  Optical Fabry-Perot cavity with a movable mirror is a paradigmatic
optomechanical systems. While usually the mirror is supported by a mechanical
spring, it has been shown that it is possible to keep one of the mirrors in a
stable equilibrium purely by optical levitation without any mechanical support.
In this work we expand previous studies of nonlinear dynamics of such a system
by demonstrating a possibility for mechanical parametric instability and
emergence of the ``phonon laser'' phenomenon.
