Femtosecond self-diffraction as a measure of the nonlinear response spectrum

Abstract

Self diffraction is a four-wave mixing process proportional to the square modulus of third-order nonlinearity susceptibility $χ^{(3)}$, which is related to the material's electronic and thermal properties. In this study, we investigate the wavelength dependence of the self-diffracted signal generated by a femtosecond pulsed laser in a dye solution to directly evaluate the electronic third-order nonlinear susceptibility spectrum. By accounting for absorption effects and phase matching conditions, we determine the $\vertχ^{(3)}\vert$ for different concentrations. Experimental results complemented with theoretical predictions, show that in the low absorption and thin sample limits, the signal reproduce the $\vertχ^{(3)}\vert$ spectral profile. These findings demonstrate the feasibility of measuring nonlinear susceptibility spectra arising solely from the bound-electronic response across a wide spectral range and for various compounds.

Figures (3)

• Figure 1: a) SD experimental setup scheme. Starting from the bottom, the fs pulse emitted by an OPA enters the optical path. A 50:50 plate beam splitter divides the pump into two equivalent beams, $1$ and $2$. Beams $1$ and $2$ are focused by a lens with focal length of $10\ {\rm cm}$ before reaching a $10\ \mu \rm m$ thick sample with angle of incidence $-\theta$ and $\theta$, respectively. Time-overlap is tuned by a delay line in beam $1$ path. The temporal chromatic dispersion on the two arms are balanced by a compensation plate. After the sample, a second lens with a focal length of $20\ {\rm cm}$ collimates the SD signal towards a CCD, whose typical example is shown in the colormap. The inset provides a visual representation of the SD process in our reference frame. b) Measured imaginary part of the linear susceptibility normalized by the molecular number density ${\rm Im}\chi^{(1)}(\lambda)/\mathcal{N}$ as a function of the wavelength for three molar concentrations (C) of Methyl Blue dye solutions dispersed in water.
• Figure 2: a) Colored dots represent SD signals normalized by the peak intensity of the beams, acquired at steps of $2\ {\rm nm}$ for different C. Peak-to-valley dynamics are observed as C increases. The black lines are a fit to the data. b) Colored triangles represent ${\rm Im}\chi^{(1)}(\lambda)$ spectra acquired linear regime, rescaled by number density $\mathcal{N}$. Green lines are fit to the data, while the green dotted and dashed lines represent the two Lorentzian components of ${\rm Im}\chi^{(1)}(\lambda)$ convoluted with the Gaussian contribution reported in \ref{['fig1']}b). c) Colored squares show the $\vert\chi^{(3)}\vert$ spectra, which were retrieved by rescaling the SD intensities using \ref{['eq:main']}. The green lines show the sum of the two Gaussian-convoluted Lorentzian components of $\vert\chi^{(3)}\vert$, which are shown as the green dotted and dashed lines.
• Figure 3: SD signal as a function of the wavelength normalized by the peak intensity measured for different impinging power, measured before the beam splitter in Figure \ref{['fig1']}a at fixed wavelength $\lambda = 640\rm \ {\rm nm}$. The error associated with the 0.5 mW-power measurement is reduced by a factor 3 for sake of clarity. Insert: integrated SD signal as a function of the impinging power. The blue line is a third-power reference curve.