The orthogonality relation for TE- and TM-modes in guided-wave optics

The orthogonality relation between two arbitrary noncollinear modes in a slab waveguide is derived. The use of noncollinear modes makes it possible to calculate the orthogonality relation between the mode amplitudes of a TE- and a TM-mode, which in the collinear case is masked by the vector orthogonality of the modes. The discrepancy between the present results and those of G.I. Stegeman et al. (1981) is discussed. The derived orthogonality relation is more complex than the corresponding relation between the amplitudes of either two TE-modes or two TM-modes. Consequently, the utility of coupled-mode analysis for solving problems involving TE-TM interactions is severely restricted.<
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