Second-order nonlinear spectroscopy

Given the interest and importance of chiral molecules, there has been considerable activity in investigating die corresponding chiral surfaces [, and 70]. From the point of view of perfomiing surface and interface spectroscopy with nonlinear optics, we must first examhie the nonlinear response of tlie bulk liquid. Clearly, a chiral liquid lacks inversion synnnetry. As such, it may be expected to have a strong (dipole-allowed) second-order nonlinear response. This is indeed true in the general case of SFG [71]. For SHG, however, the pemiutation synnnetry for the last two indices of the nonlinear susceptibility tensor combined with the... 

Hicks J M, Petralli-Mallow T and Byers J D 1994 Consequences of chirality in second-order nonlinear spectroscopy at interfaces Faraday Disc. 99 341 -57... 

Hyper-Raman spectroscopy is not a surface-specific technique while SFG vibrational spectroscopy can selectively probe surfaces and interfaces, although both methods are based on the second-order nonlinear process. The vibrational SFG is a combination process of IR absorption and Raman scattering and, hence, only accessible to IR/Raman-active modes, which appear only in non-centrosymmetric molecules. Conversely, the hyper-Raman process does not require such broken centrosymmetry. Energy diagrams for IR, Raman, hyper-Raman, and vibrational SFG processes are summarized in Figure 5.17. 

IV. COMBINATION OF TIP-ENHANCEMENT AND SECOND-ORDER NONLINEAR SPECTROSCOPY... 

Prof. Fleming, the expressions you are using for the nonlinear response function may be derived using the second-order cumulant expansion and do not require the use of the instantaneous normal-mode model. The relevant information (the spectral density) is related to the two-time correlation function of the electronic gap (for resonant spectroscopy) and of the electronic polarizability (for off-resonant spectroscopy). You may choose to interpret the Fourier components of the spectral density as instantaneous oscillators, but this is not necessary. The instantaneous normal mode provides a physical picture whose validity needs to be verified. Does it give new predictions beyond the second-order cumulant approach The main difficulty with this model is that the modes only exist for a time scale comparable to their frequencies. In glasses, they live much longer and the picture may be more justified than in liquids. 

ZINDO57-58 is a semiempirical intermediate neglect of differential overlap/spectroscopy (INDO/S) based routine. It can be combined with an SOS method to calculate second-order nonlinear optical coefficients. ZINDO is parametrized to accommodate transition-metal calculations and is therefore suited for calculation on organometallic compounds. To achieve computational efficiency, some of the terms in Eq. (2) are replaced by empirical data or neglected. To see how the INDO/S does this, the closed-shell case will be examined.57 58 It is useful to introduce the following ... 

Barnik, M. L, Blinov, L. M., Weyrauch, T, Palto, S. A., Tevosov, A. A., and Haase, W, Stark spectroscopy as a tool for the characterization of poled polymers for nonlinear optics. In G. A. Lindsay, K. O. Singer, Eds. Polymers for Second-Order Nonlinear Optics, 288 (1995). Natansohn, A., Rochon, R, Gosselin, J., and Xie, S. Azo polymers for reversible optical storage. 1. Poly[4 -[[2-(acryloyloxy)ethyl]ethylamino]-4-nitroazobenzene]. Macromolecules 25,2268 (1992). 

A number of spectroscopic techniques have already been discussed in Volume 1 (secs. 7.11-13). Here, we will focus on the application of vibrational (infrared and Raman) and UV/visible spectroscopy, fluorescence and second-order nonlinear optical techniques for the study of monolayers. The type of information obtained with these techniques refers to the chemical composition, surface coverage, molecular conformation and orientation, and dynamics of monolayers. 

Second harmonic generation has been recognized as a powerful probe to study the electronic states at surfaces and interfaces [16]. Under the electric dipole approximation, second-order nonlinear processes are forbidden in centrosymmetric systems. This principle makes the phenomena surface-specific in many cases. Indeed, the capability of SHG spectroscopy to explore surface electronic states has been demonstrated on various systems, dye molecules at solid/liquid interfaces [17], organic molecules at liquid/air interfaces [18], semiconductor surface states [19], organic molecules at metal surfaces [20], and so on. 

Sum-frequency generation (SFG) at second-order and the nonlinear Raman spectroscopy BioCARS at fourth-order can also probe chiral molecules. They have no analog in linear optics. We show that both are only symmetry allowed in a fluid, if the fluid is chiral. However, in contrast to optical activity phenomena, these processes arise entirely from induced electric-dipoles (without magnetic or quadrupolar transitions) and they are not circular differential. All laser beams can be linearly polarized and no polarization modulation is required as the detection of a sum-frequency (yiz. five-wave mixing) photon is in itself a measure of the solution s chirality. Since an achiral solvent can not contribute to the signal, these techniques are sensitive, background-free probes of molecular chirality. The SFG... 

Fischer and Champagne present an overview of linear and nonlinear optical properties of chiral molecules in isotropic media. The authors state the general symmetry requirements of chiroptical processes, and show that nonlinear chiral spectroscopies can arise within the electric dipole approximation. The authors describe sum-frequency-generation experiments at second order and demonstrate how nonlinear optics can be used to determine the absolute conformation of a chiral molecule in solution. This is discussed with recourse to electric-field induced... 

We close with three comments. First, there is preliminary work on retrieving not only the amplitude but also the phase of photon echoes [49]. This appears to be a promising avenue to acquire complete 2-dimensional time and frequency information on the dynamics, analogous to methods that have been used in NMR. Second, we note that there is a growing literature on non-perturbative, numerical simulation of nonlinear spectroscopies. In these methods, the consistency of the order of interaction with the field and the appropriate relaxation process is achieved automatically,... 

The second-order nonlinear susceptibility describing a surface or interface, as indicated by the microscopic form of equation B 1.5.30, is resonantly enhanced whenever an input or output photon energy matches a transition energy in the material system. Thus, by scanning the frequency or frequencies involved in the surface nonlinear process, we may perform surface-specific spectroscopy. This method has been successfully applied to probe both electronic transitions and vibrational transitions at interfaces. 

Other nonlinear optical spectroscopies have gained much prominence in recent years. Two techniques in particular have become quite popular among surface scientists, namely, second harmonic (SHG) [55] and sum-frequency (SFG) [56] generation. The reason why both SHG and SFG can probe interfaces selectively without being overwhelmed by the signal from the bulk is that they rely on second-order processes that are electric-dipole forbidden in centrosymmetric media by breaking the bulk symmetry, the surface places the molecular species in an environment where their second-order nonlinear susceptibility, the term responsible for the absorption of SHG and SFG signals, becomes non-zero. 

Figure 5 shows the SFG vibrational spectra of carbon monoxide obtained at 10 -700 Torr of CO and at 295 K. When the clean Pt(lll) surface was exposed to 10 L (1 L=10 Torr sec) of CO in UHV, two peaks at 1845 cm and 2095 cm were observed which are characteristic of CO adsorbed at bridge and atop sites. LEED revealed that a c(4 X 2) structure was formed in which an equal number of carbon monoxide molecules occupied atop and bridge sites [15]. Such results are in agreement with previous HREELS [16] and reflection-absoiption infrared spectroscopy (RAIRS) [17] studies. ITie much higher relative intensity of atop bonded CO to bridge bonded CO in the SFG spectra is due to the specific selection rule for the SFG process [18]. As mentioned earlier, SFG is a second order, nonlinear optical technique and requires the vibrational mode under investigation to be both IR and Raman active, so that the SFG intensity includes contributions from the Raman polarizability as well as the IR selection mle for the normal mode. 

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