  Phonon lasers or coherent amplifications of mechanical oscillations have
provided powerful tools for both fundamental studies of coherent acoustics and
diverse applications ranging from ultrasensitive force sensing to phononic
information processing. Here, we propose how to achieve directional phonon
lasing with an optomechanical resonator coupled to a nonlinear optical
resonator. We find that, by pumping the nonlinear resonator, directional
optical squeezing can occur along the pump direction. As a result, we can
achieve the directional mechanical gain by utilizing the directional optical
squeezing, thus leading to nonreciprocal phonon lasing with a well-tunable
directional power threshold. Our work shows a feasible way to build
nonreciprocal phonon lasers with various nonlinear optical mediums, which are
important for such a wide range of applications as directional acoustic
amplifiers, invisible sound sensing or imaging, and one-way phononic networks.
