Minimizing the modulus of the reflection coefficient of a polychromatic wave from an inhomogeneous absorbing layer

Abstract

The synthesis is considered of the optimum inhomogeneous absorbing layer of given thickness under the incidence of a plane polychromatic wave with a known frequency spectrum. The synthesis is treated as a problem in optimum control. The control is approximated as a step function and the problem is reduced to minimizing a function of many variables. Equations are obtained for the exact calculation of the gradient in the goodness criterion; this gradient is required in setting up the algorithm for finding the optimum solution. The principal and adjoint variables and also the Hamiltonian are written in complex form and this greatly simplifies the intermediate transformations. The optimum solution is sought by using the method of adjoint gradients [1, 2] with constraints placed on the control. To illustrate the problem, results are given of computer calculations of an optimum control.