Passage from the microscopic third-order optical polarizability tensor to the macroscopic third-order susceptibility tensor elements in coherent Raman scattering (CRS: CARS and CSRS) is reviewed with appropriate orientation averaging for an isotropic medium. The results are applied to existing polarized CARS measurements for the 991 cm-' vibration in benzene as a neat liquid IM. D. Levenson and N. Bloembergen, J. Chern. P h p . 60, 1323 (1974)] and also to new polarized interferometric data on the same system from a method called interferometric coherent Raman spectroscopy (ICRS; ICSRS in particular is used). Lineshape analysis of the CARS spectra seen in both the ZXXZ polarization (mildly dispersive) and the ZZZZ polarization (strongly dispersive) leads to ratios for tbe non-resonant to resonant parts of the corresponding susceptibility elements. Thus x;xxz/x!&z = 0.5 (from 0.3-1.7) (a new result) and ~&~~/ ; l ! &~~ = 0.042 _+ 0.002 (from Levenson and Bloembergen). It is shown that given one ratio, the second must be completely determined by the depolarization ratio from conventional Raman scattering. These same tensor element ratios are incorporated into ICSRS theory to produce polarized interferograms which qualitatively confirm the strikingly different patterns seen in the ZXXZ and ZZZZ polarized ICSRS experiments. On the quantitative level, agreement is less satisfactory.
INTRODUCTlONThe coherent Raman spectroscopic (CRS) techniques, CARS and CSRS, are nearly degenerate four-wave mixing (4WM) processes which involve Raman-type resonances. Typically, two non-collinear incident fields are incident upon a sample, one at frequency ol, the other at w 2 , (a, > w 2 , say). The third-order electrical polarization appears when one of the fields acts twice (and in-phase) to join the second (opposite in phase). This polarization launches a fourth wave at a new frequency and along a new k-vector-the single field governed by the phase-matching conditions. For CARS, field 1 acts twice to generate a signal field at o, = 2 0 , -02. For CSRS the signal is at w, = 2 0 , -a2 along a different k-vector. In contrast to the 'active' phenomena of absorption or emission (linear or non-linear), where light-matter interaction drives population changes in the material, the CRS spectroscopic methods are strictly coherent processes, and in that sense are regarded as a form of 'passive' light-matter interaction. Nevertheless, it has been shown that for resonant 4WM processes such as CARS and CSRS, despite their passive nature, there can be cycle-averaged energy transfer between the radiation and the medium. This follows from the complex nature of the third-order susceptibility, ~(~'(0,) (due to the Raman resonance) and must appear as a population change in the resonant vibrational state.' Since the CRS signal (CARS or CSRS) is the quadrature-detected fourth field, it is pro-
