Reconstruction of coherent anti-Stokes Raman scattering signals generated by means of laser pulses with asymmetric amplitude and phase

Time and frequency asymmetries in ultrashort chirped laser fields might appear as a consequence of dispersive propagation, pulse shaping techniques, or generation of auxiliary light pulses needed in nonlinear optics. Here, we try to find an answer to the question of how to solve analytically coherent anti-Stokes Raman scattering (CARS) under asymmetric conditions of chirped femtosecond laser pulses. The approach breaks in two parts. One for the field amplitudes and the other for the phases. The former revolves around Gaussian dependences that, besides being rather common in ultrashort laser physics, can be arranged and mixed to reproduce spectrally asymmetric laser amplitudes. The latter is limited to field phases with cubic frequency dependence (i.e., second-order chirp) whose asymmetry is simulated by adding a linear term to the quadratic phase. Both approximations for amplitudes and phases of the three laser pulses are mandatory to guarantee the solution to the complexity posed by the CARS problem. Comparisons with known experimental and numerical results support the validity of the model.