THEORETICAL CALCULATION OF LINE-SHAPES AND SATURATION EFFECTS IN POLARIZATION SPECTROSCOPY

The physics of polarization spectroscopy (PS) is investigated by direc t numerical integration of the time-dependent density matrix equations . The Zeeman structure of the upper and lower energy levels is include d in a multistate formulation of the density matrix equations. The num erical solution of the time-dependent density matrix equations enables us to investigate the effects of strong saturation on PS signal level s and line shapes. Bath levels not directly coupled by the laser radia tion are included in the numerical modeling to investigate the effects of collisional rates and different types of collisions on signal leve ls and Line shapes. The effects of Doppler broadening are included by solving the density matrix equations for numerous velocity groups. At low laser power we find that the homogeneously broadened PS line shape is Lorentzian-cubed, as compared to the Lorentzian predicted in sever al previous low-power analytical solutions. In the low laser power reg ime, the line-center PS signal is proportional to (collision rate)(-6) , obviously greatly complicating the application of unsaturated PS for quantitative concentration measurements in flames and plasmas. As the transition begins to saturate at higher laser intensities, the depend ences of the signal strength on the laser intensity and on the collisi on rate decrease drastically, although the line-center PS signal is st ill approximately proportional to (collision rate)(-2). The dependence of the PS signal intensity on the ratio of the population-transfer co llision rate to the dephasing collision rate Is minimized for saturati ng pump beam intensities. For resonances that are both Doppler- and co llision-broadened the low-power PS line shape is Lorentzian with a lin ewidth equal to the collisional width for the case where the Doppler w idth is much greater than the collisional width. At low pump laser int ensities, the PS signal is very dependent on the ratio of Doppler broa dening to collisional broadening when the Doppler width is greater tha n the collisional width. However, at high intensity, the Line-center P S signal intensity becomes nearly independent of collision rate when t he collisional linewidth is less than the Doppler linewidth. Quantitat ive application of polarization spectroscopy for concentration measure ments in flames and plasmas will almost certainly require resolution o f the PS line shape and/or accurate measurement of the saturation curv e. (C) 1998 American Institute of Physics.