Goos-Hiichen shifts for a one-dimensional photonic crystal with a nonlinear defect

The Goos-Hanchen effect for a one-dimensional photonic crystal containing a nonlinear defects is theoretically investigated. It´s found that there exists a hysteresis response between the incident light intensity and the lateral shift for transmitted beams and lateral shift reaches its peak at the switch-down threshold intensity of the optical bistability. The dependence of the hysteresis on the nonlinear defect and the incident angle is discussed systematically. It´s also found that for fixed structure and incident angle, the hysteresis is dependent of the frequency offset between the incident light frequency and the linear defect mode frequency. The validity of the theoretical analysis is demonstrated by numerical simulations for a Gaussian beam.