Abstract
This paper discusses a method of analyzing complex one-dimensional multilayer
waveguides in a numerically stable way. When a multilayer waveguide contains
a quite thick layer or a layer whose refractive index has a very large real
or imaginary part, conventional analysis methods tend to fail to find out
its modes. In order to solve such a problem, the discussed analysis method
is based on modified transfer matrix equations. The method consists of three
steps. At the first step, two types of modified transfer matrix equations
are used to derive two types of characteristic equations. At the next step,
the iteration method comprised of initial root-finding and root-tracking is
used to find the roots of the characteristic equations. Since the two characteristic
equations have different features, the initial root-finding is carried out
with one of them, and the root-tracking with the other. Finally, the field
profiles of waveguide modes are calculated by using the found roots and employing
a stable routine based on the modified transfer matrix equations. A few presented
examples show that the discussed method works well. In addition to the method,
it is shown that one of the characteristic equations can be expressed as an
explicit form rather than a conventional recursive matrix relation because
of the simple form of one of the transfer matrix equations.
© 2009 IEEE
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