Second-harmonic resonant excitation in optical periodic structures with nonlinear anisotropic layers

Abstract

We propose a method to derive a system of ordinary differential equations ͑coupling equations͒ in order to analyze nonlinear wave processes inside lossless layered periodic media. We solve the problem associated with the interaction between the first-and second-harmonic waves inside a structure with anisotropic nonlinear dielectric layers. An arbitrary angle between the wave propagation direction and the structure interfaces is considered. The method takes into account both the nonlinear processes occurring at the slab interfaces and the nonlinear terms that depend differently on the field components. We derive analytically the phase matching conditions that provide the maximum interaction between the first-and second-harmonic waves. A physical explanation of the increase in efficiency of the wave coupling that takes place at the frequency near the passband edges is given. ͓S1063-651X͑98͒04111-7͔PACS number͑s͒: 42.65.Tg

Nonlinear harmonic interaction in a waveguide with periodic layered walls

“…In the case analyzed, the operator˜ L for the transposed system of equations differs from the initial oneˆ L in all signs, while the solution of the system coincides with the solution of the untransposed system [2].…”

“…Experimental data (see, e.g., [15]) show that the dielectric-permittivity dispersion can be small and amount to several percent. For example, for CdS in the range in which the experiment was performed [1] (i.e., for wavelengths of the order of 500−600 nm), the variation is approximately 4% (see also [2]). …”

“…(11). We assume that the additional field must also satisfy these conditions [2]. Equation (11) means that the eigenfunctions of the transposed linear differential operator are othogonal to the right-hand side of the system of linear differential equations (4).…”

“…It is well known that in the anisotropic medium the ith component can be represented as (2) where χ ij is the linear electric susceptibility, χ ijk and χ ijkl are the nonlinear susceptibilities of the second and third orders, respectively, and E j is the jth component of the electric field. The second-order nonlinearity is responsible for the second-harmonic generation (frequency doubling), the generation of the total and difference frequencies, and the parametric amplification and generation.…”

“…Multiple studies showed that the use of periodic nonlinear structures can appreciably increase the wave-interaction intensity [2][3][4][5].…”