Coherent multidimensional optical spectroscopy.

Multidimensional optical techniques, the focus of this special issue, are analogues of their NMR counterparts; that is, rather than using spin transitions as little spies within a molecule, we use vibrational or optical transitions. Similar to NMR, the spectroscopic states often respond in a very sensitive way to their chemical environment. By modeling the coupling of one of these states to either other states within the same molecule, another molecule, or the solvent, we can extract a wealth of information about molecular structure and dynamics. The interpretation and analysis of these signals requires support from extensive electronic structure calculations as a function of molecular configuration. These provide some critical tests for the accuracy of state of the art methods of theoretical chemistry, and stimulate future developments. The most notable difference from NMR is the greatly-improved temporal resolution, which changes from milliseconds to about 100 fs for vibrational spectroscopy, and even into the 20 fs range for electronic spectroscopy. Looking at the comparison between NMR and optical multidimensional spectroscopy in more detail, we find that many other technical and conceptual differences exist. Hence, NMR ideas may not be directly transferred to the optical regime and new methods and tools are required for the design of novel optical pulse sequences. Multidimensional optical techniques provide a very different window into molecular structure and dynamics that is complementary to NMR spectroscopy. Conventional optical spectroscopy techniques, such as ordinary infrared, Raman, and UV-visible spectroscopies, provide a one dimensional (1D) projection of the available molecular information of a sample onto a single frequency axis. In contrast, optical multidimensional (2D, 3D) spectroscopy techniques provide a multidimensional projection of the relevant molecular motions offering dramatically more information. In 1D spectroscopy, the linear electrical polarization of the sample induced by the optical field is probed, while in the nonlinear 2D and 3D spectroscopic techniques, the coherent higher order polarization of the sample induced by the sequence of optical pulses is projected in multidimensions. The parametric dependence of the signals on the time intervals between pulses carries a wealth of information. Signals are typically displayed as two-dimensional correlation plots with respect to two of these intervals, say t1 and t3, holding the third (t2) fixed (see Figure 1). The signal is double Fourier transformed with respect to the two desired time variables to generate frequency/frequency correlation plots such as S(ω1;t2;ω3) where ω1 and ω3 are the frequency conjugates to t1 and t3. Just like in NMR, heterodyne-detected (i.e., stimulated) signals record the signal field itself (both amplitude and phase), rather than just its intensity. We can thus display both the real (in-phase) and the imaginary (out-of-phase) components of the response. Coupled vibrational or electronic chromophores generate new resonances, cross-peaks, whose magnitudes and line shapes give direct zero-background signatures of the correlations between transitions. The resulting correlation plots of dynamical events taking place during controlled evolution periods can be interpreted in terms of multipoint correlation functions. These carry considerably more information than the two-point functions of linear 1D spectroscopy. The positions and profiles of the peaks in the 2D contour maps of the signals reflect the variations of the nonlinear response functions on a selected time window, which are sensitive to fine details of the molecular motions and couplings. The origin of multidimensional vibrational spectroscopy can be traced to the picosecond, electronically off-resonant, coherent anti-Stokes Raman spectroscopy (CARS) measurements of FIGURE 1. Pulse configuration for a heterodyne-detected multidimensional four-wave mixing experiment. Signals are recorded vs the three time delays, t1, t2, and t3, and displayed as 2D correlation plots involving two of the time delays, holding the third fixed.