017

  • Avayu, Ori; Almeida, Euclides; Prior, Yehiam
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms14992

A review of dielectric optical metasurfaces for wavefront control
journal, June 2018


Single-Layer Metasurface with Controllable Multiwavelength Functions
journal, February 2018


Dielectric gradient metasurface optical elements
journal, July 2014


Topology optimization for nano-photonics
journal, December 2010


Polarization-Insensitive Metalenses at Visible Wavelengths
journal, October 2016


Polarization-Independent Silicon Metadevices for Efficient Optical Wavefront Control
journal, July 2015


Topology optimization of freeform large-area metasurfaces
journal, January 2019

  • Lin, Zin; Liu, Victor; Pestourie, Raphael
  • Optics Express, Vol. 27, Issue 11
  • DOI: 10.1364/OE.27.015765

Metasurface Polarization Optics: Independent Phase Control of Arbitrary Orthogonal States of Polarization
journal, March 2017


Fabrication-constrained nanophotonic inverse design
journal, May 2017


Phase retrieval algorithms: a comparison
journal, January 1982


Hybrid optical-electronic convolutional neural networks with optimized diffractive optics for image classification
journal, August 2018


All-optical nonlinear activation function for photonic neural networks [Invited]
journal, January 2018

  • Miscuglio, Mario; Mehrabian, Armin; Hu, Zibo
  • Optical Materials Express, Vol. 8, Issue 12
  • DOI: 10.1364/OME.8.003851

Diffractive doublets corrected at two wavelengths
journal, January 1991

  • Farn, Michael W.; Goodman, Joseph W.
  • Journal of the Optical Society of America A, Vol. 8, Issue 6
  • DOI: 10.1364/JOSAA.8.000860

Broadband achromatic dielectric metalenses
journal, November 2018


A multi-directional backlight for a wide-angle, glasses-free three-dimensional display
journal, March 2013

  • Fattal, David; Peng, Zhen; Tran, Tho
  • Nature, Vol. 495, Issue 7441, p. 348-351
  • DOI: 10.1038/nature11972

Topology-Optimized Multilayered Metaoptics
journal, April 2018


Broadband high-efficiency dielectric metasurfaces for the visible spectrum
journal, September 2016

  • Devlin, Robert C.; Khorasaninejad, Mohammadreza; Chen, Wei Ting
  • Proceedings of the National Academy of Sciences, Vol. 113, Issue 38
  • DOI: 10.1073/pnas.1611740113

Huygens’ Metasurfaces Enabled by Magnetic Dipole Resonance Tuning in Split Dielectric Nanoresonators
journal, June 2017


Gradient-based learning applied to document recognition
journal, January 1998

  • Lecun, Y.; Bottou, L.; Bengio, Y.
  • Proceedings of the IEEE, Vol. 86, Issue 11
  • DOI: 10.1109/5.726791

Multicolour localization microscopy by point-spread-function engineering
journal, August 2016


High-efficiency, large-area, topology-optimized metasurfaces
journal, May 2019


Recent advances in planar optics: from plasmonic to dielectric metasurfaces
journal, January 2017


All-optical machine learning using diffractive deep neural networks
journal, July 2018


Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging
journal, June 2016

  • Khorasaninejad, Mohammadreza; Chen, Wei Ting; Devlin, Robert C.
  • Science, Vol. 352, Issue 6290
  • DOI: 10.1126/science.aaf6644

Visible-Frequency Dielectric Metasurfaces for Multiwavelength Achromatic and Highly Dispersive Holograms
journal, July 2016


Colored point spread function engineering for parallel confocal microscopy
journal, January 2016

  • Jesacher, Alexander; Bernet, Stefan; Ritsch-Marte, Monika
  • Optics Express, Vol. 24, Issue 24
  • DOI: 10.1364/OE.24.027395

Cascaded metasurfaces for complete phase and polarization control
journal, June 2013

  • Pfeiffer, Carl; Grbic, Anthony
  • Applied Physics Letters, Vol. 102, Issue 23
  • DOI: 10.1063/1.4810873

    Works referencing / citing this record:

    VIPR: vectorial implementation of phase retrieval for fast and accurate microscopic pixel-wise pupil estimation
    journal, January 2020

    • Ferdman, Boris; Nehme, Elias; Weiss, Lucien E.
    • Optics Express, Vol. 28, Issue 7
    • DOI: 10.1364/oe.388248