Abstract
We present an efficient numerical algorithm for the design of anti-reflection coating (ARC). In contrast to the widely used direct design where the behaviour of the field is investigated, we consider the inverse problem. Our purpose is to determine the best material for the ARC which matches with some sought values of the field at the surface. Mathematically, we solve an inverse scattering problem to identify the refractive index of the ARC. For modelling, the light propagation throughout a stratified ARC the time-harmonic Maxwell equations are reduced into one dimensional Helmholtz equation with prescribed boundary conditions. From this BVP, we derive an equivalent formulation as a Fredholm integral equation. The problem is nonlinear and ill-posed. We apply Born approximation for linearisation. To obtain stable solutions, we present numerical results using the method of approximate inverse (AI). We also carry out numerical tests to compare AI to Tikhonov-Phillips method.
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