Cubic hyperpolarizability

Numerous compounds of the types (L)AuC=CR and Q+[Au(C=C-R)2] were investigated for their properties as NLO materials. Some of the examples were found to have the largest cubic optical non-linearity for monomeric organometallics.103 Examples are given in Scheme 18. For all of these compounds, the quadratic/cubic hyperpolarizability (linear optical and quadratic NLO response) have been determined. The studies were complemented by cyclovoltammetric measurements.58,59,103,112-117... 

The fundamental equation (1) describes the change in dipole moment between the ground state and an excited state jte expressed as a power series of the electric field E which occurs upon interaction of such a field, as in the electric component of electromagnetic radiation, with a single molecule. The coefficient a is the familiar linear polarizability, ft and y are the quadratic and cubic hyperpolarizabilities, respectively. The coefficients for these hyperpolarizabilities are tensor quantities and therefore highly symmetry dependent odd order coefficients are nonvanishing for all molecules but even order coefficients such as J3 (responsible for SHG) are zero for centrosymmetric molecules. Equation (2) is identical with (1) except that it describes a macroscopic polarization, such as that arising from an array of molecules in a crystal (10). 

Equation (2) is, strictly speaking, not suitable for optical fields, which are rapidly varying in time. The damping of the oscillating dipole, and the resultant phase shift, is then conveniently expressed by treating the hyperpolarizabilities as complex, frequency-dependent quantities. For the cubic hyperpolarizability, the relation between the Fourier components of the electric field and the Fourier amplitude of the oscillation of the electric dipole gives... 

Whittall, LR., Humphrey, M.G., Samoc, M., Swiatkiewicz, J., Luther-Davies, B. Organometalhc complexes for nonlinear ophcs. 4. Cubic hyperpolarizabilities of (cyclopentadienyl)bis(phos-phine)ruthenium cr-arylacetyhdes. Organometalhcs 14, 5493-5495 (1995)... 

Whittall, I.R., Cifuentes, M.P., Humphrey, M.G., Luther-Davies, B., Samoc, M., Houbrechts, S., Persoons, A., Heath, G.A., Hockless, D.C.R. Organometalhc complexes for nonlinear optics. X. Molecular quadratic and cubic hyperpolarizabilities of systematically varied (cyclopentadienyl)bis(phosphine)ruthenium cr-arylacetylides X-ray crystal structure of Ru(( )-4,4 -C=CCsH4CH=CHC5H4NO2)(PPh3)2(r)-C5H5). J. Organomet. Chem. 549, 127-137 (1997)... 

Here, / (0) is the permanent dipole moment and the tensors a, fi and are respectively the linear polarizability and the first (quadratic or second order polarizability)) and second (third order or cubic) hyperpolarizabilities. 

Kobayashi, Sasagane and Yamaguchi" have developed the theory of the time-dependent spin-restricted Hartree-Fock method for application to open shell systems (TDROHF). The expression for the cubic hyperpolarizability is obtained from the quasi-energy derivative (QED) method. The theory is applied to the investigation of the frequency-dependent y susceptibility of the Li, Na, K and N atoms. 

In liquids, the EFISH method is used to measure the total average microscopic cubic hyperpolarizability of a single molecule, y. The principle of this experiment has been described in a number of papers [35-37]. The nonlinearity y measured using EFISH contains contributions from electronic, vibrational, and rotational motions. This can be seen by considering the harmonic polarization Pf" for a single molecule [38]. 

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