Second-harmonic generation in a layer with variable susceptibility

The weak nonlinearity limit of the second-harmonic generation in a medium with variable second-order susceptibility, changing along the direction of propagation of interacting waves according to the hyperbolic secant law, is considered. It is shown that the variation of the second harmonic’s normalized intensity with the spatial coordinate is given in terms of the solution to an auxiliary linear problem, which is known as the Rosen-Zener quantum two-level model. The final intensity of the second harmonic at the exit from the medium is calculated and analyzed. It is shown that, for the particular Rosen-Zener profile under consideration, because of its inherent properties, the variation range of the peak susceptibility of the layer for which the medium can be strictly considered as weakly nonlinear is narrower than the corresponding parameter range for a homogeneous medium.