Abstract
We develop a generalized formalism for describing the propagation of
an electromagnetic wave along the z-direction
of a dielectric medium. The derivation is achieved by casting the 2-D transverse
part of the Maxwell equations in a Schrodinger-like form whose Hamiltonian
is identified to be pseudo-Hermitian. The developed formalism is combined
with the variational principle to derive a set of nonorthogonal coupled-mode
theory which is slightly different from that derived using the same variational
principle but with the 3-D Maxwell equations. By showing that the 3-D variational
approach suffers from a mode-expansion incompatibility issue that is absent
in our 2-D case, we conclude that our nonorthogonal coupled-mode theory is
more rigorous. Owing to the complexity of the second-order error of the propagation
constant as revealed by further analysis, it is found that our nonorthogonal
coupled-mode theory may not necessarily be more accurate in practice. The
developed pseudo-Hermitian formalism may provide a good framework for the
analysis and design of various integrated optical devices.
© 2011 IEEE
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