Phase-Tunable Non-Reciprocal Light Routing in Multimode Quadratic Optomechanical Systems

Nonreciprocal optical devices are key components of integrated photonics and quantum information processing. However, achieving dynamically reconfigurable nonreciprocal transport without magnetic materials or structural asymmetry remains challenging. A phase-controlled nonreciprocal optical isolator based on a multimode quadratic optomechanical system is theoretically investigated through numerical analysis. Unlike linear optomechanical systems, quadratic optomechanical interactions and position-dependent photon hopping combine through radiation-pressure-induced mechanical displacements to tailor the effective photon hopping, enabling nonlinear control of photon transport. The relative phase between the coherent driving fields induces a synthetic gauge field that controls the interference between direct and mechanically mediated transport pathways. This interference produces nonreciprocal transmission in a structurally symmetric system without magnetic bias or static parameter asymmetry. Steady-state calculations and probe transmission spectra predict isolation ratios exceeding 30 dB. The propagation direction is reversed only by tuning the relative phase of the driving fields, without changing the device geometry, probe frequency, or pump power. The proposed scheme combines large isolation, reversible transport, and magnetic-free operation without structural or mechanical reconfiguration.