Third-order hyperpolarizability

If we neglect pure dephasing, the general tensor element of the third order hyperpolarizability relates to those of the first order polarizability tensor according to... 

In this expression, the Einstein convention of summation over repeated indices has been followed p0 is the permanent dipole moment, while al7, fiijk, and yiJkl are the tensorial elements of the linear polarizability, and the second- and third-order hyperpolarizabilities of the molecule, respectively. 

It should be noted that polarizabilities of various orders can be defined in an alternative way in the SI system of units to that discussed previously. A quantity having the dimension of volume a = a/47re0 can be considered to be an SI analogue of the cgs polarizability. Analogously, y = -y/47re0 (or y = y/eo) can be used as the third-order hyperpolarizability in the SI system, with y having the units of m5 V 3. The presence or absence of the factor of An in the definition of the hyperpolarizability is, unfortunately, not always obvious in literature data. 

Ab initio methods have thus far only been used to calculate the static third-order hyperpolarizabilities of ligated organometallic fragments. The CFIF finite field (FF) method was utilized with MP2, MP3, MP4(SDTQ), QCISD(T), and CCSD(T) electron correlation corrections applied. The reader is directed elsewhere for a more detailed description of these electron correlation corrections.10... 

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. 

All applications quoted so far were for the linear response. Very few investigations have dealt with the higher-order response described in Sect. 5.2. The frequency-dependent third-order hyperpolarizabilities of rare-gas atoms were calculated by Senatore and Subbaswamy [86] within the ALDA the calculated values turned out to bee too large by a factor of two, further indicating the need for self-interaction corrected functionals in the calculation of response properties. The effect of adsorbates on second-harmonic generation at simple metal surfaces was invested by Kuchler and Rebentrost [205, 206]. Most recently, the second-order harmonic generation in bulk insulators was calculated within the ALDA [207]. 

The formulae for effecting the conversion have been discussed in section (7.1). Data is not completely available to apply the general formula of Teng and Garito, but the simplified versions can readily be applied to the macroscopic measurements described in the previous section. A number of different values of the dipole moment have been adopted in extracting Pz from y. In all cases other than in refs. 42 and 43 the values of and a form of p are given and it is possible to reconstruct the quantity fiPz- In comparing the interpretations of different studies this product, expressed in units of (au.Debye), has been used. The third order hyperpolarizability term, y of... 

Levine, B.F., Bethea, C.G. Second and third order hyperpolarizabilities of organic molecules, J. Chem. Phys. 63, 2666-2682 (1975)... 

Most of the linear optical properties and also some of the nonlinear properties like photo-induced absorption were reported in Section 4.1.2 above. We will here concentrate on phenomenological properties like the refractive index and the second and third order hyperpolarizabilities. 

Rinkevicius et al. [12] have shown that when ultra-small metallic nanoparticles are combined with organic derivatives with large second- and third-order hyperpolarizabilitis, lead to enhancement of the overall third-order response of the... 

The third order hyperpolarizability coefficients x have been determined under double resonance conditions for thin films of PcGaCl and PcAlF [187a]. Depending on the deposition conditions, the films consist, in variable ratios, of cofacially stacked (triclinic) and slipstacked (monoclinic) small crystallites. The samples were irradiated at 1064 nm, a frequency where the compounds are... 

Risser, S, M., and Ferris, K. F., Third-order hyperpolarizabilities of conjugated inorganic polymers, Chem. Phys. Lett., 170, 349 (1990). 

Here, f, Fx and are local field factors, a is a molecular parameter including the dipole moment, second order and third order hyperpolarizabilities. Under condition F = Fx = the formula does not agree with the experiment for 8CB. Indeed, it follows that rji should increase at the transition from the nematic to smectic A phase according to the increase in (F2) However, in the experiment, Fn markedly decreases. The similar temperature behavior was earlier observed for dielectric permittivity of 8CB. In the latter case the decrease in is due to the antiparallel correlation of molecular dipoles in the smectic A phase, which results in a decrease in the effective dipole moment /x Thus, the decrease... 

The imaginary part of the third-order hyperpolarizability (y) was measured for a series of platinum poly-ynes in both solution and thin-film form, and for a group of related platinum-organic species. 

Transition metal poly-ynes have large third-order optical susceptibilities (X ) which consist of contributions from the real and imaginary parts of the third-order hyperpolarizabilities (y and y", respectively). In previous studies, various optical measurements were used to determine the nonlinear hyper-polarizabilities of the polymers.Most recently, an extensive study of the structural dependence of the hyperpolarizabilities of the platinum and palladium... 

Guha, S., Frazier, C.C., Porter, P.L., Kang, K., and Finberg, S., "Measurement of the third-order hyperpolarizability of platinum poly-ynes," Optics Letters 14 952 (1989). 

The contributions to the fifth-order nonlinear optical susceptibility of dense medium have been theoretically estimated by using both the local-field-corrected Maxwell-Bloch equations and Bloembergen s approach. In addition to the obvious fifth-order hyperpolarizability contribution, the fifth-order NLO susceptibility contains an extra term, which is proportional to the square of the third-order hyperpolarizability and which originates purely from local-field effects, as a cascaded contribution. Using as model the sodium 3s 3p transition system, it has been shown that the relative contribution of the cascaded term to the fifth-order NLO susceptibility grows with the increase of the atomic density and then saturates. 

Contributions to the third-order susceptibility (-G) CO-O), co) from third-order hyperpolarizability have received considerable attention. Picosecond measurements have been carried out on liquid crystals in the isotropic phase [69, 70] from the criti-... 

Assuming that arises from the third-order hyperpolarizability, elements of give information about the degree of orientational order. Measurements of electric-field-induced second-harmonic generation (EFISH) have been carried out [88] on 5CB, showing the expected temperature dependence. In liquid crystals, may originate from order or flexoelectric effects, or other mechanisms resulting in electric polarization. 

---