G. S. Malyshev - Post-graduate Student of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev. E-mail: physics@nntu.nnov.ru A. S. Raevsky - Dr.Sc. (Phys.-Math.), Professor, Head of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev S. B. Raevsky - Dr.Sc. (Eng.), Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev; Honored Scientist of RF A. A. Titarenko - Dr.Sc. (Eng.), Associate Professor of Department of Physics and Technology of Optical Communication, Nizhny Novgorod State Technical University n.a. R.E. Alekseev; Deputy Chief Designer of FSUE FRPC - Measuring System Research Institute n.a. Yu.Ye. Sedakov?

The article describes the process of solving the self-consistent problem of radiation from a hole in a perfectly conducting screen. The self-consistent problem leads to a system of homogeneous integral equations. The solutions of these equations form the basis for ex-pansion of the fields produced by the sources in open space. The unknown field components from the system are represented as independent expansions. Expansions fields must satisfy the condition on the edge and zero conditions at infinity. The components of the electric field must vanish on the metal surface. The connection between the expansion coefficients determined in the process of solving the system. This is the principle of spectral method. The collocation method was used for solving the systems of integral equations. The systems are written in the nodes of collocation. The result is a system of homogeneous algebraic equations. From the requirement of non-trivial solutions of systems we obtain the characteristic equation. The joint solution of these equations gives the eigenvalues. It has been found that by increasing the number of nodes of collocation and changing their coordinates, the real component of the electric field components preserves the order. The qualitative dependence of the components of the electric field by the radial coordinate is not changed. This indicates the stability of the solutions obtained on the basis of the collocations method. Similar calculations for the magnetic field have shown that the components of the field become small outside the hole. Magnetic field components are tends to zero by removal to infinity. This corresponds to the approximation of geometric optics.

 

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