Optical second harmonic generation in a cavity with moving boundaries

The study of nonlinear wave dynamics in optical media is of fundamental and practical importance. An important phenomenon appearing in wave propagation in nonlinear optical media is second and higher harmonic generation which appears due to the interaction of light with nonlinear media. This phenomenon implies the change of such fundamental characteristics of a wave as frequency and apmplitude during its propagation. Despite the great progress in the study of harmonic generationt investigation of the role of size and shape of the optical domain where wave propagates is still remaining as less studied problem. In this work we explore nonlinear wave propagation and second harmonic generation in a passive second harmonic generating cavity having different shapes and finite size. System of first-order nonlinear differential equations describing the interaction of two wave nonlinear waves (harmonics) is solved by imposing of billiard boundary conditions. The boundaries are considered as moving with a constant velocity. Appearing of chaotic motion in the system is studied by considering the above equations as a classical equations of motion.