Abstract
Cavity-optomechanics-based phonon lasers are traditionally described in terms of three-mode resonance, while the energy nonconservation optomechanical terms are conventionally ignored. Here, we present a complete theory of phonon lasers, emphasizing the importance of the previously omitted optomechanical interaction. We show that this indispensable optomechanical interaction is equivalent to a Kerr nonlinear interaction. Analytical results show that the interference between this Kerr-type interaction and three-mode resonance adds a transition channel with no phonon emission or absorption, thus enhancing phonon lasing and realizing an ultralow-threshold phonon laser and even a phonon cooler. The interference effect produces an asymmetric gain profile with a Fano spectral shape in addition to the traditional Lorentzian shape. Our complete theory shows perfect agreement with existing experiments and provides a new degree of freedom to manipulate optomechanical phonon lasers.
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