Optical feedback characteristics of frequency modulated microchip Nd:YAG lasers with anisotropic external cavity are investigated. With isotropic optical feedback, the modulation frequency of output intensity is proportional to the ratio of external cavity length to internal cavity length. With anisotropic optical feedback, the laser polarization periodically hops between two orthogonal directions with equal bandwidth. The times of polarization flipping in the longitudinal mode bandwidth is proportional to the ratio of external cavity length to internal cavity length, resulting in double frequency of original fringes. The theoretical analysis based on Fabry-Perot cavity equivalent model is in good agreement with the experimental results. The potential applications of this phenomenon in precision measurement are discussed.