Second-order nonlinear thin film characterization using logarithmic Hilbert transform

A new technique based on logarithmic Hilbert transform processing of Maker-fringe (MF) curves to characterize second-order optical nonlinear depth profile of thin films is described. Such characterization methods are important for several fields, for example to characterize the nonlinear coefficient profile of poled glass samples, which hold an important potential for fiber based nonlinear devices in telecommunication links. In the classical MF measurement system, a laser beam is focused onto the nonlinear film and the generated second-harmonic power is recorded vs. the laser incidence angle. The resulting MF curve is proportional to the square of the magnitude of the Fourier transform of the spatial profile d(z) of the nonlinear coefficient, where z is perpendicular to the film surface. Our new analytical method requires only the measurement of the MF curve of the nonlinear sample alone. It is based on the computation of the logarithmic Hilbert transform of the measured MF curve of the sample. Being analytical, this approach provides speed advantage over its iterative alternative. This new technique is verified experimentally with two germanosilicate-Infrasil structures, thermally poled at similar to 5 kV and 280 degrees C in air. This choice of material was primarily made because germanosilicate films form excellent waveguides with a refractive index close to that of silica, which makes them compatible with fiber-optic technology. This is the first time that a Hilbert transform based analytical tool has been applied to uniquely characterize nonlinear thin films.