Non-specular reflection of a narrow spatially phase-modulated Gaussian beam

The lateral and angular Goos-Hänchen shifts undergone upon reflection on a dielectric plate by a spatially phase-modulated Gaussian beam are derived. It is shown that the amplitude and direction of both lateral and angular shifts are very sensitive to the degree of spatial phase modulation of the incident beam, so that such modulation thus provides a means to control those shifts. It is also shown that the modulation incurs some beam reshaping upon reflection. Analytical calculations of the lateral shift are found to be in good agreement with numerical simulations of beam propagation before and after reflection. In these simulations, the required spatial transverse phase modulation is achieved by focusing a microwave Gaussian beam onto the dielectric plate with a non-spherical lens or a flat-surfaced thin lamella exhibiting a suitable gradient of its refractive index. The optimal parameters governing the spatial phase modulation are discussed to achieve: (i) enhancement of the lateral shift of a spatially phase-modulated beam in comparison to that of a non-modulated beam and (ii) simultaneous large values of reflectivity and of the lateral shift, while keeping the reshaping of the reflected beam to a minimum.