Single-photon description of the lossless optical Y coupler

TL;DR

This paper derives a unique, symmetry-based scattering matrix for a lossless optical Y-coupler, revealing its hybrid reflection properties and proposing novel quantum and classical optical systems utilizing its symmetry features.

Contribution

It introduces a symmetry-derived, unique scattering matrix for the optical Y-coupler and explores its applications in quantum walks and optical system design.

Findings

The Y-coupler exhibits strong coherent back-reflections unlike traditional splitters.

The derived scattering matrix is unique up to external phase shifts.

Proposed optical systems include a resource-efficient Grover four-port and a tunable Fabry-Perot interferometer.

Abstract

Using symmetry considerations, we derive a unitary scattering matrix for a three-port optical Y-coupler or Y-branch. The result is shown to be unique up to external phase shifts. Unlike traditional passive linear-optical one-way splitters, coupling light into the conventional output ports of the Y-coupler results in strong coherent back-reflections, making the device a hybrid between feed-forward devices like the beam splitter, which do not reverse the direction of light, and a recently considered class of directionally unbiased multiport scatterers (with dimension greater than two) which do. While the device could immediately find use as a novel scattering vertex for the implementation of quantum walks, we also design a few simple but nonetheless useful optical systems that can be constructed by taking advantage of the symmetry of the scattering process. This includes an interference-free, resource-efficient implementation of the Grover four-port and a higher-dimensional Fabry-Perot interferometer with tunable finesse. Symmetry-breaking generalizations are also considered.