Analysis of lossy optical materials possessing graded refractive index profiles

Abstract

Analytical expressions for reflectance, transmittance, and bilinear transformed reflectance of processed materials containing complex graded refractive index profiles are presented. Oblique incidence is considered. Substantial changes in complex refractive index are modeled by means of a second-order theory, whereas moderate refractive index changes are described by means of a much simpler first-order approximation. An ellipsornetric expression for inhornogeneous layers is also derived using this theory. The performance of the integral formulation is compared to that of the matrix technique by simulations and analysis of experimental data. Simulations using our first-order formulas have a time savings benefit of more than a factor of 10 over reflectance curves calculated by the well-known matrix method. Experimental infrared reflectance of semi-insulating (100) GaAs samples implanted with 280-keV beryllium ions is also analyzed and is compared with our theoretical results obtained from a first-order theory. The Fourier spectrum in the optical thickness domain yielded the position of the peak carrier concentration accurately.