ISSN:
1432-0649
Keywords:
42.80
;
42.82
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract Guided modes of a planar dielectric waveguide which encounter a nondiagonal permittivity tensor are neither TE nor TM, but hybrid. They are described by a pair of coupled second-order differential equations for the transversal electric and magnetic field components. We construct a real-valued function which plays the role of the transversal electric or magnetic field in the uncoupled Sturm-Liouville differential equation for TE or TM modes. The number of zeroes, or nodes, of this function labels the modes. The nodes increase with the prospective propagation constant. This fact is proven by constructing suitable self-adjoint operators and referring to the minimax principle. The nodal properties allow to formulate an efficient bisection algorithm for effective indices and field distributions of guided hybrid modes.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00692123
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