Analytic spectrum of multifrequency Raman generation with chirped pulses

Multifrequency Raman generation is a promising method of producing ultrashort laser pulses with high intensities and visible wavelength frequencies. Experimental realizations of multifrequency Raman generation have a spectrum that displays several behaviors that are not explained by theories calculating the relative Raman order amplitudes. We derive an analytic and perturbative expression for the spectra of the individual Raman orders radiated by a Raman medium excited by multiple Gaussian laser pulses. We use a method of Dawson function approximations to derive an analytic spectrum showing that the Raman order spectra are dependent on both the energy and chirp of the pumps, as observed experimentally.