# Polarization Multiplexed Diffractive Computing: All-Optical Implementation of a Group of Linear Transformations Through a Polarization-Encoded Diffractive Network arXiv: https://arxiv.org/abs/2203.13482 ยท HTML: https://mlsanity.com/paper/2203.13482/ ## Key facts - Cited by 10 papers in the map (data through 14 Oct 2026). - Builds on 23 of its 86 references that are in the map. - First posted on arXiv 25 Mar 2022. ## Builds on (most cited first, 23 of 23) - [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014) - [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018) - [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021) - [Photonics for artificial intelligence and neuromorphic computing](https://mlsanity.com/paper/2011.00111/) (2020) - [Neuromorphic Silicon Photonic Networks](https://mlsanity.com/paper/1611.02272/) (2016) - [Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit](https://mlsanity.com/paper/2008.11659/) (2020) - [Deep Polarization Imaging for 3D shape and SVBRDF Acquisition](https://mlsanity.com/paper/2105.02875/) (2021) - [Wave Physics as an Analog Recurrent Neural Network](https://mlsanity.com/paper/1904.12831/) (2019) - [Misalignment Resilient Diffractive Optical Networks](https://mlsanity.com/paper/2005.11464/) (2020) - [Reinforcement Learning in a large scale photonic Recurrent Neural Network](https://mlsanity.com/paper/1711.05133/) (2017) - [Analysis of Diffractive Optical Neural Networks and Their Integration with Electronic Neural Networks](https://mlsanity.com/paper/1810.01916/) (2018) - [Design of Task-Specific Optical Systems Using Broadband Diffractive Neural Networks](https://mlsanity.com/paper/1909.06553/) (2019) - [All-Optical Synthesis of an Arbitrary Linear Transformation Using Diffractive Surfaces](https://mlsanity.com/paper/2108.09833/) (2021) - [Diffractive all-optical computing for quantitative phase imaging](https://mlsanity.com/paper/2201.08964/) (2022) - [Ensemble learning of diffractive optical networks](https://mlsanity.com/paper/2009.06869/) (2020) - [Scalable Optical Learning Operator](https://mlsanity.com/paper/2012.12404/) (2020) - [Computational Imaging Without a Computer: Seeing Through Random Diffusers at the Speed of Light](https://mlsanity.com/paper/2107.06586/) (2021) - [Photonic tensor cores for machine learning](https://mlsanity.com/paper/2002.03780/) (2020) - [Class-specific Differential Detection in Diffractive Optical Neural Networks Improves Inference Accuracy](https://mlsanity.com/paper/1906.03417/) (2019) - [Scale-, shift- and rotation-invariant diffractive optical networks](https://mlsanity.com/paper/2010.12747/) (2020) - [Deep learning-based holographic polarization microscopy](https://mlsanity.com/paper/2007.00741/) (2020) - [Cascadable all-optical NAND gates using diffractive networks](https://mlsanity.com/paper/2111.01404/) (2021) - [Classification and reconstruction of spatially overlapping phase images using diffractive optical networks](https://mlsanity.com/paper/2108.07977/) (2021) ## Built on by (most cited first, 10 of 10) - [Snapshot Multispectral Imaging Using a Diffractive Optical Network](https://mlsanity.com/paper/2212.05217/) (2022) - [Super-resolution image display using diffractive decoders](https://mlsanity.com/paper/2206.07281/) (2022) - [Unidirectional Imaging using Deep Learning-Designed Materials](https://mlsanity.com/paper/2212.02025/) (2022) - [Multispectral Quantitative Phase Imaging Using a Diffractive Optical Network](https://mlsanity.com/paper/2308.02952/) (2023) - [All-optical image denoising using a diffractive visual processor](https://mlsanity.com/paper/2309.09215/) (2023) - [All-optical image classification through unknown random diffusers using a single-pixel diffractive network](https://mlsanity.com/paper/2208.03968/) (2022) - [Time-lapse image classification using a diffractive neural network](https://mlsanity.com/paper/2208.10802/) (2022) - [Multiplexed all-optical permutation operations using a reconfigurable diffractive optical network](https://mlsanity.com/paper/2402.02397/) (2024) - [SP2RINT: Spatially-Decoupled Physics-Inspired Progressive Inverse Optimization for Scalable, PDE-Constrained Meta-Optical Neural Network Training](https://mlsanity.com/paper/2505.18377/) (2025) - [Snapshot 3D image projection using a diffractive decoder](https://mlsanity.com/paper/2512.20464/) (2025) ## Abstract (arXiv) Research on optical computing has recently attracted significant attention due to the transformative advances in machine learning. Among different approaches, diffractive optical networks composed of spatially-engineered transmissive surfaces have been demonstrated for all-optical statistical inference and performing arbitrary linear transformations using passive, free-space optical layers. Here, we introduce a polarization multiplexed diffractive processor to all-optically perform multiple, arbitrarily-selected linear transformations through a single diffractive network trained using deep learning. In this framework, an array of pre-selected linear polarizers is positioned between trainable transmissive diffractive materials that are isotropic, and different target linear transformations (complex-valued) are uniquely assigned to different combinations of input/output polarization states. The transmission layers of this polarization multiplexed diffractive network are trained and optimized via deep learning and error-backpropagation by using thousands of examples of the input/output fields corresponding to each one of the complex-valued linear transformations assigned to different input/output polarization combinations. Our results and analysis reveal that a single diffractive network can successfully approximate and all-optically implement a group of arbitrarily-selected target transformations with a negligible error when the number of trainable diffractive features/neurons (N) approaches N_p x N_i x N_o, where N_i and N_o represent the number of pixels at the input and output fields-of-view, respectively, and N_p refers to the number of unique linear transformations assigned to different input/output polarization combinations. This polarization-multiplexed all-optical diffractive processor can find various applications in optical computing and polarization-based machine vision tasks.