Quasinormal Modes of Analog Rotating Black Holes in 2-Dimensional Photon-Fluid Model

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.