Third-order spectroscopies

B1.3.2.2 THE GENERATORS FOR ALL THIRD ORDER SPECTROSCOPIES FROM THE COMPLEX REPRESENTATION OF THE FIELD... 

We model the amide band as a system of N interacting localized vibrations. For the sake of third-order spectroscopies, we only need to consider the lowest three levels of each peptide group with energies 0, Gm, Gnl(m = 1,..., N). The matrix elements of the dipole operator corresponding to the 0-1 and 1-2 transitions are denoted /j.m and //ra, respectively, and their ratio is Km = To introduce the vibrational Frenkel exciton model,... 

Murry RL, Fourkas JT, Keyes T. Nonresonant intramolecular spectroscopy beyond the Placzek approximation. I. Third-order spectroscopy. J Chem Phys 1998 109 2814-2825. 

Fig. 1.3 Pulse sequence top) and energy level diagram bottom) for third-order left) and fifth-order right) Raman spectroscopy. The nonresonant third-order spectroscopy consists of a pair of time-coincident pump pulses (ki, k2) followed by a probe pulse (ks) after a time delay t. The fifth-order nonresonant spectroscopy consists of two pump pulse pairs (ki, k2, and ks, k4) separated by a time delay T2, followed by a probe pulse (ks) after a second time delay T4. In both cases a signal field (ks) is generated by the scattering of the probe off the pump-induced grating in the sample...

The ability to heterodyne detect the signal is extremely important in nonlinear spectroscopy where the phase of the signal field often contains information about what physical process generated it. In third-order spectroscopy heterodyne detection allows the separation of the resonant from the noiuesonant... 

Murry, R.L., Fourkas, J.T., Keyes, T. (1998). Nonresonant intermole-cular spectroscopy beyond the Placzek approximation. I. Third-order spectroscopy. J. Chem. Phys. 109 2814—2825 Murry, R.L., Fourkas, J.T., Keyes, T. (1998). Nonresonant intermolecular spectroscopy beyond the Placzek approximation. II. Fifth-order spectroscopy. J. Chem. Phys. 109 7913-7922. 

All nonlinear (electric field) spectroscopies are to be found in all temis of equation (B 1.3.1) except for the first. The latter exclusively accounts for the standard linear spectroscopies—one-photon absorption and emission (Class I) and linear dispersion (Class II). For example, the temi at third order contains by far the majority of the modem Raman spectroscopies (table B 1.3.1 and tableBl.3.2). 

Consider all of the spectroscopies at third order s = 3). To be as general as possible, suppose the total incident field consists of the combination of three experimentally distinct fields (/ = 1, 2, 3). These can differ in any combination of their frequency, polarization and direction of incidence (wavevector). Thus the total field is written as... 

B1.3.2.3 THE FIELD GENERATORS FOR ALL THIRD ORDER RAMAN SPECTROSCOPIES... 

B1.3.2.4 TIME EVOLUTION OF THE THIRD ORDER POLARIZATION BY WAVE MIXING ENERGY LEVEL (WMEL) DIAGRAMS. THE RAMAN SPECTROSCOPIES CLASSIFIED... 

The general task is to trace the evolution of the third order polarization of the material created by each of the above 12 Raman field operators. For brevity, we choose to select only the subset of eight that is based on two colours only—a situation that is connnon to almost all of the Raman spectroscopies. Tliree-coloiir Raman studies are rather rare, but are most interesting, as demonstrated at both third and fifth order by the work in Wright s laboratory [21, 22, 23 and 24]- That work anticipates variations that include infrared resonances and the birth of doubly resonant vibrational spectroscopy (DOVE) and its two-dimensional Fourier transfomi representations analogous to 2D NMR [25]. 

Interestingly, tliree-coloiir spectroscopies at third order can only be of Class II, since the generators cannot possibly contain any quadrature. Maximal quadrature is necessary for Class I. 

Plenary 7(5. N I Koroteev et al, e-mail address Koroteev nik.phys.iusu.su (CARS/CSRS, CAHRS, BioCARS). A survey of the many applications of what we call the Class II spectroscopies from third order and beyond. 2D and 3D Raman imaging. Coherence as stored infonuation, quantum infonuation (the qubit ). Uses tenus CARS/CSRS regardless of order. BioCARS is fourtli order in optically active solutions. 

The cadmium chalcogenide semiconductors (qv) have found numerous appHcations ranging from rectifiers to photoconductive detectors in smoke alarms. Many Cd compounds, eg, sulfide, tungstate, selenide, teUuride, and oxide, are used as phosphors in luminescent screens and scintiUation counters. Glass colored with cadmium sulfoselenides is used as a color filter in spectroscopy and has recently attracted attention as a third-order, nonlinear optical switching material (see Nonlinear optical materials). DiaLkylcadmium compounds are polymerization catalysts for production of poly(vinyl chloride) (PVC), poly(vinyl acetate) (PVA), and poly(methyl methacrylate) (PMMA). Mixed with TiCl, they catalyze the polymerization of ethylene and propylene. 

Ohta, K., M. Yang, and G. R. Fleming. 2001. Ultrafast exciton dynamics of J-aggregates in room temperature solution studied by third-order nonlinear optical spectroscopy and numerical simulations based on exciton theory. J. Chem. Phys. 115 7609-7621. 

Scheme 15 could be a reaction pathway parallel to the classical reaction (equation 1), and it was postulated to explain the third order in amine observed in the reactions of FDNB and aromatic amines in benzene and in chloroform184. The K values were calculated from the absorbances of the reaction mixture extrapolated to zero reaction time, in a wavelength range in which the starting materials do not show an appreciable absorbance value. Good agreement was observed between the values of K for the FDNB/aniline complex in chloroform by U.V. and 111-NMR spectroscopy, as well as for the K obtained kinetically (based on Scheme 15) and spectroscopically. 

Diels-Alder dimer or its reaction with styrene is the rate-determining step in initiation is not completely established. The dependence of Rp on [M] is closer to third-order than second-order, indicating that Eq. 3-63b is the slow step. The Diels-Alder dimer has not heen isolated, but ultraviolet spectroscopy of the reaction system is entirely compatible with its presence. There are indications that the photopolymerization of neat styrene proceeds by a similar mechanism. 

---