Leveraging Chaos for Wave-Based Analog Computation: Demonstration with Indoor Wireless Communication Signals

In sight of fundamental thermal limits on further substantial performance improvements of modern digital computational processing units, wave-based analog computation is becoming an enticing alternative. A wave, as it propagates through a carefully tailored medium, performs the desired computational operation. Yet, the necessary designs are so intricate that experimental demonstrations will necessitate further technological advances. Here, we show that, counterintuitively, the carefully tailored medium can be replaced with a random medium, subject to an appropriate shaping of the incident wave front. Using tunable metasurface reflect-arrays, we demonstrate our concept experimentally in a chaotic microwave cavity. We conclude that off-the-shelf wireless communication infrastructure in combination with a simple reflect-array suffices to perform analog computation with Wi-Fi waves reverberating in a room.

[1]  David A. B. Miller,et al.  Self-configuring universal linear optical component [Invited] , 2013, 1303.4602.

[2]  E. G. van Putten,et al.  Scattering lens resolves sub-100 nm structures with visible light. , 2011, Physical review letters.

[3]  D. Sievenpiper,et al.  Metasurfaces and their applications , 2018, Nanophotonics.

[4]  Aris L. Moustakas,et al.  Communication in a Disordered World , 2001 .

[5]  G. Lerosey,et al.  Controlling waves in space and time for imaging and focusing in complex media , 2012, Nature Photonics.

[6]  Stein,et al.  Microwave studies of billiard Green functions and propagators. , 1995, Physical review letters.

[7]  P. Winzer,et al.  Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages , 2018, Nature.

[8]  G. Lerosey,et al.  Hybridized resonances to design tunable binary phase metasurface unit cells. , 2014, Optics express.

[9]  Edward Ott,et al.  Universal statistics of the scattering coefficient of chaotic microwave cavities. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  S. Popoff,et al.  Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media. , 2009, Physical review letters.

[11]  Michael S Feld,et al.  Overcoming the diffraction limit using multiple light scattering in a highly disordered medium. , 2011, Physical review letters.

[12]  Karthikeyan Sankaralingam,et al.  Dark Silicon and the End of Multicore Scaling , 2012, IEEE Micro.

[13]  Yi Yang,et al.  Nanophotonic particle simulation and inverse design using artificial neural networks , 2018, Science Advances.

[14]  Dieter Gromes,et al.  Über die asymptotische Verteilung der Eigenwerte des Laplace-Operators für Gebiete auf der Kugeloberfläche , 1966 .

[15]  Laurent Daudet,et al.  Intensity-only measurement of partially uncontrollable transmission matrix: demonstration with wave-field shaping in a microwave cavity. , 2016, Optics express.

[16]  Wolfgang Arendt,et al.  Weyl's Law: Spectral Properties of the Laplacian in Mathematics and Physics , 2009 .

[17]  S. Gigan,et al.  Light fields in complex media: Mesoscopic scattering meets wave control , 2017, 1702.05395.

[18]  Sun K. Hong,et al.  Nonlinear Electromagnetic Time Reversal in an Open Semireverberant System , 2014 .

[19]  Brian J. Smith,et al.  Two-photon quantum walk in a multimode fiber , 2015, Science Advances.

[20]  Tom A W Wolterink,et al.  Programmable multiport optical circuits in opaque scattering materials. , 2014, Optics express.

[21]  Ari Sihvola,et al.  Enabling Optical Analog Computing with Metamaterials , 2014, Science.

[22]  Hyok J. Song,et al.  Two-dimensional beam steering using an electrically tunable impedance surface , 2003 .

[23]  H. Zimmermann,et al.  Zero-bias 40Gbit/s germanium waveguide photodetector on silicon. , 2012, Optics express.

[24]  Dimitris Bertsimas,et al.  Robust optimization with simulated annealing , 2010, J. Glob. Optim..

[25]  I. Freund Looking through walls and around corners , 1990 .

[26]  Jing Wang,et al.  Transport through modes in random media , 2011, Nature.

[27]  U. Kuhl,et al.  Classical wave experiments on chaotic scattering , 2005 .

[28]  David R. Smith,et al.  Large Metasurface Aperture for Millimeter Wave Computational Imaging at the Human-Scale , 2017, Scientific Reports.

[29]  Aobo Li,et al.  High-Power Transistor-Based Tunable and Switchable Metasurface Absorber , 2017, IEEE Transactions on Microwave Theory and Techniques.

[30]  Andrea Alù,et al.  Performing Mathematical Operations with Metamaterials , 2014, Science.

[31]  J. Barthélemy,et al.  Complete S matrix in a microwave cavity at room temperature. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Mathias Fink,et al.  Shaping Microwave Fields Using Nonlinear Unsolicited Feedback: Application to Enhance Energy Harvesting , 2017, 1706.00450.

[33]  R. Boyd,et al.  Custom-tailored spatial mode sorting by controlled random scattering , 2017, 1701.05889.

[34]  Vivienne Sze,et al.  Efficient Processing of Deep Neural Networks: A Tutorial and Survey , 2017, Proceedings of the IEEE.

[35]  David A. Hill,et al.  Electromagnetic Fields in Cavities , 2009 .

[36]  A. Mosk,et al.  Phase control algorithms for focusing light through turbid media , 2007, 0710.3295.

[37]  A. Alú,et al.  Full control of nanoscale optical transmission with a composite metascreen. , 2013, Physical review letters.

[38]  M Fink,et al.  Random multiple scattering of ultrasound. II. Is time reversal a self-averaging process? , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  David R. Smith,et al.  Microwave Imaging Using a Disordered Cavity with a Dynamically Tunable Impedance Surface , 2016 .

[40]  Sergio Gomez Colmenarejo,et al.  Hybrid computing using a neural network with dynamic external memory , 2016, Nature.

[41]  Shanhui Fan,et al.  Plasmonic computing of spatial differentiation , 2017, Nature Communications.

[42]  D. Sievenpiper,et al.  High-impedance electromagnetic surfaces with a forbidden frequency band , 1999 .

[43]  J. Goodman Introduction to Fourier optics , 1969 .

[44]  O. Katz,et al.  Focusing and compression of ultrashort pulses through scattering media , 2010, 1012.0413.

[45]  Philipp Ambichl,et al.  Super- and Anti-Principal Modes in Multi-Mode Waveguides , 2017, 1704.05117.

[46]  David R Smith,et al.  Dynamic Metasurface Aperture as Smart Around-the-Corner Motion Detector , 2018, Scientific Reports.

[47]  M. Fink Time reversed acoustics , 2001 .

[48]  A. Mosk,et al.  Control of light transmission through opaque scattering media in space and time. , 2010, Physical review letters.

[49]  David R. Smith,et al.  Precise Localization of Multiple Noncooperative Objects in a Disordered Cavity by Wave Front Shaping. , 2018, Physical review letters.

[50]  Mathias Fink,et al.  Shaping complex microwave fields in reverberating media with binary tunable metasurfaces , 2014, Scientific Reports.

[51]  Lorien Y. Pratt,et al.  A Survey of Connectionist Network Reuse Through Transfer , 1998, Learning to Learn.

[52]  Trevor Darrell,et al.  Caffe: Convolutional Architecture for Fast Feature Embedding , 2014, ACM Multimedia.

[53]  Maokun Li,et al.  A programmable metasurface with dynamic polarization, scattering and focusing control , 2016, Scientific Reports.

[54]  Yongkeun Park,et al.  Subwavelength light focusing using random nanoparticles , 2013, Nature Photonics.

[55]  G. Lerosey,et al.  Wave-Field Shaping in Cavities: Waves Trapped in a Box with Controllable Boundaries. , 2015, Physical review letters.

[56]  Mark Horowitz,et al.  1.1 Computing's energy problem (and what we can do about it) , 2014, 2014 IEEE International Solid-State Circuits Conference Digest of Technical Papers (ISSCC).

[57]  Nikos D. Sidiropoulos,et al.  Transmit beamforming for physical-layer multicasting , 2006, IEEE Transactions on Signal Processing.

[58]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[59]  Andrew S. Cassidy,et al.  Convolutional networks for fast, energy-efficient neuromorphic computing , 2016, Proceedings of the National Academy of Sciences.

[60]  A. Mosk,et al.  Focusing coherent light through opaque strongly scattering media. , 2007, Optics letters.

[61]  Florent Krzakala,et al.  Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques. , 2015, Optics express.

[62]  G.E. Moore,et al.  Cramming More Components Onto Integrated Circuits , 1998, Proceedings of the IEEE.

[63]  Tom Minka,et al.  You are facing the Mona Lisa: spot localization using PHY layer information , 2012, MobiSys '12.

[64]  J. O'Brien,et al.  Universal linear optics , 2015, Science.

[65]  Juerg Leuthold,et al.  100 GHz Plasmonic Photodetector , 2018, ACS Photonics.

[66]  Joe LoVetri,et al.  Use of Field-Perturbing Elements to Increase Nonredundant Data for Microwave Imaging Systems , 2017, IEEE Transactions on Microwave Theory and Techniques.

[67]  A. Mosk,et al.  Exploiting disorder for perfect focusing , 2009, 0910.0873.

[68]  P. Marko,et al.  ABSENCE OF DIFFUSION IN CERTAIN RANDOM LATTICES , 2008 .

[69]  Ari Sihvola,et al.  Metamaterials in electromagnetics , 2007 .

[70]  Wonjun Choi,et al.  Transmission matrix of a scattering medium and its applications in biophotonics. , 2015, Optics express.

[71]  Mathias Fink,et al.  Spatiotemporal Wave Front Shaping in a Microwave Cavity. , 2016, Physical review letters.

[72]  Wim Bogaerts,et al.  Demonstration of a 4 × 4-port universal linear circuit , 2016 .

[73]  Florent Krzakala,et al.  Random projections through multiple optical scattering: Approximating Kernels at the speed of light , 2015, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[74]  Matthew S. Reynolds,et al.  An analysis of beamed wireless power transfer in the Fresnel zone using a dynamic, metasurface aperture , 2016, 1610.06799.

[75]  David A. B. Miller,et al.  Meshing optics with applications , 2017, Nature Photonics.

[76]  Bahram Jalali,et al.  Analog optical computing , 2015, Nature Photonics.

[77]  David R. Smith,et al.  Focusing Microwaves in the Fresnel Zone With a Cavity-Backed Holographic Metasurface , 2018, IEEE Access.

[78]  H. Stöckmann,et al.  Quantum Chaos: An Introduction , 1999 .

[79]  L. R. Arnaut,et al.  Reverberation chambers a la carte: An overview of the different mode-stirring techniques , 2017, IEEE Electromagnetic Compatibility Magazine.