Dark-mode-controlled Goos-Hachen Shift in a Phonon-Coupled Optomechanical System

초록

We investigate the Goos-H & auml;nchen shift (GHS) in a phonon-coupled optomechanical system consisting of an optical cavity interacting with two degenerate mechanical resonators. The optical reflection is evaluated using the transfer matrix method, and the lateral beam displacement is extracted from the phase of the complex reflection coefficient. In the dark-mode-unbroken regime, the reflected field exhibits interference-driven phase behavior that produces both positive and negative GHS as the incident angle is varied. When the dark-mode condition is broken by introducing a finite phonon-phonon interaction, mechanical hybridization reshapes the reflection phase and the GHS response becomes predominantly negative, demonstrating a clear route to control the sign and magnitude of the beam shift. We further characterize the tunability of the shift as a function of the incident angle, the phonon-phonon interaction strength, and the driving power, and present a two-parameter map that identifies operating regions where the negative beam displacement is maximized. Using experimentally accessible parameters and a fixed wavelength of 1064 nm, our results establish phonon-mediated mode control as an effective mechanism for engineering and tuning GHS in hybrid optomechanical platforms.

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