Abstract
For a nonhomogeneous waveguide, whose refractive index is not a constant,
the problem is very complicated since the nonlinear eigenvalue problems are
unable to reduce to algebraic equations yet. When the refractive index is
varied, the dispersion relation cannot be derived by using the analytic expressions
of the solutions in each layer. In this paper, this problem is solved by using
the differential transfer matrix method, which is introduced to deduce the
dispersion relations of leaky modes for TE and TM cases, respectively. Moreover,
for the waveguide whose refractive index is gradually varied, the dispersion
relations can be approximated by some simpler algebraic equations, which are
close to the exact relations and very easy to analyze. Asymptotic solutions
are used as initial guesses, and followed by Newton's method, to give very
accurate solutions. This paper is a generalization of the asymptotic method
of slab waveguides; all the results therein are consistent with the analysis
here.
© 2011 IEEE
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