Photonic Circuit of Arbitrary Non-Unitary Systems

TL;DR

This paper presents a novel design framework for implementing arbitrary non-unitary operations in photonic circuits by leveraging the cosine-sine decomposition, enabling advanced functionalities in neuromorphic photonics and signal processing.

Contribution

The paper introduces a method to realize non-unitary operations in photonic circuits through unitary matrix completion and decomposition, expanding the capabilities of photonic integrated systems.

Findings

Demonstrates the feasibility of implementing arbitrary non-unitary matrices in photonic circuits.

Shows the scalability and robustness of the proposed design approach.

Applicable to various linear functions in neuromorphic photonics, sensing, and communications.

Abstract

A design framework to implement non-unitary input-output operations to a practical unitary photonic integrated circuit is described. This is achieved by utilising the cosine-sine decomposition to recover the unitarity of the original operation. The recovered unitary operation is decomposed into fundamental unitary building blocks, forming a photonic integrated circuit network based on directional couplers and waveguide phase shifters. The individual building blocks are designed and optimised by three-dimensional full-wave simulations and scaled up using a circuit approach. The paper investigates the scalability and robustness of the design approach. Our study demonstrates that the proposed approach of performing unitary matrix completion can be applied to any arbitrary matrices. This design approach allows for implementation of non-unitary operations to perform various linear functions in neuromorphic photonics for computing, sensing, signal processing and communications.