Determination of the spatial profiles of all components of the quadratic susceptibility tensor $\hat \chi ^{(2)} $ (z, 2ω; ω, ω) of a one-dimensionally inhomogeneous absorbing medium

Abstract

For a one-dimensionally inhomogeneous plate whose linear dielectric properties are also inhomogeneous and are characterized by a diagonal permittivity tensor, it is proved that the spatial profiles of all components of the complex quadratic susceptibility tensor \(\hat \chi ^{(2)} \)(z, 2ω; ω, ω responsible for the second harmonic generation can be uniquely determined, and an appropriate method is proposed. To implement this method, one should measure the complex coefficient of transformation of a fundamental plane wave incident on the plate into a reflected second-harmonic wave in a certain range of angles of incidence. By varying the plane of incidence of the wave and (or) its polarization and measuring the coefficients of transformation into s- and p-polarized waves of double frequency, one can uniquely determine the spatial profiles of all components of the quadratic susceptibility tensor. The method involves the measurement of the intensities of the second-harmonic waves generated under special conditions with the use of two auxiliary reference plates and thus allows one to avoid complicated phase measurements.