Numerical Study of Optical Bistability in a Nonlinear Photonic Crystal Notch Filter

Abstract

Optical bistability occurs when the effects of nonlinear behaviour of materials cause hysteresis in the transmission and reflection of a device. A possible mechanism for this is a strong dependence of the optical intensity on the index of refraction, e.g. in a cavity near resonance. In a 2-dimensional photonic crystal composed of rods of high-index material in air, a waveguide can be created by removing a line of rods. When a cavity is made by taking away several rods perpendicular to the waveguide, a notch filter characteristic in the transmission occurs. Due to the high intensity in the cavity in resonance, nonlinear effects are enhanced. This paper shows numerical simulations of bistability in the transmission and in the field inside the cavity both when a material inside the cavity has third-order (Kerr-type) nonlinear effects, and when the high-index rods themselves are nonlinear.