Study of polarization CRS and polarization ICRS with application to benzena

Abstract

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-

Two-Dimensional Electronic Spectroscopy Using Incoherent Light: Theoretical Analysis

“…Although noisy light offers some advantages, it is not as generally useful as its shortpulse counterpart. One exception is coherent anti-Stokes Raman scattering spectroscopy (I (2) CARS), where the noisy-light version has proven to be a very useful tool that is still being used to investigate a variety of systems [87,[102][103][104][105][106][107][108][109][110][111][112][113][114][115][116]. Noisy sources have found occasional uses and advantages in other spectral regimes as well [117][118][119][120][121].…”

Direct observation of the resonant-non-resonant cross-term contribution to coherent Raman scattering of quasi-continuous-wave noisy light in molecular liquids

“…R zzzz The experiment is based on the theory of "monochromaticallyÏ detected I(2)CARS developed by Dugan and co-workers2 and expanded upon by Schaertel and coworkers. 4 This down-conversion is one of the primary advantages of the I(2)CARS technique. It allows for the characterization of vibrations with a much smaller interferometric sampling rate than would be required if the modes themselves were interferometrically detected (as in FTIR or FT-Raman methods).…”

“…The characteristics of the hyperpolarizability tensor and its relationship to other common parameters familiar in Raman spectroscopy such as the Raman polarizability tensor and the Raman depolarization ratio have been discussed in detail. 4,6 When is determined through lineshape analysis R ABCD in traditional CRS spectroscopy, the frequency separation of the zeros of the derivative of the dispersive CRS spectrum are measured and used with the Raman linewidth to determine the ratio.7 However, analysis of the timeÈfrequency detection version of I(2)CRS incorporates line position, linewidth and simulta-R ABCD neously and o †ers an exceptionally large redundancy in the determination of these three parameters.3 It also eliminates the need for scanning a monochromatic excitation source, and careful calibration of only the narrowband source and the detection window is required (the broadband source need not be Ðnely calibrated). Furthermore, in I(2)CRS the spectrum is uncoupled from the linewidth (dephasing rate constant) which instead determines the interferometric decay.…”

“…4 The two dimensional timeÈ frequency domain I(2)CRS technique employed in this work does not suppress the non-resonant contribution ; instead, the non-resonant components can be clearly identiÐed in both the theoretical expression for the I(2)CRS signal and the experimentally observed signal. For any given polarization geometry twodimensional I(2)CRS yields with high precision not only the Raman frequency, and the dephasing conu R , stant, but also the ratio of the absolute values of the c R , orientationally averaged non-resonant to resonant hyperpolarizability tensor components, and Sc ABCD N T respectively, which we notate Sc ABCD R T, as…”

Interferometric coherent Raman spectroscopy: Resonant and non‐resonant contributions

“…{ I x!&D(os; -0 1 , w2 + 0, 0 2 ' + 0') 1 ' (17) In this equation, the f 3 ) s are the standard expressions for monochromatic CRS (CARS or CSRS) as calculated by Bloembergen et The delta function is analogous to the 6(2w, -o1 -0,) which is implicit for monochromatic CRS. The subscripts ABCD refer to the Cartesian polarization directions in the laboratory coordinate frame of the signal and the incident fields (incident field magnitudes given by E l , E, and E,,) at w,, w 2 , w,, and wI , respectively.…”