S. A. Kapustin – Post-graduate Student,

Department of Physics and Technology of Optical Communication,

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

E-mail: physics@nntu.ru

S. B. Raevskij – Dr.Sc. (Eng.), Professor,

Department of Physics and Technology of Optical Communication,

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

L. G. Rudoyasova – Ph.D. (Eng.), Associate Professor,

Department of Physics and Technology of Optical Communication,

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

The article compares coupled and complex waves, including those connected to the source. The dispersion equations of the attached waves are formed by equating to zero the main and additional determinants of the systems of, in the general case, inhomogeneous linear algebraic equations obtained from the boundary conditions of the boundary value problem. Attached waves should not be attributed to their own waves, since they are described by the inhomogeneous (attached) Helmholtz equation. Their existence is explained by the distributed interaction with a source such as a traveling wave antenna. Coupled waves are the result of the interaction of own waves with the same phase characteristics.

In this work, to compare coupled waves with complex waves, a model of a directional coupler on distributed-guided waveguides is used.

Coupled waves in the guiding structures are usually their own waves of these structures or their fragments, on which, in one way or another, additional bonds are superimposed. The guiding structures have eigenwave spectra that turn out to be interconnected either discretely or distributed. These waves are interconnected within each line and with the waves of other lines. When these waves propagate, their energies are constantly exchanged.

As a result, coupled transmission lines are formed, the own waves of which can be described in the general case by both self-adjoint and non-self-adjoint boundary value problems. In the first case, the complexity of the wave numbers of coupled waves is caused by their interaction, in the second case, it is embedded in the own waves themselves, because the eigenvalues of non-self-adjoint boundary value problems in the general case are complex quantities (this is the so-called “intrinsic” complexity), and in addition, “external” complexity associated with the interaction of own waves is occurred.

The complexity of the wave numbers is explained by the non-self-adjointness of the boundary value problems describing these waves. The complexity of the wave numbers of coupled waves is explained by their interaction, which is influenced by the "intrinsic" complexity of wave numbers if the own waves in the absence of their coupling are described by solutions of non-self-adjoint boundary value problems. Thus, the complexity of the wave numbers of coupled and complex waves is due to various reasons. The complexity of the wave numbers of complex waves is caused by the spectral interaction of the partial waves that form the field of each own wave. This interaction leads to the formation of oncoming power flows. The complexity of the wave numbers of coupled waves is caused by the interaction of their own waves with each other, as a result of which a constant redistribution of energy between the waves occurs during the propagation of the electromagnetic field.

In nonreciprocal guiding structures, complex waves can exist that do not satisfy the orthogonality condition in the energy sense and exist due to pair interaction, as a result of which energy is transferred from one wave to another.

Studies have shown that the intrinsic power fluxes of Ke waves through the cross section of the waveguide are nonzero. In this case, the waves can be divided into two pairs, inside each of which the waves interact with each other. The interaction is evidenced by the presence of a mutual power flow in these waves.

The presented results can be used in the electrodynamic calculation of devices such as directional couplers and limit attenuators.

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