# Physical Interpretation of Diffractive Optical Networks for High‐Dimensional Vortex Mode Sorting

## TL;DR

This paper explains how layers in diffractive optical networks perform vortex mode sorting, linking their structure to physical principles for better design and understanding.

## Contribution

The first layer-resolved physical interpretation of diffractive optical networks for high-dimensional vortex mode sorting is presented.

## Key findings

- Layer-level physical transformation rules are revealed for vortex mode sorting in diffractive networks.
- A transformation division phenomenon is observed, linked to performance saturation with more masks.
- Physical interpretation enables efficient design of parameter-varying networks with high performance.

## Abstract

Despite the significant progress achieved by diffractive optical networks in diverse computing tasks, such as mode multiplexing and demultiplexing, investigations into the physical meanings behind complex diffractive networks at the layer level have been quite limited. Here, for high‐dimensional vortex mode sorting tasks, the physical transformation rules for each layer within trained diffractive networks are shown to be revealed under properly defined input/output mode relations. An intriguing physical transformation division phenomenon, associated with the saturated sorting performance of the system, has been observed with an increasing number of masks. In addition, the use of physical interpretation for efficiently designing parameter‐varying networks with high performance is also demonstrated. The physical interpretation of optical networks resolves the contradiction between rigorous physical theorems and operationally vague network structures, paving the way for designing and understanding systems for various mode conversion tasks, and inspiring further interpretation of diffractive networks in advanced tasks and other network structures.

The first layer‐resolved physical interpretation of diffractive optical networks trained for high‐dimensional vortex mode sorting is presented, revealing transformation division phenomena linked to saturated performance as layer numbers increase. This analysis reconciles physical theorems with network operations, enabling physics‐driven design of parameter‐varying architectures, and will inspire further interpretation of advanced diffractive network structures.