Numerical analysis of the longitudinal component of electric field in electromagnetic wave

Optical phenomena connected with the influence of the longitudinal component (i.e. parallel to the wave vector) of the electric field in electromagnetic wave are considered. The topicality of the study is connected with the analysis of the objects of subwave scales and additional degrees of freedom of spatially inhomogeneous optical fields in new areas of optics; they are photonics, plasmonics and nanooptics. The numerical analysis is carried out for plane waves with Gauss intensity profile and homogeneous (linear or circular) polarization. The solution of Maxwell equations is carried by the method of finite differences. To test the accuracy of the program the reflection coefficients of an electromagnetic wave on the boundary of a transparent dielectric medium with analytic Fresnel solution are compared. The distribution of the electromagnetic field at focusing with a thick symmetrical lens is calculated. The increase in the intensity of the longitudinal component in the focal plane of the lens is found to be ~ 25 fold compared with the value of E|| in the incident radiation. A numerical analysis of the geometric spin Hall effect is carried out for the first time when focusing an asymmetrically converging light beam. The effect is in shifting the center of gravity of the intensity distribution of the longitudinal component of the light beam for different states of circular polarization. The calculated shift is ~0,5λ for right-handed and left polarized light with a focal spot diameter of ~2λ which agrees with experimental data well. Carried out research has shown that the developed package can be used to calculate field distribution in the propagation of electromagnetic waves of arbitrary configuration in optically inhomogeneous media.