As it is known [1], some freedom in choosing the integral representation of electromagnetic fields in diffraction problems makes it possible to get various integral equations. The essence of the proposed method comes down to determining the intermediate characteristic — the charge distribution over the metal plate and then by means of integration — the electric current. The vectors of the electromagnetic field are determined via the vector potential of electric currents using the known equations:

(1) |

where .

The radiator is regarded as part of an infinite periodic antenna array, which makes it possible to proceed to the analysis of the field within one period. Due to this, it is reasonable to use a representation in the form of expansion in plane waves for the vector potential [2]:

(2) |

where

and is the vector of the electric current volume density, (*x*,*y*,*z*), (*x'*,*y'*,*z'*) are the coordinates of the point of observation and the point of integration respectively.

Fig.1

Presuming that the metal radiators are ideal conductors and they are also infinitely thin, the vector of the electric current volume density can be written down in the following way:

(3) |

and it is reasonable to replace the effect of the screen with a mirror view of the radiator:

(4) |

where is the vector of the electric charge surface density, is the Dirac delta function.

By integrating expression (2) using the axial coordinate *z* and taking into account (3) and (4), it is possible to get the values of the vector potential harmonic in two characteristic areas of the structure:

(5) |

The wave of the potential is presented in the form of the superposition of waves related to *Е*- and *Н*-waves of the spatial waveguide:

(6) |

The specified waves are determined by the following expressions:

(7) |

where .