PT-symmetric phonon laser under gain saturation effect

As an analog of optical laser, phonon laser has potential applications in various areas. We study a type of phonon laser implemented by two coupled micro-cavities, one of which carries optical gain medium. The phonon laser operation is under a blue detuned external drive leading to dynamical instability. The saturation of the optical gain is considered, and its induced nonlinearity results in more complicated behaviors in stimulated phonon emission. To deal with such complex dynamics, we apply a composite numerical approach, in addition to a previously used dynamical approach, to the time evolution of the system. The workable phonon laser operation is found to be achievable by choosing the proper system parameters. Moreover, low threshold for the phonon laser operation is possible with the suitable coupling between the cavities and an optimum damping rate in one cavity.