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On the classification of electrodynamic operators describing inhomogeneous and irregular guide structure

Keywords:

E. V. Pavlovich – Head of 1203 VP of RF DoD
Yu. V. Raevskaya – Ph.D. (Eng.), Associate Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev
E-mail: raevskaja@forum.nn.ru


We consider the formulation of boundary value problems describing irregular guide electrodynamic structures. It is noted that in the vast majority these problems are classified as nonself-adjoint. The most common solutions of their dispersion equations are complex values, corresponding to complex waves. The article contains specific examples of such solutions.
The problems of classification of electrodynamic operators describing cross-inhomogeneous and longitudinally irregular guide structures have been considered. It has been noted that if at least for one of the areas of the structure, formed as a result of decomposition of the latter, the boundary value problem is nonself-adjoint, the boundary value problem will be nonself-adjoint for the entire structure as a whole. It has been shown that periodically irregular structures in the rigorous formulation of boundary value problems are described by the nonself-adjoint operators, so that they can guide complex waves. Complex eigenvalues (existence of complex waves) is the prerogative of self-conjugate boundary value problems and their main feature. The solutions corresponding to these eigenvalues are the most common. In the case of open guiding structures in the absence of a zero condition at infinity it is expedient to replace the term "eigenvalue" by the term "characteristic value", as a boundary value problem ceases to be homogeneous.

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