Accession Number : ADP008224
Title : Finite Difference Generalized Pade Approximant Propagation Methods,
Corporate Author : QUEEN'S UNIV KINGSTON (ONTARIO) DEPT OF ELECTRICAL ENGINEERING
Personal Author(s) : Yevick, David ; Glasner, Moses ; Hermansson, Bjorn
Report Date : APR 1992
Pagination or Media Count : 4
Abstract : We present a simple series of high-order finite difference and finite element propagation procedures based on approximating the exponential of two noncommuting operators as a product of single-operator Pade approximants. We have previously generated a class of precise split-step fast Fourier transform propagation techniques from an expansion of eA+B, where A and B are noncommuting operators, into an alternating product of exponentials of the individual component operators. We here extend this formalism to split-operator finite difference and finite element alternating direction implicit procedures by defining the generalized Pade approximant of eA+B as a product of Pade approximants of each individual operator. We demonstrate the central fact that that high-order propagation methods often require only (1,1) component approximants. Our results, which are found numerically to apply in fourth and sixth order even to longitudinally varying refractive index distributions, are verified by analyzing light propagation through an integrated optic microlens.
Descriptors : *PROPAGATION, EXPANSION, FAST FOURIER TRANSFORMS, LIGHT, OPTICS, REFRACTIVE INDEX, FINITE DIFFERENCE THEORY, FINITE ELEMENT ANALYSIS.
Subject Categories : Radiofrequency Wave Propagation
Distribution Statement : APPROVED FOR PUBLIC RELEASE