ИСТИНА

A 2D problem of diffraction by an aperture line is studied. The line is formed by absorptive screens(Fig. 1). This problem can be interpreted as a reduction of a waveguide problem[1]. It corresponds to the Fabry - Perot resonator with displaced mirrors(Fig. 2). The incident wave is assumed to have wavelength short comparatively to the scale of the aperture line, and the incidence angle is small, i.e. the incident wave propagates almost parallel to the edge of the aperture line. We assume that the scattering occurs mainly under small angles and use the parabolic approximation to describe the wave process. A recently developed approach[2][3] based on the embedding formula and the spectral equation for the directivity of an edge Greens function is applied to the problem. We prove the embedding formula for this problem, which express reflection coefficients through the directivity of an edge Greens function. Then we introduce spectral equation,which is an ordinary differential equation with unknown coefficient but with known boundary conditions. To determine this coefficient we construct Ordered Exponential (OE) equation. Then we solve OE - equation numerically.