Method of Additive Regularization of Field Integrals in the Problem of Electromagnetic Diffraction by a Slot in a Conducting Screen, Placed Before a Dielectric Layer

Abstract

We present a rigorous solution of a two-dimensional problem of stationary electromagnetic plane wave diffraction by a slot in a perfectly conducting screen having finite thickness in the presence of a plane dielectric layer behind the screen. For obtaining this solution, the method of additive regularization of singularities for field diffraction integrals is developed. This method is suitable for the cases of transparent, absorbing and amplifying dielectric. It reduces to explicit extraction of singularities in the form of supplementary singular integral terms, which describe waveguide modes of a dielectric layer. On the bases of the obtained solution, the conditions of optimum diffraction excitation for such modes are investigated in dependence of geometrical parameters of the problem for the cases, when these parameters are of the order of the radiation wavelength.

Asymptotic regularisation of the solution to the problem of electromagnetic field scattering from a set of small impedance particles

“…Error of asymptotic solution (17) at small distance d between particles in the range of GHz frequencies for the ellipsoid particles ANDRIYCHUK -7 depends slightly on the distance d between the particles if the value of b remains the same. This was confirmed by the data in Figure 2, where the results for d = 20b are presented.…”

“…One can show that if b → 0, then the sum in (17) converges to the respective integral and (11) becomes…”

“…F I G U R E 1Error of asymptotic solution(17) at small distance d between particles in the range of GHz frequencies for the ellipsoid particles 1336 -ANDRIYCHUK…”

Theory of Gaussian Beam Diffraction by a Transmission Dielectric Grating

“…The exponential multiplier exp(±ikαx) describes such propagation exactly, and the condition (23) provides the satisfaction of the wave Helmholtz Equation ( 2) for the total field ( 22) as a whole and for every its plane-wave component separately. Expression ( 22) is mathematical appearance of the principal of superposition, which establishes that various components exp(ik[±αx + βy]) of the compound field (22) propagate in homogeneous linear medium independently of one another and conserve their starting amplitudes U (β).…”

“…Strictly speaking, in addition to waveguide modes of a grating, taking into account by the present theory, waveguide modes of a substrate can also exist, whose field propagates along the normal in a grating and in a substrate, but undergoes total internal reflection on the lower boundary of a substrate with air. There is a special technique for solving diffraction problems with the participation of waveguide Serdyuk modes in a plane dielectric layer [22], which is reduced to the regularization of integral expressions for the fields inside a layer. However, the amplitudes of such modes are negligibly small because of large thickness of a dielectric layer (a substrate), in which they are excited.…”