Determination of the spatial dependence of the complex components of the tensor $$\hat \chi ^{(2)}$$ (z, ω 1 + ω 2; ω 1, ω 2) of a medium with one-dimensional inhomogeneity using a biharmonic wave

Abstract

It is proven that the spatial profiles of different components of the complex quadratic susceptibility tensor \(\hat \chi ^{(2)}\) (z,ω1+ω2; ω1, ω2), which is responsible for the generation of sum-frequency wave in a plate with one-dimensional inhomogeneity, can be reconstructed unambiguously. A reconstruction technique is proposed. To implement it, one has to direct a plane biharmonic wave with monochromatic components at frequencies ω1 and ω2 onto a plate and measure (in some range of the angles of incidence) the complex amplitude of the sum-frequency wave reflected from the plate. Changing the plane of incidence of the initial wave and (or) the polarization of its monochromatic components, one can determine the coordinate dependences for more than half of the components of \(\hat \chi ^{(2)}\) (z,ω1+ω2; ω1, ω2). This reconstruction can be performed if the symmetry of the plate medium provides a diagonal form for its linear permittivity tensor. The technique proposed implies measurement of the intensities of the sum-frequency waves generated under special conditions using an auxiliary reference plate; this approach allows one to do without complex phase measurements.