Title :
Scalar analysis of general dielectric waveguides by Fourier decomposition method
Author :
Forastiere, Michele A. ; Righini, Giancarlo C.
Author_Institution :
Ist. di Ricerca sulle Onde Elettromagnetiche, CNR, Firenze, Italy
fDate :
2/1/1999 12:00:00 AM
Abstract :
The scalar Helmholtz eigenproblem for dielectric waveguides is solved by expressing the field in a series of sines in the transverse plane (Fourier decomposition). A matrix eigenproblem is correspondingly built up, where the refractive index distribution is represented either by a grid of homogeneous rectangles or by polynomial functions defined over rectangular domains. Finally, the Lanczos reduction technique is used to calculate the matrix eigenpairs corresponding to guided modes. This allows to examine very large-sized cases without physically storing huge nonsparse matrices. 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 a commercial simulation software and the effective index method
Keywords :
Helmholtz equations; dielectric waveguides; eigenvalues and eigenfunctions; gradient index optics; optical waveguide theory; optical waveguides; refractive index; Fourier decomposition; Fourier decomposition method; GRIN integrated optical structures; Lanczos reduction technique; effective index method; general dielectric waveguides; graded-index integrated optical structures; guided modes; homogeneous rectangles; matrix eigenpairs; matrix eigenproblem; optical waveguide theory; polynomial functions; propagation analysis; refractive index distribution; scalar Helmholtz eigenproblem; scalar analysis; simulation software; step-index integrated optical structures; transverse plane; Dielectrics; Integrated optics; Matrix decomposition; Optical propagation; Optical refraction; Optical waveguides; Planar waveguides; Polynomials; Refractive index; Transmission line matrix methods;
Journal_Title :
Lightwave Technology, Journal of
