Electronic resonance enhancement of coherent anti-Stokes Raman scattering

We analyze the enhancement of the coherent anti-Stokes Raman-scattering (CARS) susceptibility when the frequencies of the waves involved are tuned into resonance with discrete and continuum one-photon absorptions, and discuss the applications. We first derive the expression for the susceptibility by means of the usual iterative treatment of density-matrix perturbations. We then show that this derivation can be done in a straightforward manner by means of a time-ordered diagrammatic representation, which brings novel physical insight into CARS mechanisms. This representation can also be used to analyze the transient behavior of CARS as the pump fields are turned on and off. In addition, we discuss resonant CARS spectroscopy in the gas phase. The spectrum is composed of the expected enhanced Raman lines and also of double-electronic-resonance lines. All these lines occur as doublets. We derive their relative intensities based on detunings, collisional broadening, Franck-Condon overlap integrals, and rotational transition moments. The line contours are predicted by representing the susceptibility in the complex plane. The problems arising from saturation and the optical Stark effect are also considered; all should be small below pump densities of 100 MW/${\mathrm{cm}}^2$ in gas mixtures near STP. Fluorescence interference is negligible, except at power densities high enough for the Stark effect to be large. Beam absorption is also negligible at STP if the resonant species' concentration is less than 1000 ppm; phase matching is then satisfied. Finally, an experimental resonant CARS spectrum of ${\mathrm{I}}_2$ at 1 mb in air near STP is presented and interpreted; the susceptibility is about 400 times larger than that of ${\mathrm{O}}_2$ off resonance and under the same thermodynamic conditions.