G. S. Malyshev – Ph.D. (Eng.), Assistant, Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev
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
A. A. Titarenko – Dr.Sc. (Eng.), Professor, Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev; Chief Designer for Microelectronics, Russian Federal Nuclear Center – All-Russian Research Institute of Experimental Physics (Sarov)
The self-consistent radiation problem has been formulated. This problem leads to homogeneous Fredholm integral equations of the second kind. The eigenfunctions of this problem are the basis for decomposition of fields on the radiation surface. This basis, obtained as a solution to the self-consistent problem, allows one to take into account the reverse effect of the radiation field on the source.
On the basis of this self-consistent task, the task was to synthesize the function of a radiation source for the case of radiation from the end of a round open dielectric waveguide. The initial self-consistency of the problem allowed us to take into account the reverse effect of the radiation field on the source. It has been shown that the problem of synthesizing a given radiation field is reduced to a system of Fredholm integral equations of the first kind, whose integrands are the source functions that determine the coordinate distributions of the primary fields on the radiating surface. The free parts of integral equations correspond to the components of a given field.
The procedure of algebraization of systems of equations on the basis of which the synthesis problem is solved has been considered. It is implemented using the collocation method. It has been shown that for a symmetric radiation field the synthesis problem can be solved with high accuracy, since the result of the solution doesn’t depend on the choice of the azimuthal coordinate of the collocation node.
For a symmetric field, the ratio between the amplitude coefficients of the symmetric waves of a round open dielectric waveguide has been calculated, which ensures the required field distribution. The good convergence of the solution obtained using the collocation method has been shown. This indicates the correctness of its use in the algebraization of the initial system of equations.
It has been shown that in the case of synthesis of an asymmetric field the collocation method also makes it possible to ensure good convergence of the solution. However, to calculate the amplitude coefficients of asymmetric waves of a round open dielectric waveguide, it is necessary to locate collocation nodes with high accuracy over the entire radiation plane, which significantly increases the computation time.
- Raevskij A.S., Raevskij S.B. Samosoglasovannost' kraevykh zadach teorii izlucheniya. Antenny. 2014. № 2. S. 3–6.
- Malyshev G.S., Novoselova N.A., Raevskij S.B., Sedakov A.Yu. Samosoglasovannaya zadacha ob izluchenii iz kruglogo otverstiya v beskonechnom ideal'no provodyashchem ekrane. Antenny. 2015. № 3. S. 3–9.
- Malyshev G.S., Novoselova N.A., Raevskij S.B., Sedakov A.Yu. Zadacha sintezirovaniya istochnika, sozdayushchego zadannoe pole izlu¬cheniya. Antenny. 2016. № 3. S. 67–72.
- Aleksidze M.A. Fundamental'nye funktsii v priblizhennykh resheniyakh granichnykh zadach. M.: Nauka. 1991.
- Malyshev G.S., Raevskij A.S., Raevskij S.B. Formirovanie funktsii istochnika, sozdayushchego zadannoe pole izlucheniya. Radiotekhnika i elektronika. 2018. № 7 (63). S. 673–681.
- Unger Kh.G. Planarnye i volokonnye opticheskie volnovody. M.: Mir. 1980.