Optimization-based calculation of optical nonlinear processes in a micro-resonator

We present a new method of calculating the performance of nonlinear processes in a resonator. An optimization-based approach, conceptually similar to techniques used in nonlinear circuit analysis, is formulated and used to find the wave magnitudes that satisfy all of the boundary conditions and account for nonlinear optical effects. Unlike previous solution methods, this technique is applicable to any nonlinear process (second-order, third-order, etc.) and multiple coupled resonators, maintains the phase relations between the waves, and is exact. Examples are given for second-order nonlinear processes in a one-dimensional resonator.