Reflection and transmission of optical vortex beams at a dielectric interface

This paper discusses the paraxial vortex beams (Laguerre-Gaussian modes) incident on a homogeneous, isotropic and lossless dielectric plane. Using Fourier transform, vortex beams are decomposed into plane waves and then multiplied by the Fresnel coefficients. The reflected or transmitted vortex beams can be obtained via inverse Fourier transformation. The results show that the centre of the intensity gravity for both reflection and transmission of light beams undergoes a transverse shift. In particular, the intensity distribution of the transmitted beam is similar to that of diagonal Hermite-Gaussian beams.