Stability of Self-Configuring Large Multiport Interferometers

TL;DR

This paper investigates the stability of self-configuration algorithms for large multiport interferometers, emphasizing the superiority of power ratio methods over naive approaches, and proposes a robust scheme requiring minimal external detectors.

Contribution

It introduces a stable self-configuration scheme for triangular and rectangular interferometer meshes that does not rely on prior component knowledge and is robust to large errors.

Findings

Power ratio methods outperform naive sequential approaches.

The proposed scheme works without prior knowledge of imperfections.

It extends to rectangular meshes with minimal additional detectors.

Abstract

Realistic multiport interferometers (beamsplitter meshes) are sensitive to component imperfections, and this sensitivity increases with size. Self-configuration techniques can be employed to correct these imperfections, but not all techniques are equal. This paper highlights the importance of algorithmic stability in self-configuration. Naive approaches based on sequentially setting matrix elements are unstable and perform poorly for large meshes, while techniques based on power ratios perform well in all cases, even in the presence of large errors. Based on this insight, we propose a self-configuration scheme for triangular meshes that requires only external detectors and works without prior knowledge of the component imperfections. This scheme extends to the rectangular mesh by adding a single array of detectors along the diagonal.