Yu. V. Raevskaya  Ph.D. (Eng.), Associate Professor,

Department of Physics and Technology of Optical Communication,

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

E-mail: physics@nntu.nnov.ru

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

Department of Physics and Technology of Optical Communication,

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

We consider a boundary value problem on the Helmholtz equation about an attached wave, in which the source function on the right side of this equation is the solution of a homogeneous boundary value problem on this equation. It is shown that such a source, along with its own wave, creates an attached wave.

Two variants of the boundary-value problem are considered for traveling waves attached to a source (existing only in its presence) and oscillations of a circular two-layer shielded waveguide. The first variant of the attached boundary value problem (when the field is formed by superposition of eigen complex waves) and the second variant (when the field of the attached wave is excited) correspond to different functions on the right side of the attached Helmholtz equation. In the first case, we have an oscillation connected to the source, in the second case – a wave.

The function on the right side of the equation of the attached Helmholtz equation can be viewed either as a function of a distributed source of the traveling wave type, and the attached boundary value problem on this equation as the problem of excitation of waves “attached” to the specified source, or as a function of the source creating complex resonance.

The boundary self-consistent tasks are formulated, which describe oscillations and waves attached to the source. They take into account the reverse effect of the field on the source, since the wave numbers in the field functions and in the source functions are the same. The amplitudes of the indicated waves and oscillations depend on the longitudinal coordinate. The oscillations and waves are attached because they are described by the adjoining Helmholtz equations, the right-hand sides of which are solutions of the corresponding homogeneous boundary value problems.

The boundary value problems thus formed should be called self-consistent. Waves (oscillations) described by them are “attached” to the source, have the opposite effect on it, they exist only if it is present. In this sense, they cannot be called own. It is proposed to call them attached to the source.

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