Diffraction of E-polarized Photons on Periodic Grating of Metal Strips

The problem of diffraction of E-polarized light at normal falling on a grating of infinitely thin metallic strips is solved. Light is represented as a flux of particles – photons. The problem of determining the psi-function of a photon scattered by the grating is led down to the Riemann-Hilbert boundary problem. A strict solution is obtained in the form of a convergent infinite system of linear algebraic equations. The system equations are valid for any relation between wavelength and period of the structure and any relation between slit width and strip width. As follows from a comparison of the de Broglie representation of the psi-function and its decomposition into Fourier series, the possible values of the photon momentum component perpendicular to its initial direction of motion are determined by even values of the "quantum" of momentum, whose magnitude is determined by the grating period. Photons passed through or reflected by the grating get discrete values of momentum when interacting with the grating and deviate at discrete angles. Numerical calculations show that the diffraction maxima are located in front of the slit and have some internal structure that depends on the ratio between the grating period and the photon wavelength. As the ratio of the grating period to the photon wavelength increases, the diffraction peak splits. When the ratio becomes less than unity, the diffraction pattern disappears, we have a uniform illumination. Therefore, the value of the specified ratio, equal to one, is the threshold.Key words: diffraction, grating, quantum, psi-function, probability amplitude, diffraction pattern, photon.