Hyperpolarizability measurement techniques

It has been suggested that this increase in nonlinearity may be an artifact (two-photon fluorescence) of the hyperpolarizability measurement technique (hyper-Rayleigh scattering). Studies are currently under way at the University of Southern California (USC) to resolve this question, by using both electric field-induced... 

The slightly larger exponent in the power law for DFWM compared to THG can be explained by the fact that the resonance is closer in DFWM than in THG (Fig. 24). This also agrees with the tendency of yielding larger differences in the hyperpolarizabilities measured by the two techniques for longer PTA oligomers. 

In DFWM vibrational contribution can add to the electronic part of the second-order hyperpolarizability measured by THG. For the measurements of the short PTAs far from any resonance the same values by both techniques were obtained which would indicate that this vibrational contribution is small relative to the electronic one. 

The HRS technique [25-27] involves the detection of the incoherently scattered second harmonic generated by the molecule in solution under irradiation with a laser of wavelength 2, leading to the mean value of the x tensor product. By analysis of the polarization dependence of the second harmonic signal, which can be evaluated selecting the polarization of the incident and scattered radiation, it is possible to obtain information about the single components of the quadratic hyperpolarizability tensor jS. Unlike EFISH, HRS can also be used for ionic molecular species and for nondipolar molecules such as ocmpolar molecules. In this chapter, the quadratic hyperpolarizability measured with an incident wavelength 2 by the EFISH and HRS techniques will be indicated as /l i(EFISH) and / (HRS), respectively. 

As in the case of molecular orientation at the interface of neat liquids, solute molecular orientation can provide insight into the local intermolecular interactions at the interface, which, in turn, is useful for interpreting dynamics, spectroscopy, and reactivity. The simple picture that the hydrophilic part of an asymmetric solute molecule tends to point toward the bulk aqueous phase, while the hydrophobic part points toward the opposite direction, has been confirmed in both simulations and experiments. Polarization-dependent SHG and SFG nonlinear spectroscopy can be used to determine relative as well as absolute orientations of solute molecules with significant nonlinear hyperpolarizability. The technique is based on the fact that the SFG and the SHG signals coming from an interface depend on the polarization of the two input and one output lasers. Because an interface with a cylindrical symmetry has only four elements of the 27-element second-order susceptibility tensor being nonzero, these elements (which depend on the molecular orientation) can be measured. This enables the determination of different moments of the orientational distribution ... 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

The SH signal directly scales as the square of the surface concentration of the optically active compounds, as deduced from Eqs. (3), (4), and (9). Hence, the SHG technique can be used as a determination of the surface coverage. Unfortunately, it is very difficult to obtain an absolute calibration of the SH intensity and therefore to determine the absolute number for the surface density of molecules at the interface. This determination also entails the separate measurement of the hyperpolarizability tensor jS,-, another difficult task because of local fields effects as the coverage increases [53]. However, with a proper normalization of the SH intensity with the one obtained at full monolayer coverage, the adsorption isotherm can still be extracted through the square root of the SH intensity. Such a procedure has been followed at the polarized water-DCE interface, for example, see Fig. 3 in the case of 2-( -octadecylamino)-naphthalene-6-sulfonate (ONS) [54]. The surface coverage 6 takes the form ... 

The non-linear optical properties of a material are evaluated by measuring (using techniques from the field of physics) its molecular hyperpolarizability coefficient (3. 

The tables in this section contain data from approximately 35 research papers that have mostly employed THG, DFWM, or Z-scan techniques to measure the third-order hyperpolarizabilities of organometallic complexes. 

As mentioned above, the powder SHG method is a useful technique for the screening of second-order nonlinear materials. However, because of the sensitivity of the SHG coefficients of crystalline materials to the orientational aspects of the molecular packing and because the measurement is performed on an essentially random distribution of microcrystalline particles, the powder SHG method is not generally useful for obtaining information about molecular hyperpolarizabilities. 

From the complementary nature of EFISHG and HRS, application of both techniques to (neutral and dipolar) molecules can lead to the measurement of more tensor components, to the experimental determination of structural parameters [22], or to the independent confirmation of experimentally obtained values for hyperpolarizability tensor components [25]. 

Ever since HRS has been developed as an experimental technique to determine the first hyperpolarizability p of molecules in solution, it has been realized that multiphoton fluorescence is a competing nonlinear process, contributing to the HRS signal [26]. For the classical dipolar and neutral molecules that may exhibit multiphoton fluorescence, electric-field-induced second-harmonic generation (EFISHG) experiments are possible. However, for ionic and non-dipolar compounds, no electric field can be applied over the solution. Hence, no EFISHG measurements are possible. Then it is very tempting to rely on the HRS measurement only. When there is, however, a multi-photon fluorescence (MPF) contribution, an overestimation of the first hyperpolarizability value results [27]. 

The first common method for molecular first hyperpolarizability determination is the electric field-induced second harmonic generation (EFISH) technique in solution [6-10]. This technique can be applied only to dipolar molecules. Under an applied external electric field, molecules in solution orient approximately in the direction of the field giving rise to second harmonic generation. The measured third-order nonlinear optical susceptibility is given by the following expression ... 

Schmalzlin et al. [90] have used the HRS technique to determine the molecular first hyperpolarizabilities (3 values of retinal Schiff base in its protonated and unprotonated form. Results of their HRS measurements performed at 1064,1300 and ISOOnm were reported. The derived hyperpolarizabilities are self-consistent with the two-state model for all three wavelengths, but they are an order of magnitude lower than those reported by Hendrickx et al. 

The Electric-Field-Induced Second-Harmonic Generation (EFISHG) technique makes it possible to measure the molecular hyperpolarizability, p, on liquids or molecular solutions. The centrosymmetry of tire solution is broken by applying a DC electric field to induce an average orientation of the molecules due to interactions of the permanent dipoles of the molecules and the electric field. The energy of a dipole with a permanent dipole fi in an electric field E is given by ... 

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