# Massively Parallel Universal Linear Transformations using a Wavelength-Multiplexed Diffractive Optical Network

arXiv: https://arxiv.org/abs/2208.10362 · HTML: https://mlsanity.com/paper/2208.10362/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2022.

## Built on by (most cited first, 9 of 9)

- [Snapshot Multispectral Imaging Using a Diffractive Optical Network](https://mlsanity.com/paper/2212.05217/) (2022)
- [Unidirectional Imaging using Deep Learning-Designed Materials](https://mlsanity.com/paper/2212.02025/) (2022)
- [All-Optical Phase Conjugation Using Diffractive Wavefront Processing](https://mlsanity.com/paper/2311.04473/) (2023)
- [All-optical image denoising using a diffractive visual processor](https://mlsanity.com/paper/2309.09215/) (2023)
- [Pyramid diffractive optical networks for unidirectional image magnification and demagnification](https://mlsanity.com/paper/2308.15019/) (2023)
- [Multiplane Quantitative Phase Imaging Using a Wavelength-Multiplexed Diffractive Optical Processor](https://mlsanity.com/paper/2403.11035/) (2024)
- [Integration of Programmable Diffraction with Digital Neural Networks](https://mlsanity.com/paper/2406.10688/) (2024)
- [1-bit Quantized On-chip Hybrid Diffraction Neural Network Enabled by Authentic All-optical Fully-connected Architecture](https://mlsanity.com/paper/2404.07443/) (2024)
- [Wavelength-Multiplexed 2D Beam Steering via a Passive Diffractive Network](https://mlsanity.com/paper/2606.16261/) (2026)

## Abstract (arXiv)

We report deep learning-based design of a massively parallel broadband diffractive neural network for all-optically performing a large group of arbitrarily-selected, complex-valued linear transformations between an input and output field-of-view, each with N_i and N_o pixels, respectively. This broadband diffractive processor is composed of N_w wavelength channels, each of which is uniquely assigned to a distinct target transformation. A large set of arbitrarily-selected linear transformations can be individually performed through the same diffractive network at different illumination wavelengths, either simultaneously or sequentially (wavelength scanning). We demonstrate that such a broadband diffractive network, regardless of its material dispersion, can successfully approximate N_w unique complex-valued linear transforms with a negligible error when the number of diffractive neurons (N) in its design matches or exceeds 2 x N_w x N_i x N_o. We further report that the spectral multiplexing capability (N_w) can be increased by increasing N; our numerical analyses confirm these conclusions for N_w > 180, which can be further increased to e.g., ~2000 depending on the upper bound of the approximation error. Massively parallel, wavelength-multiplexed diffractive networks will be useful for designing high-throughput intelligent machine vision systems and hyperspectral processors that can perform statistical inference and analyze objects/scenes with unique spectral properties.