Second- and third-order nonlinearities

Fig. 8. Examples of some of the donor-acceptor substituted TEEs prepared for the exploration of structure-property relationships in the second- and third-order nonlinear optical effects of fully two-dimensionally-conjugated chromophores. For all compounds, the second hyperpolarizability y [10 esu], measured by third harmonic generation experiments in CHCI3 solution at a laser frequency of either A = 1.9 or 2.1 (second value if shown) pm is given in parentheses. n.o. not obtained...

In Equation 1, x is the linear susceptibility which is generally adequate to describe the optical response in the case of a weak optical field. The terms x and X are the second and third-order nonlinear optical susceptibilities which describe the nonlinear response of the medium. At optical frequencies (4)... 

This paper is a tutorial overview of the techniques used to characterize the nonlinear optical properties of bulk materials and molecules. Methods that are commonly used for characterization of second- and third-order nonlinear optical properties are covered. Several techniques are described briefly and then followed by a more detailed discussion of the determination of molecular hyperpolarizabilities using third harmonic generation. 

THG has become an important technique for characterization of the second- and third-order nonlinearities of materials and molecules. This is largely due to the interest in determining the purely electronic nonlinearity of molecules without major complications due to orientational or other motional contributions to the observed signals. The... 

Gold nanoparticles have large second- and third-order nonlinear susceptibilities and are therefore a promising class of nonlinear optical materials.214 We will briefly discuss several nonlinear optical processes from metal nanoparticles, such as multiphoton luminescence, hyper-Rayleigh scattering, and multiharmonic generation. 

Since Chapter 6 (352) in this volume is devoted to the luminescence and photochemistry of dithiolene complexes, these aspects will not be developed here. In this section, we restrict ourselves to the review of dithiolene complex-based compounds exhibiting optical properties, such as strong infrared (IR) absorption and second- and third-order nonlinear optical properties. In the last part of this section, we will review the use of some dithiolene complexes for optical data storage (printers, developer, CD-ROM, etc.). Contrary to what was observed throughout the two previous sections, no particular dithiolene complex really dominates the domain of the molecular materials exhibiting interesting optical properties. 

Donor/acceptor substituted azobenzenes, which have large second-and third-order nonlinear optical properties, show a fast thermal Z-F (cis-trans) conversion. 

Sekkat, Z., Pretre, P., Knoesen, A., Volksen, W., Lee, Y. Y., Miller, R. D., Wotxl, J., and Knoll, W. Correlation between polymer architecture and sub-glass-transiiion-temperature light-induced molecular movement in azo-polyimide polymers influence on linear and second- and third-order nonlinear optical processes. Journal of the Optical Society of America B (Optical Physics), vol. I S, (no. 1), Opt. Soc. America, m. 1998, p. 401-41.1. 

The second and third terms of the right hand side of Eq. (25) constitute the second- and third-order nonlinear contributions to the total polarization. These corrections to the polarization are responsible for numerous nonlinear optical processes such as the generation of light beams with new frequencies or an intensity dependent refractive index. 

The same year, Levine [182] proposed a model that related the anharmonic motion of the bond charge, located approximately halfway between two neighboring atoms, to the second- and third-order nonlinear optical susceptibilities of... 

Aside from these approaches, empirical relations have been proposed to relate the second- and third-order nonlinear susceptibilities to their linear analogs. Among them are Miller s rule [209] for the second-order nonlinear susceptibility of ionic crystals as well as the expressions of Wang [210] and of Boling, Glass, and Owyoung [211] for the third-order nonlinear susceptibility in the low-frequency limit. The latter have been shown, by comparison with experiment, to possess their own range of validity. 

Abstract Different techniques to characterize the strength of the second- and third-order nonlinear... 

The EFISHG technique obtains x from both second- and third-order nonlinearities. In the case of solutions, x will be related to the microscopic third-order polaiizability of the dissolved molecules which is given by ... 

The tensors and 7 constitute the molecular origin of the second-and third-order nonlinear optical phenomena such as electro-optic Pock-els effect (EOPE), optical rectification (OR), third harmonic generation (THG), electric field induced second harmonic generation (EFI-SHG), intensity dependent refractive index (IDRI), optical Kerr effect (OKE), electric field induced optical rectification (EFI-OR). To save space we do not indicate the full expressions for and 7 related to the different second and third order processes but we introduce the notations —(Ajy,ui,cj2) and 7(—a , o i,W2,W3), where the frequency relations to be used for the various non-linear optical processes which can be obtained in the case of both static and oscillating monochromatic fields are reported in Table 1.7. 

The problem becomes more complex when studying solid phases because the microscopic NLO responses do not provide the full information about their macroscopic coimterparts, the second- and third-order nonlinear susceptibilities, and To make the transition between the microscopic and macroscopic, it is necessary to know the structure of the condensed phases as well as the nature and the effects of the intermolecular interactions in the bulk of the material. In both the Physics and Chemistry arena, several schemes have been proposed to characterize the NLO responses of solid phases. One of the authors has recently contributed to review these approaches [3] of which one of the extremes is occupied by the oriented gas approximation that consists in performing a tensor sum of the microscopic NLO properties to obtain the macroscopic responses of the crystal. The other extreme consists in performing a complete treatment of the solid by using the supermolecule method or by taking advantage of the spatial periodicity in crystal orbital calculations. In between these techniques, one finds the interaction schemes and the semi-empirical approaches. 

Here, Pq is the permanent polarization, and and denote the second- and third-order nonlinear optical three-dimensional susceptibility tensors. The indices attached to the x tensors refer to the tensor elements, and the indices associated with the E values refer to the components of the electric field strength, here expressed in the laboratory frame. 

X and x are the second and third-order nonlinear optical susceptibilities. Two important manifestations of optical nonlinearities are harmonic generation and refractive fndex modulation by electric and optical fields. Their origin can conveniently be explained by considering a plane wave propagation through the nonlinear medium. The polarization is then given by... 

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