<title>Application of wavelet transform in characterization of nonlinear optical materials</title>

Abstract

Wavelet transform technique is applied to the analysis of data collected in experiments on the characterization of nonlinear optical materials which may be in the form of liquid, thin film or crystal. Many characterization techniques are based on nonlinear optical processes such as higher harmonic generation in which second harmonic or third harmonic signals may be generated by the nonlinear material. When the optical path length of the material is changed, the interference between bound and free waves forms a fringe pattern. Conventional Fourier transform techniques are not suitable for analyzing such fringes when they have a variable periodicity and a low signal-to-noise ratio. However, the wavelet transform method is best suited for such signals because it provides a better resolution in both space and frequency domains. In this study, optical properties of materials are extracted from these fringe patterns by decomposing them into coefficients which are inner products of the signal and a family of wavelets generated from a mother wavelet by dilation and shift operations.