All-optical synthesis of an arbitrary linear transformation using diffractive surfaces

Onur Kulce; Deniz Mengu; Yair Rivenson; Aydogan Ozcan

doi:10.1038/s41377-021-00623-5

Go to Nature Website

Your Location：

Home >

Browse articles >

All-optical synthesis of an arbitrary linear transformation using diffractive surfaces

Article

- All-optical synthesis of an arbitrary linear transformation using diffractive surfaces
- Light: Science & Applications Vol. 10, Issue 10, Pages: 1928-1948(2021)
- Affiliations：
  
  1.Electrical and Computer Engineering Department, University of California, Los Angeles, CA, 90095, USA
  2.Bioengineering Department, University of California, Los Angeles, CA, 90095, USA
  3.California NanoSystems Institute, University of California, Los Angeles, CA, 90095, USA
- Author bio：
  
  Aydogan Ozcan (ozcan@ucla.edu)
- Funds：
- DOI：10.1038/s41377-021-00623-5
  CLC：
- Published：31 October 2021，
  
  Published Online：24 September 2021，
  
  Received：20 April 2021，
  
  Revised：20 August 2021，
  
  Accepted：23 August 2021
- Accepted：
Scan QR Code
Kulce, O. et al. All-optical synthesis of an arbitrary linear transformation using diffractive surfaces. Light: Science & Applications, 10, 1928-1948 (2021).
DOI：

Kulce, O. et al. All-optical synthesis of an arbitrary linear transformation using diffractive surfaces. Light: Science & Applications, 10, 1928-1948 (2021). DOI： 10.1038/s41377-021-00623-5.

摘要

Abstract

Spatially-engineered diffractive surfaces have emerged as a powerful framework to control light-matter interactions for statistical inference and the design of task-specific optical components. Here

we report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input (

) and output (

)

where

and

represent the number of pixels at the input and output fields-of-view (FOVs)

respectively. First

we consider a single diffractive surface and use a matrix pseudoinverse-based method to determine the complex-valued transmission coefficients of the diffractive features/neurons to all-optically perform a desired/target linear transformation. In addition to this data-free design approach

we also consider a deep learning-based design method to optimize the transmission coefficients of diffractive surfaces by using examples of input/output fields corresponding to the target transformation. We compared the all-optical transformation errors and diffraction efficiencies achieved using data-free des

igns as well as data-driven (deep learning-based) diffractive designs to all-optically perform (i) arbitrarily-chosen complex-valued transformations including unitary

nonunitary

and noninvertible transforms

(ii) 2D discrete Fourier transformation

(iii) arbitrary 2D permutation operations

and (iv) high-pass filtered coherent imaging. Our analyses reveal that if the total number (

) of spatially-engineered diffractive features/neurons is ≥

both design methods succeed in all-optical implementation of the target transformation

achieving negligible error. However

compared to data-free designs

deep learning-based diffractive designs are found to achieve significantly larger diffraction efficiencies for a given

and their all-optical transformations are more accurate for

. These conclusions are generally applicable to various optical processors that employ spatially-engineered diffractive surfaces.

关键词

Keywords

references

Wetzstein, G. et al. Inference in artificial intelligence with deep optics and photonics.Nature588, 39–47 (2020)..

Ozaktas, H. M., Zalevsky, Z.&Kutay, M. A.The Fractional Fourier Transform: With Applications in Optics and Signal Processing.(Wiley, New York, 2001).

Goodman, J. W.Introduction to Fourier Optics, 3rd edn (Greenwoood Village: Roberts&Company Publishers, 2005).

Athale, R.&Psaltis, D. Optical computing: past and future.Opt. Photonics N.27, 32–39 (2016)..

Solli, D. R.&Jalali, B. Analog optical computing.Nat. Photonics9, 704–706 (2015)..

Zangeneh-Nejad, F. et al. Analogue computing with metamaterials.Nat. Rev. Mater.6, 207–225 (2021)..

Miller, D. A. B. Self-configuring universal linear optical component.Photonics Res.1, 1–15 (2013)..

Reck, M. et al. Experimental realization of any discrete unitary operator.Phys. Rev. Lett.73, 58–61 (1994)..

Goodman, J. W., Dias, A. R.&Woody, L. M. Fully parallel, high-speed incoherent optical method for performing discrete Fourier transforms.Opt. Lett.2, 1–3 (1978)..

Slavík, R. et al. Photonic temporal integrator for all-optical computing.Opt. Express16, 18202–18214 (2008)..

Goodman, J. W.&Woody, L. M. Method for performing complex-valued linear operations on complex-valued datausing incoherent light.Appl. Opt.16, 2611–2612 (1977)..

Farhat, N. H. et al. Optical implementation of the Hopfield model.Appl. Opt.24, 1469–1475 (1985)..

Athale, R. A.&Collins, W. C. Optical matrix–matrix multiplier based on outer product decomposition.Appl. Opt.21, 2089–2090 (1982)..

Sawchuk, A. A.&Strand, T. C. Digital optical computing.Proc. IEEE72, 758–779 (1984)..

Moeini, M. M.&Sounas, D. L. Discrete space optical signal processing.Optica7, 1325–1331 (2020)..

Silva, A. et al. Performing mathematical operations with metamaterials.Science343, 160–163 (2014)..

Miscuglio, M. et al. Massively parallel amplitude-only Fourier neural network.Optica7, 1812–1819 (2020)..

Yu, F. T. S.&Jutamulia, S.Optical Signal Processing, Computing, and Neural Networks(Wiley, Hoboken, 1992).

Duport, F. et al. All-optical reservoir computing.Opt. Express20, 22783–22795 (2012)..

Knill, E., Laflamme, R.&Milburn, G. J. A scheme for efficient quantum computation with linear optics.Nature409, 46–52 (2001)..

Shen, Y. C. et al. Deep learning with coherent nanophotonic circuits.Nat. Photonics11, 441–446 (2017)..

Pendry, J. B. Negative refraction makes a perfect lens.Phys. Rev. Lett.85, 3966–3969 (2000)..

Pendry, J. B., Schurig, D.&Smith, D. R. Controlling electromagnetic fields.Science312, 1780–1782 (2006)..

Cai, W. S. et al. Optical cloaking with metamaterials.Nat. Photonics1, 224–227 (2007)..

Valentine, J. et al. An optical cloak made of dielectrics.Nat. Mater.8, 568–571 (2009)..

Oulton, R. F. et al. Plasmon lasers at deep subwavelength scale.Nature461, 629–632 (2009)..

Estakhri, N. M., Edwards, B.&Engheta, N. Inverse-designed metastructures that solve equations.Science363, 1333–1338 (2019)..

Lin, X. et al. All-optical machine learning using diffractive deep neural networks.Science361, 1004–1008 (2018)..

Li, J. X. et al. Spectrally encoded single-pixel machine vision using diffractive networks.Sci. Adv.7, eabd7690 (2021)..

Rahman, M. S. S. et al. Ensemble learning of diffractive optical networks.Light Sci. Appl.10, 14 (2021)..

Mengu, D. et al. Misalignment resilient diffractive optical networks.Nanophotonics9, 4207–4219 (2020)..

Veli, M. et al. Terahertz pulse shaping using diffractive surfaces.Nat. Commun.12, 37 (2021)..

Mengu, D., Rivenson, Y.&Ozcan, A. Scale-, shift-, and rotation-invariant diffractive optical networks.ACS Photonics8, 324–334 (2021)..

Luo, Y. et al. Design of task-specific optical systems using broadband diffractive neural networks.Light Sci. Appl.8, 112 (2019)..

Kulce, O. et al. All-optical information-processing capacity of diffractive surfaces.Light Sci. Appl.10, 25 (2021)..

Zuo, Y. et al. All-optical neural network with nonlinear activation functions.Optica6, 1132–1137 (2019)..

Dinc, N. U. et al. Computer generated optical volume elements by additive manufacturing.Nanophotonics9, 4173–4181 (2020)..

Kulce, O., Onural, L.&Ozaktas, H. M. Evaluation of the validity of the scalar approximation in optical wave propagation using a systems approach and an accurate digital electromagnetic model.J. Mod. Opt.63, 2382–2391 (2016)..

Kulce, O.&Onural, L. Power spectrum equalized scalar representation of wide-angle optical field propagation.J. Math. Imaging Vis.60, 1246–1260 (2018)..

Kulce, O.&Onural, L. Generation of a polarized optical field from a given scalar field for wide-viewing-angle holographic displays.Opt. Lasers Eng.137, 106344 (2021)..

Moon, T. K.&Stirling, W. C.Mathematical Methods and Algorithms for Signal Processing(Upper Saddle River: Prentice Hall, 2000).

Oppenheim, A. V., Schafer, R. W.&Buck, J. R.Discrete-Time Signal Processing(Prentice Hall, Upper Saddle River, 1999).

Hayes, M. H.Statistical Digital Signal Processing and Modeling(Wiley, New York, 1996).

Wang, H. Y.&Piestun, R. Dynamic 2D implementation of 3D diffractive optics.Optica5, 1220–1228 (2018)..

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

⁰