There has been increasing interest during the last decade in the processes of electromagnetic wave propagation in complex guiding systems with inhomogeneous filling. Although different types of them have been widely used in various practical applications for more than 30 years and a lot of their physical properties have been established, interest in developing rigorous mathematical technique in this field of electrodynamics has appeared only recently. Modern guiding systems such as microstrip transmission lines and other types of open waveguides with non-compact boundaries produce new problems to be solved and require working out special methods for their studies. Typical here are nonself adjoint boundary eigenvalue problems for the systems of Helmholtz equations with piecewise-constant coefficients and transmission conditions where the spectral parameter enters in a nonlinear way. The methods developed in this chapter for solving such problems are based on the spectral theory of operator-valued functions and operator pencils.

Inspec keywords: optical waveguides; eigenvalues and eigenfunctions; microstrip lines; transmission line theory; Helmholtz equations; piecewise constant techniques; electromagnetic wave propagation; electrodynamics

Other keywords: electrodynamics; physical properties; piecewise-constant coefficients; operator pencils; electromagnetic wave propagation; eigenwaves; operator-valued functions; open waveguides; spectral theory; boundary eigenvalue problems; Helmholtz equations; microstrip transmission lines; mathematical technique; transmission conditions; noncompact boundaries; inhomogeneous filling; complex guiding systems

Subjects: Optical waveguides and couplers