Effect of pump fluctuations on line shapes in coherent anti-Stokes Raman scattering

The theory of coherent anti-Stokes Raman scattering (CARS) is extended to include the effect of pump fluctuations. The intensities and spectra of lines in resonant CARS are calculated to all orders in fields assuming a phase-diffusion model for waves at the two pump frequencies. The bandwidth of the two lasers enters in a much more complicated way than following a simple scaling of $T_1$ or $T_2$. Various resonances in CARS spectra due to dynamic splitting of the energy levels are discussed for a range of detunings, field intensities, and bandwidths. In contrast to the usual spectra in strong fields, the Rabi sidebands appear as dispersion-shaped structures. The laser linewidth is shown to change dramatically the CARS line shape. The case of no saturation is also treated, thus allowing for the inclusion of more general line shapes and fluctuations of the pump waves and the nonlinear susceptibility tensor ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$. Gaussian statistics of the pump field are shown to lead to enhancement factors in CARS intensity, similar to those appearing in the context of multiphoton absorption processes.