An exact solution for the nonlinear birefringent medium model is obtained by using SO(3) rotation group property. It is proved that coherent light entering the medium will evolve into a superposition of maorosoopioally distinguishable quantum states. In order to detect their interference fringes, holodyne detection scheme is used and the probability distribution for the output of homodyne detector is calculated when the intial states being linear and circular polarization coherent light.