Orthogonality of Diffractive Deep Neural Networks

TL;DR

This paper establishes fundamental laws governing Diffractive Deep Neural Networks (D2NN), showing they preserve inner products and act as unitary transformations, making them suitable for optical mode classification and conversion tasks.

Contribution

It reveals the orthogonality properties and unitary nature of D2NN, providing theoretical insights and demonstrating their effectiveness in optical mode applications.

Findings

D2NN preserves inner products of light fields

D2NN acts as a unitary transformation for optical fields

D2NN performs well in mode conversion and recognition

Abstract

Several laws are found for the Diffractive Deep Neural Networks (D2NN). They reveal the inner product of any two light fields in D2NN is invariant and the D2NN act as a unitary transformation for optical fields. If the output intensities of the two inputs are separated spatially, the input fields must be orthogonal. These laws imply that the D2NN is not only suitable for the classification of general objects but also more suitable for applications aim to the optical orthogonal modes. Additionally, our simulation shows D2NN do well in applications like mode conversion, mode multiplexer, and optical mode recognition.