Numerical Simulation of the Transverse and Longitudinal Shifts of Reflected Beam

Abstract

The effects of the spin-orbit interaction of light are observed at the wavelength scale and can be used in nanophotonics. The computer simulation of these effects is a necessary tool for creating devices, based on the spin-orbit interaction of light. We have developed a software package in Python to simulate two known effects, namely, transverse and longitudinal shifts of the center of gravity of beams at the total internal reflection. The package is based on the algorithm for the numerical solution of Maxwell's equations by the finite difference time domain method. We have used the modification of PML - UPML as absorbing boundary conditions. We simulated the refraction and total internal reflection of an electromagnetic wave at the plane interface between two transparent dielectrics and calculated the depth of penetration of a non-uniform electromagnetic wave, occurring at total 1 internal reflection in the optically less dense medium. To test the software package, we have compared the reflection coefficients of the electromagnetic wave for the normal and oblique incidence on the plane interface, calculated by the simulation with the coefficients, obtained by Fresnel formulas for the s-polarization of the wave. We have numerically simulated the shifts of the center of gravity of beams of finite size in the plane of incidence and perpendicular to it, namely, the effects of Goos-Hanchen and Fedorov. The dependence of the direction of the transverse shift on the sign of the circular polarization of the incident beam was demonstrated. The dependence of the longitudinal shift on the direction of linear polarization is also demonstrated. It should be stressed that the developed software package can be applied for simulating of the longitudinal and transverse shifts in anisotropic media, media with optical activity, as well as thin films on the dielectric surface.