We fabricated the asymmetric Fabry-Perot etalon which contains amorphous $As_2S_3$ as a spacer layer by using the method of optical multilayer coating and observed the optical bistability with the polarization. Optical thickness of the spacer layer is 2$lambda$ at $Ar^+$ ($lambda $=514.5 nm) laser wavelength. Optical bistability was observed at the intensities between 80~100 mW and the experiment shows us that the trends of bistable loop of the reflected and the transmitted lights are quite different depending on the state of polarization. This phenomena can be explained as the phase differences of each polarizations are different in the nonlinear Fabry-Perot etalon.