Distortion-suppression optimization for a class of nonlinear optical systems with feedback

Abstract

We consider the initial boundary-value problem for the quasilinear diffusion equation ∂tu + u − D∆u = K(x, y)`1 + γ(u + ϕ(x, y))´describing the dynamics of optical systems with controlled feedback wave intensity modulation K(x, y) in the presence of incoming-wave phase perturbations ϕ(x, y). The control problem for the parameter K(x, y) is formulated with the objective of smoothing out the spatial nonhomogeneities of the total output phase u(x, y, T ) + ϕ(x, y). We prove existence and uniqueness theorems for the generalized solutions of the direct and conjugate problems, solvability theorems for the optimization problems, and Frechet-differentiability of the objective functional. A formula for the functional gradient is derived and the efficiency of the gradient projection method is demonstrated numerically.