Goos-Hanchen and Imbert-Fedorov shifts of higher-order Laguerre-Gaussian beams reflected from a dielectric slab

We consider reflection of the Laguerre–Gaussian light beams by a dielectric slab. In view of the unified operator approach, the higher-order Laguerre–Gaussian beams represent a parametric family with the transverse beam profile given by an arbitrary generating parameter. Relying on the Fourier expansion in the focal plane of the beam, we compute the Goos–Hänchen and the Imbert–Fedorov shifts for light beams with non-zero order and azimuthal index. It is demonstrated that both shifts exhibit resonant behavior as functions of the angle of incidence due to the interference between the waves reflected from the upper and lower interfaces. The centroid shifts strongly depend on the order and azimuthal index of the beam. Most interestingly, it is found that the generating parameter of the higher-order beam families strongly affects the shifts. Thus, reshaping of the incident wavefront with fixed order and azimuthal index changes the linear Goos–Hänchen shift up to one half of the beam radius, both negative and positive.