# Transmission Nonreciprocity in a Mutually Coupled Circulating Structure

## TL;DR

This paper proposes a linear optical structure of mutually coupled microcavities or fiber rings that achieves nonreciprocal light transmission without breaking Lorentz reciprocity, enabling optical isolation and isolator functions.

## Contribution

It introduces a novel linear optical system with mutual coupling that achieves nonreciprocity through gain saturation or asymmetric coupling, challenging traditional reciprocity assumptions.

## Key findings

- Achieves nonreciprocal transmission in a linear system without breaking Lorentz reciprocity.
- Enables optical isolation for inputs from two different ports.
- Supports approximate optical isolator operations.

## Abstract

Breaking Lorentz reciprocity was believed to be a prerequisite for nonreciprocal transmissions of light fields, so the possibility of nonreciprocity by linear optical systems was mostly ignored. We put forward a structure of three mutually coupled microcavities or optical fiber rings to realize optical nonreciprocity. Although its couplings with the fields from two different input ports are constantly equal, such system transmits them nonreciprocally either under the saturation of an optical gain in one of the cavities or with the asymmetric couplings of the circulating fields in different cavities. The structure made up of optical fiber rings can perform nonreciprocal transmissions as a time-independent linear system without breaking Lorentz reciprocity. Optical isolation for inputs simultaneously from two different ports and even approximate optical isolator operations are implementable with the structure.