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Asymptotic analysis of planar and cylindrical inhomogeneous waveguides
Author(s) -
Arnold J. M.
Publication year - 1981
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs016i004p00511
Subject(s) - planar , cladding (metalworking) , eigenvalues and eigenvectors , mathematical analysis , boundary value problem , mathematics , transformation (genetics) , homogeneous , waveguide , differential equation , asymptotic analysis , nonlinear system , method of matched asymptotic expansions , optics , physics , computer science , materials science , biochemistry , chemistry , computer graphics (images) , quantum mechanics , combinatorics , metallurgy , gene
The problem of determining the eigenvalues of an inhomogeneous waveguide, subject to boundary conditions at an interface with an exterior homogeneous medium (cladding) is considered. A recently developed asymptotic method is summarised. Previous work dealt with planar waveguides; here we incorporate the extensions necessary to accommodate cylindrical waveguides, as encountered in optical fibres. The method uses a nonlinear transformation between variables to reduce a given differential equation to canonical form; this transformation has more tractable asymptotic properties than the original differential equation.