All-Optical Synthesis of an Arbitrary Linear Transformation Using Diffractive Surfaces

Abstract

We report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input (N_i) and output (N_o), where N_i and N_o 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 designs 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 (N) of spatially-engineered diffractive features/neurons is N_i x N_o or larger, 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 N and their all-optical transformations are more accurate for N < N_i x N_o. These conclusions are generally applicable to various optical processors that employ spatially-engineered diffractive surfaces.

arXiv comment46 Pages, 12 Figures

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• All-optical image classification through unknown random diffusers using a single-pixel diffractive network
• Super-resolution image display using diffractive decoders
• Data class-specific all-optical transformations and encryption
• Unidirectional Imaging using Deep Learning-Designed Materials
• Cascadable all-optical NAND gates using diffractive networks
• Universal metasurfaces for complete linear control of coherent light transmission
• Quantitative phase imaging (QPI) through random diffusers using a diffractive optical network
• Time-lapse image classification using a diffractive neural network
• Diffractive Interconnects: All-Optical Permutation Operation Using Diffractive Networks