# Optimal unidirectional amplification induced by optical gain in optomechanical systems

## TL;DR

This paper introduces a three-mode optomechanical system with optical gain that achieves unidirectional amplification and nonreciprocal transmission, advancing the design of high-quality nonreciprocal devices.

## Contribution

It presents a novel three-mode optomechanical system with optical gain enabling unidirectional amplification and nonreciprocal transmission, with analytical expressions for optimal transmission and isolation.

## Key findings

- Optical gain enhances transmission in one direction.
- The system achieves high isolation ratios.
- Analytical formulas for transmission and isolation are derived.

## Abstract

We propose a three-mode optomechanical system to realize optical nonreciprocal transmission with unidirectional amplification, where the system consists of two coupled cavities and one mechanical resonator which interacts with only one of the cavities. Additionally, the optical gain is introduced into the optomechanical cavity. It is found that for a strong optical input, the optical transmission coefficient can be greatly amplified in a particular direction and suppressed in the opposite direction. The expressions of the optimal transmission coefficient and the corresponding isolation ratio are given analytically. Our results pave a way to design high-quality nonreciprocal devices based on optomechanical systems.