Oblique Incidence E-polarized Photons on Infinite Periodic Grating of Metal Strips

Diffraction of a homogeneous unit density flow of E-polarized photons on a grating of infinitely thin metallic strips is considered. Probability of finding a photon in any point is represented by psi-function, satisfying to Schrödinger equation and boundary conditions of equality zero on the strips and continuity on the slits. This work provides further development of quantum-mechanical contemplation of the diffraction problem on the periodical structures. To solve the problem, the strict Riemann-Hilbert boundary value problem method is used. The essence of it is that the solution of the functional equations system is reduced to the restoration of the analytical function in the entire plane of the complex variable, based on the sum of its limit values on the arc of the unit circle. The unknown coefficients of the function, represented as a Fourier series, are determined from a well-converging infinite system of algebraic equations.Using PC, numerical experiments were performed to study the probability distribution of E-polarized photons with a wide change in the parameters of the problem. The dependences of the square of the psi-function module on the ratio between the wavelength and the grating period, on the ratio between the slit width and the grating period are presented for different values of the angle of incidence of the photon flux and the distance from the grating. Based on the analysis of the obtained dependencies, conclusions about the ratios of parameters at which the grating constant can be determined more accurately from the observed diffraction pattern were made. With normal incidence on the grating, it is more convenient to do this by observing the diffraction pattern behind the grating, with oblique incidence - in front of the grating.