Goos-H\"anchen Shift in $\mathcal{PT}$-Symmetric and Passive Cavity Optomechanical Systems

TL;DR

This paper theoretically explores how the Goos-H"anchen shift can be controlled in $ ext{PT}$-symmetric and passive optomechanical systems, revealing phase-dependent enhancements and tunability for potential photonic applications.

Contribution

It introduces a novel optomechanical setup with active and passive components, demonstrating phase-dependent control of the GHS and active tuning methods.

Findings

GHS is significantly enhanced in the unbroken $ ext{PT}$ phase.

GHS can be actively tuned via cavity detuning and medium length.

An exceptional point emerges at balanced gain-loss conditions.

Abstract

We theoretically investigate the control of the Goos-H\"anchen shift (GHS) of a reflected weak probe field in both parity-time ($\mathcal{PT}$)-symmetric and conventional optomechanical systems. The proposed scheme consists of a single optomechanical platform where a passive optical cavity is coupled to an active mechanical resonator, in contrast to standard passive-passive configurations. Analysis of the eigenfrequency spectrum reveals the emergence of an exceptional point under balanced gain-loss conditions at a tunable effective optomechanical coupling strength. Using the transfer-matrix method combined with stationary-phase analysis, we examine the GHS across broken and unbroken $\mathcal{PT}$ phases and compare it with that in the conventional system. The lateral shift exhibits strong phase dependence: it is markedly enhanced in the unbroken regime relative to both the broken phase and the passive configuration. We further show that the GHS can be actively tuned through the cavity detuning and the intracavity medium length. These results provide a controlled means for manipulating beam shifts in optomechanical systems and suggest pathways toward tunable photonic components and precision optical sensing.