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Optomechanical interactions in non-Hermitian photonic molecules

We study optomechanical interactions in non-Hermitian photonic molecules that support two photonic states and one acoustic mode. The nonlinear steady-state solutions and their linear stability landscapes are investigated as a function of the system's parameters and excitation power levels. We also examine the temporal evolution of the system and uncover different regimes of nonlinear dynamics. Our analysis reveals several important results: (1) Parity-time ($\mathcal{PT}$) symmetry is not necessarily the optimum choice for maximum optomechanical interaction. (2) Stable steady-state solutions are not always reached under continuous wave (CW) optical excitations. (3) Accounting for gain saturation effects can regulate the behavior of the otherwise unbounded oscillation amplitudes. Our study provides a deeper insight into the interplay between optical non-Hermiticity and optomechanical coupling and can thus pave the way for new device applications.