An inverse problem in nonlinear optics

摘要

In nonlinear optics, the electromagnetic field in semi-infinite medium is often described by the equation ∂2∂z2E(z, t)−1c2∂2∂t2(ε(z)E(z,t)+ 4πα|E(z, t)|2E(z, t)) = 0. In this paper, we discuss its inverse problem of a nonharmonic electromagnetic wave acting on the surface of the medium from the mathematical physics point of view. A method to solve the ε(z) inversely is proposed.