Numerical evaluation of truncated Kramers-Kronig transforms

摘要

The truncated Kramers-Kronig transform, used widely in the analysis of optical data, is recast into a form that avoids the need to evaluate a Cauchy principal-value integral. A specialized Gaussian quadrature involving the weight function log(e) x(-1) is employed. This approach yields accurate results for functions that lead to kernels with relatively rapid decay, which covers the cases most commonly encountered in optical data analysis. An application to the reststrahlen region of the GaAs spectrum is made. (c) 2007 Optical Society of America.