Analysis of signal optimization problems for dielectric media

The authors have recently presented the results of the numerical implementation of a scheme for designing an incident electromagnetic plane wave which will deposit a maximum amount of energy in any selected portion of an inhomogeneous dielectric slab. This paper presents the mathematical analysis underlying this scheme for solving the signal design problem. The analysis indicates that the maximum energy is achieved by choosing the incident signal to be an appropriately normalized eigenfunction of a compact Fredholm integral operator. A numerical scheme for solving the optimization problem is discussed briefly.This research was supported by Ames Laboratory-USDOE under Contract No. W-7405-Eng-82.