  A conventional optomechanical system is composed of a mechanical mode and an
optical mode interacting through a linear optomechanical coupling (LOC). We
study how the presence of quadratic optomechanical coupling (QOC) in the
conventional optomechanical system affects the system's stability and optical
quadrature squeezing. We work in the resolved side-band limit with a high
quality factor mechanical oscillator. In contrast to the conventional
optomechanical systems, we find that strong squeezing of the cavity field can
be achieved in presence of QOC along with LOC at lower pump powers and at
higher bath temperatures. Using detailed numerical calculations we also find
that there exists an optimal QOC where one can achieve maximum squeezing.
