# Diffractive Interconnects: All-Optical Permutation Operation Using Diffractive Networks

arXiv: https://arxiv.org/abs/2206.10152 · HTML: https://mlsanity.com/paper/2206.10152/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 89 references that are in the map.
- First posted on arXiv 21 Jun 2022.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [DeepISP: Towards Learning an End-to-End Image Processing Pipeline](https://mlsanity.com/paper/1801.06724/) (2018)
- [Deep learning-based virtual histology staining using auto-fluorescence of label-free tissue](https://mlsanity.com/paper/1803.11293/) (2018)
- [Neuromorphic Silicon Photonic Networks](https://mlsanity.com/paper/1611.02272/) (2016)
- [Deep Optics for Single-shot High-dynamic-range Imaging](https://mlsanity.com/paper/1908.00620/) (2019)
- [Phase recovery and holographic image reconstruction using deep learning in neural networks](https://mlsanity.com/paper/1705.04286/) (2017)
- [Lensless computational imaging through deep learning](https://mlsanity.com/paper/1702.08516/) (2017)
- [PhaseStain: Digital staining of label-free quantitative phase microscopy images using deep learning](https://mlsanity.com/paper/1807.07701/) (2018)
- [Misalignment Resilient Diffractive Optical Networks](https://mlsanity.com/paper/2005.11464/) (2020)
- [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)
- [To image, or not to image: Class-specific diffractive cameras with all-optical erasure of undesired objects](https://mlsanity.com/paper/2205.13122/) (2022)
- [Computational Imaging Without a Computer: Seeing Through Random Diffusers at the Speed of Light](https://mlsanity.com/paper/2107.06586/) (2021)
- [Quantitative Phase Imaging and Artificial Intelligence: A Review](https://mlsanity.com/paper/1806.03982/) (2018)
- [Super-resolution image display using diffractive decoders](https://mlsanity.com/paper/2206.07281/) (2022)
- [Three-dimensional virtual refocusing of fluorescence microscopy images using deep learning](https://mlsanity.com/paper/1901.11252/) (2019)
- [Deep learning enhanced mobile-phone microscopy](https://mlsanity.com/paper/1712.04139/) (2017)
- [Resolution enhancement in scanning electron microscopy using deep learning](https://mlsanity.com/paper/1901.11094/) (2019)
- [Graph-Embedded Multi-Agent Learning for Smart Reconfigurable THz MIMO-NOMA Networks](https://mlsanity.com/paper/2107.07198/) (2021)
- [50 Years of Permutation, Spatial and Index Modulation: From Classic RF to Visible Light Communications and Data Storage](https://mlsanity.com/paper/1803.03939/) (2018)

## Built on by (most cited first, 6 of 6)

- [Training of Physical Neural Networks](https://mlsanity.com/paper/2406.03372/) (2024)
- [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)
- [Multispectral Quantitative Phase Imaging Using a Diffractive Optical Network](https://mlsanity.com/paper/2308.02952/) (2023)
- [Pyramid diffractive optical networks for unidirectional image magnification and demagnification](https://mlsanity.com/paper/2308.15019/) (2023)
- [Multiplexed all-optical permutation operations using a reconfigurable diffractive optical network](https://mlsanity.com/paper/2402.02397/) (2024)

## Abstract (arXiv)

Permutation matrices form an important computational building block frequently used in various fields including e.g., communications, information security and data processing. Optical implementation of permutation operators with relatively large number of input-output interconnections based on power-efficient, fast, and compact platforms is highly desirable. Here, we present diffractive optical networks engineered through deep learning to all-optically perform permutation operations that can scale to hundreds of thousands of interconnections between an input and an output field-of-view using passive transmissive layers that are individually structured at the wavelength scale. Our findings indicate that the capacity of the diffractive optical network in approximating a given permutation operation increases proportional to the number of diffractive layers and trainable transmission elements in the system. Such deeper diffractive network designs can pose practical challenges in terms of physical alignment and output diffraction efficiency of the system. We addressed these challenges by designing misalignment tolerant diffractive designs that can all-optically perform arbitrarily-selected permutation operations, and experimentally demonstrated, for the first time, a diffractive permutation network that operates at THz part of the spectrum. Diffractive permutation networks might find various applications in e.g., security, image encryption and data processing, along with telecommunications; especially with the carrier frequencies in wireless communications approaching THz-bands, the presented diffractive permutation networks can potentially serve as channel routing and interconnection panels in wireless networks.