Second-harmonic generation by reflection of a two-dimensional Gaussian beam from the surface of an isotropic gyrotropic medium

A theoretical investigation is reported of the influence of the finite spatial size of a pump wave on second-harmonic generation by surface reflection of a two-dimensional Gaussian beam (treated as an example) incident on the surface of a nonabsorbing isotropic gyrotropic medium. Formulas are obtained for expressing the field of the reflected second-harmonic wave in terms of parameters representing the geometry of the problem and in terms of the components of the material tensors which describe the quadratic optical response of the surface and the spatial dispersion of the nonlinearity of the medium. It is shown that in this case the doubled-frequency signal can be represented by a superposition of a two-dimensional Gaussian beam and a non-Gaussian component. This component appears most clearly for normal incidence of the pump wave when second-harmonic generation is altogether impossible in the plane-wave approximation. The inhomogeneity of the surface region and the spatial dispersion of the optical response of the medium are taken into account by adopting modified boundary conditions for an electromagnetic field. These conditions include the surface density of the bound-charge current.