Longitudinal and transverse effects of nonspecular reflection

A rigorous spectral analysis is given for the nonspecular reflection of a three-dimensional Gaussian beam at a dielectric isotropic planar structure. For the first time all independent nonspecular effects are derived in a self-consistent manner for the three-dimensional case. It is shown that the longitudinal nonspecular effects in the incidence plane, that is, the lateral and focal shifts of the beam waist position, the angular rotation of the reflected-beam axis, and the modifications of the beam waist width and complex amplitude, have their direct analogies in the plane transverse to the incidence and interface planes that gives transverse nonspecular effects. Moreover, the existence of the other, not yet reported, effect of nonspecular modification of the beam polarization is also proved. A role for TM and TE polarizations in reflected-beam formation is indicated. The results show that, up to the symmetric second-order terms in approximation of Fresnel coefficients, each of the longitudinal and transverse beam factors independently preserves its shape under reflection at the expense of changes of the beam reference frame, width, amplitude, and polarization parameters.