  It was recently found that the optical field fluctuations in self-defocusing
media can be described by sound waves propagating in a two-dimensional
photon-fluid. This photon-fluid is controlled by the driving beam and serves as
the background in which the sound waves can experience an effective curved
spacetime, such that it provides a new platform of studying analog black holes.
In this paper, we are interested in investigating the quasinormal modes (QNMs)
of this analog black hole in the photon-fluid model. Based on the master
equation of motion of the optical field fluctuations, we calculate the
frequencies of quasinormal modes (QNF) with three different numerical methods
to make sure the QNF we get are reliable. Besides fundamental modes, we also
try to calculate the overtones up to $n=3$ aiming to uncover more properties of
QNF. The effects of angular velocity $\Omega_H$ of the black hole, the overtone
number $n$ and the winding number $m$ on the QNF are investigated. Under the
$m$ with opposite sign, we find that both the real and imaginary part of the
QNF will show strikingly contrasting behaviors when the QNF is plotted against
$\Omega_H$, and the similar contrast effects are also found when comparing the
influences from winding number and overtone number. We hope that this work may
potentially contribute to the future detections of QNMs in experimental
settings of photon-fluid.
