Femtosecond polarization spectroscopy: A density matrix description

A density matrix treatment of the time evolution of the third order polarization response describing the optical heterodyne detected (OHD) transient birefringence and dichroism excited by ultrafast pulses is given. The relationship between frequency domain (Raman scattering) and time domain (pump-probe) spectroscopies is revealed by this pathway explicit description. Constructive and destructive interferences between time evolution density matrix pathways account for the respective strong birefringent and weak dichroic ground state nuclear response when the pulses are electronically nonresonant. However, for electronically resonant chromophores, the dichroic response is larger than the corresponding birefringent response due to constructive and destructive interferences respectively between density matrix time evolution histories. No such interferences contribute to spontaneous Raman scattering. The relative magnitude of the resonant dichroic and birefringent responses is pulse width dependent in the fast pulse limit and dependent on the relative rates of optical dephasing and ground state nuclear motion in the rapid optical dephasing limit. The spatial interpretation of the ground and excited state OHD polarization responses is given within the context of this polarization approach and the familiar Maker-Terhune notation. These relationships between time and frequency domain spectroscopies are illustrated by the observed OHD birefringence and dichroism and the spontaneous Raman spectra of both a nonresonant liquid (chloroform) and a resonant solution ( I2 in n-hexane).