Digital simulation of electromagnetic wave diffraction by a rectangular groove in a conducting screen

When optimizing the directivity and energy characteristics of the antennas with flat reflectors and the leaky-wave antennas, high-speed computational algorithms are required for a reliable analysis of the diffraction of electromagnetic waves on a conducting screen, accounting for the inhomogeneities with the dimensions commensurate with the wavelength. To calculate the diffraction field of an electromagnetic wave with an arbitrary-shaped front on a rectangular groove in the screen, a numerical model has been developed. This model is based on the approximation of the wave front by finite locally flat patches and the use of the authors’ rigorous solution of the problem of locally flat wave diffraction on a conducting screen with a groove. The field above the screen is represented by the Fourier integral, while the field in the groove – by the sum of waveguide modes. The set of functional equations is obtained using the method of partial domains. Through a re-expansion of the modal functions of the field of partial domains in terms of the basis of the adjacent domain, the functional equations are reduced to a set of linear algebraic equations with respect to the complex amplitudes of the waveguide modes of the groove. The implementation of the main computational procedures is described. Based on the analysis of the particular results, the reliability of the developed model is proved. The influence of the quality of the wave front interpolation on the accuracy of the solution is studied. Recommendations on the frequency of a wave-front fragmentation are formulated. The proposed digital algorithm can be used to analyze and synthesize antennas with the flat perforated distributing and radiating systems.