Theoretical modeling of single-laser-shot, chirped-probe-pulse femtosecond coherent anti-Stokes Raman scattering thermometry

Chirped-probe-pulse (CPP) femtosecond (fs) coherent anti-Stokes Raman scattering (CARS) spectroscopy for single-laser-shot temperature measurements in flames is discussed. In CPP fs CARS, a giant Raman coherence is created in the medium by impulsive pump-Stokes excitation, and the temperature-dependent temporal decay of this initial coherence is mapped into the frequency of the CARS signal using a CPP. The theory of the CPP fs CARS technique is presented. A computer code has been developed to calculate theoretical CPP fs CARS spectra. The input parameters for the calculation of the theoretical spectra include the temperature, probe time delay, ratio of the resonant and nonresonant susceptibilities, and parameters for characterizing the pump, Stokes and probe pulses. The parameters for characterizing the pump, Stokes and probe pulses are determined from the best fit of theoretical spectra to experimental spectra acquired from calibration flames at a known temperature. For spectra acquired in subsequent measurements, these laser parameters are fixed and temperature is determined as one of the fit parameters from the best fit of theoretical spectra to experimental spectra. For single-laser-shot CPP fs CARS temperature measurements performed in steady, near-adiabatic flames, the best-fit temperature distribution width is typically less than 1.5% of the mean temperature. The mean temperature is accurate to within approximately 3% with respect to the adiabatic flame temperature. The most significant limitation on temperature measurement accuracy is associated with the evaluation of the theoretical laser parameters. Significant improvements in the temperature measurement accuracy are expected once monitoring equipment capable of characterizing the spectrum and phase of each laser pulse is incorporated in the experiments.