The Schur algorithm applied to the design of optical multi-mirror structures

Abstract

We show how to use the classical Schur algorithm to design multi-mirror optical interferometers (or filters). Our derivation is simple and straightforward, clearly revealing its connection to the previously known orthogonal digital filter structures. We also give a complete detailed description of an FFT-based algorithm for the reciprocal polynomial approximation of an arbitrary curve (or spectrum). The Schur algorithm can, in turn, be applied to the obtained polynomial to get the desired reflection coefficients of the mirrors. Copyright (c) 2004 John Wiley W Sons, Ltd.