Abstract
A new approach to the calculation of the nonlinear optical response of a crystalline slab is presented. Analytical expressions for the reflected and transmitted second harmonic wave are derived, in a form allowed by symmetry of a medium including time-reversal symmetry. The main advantage of the approach is that it takes into account both the non-local behavior of the optical susceptibilities and inhomogeneity of a medium. The theory is especially suited to the analysis of the experiments in which the symmetry of the medium should be taken into account exactly, e.g., in the case of magnetic crystals. It is shown that a consistent derivation of the optical response of the surface with a regular structure requires of using the space group of the crystal but not the point group.
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