Exact Solutions For TM Modes in Graded Index Slab Waveguides
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Three continuous profiles for the dielectric constant are derived, which allow exact solutions of the vector wave equation, including all terms in the gradient of the profile, for both TE and TM modes on slab waveguides. The dielectric constant has been assumed to be a scalar quantity; i.e., the medium is isotropic.
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IEEE Journal of Quantum Electronics