Second-order coherent Raman scattering

Abstract

Detailed dispersion curves of second-order coherent anti-Stokes Raman scattering (CARS) (${\ensuremath{\omega}}_{4}=3{\ensuremath{\omega}}_{1}\ensuremath{-}2{\ensuremath{\omega}}_{2}$) are reported for benzene with the laser frequency difference ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ near the 992-${\mathrm{cm}}^{\ensuremath{-}1}$ Raman line. The results are compared with the first-order CARS (${\ensuremath{\omega}}_{3}=2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$) dispersion curves. Several experimental parameters were manipulated in order to distinguish between a direct six-wave mixing process, which depends on the fifth-order nonlinear susceptibility ${\ensuremath{\chi}}^{(5)}$ and a cascaded four-wave mixing process involving ${\ensuremath{\chi}}^{(3)}$ twice. The observed characteristic interference line shape, the dependence on laser power, and the concentration dependence of the effect indicate that the cascaded process dominates. Additional evidence for the cascaded mechanism is derived from second-order CARS experiments using three incident laser frequencies. It is shown theoretically that if simultaneous phase matching occurs for both first- and second-order CARS, then the electric-field amplitude of the cascaded four-wave mixing should dominate the direct six-wave mixing by a factor of the order of $\frac{1}{\ensuremath{\lambda}}$, where $l$ is the interaction length and $\ensuremath{\lambda}$ is the second-order anti-Stokes wavelength. The second-order CARS reported here is to be distinguished from a possible "overtone" coherent Raman process which would require the frequency separation of the two lasers to be twice the Raman fundamental.