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A unified electrodynamic approach to the guided wave excitation by external sources in the waveguiding structures with bianisotropic media is developed. Effect of electric, magnetic, and magneto-electric losses in such media manifests itself in the special form of eigenmode orthogonality referred to as the quasi-orthogonality relation. It reflects the existence of the cross-power flow P kl and loss Q kl for any pair (k, l) of modes which are rigidly linked to each other by this relation. The quasi-orthogonality relation remains true in the limiting case of lossless waveguides yielding the customary relations of orthogonality and normalization for propagating (active) modes and also their generalization for nonpropagating (reactive) modes.It is shown that the eigenmode set for a waveguiding structure is complete only outside the region of exciting sources. Inside this region the modal expansions of fields are incomplete and must be supplemented with the orthogonal complementary fields which extend the proper Hilbert space spanned by waveguide eigenfunctions. Among exciting sources there are the external bulk sources (currents, fields, and medium perturbations) and the external surface currents. Besides, the orthogonal complementary fields generate the effective surface currents on boundaries of the bulk exciting sources.The problem of waveguide excitation by external sources is solved by means of determining both the mode amplitudes for the modal field expansions and the orthogonal complementary fields inside the source region. The equations of mode excitation are derived on the basis of three approaches applying the direct use of Maxwell's equations, the electrodynamic analogy with the mathematical method of variation of constants, and the conjugate reciprocity theorem.

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This article evolves an analytical theory of nonuniform P N -junctions by employing the transverse averaging technique (TAT) to reduce the three-dimensional semiconductor equations to the quasione-dimensional (quasi-1D) form involving all physical quantities as averaged over the longitudinallyvarying cross section S(z). Solution of the quasi-1D Poisson's equation shows that, besides the usual depletion capacitance Cp and Cn due to the p-and n-layers, there is an additional capacitance Cs produced by nonuniformity of the cross-section area S(z). The general expressions derived yield the particular formulas obtained previously for the abrupt and linearly-graded junctions with uniform cross-section. The quasi-1D theory of nonuniform structures is demonstrated by applying the general formulas to the P N -junctions of exponentially-varying cross section S(z) = S0 exp(αz) as most universal and applicable to any polynomial approximation S(z) ≃ S0(1 + αz) n .

A rigorous and consistent approach is demonstrated to develop a model of the 4M structure (the four-media structure of a film on a substrate of finite thickness). The general equations obtained for the reflectance and transmittance spectra of the 4M structure are simplified by employing a procedure of the so-called device averaging to reduce them to a succinct form convenient for processing of experimental spectra for the structures with a thick substrate. The newly derived equations are applied to two special cases: (i) an arbitrary film on highly absorbing substrates and (ii) a slightly absorbing film on transparent substrates. The reflectance and transmittance spectra represented in the simplified (with the device averaging) form have a practical application for determining the film thickness and optical constants from experimental spectra by using the known techniques.