# Multiplexed all-optical permutation operations using a reconfigurable diffractive optical network

arXiv: https://arxiv.org/abs/2402.02397 · HTML: https://mlsanity.com/paper/2402.02397/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 43 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 21 of 21)

- [All-Optical Machine Learning Using Diffractive Deep Neural Networks](https://mlsanity.com/paper/1804.08711/) (2018)
- [Large-scale neuromorphic optoelectronic computing with a reconfigurable diffractive processing unit](https://mlsanity.com/paper/2008.11659/) (2020)
- [Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networks](https://mlsanity.com/paper/2205.08501/) (2022)
- [Misalignment Resilient Diffractive Optical Networks](https://mlsanity.com/paper/2005.11464/) (2020)
- [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)
- [Ensemble learning of diffractive optical networks](https://mlsanity.com/paper/2009.06869/) (2020)
- [Scalable Optical Learning Operator](https://mlsanity.com/paper/2012.12404/) (2020)
- [Universal Linear Intensity Transformations Using Spatially-Incoherent Diffractive Processors](https://mlsanity.com/paper/2303.13037/) (2023)
- [Snapshot Multispectral Imaging Using a Diffractive Optical Network](https://mlsanity.com/paper/2212.05217/) (2022)
- [Data class-specific all-optical transformations and encryption](https://mlsanity.com/paper/2212.12873/) (2022)
- [Scale-, shift- and rotation-invariant diffractive optical networks](https://mlsanity.com/paper/2010.12747/) (2020)
- [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)
- [Polarization Multiplexed Diffractive Computing: All-Optical Implementation of a Group of Linear Transformations Through a Polarization-Encoded Diffractive Network](https://mlsanity.com/paper/2203.13482/) (2022)
- [Multispectral Quantitative Phase Imaging Using a Diffractive Optical Network](https://mlsanity.com/paper/2308.02952/) (2023)
- [Cascadable all-optical NAND gates using diffractive networks](https://mlsanity.com/paper/2111.01404/) (2021)
- [Universal Polarization Transformations: Spatial programming of polarization scattering matrices using a deep learning-designed diffractive polarization transformer](https://mlsanity.com/paper/2304.05724/) (2023)
- [Diffractive Interconnects: All-Optical Permutation Operation Using Diffractive Networks](https://mlsanity.com/paper/2206.10152/) (2022)
- [Information hiding cameras: optical concealment of object information into ordinary images](https://mlsanity.com/paper/2401.07856/) (2024)
- [All-optical image classification through unknown random diffusers using a single-pixel diffractive network](https://mlsanity.com/paper/2208.03968/) (2022)

## Built on by (most cited first, 2 of 2)

- [Structural Vibration Monitoring with Diffractive Optical Processors](https://mlsanity.com/paper/2506.03317/) (2025)
- [Illumination Angular Spectrum Encoding for Controlling the Functionality of Diffractive Networks](https://mlsanity.com/paper/2601.04825/) (2026)

## Abstract (arXiv)

Large-scale and high-dimensional permutation operations are important for various applications in e.g., telecommunications and encryption. Here, we demonstrate the use of all-optical diffractive computing to execute a set of high-dimensional permutation operations between an input and output field-of-view through layer rotations in a diffractive optical network. In this reconfigurable multiplexed material designed by deep learning, every diffractive layer has four orientations: 0, 90, 180, and 270 degrees. Each unique combination of these rotatable layers represents a distinct rotation state of the diffractive design tailored for a specific permutation operation. Therefore, a K-layer rotatable diffractive material is capable of all-optically performing up to 4^K independent permutation operations. The original input information can be decrypted by applying the specific inverse permutation matrix to output patterns, while applying other inverse operations will lead to loss of information. We demonstrated the feasibility of this reconfigurable multiplexed diffractive design by approximating 256 randomly selected permutation matrices using K=4 rotatable diffractive layers. We also experimentally validated this reconfigurable diffractive network using terahertz radiation and 3D-printed diffractive layers, providing a decent match to our numerical results. The presented rotation-multiplexed diffractive processor design is particularly useful due to its mechanical reconfigurability, offering multifunctional representation through a single fabrication process.