Optical complex media as universal reconfigurable linear operators

Abstract

Performing linear operations using optical devices is a crucial building block in many fields ranging from telecommunication to optical analogue computation and machine learning. For many of these applications, key requirements are robustness to fabrication inaccuracies and reconfigurability. Current designs of custom-tailored photonic devices or coherent photonic circuits only partially satisfy these needs. Here, we propose a way to perform linear operations by using complex optical media such as multimode fibers or thin scattering layers as a computational platform driven by wavefront shaping. Given a large random transmission matrix (TM) representing light propagation in such a medium, we can extract a desired smaller linear operator by finding suitable input and output projectors. We discuss fundamental upper bounds on the size of the linear transformations our approach can achieve and provide an experimental demonstration. For the latter, first we retrieve the complex medium's TM with a non-interferometric phase retrieval method. Then, we take advantage of the large number of degrees of freedom to find input wavefronts using a Spatial Light Modulator (SLM) that cause the system, composed of the SLM and the complex medium, to act as a desired complex-valued linear operator on the optical field. We experimentally build several 16 × 16 complex-valued operators, and are able to switch from one to another at will. Our technique offers the prospect of reconfigurable, robust and easy-to-fabricate linear optical analogue computation units. * sebastien.popoff@espci.psl.eu 1 arXiv:1810.05688v1 [physics.optics]

Compressively sampling the optical transmission matrix of a multimode fibre

“…The control of light fields through MMFs has recently attracted growing attention, as MMF-based micro-endoscopy promises video-rate imaging with sub-cellular resolution deep within tissue at the tip of a needle 28 – 30 . MMFs have also been used as mixing elements for classical and quantum optical computing schemes 19 , 20 . Modal dispersion means that an image projected onto one end of an MMF is scrambled into a speckle pattern at the other end, and so, before an MMF can be deployed as a micro-endoscope, it is necessary to first characterise its TM to understand how to invert this scrambling process 7 – 9 .…”

“…Beyond imaging, the information-rich nature of the high-dimensional TM is finding applications in a growing number of areas. Examples include the identification of the principal modes of MMFs to maximise spatial coherence for high-capacity telecom applications 14 , the optimisation of energy delivery inside scattering materials 15 , 16 , the design of optimised optical trapping fields through random scattering systems 17 , 18 , and the creation of new forms of all-optical classical 19 and quantum 20 information processing.…”

Speckle-Correlation Scattering Matrix Approaches for Imaging and Sensing through Turbidity

“…where T is deterministic for a given optical configuration. Thus, for exact knowledge about TM, a scattering medium can be utilized for imaging and wavefront shaping [42][43][44][45][46][47]. However, TM-based techniques generally require interferometric systems to calibrate the TMs and transmitted fields [46,48,49], or they are limited to the imaging of the amplitude of light [50].…”

Living optical random neural network with three dimensional tumor spheroids for cancer morphodynamics

“…Random NNs do not require the precise control of each of the deep computational layers and are trained only at the input and output layers. Random NNs enable new hardware with thousands of nodes and are rapidly emerging in classical and quantum optical computing [8][9][10][11][12][13][14] . Optical neuromorphic computing processes information at the speed of light [15][16][17][18][19] , and recently, photonic spin-glasses and Ising machines have been experimentally demonstrated [20][21][22][23][24][25] .…”