12 January 1998 Analysis of step- and graded-index optical waveguides by solving Helmholtz eigenproblem through Fourier analysis and iterative Lanczos reduction
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Abstract
A method of solution of the scalar Helmholtz eigenproblem for dielectric waveguides is presented. The fundamental idea is the expansion of the electric field on a discrete basis of sine functions which go to zero at the calculation window boundaries, for both transverse directions. A matrix eigen problem is correspondingly built up from the Helmholtz polynomial functions defined over rectangular domains. The solution algorithm takes advantage of the well-known Lanczos reduction technique, allowing for the straightforward evaluation of discrete eigen values within any desired precision order. The Lanczos algorithm, here combined with the Fourier-analysis technique, allows to examine very large-sized cases without the problem of storage space lacing. In this work, a few examples of propagation analysis are shown referring to both step-index and graded-index integrated optical structures, and the calculation results are compared with those obtained by commercial BPM algorithms and the effective index method.
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Michele A. Forastiere, Michele A. Forastiere, Giancarlo C. Righini, Giancarlo C. Righini, "Analysis of step- and graded-index optical waveguides by solving Helmholtz eigenproblem through Fourier analysis and iterative Lanczos reduction", Proc. SPIE 3278, Integrated Optic Devices II, (12 January 1998); doi: 10.1117/12.298216; https://doi.org/10.1117/12.298216
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