Optical hyperpolarizabilities, origins

We have shown the molecular orbital theory origin of structure - function relationships for electronic hyperpolarizability. Yet, much of the common language of nonlinear optics is phrased in terms of anharmonic oscillators. How are the molecular orbital and oscillator models reconciled with one another The potential energy function of a spring maps the distortion energy as a function of its displacement. A connection can indeed be drawn between the molecular orbitals of a molecule and its corresponding effective oscillator . 

Exact static optical susceptibilities are conveniently calculated as successive derivatives on an applied electric field of the gs polarization, defined, in linear aggregates, as the dipole moment per unit length. The linear polarizability (a), the first and second hyperpolarizabilities (jS and y, respectively) obtained for 16-sites clusters are shown as full lines in Fig. 5. Left, middle and right panels refer to A, B and C clusters, respectively, for the parameters that, in Fig. 4 drive the system through the neutral-zwitterionic interface. Susceptibilities show a strong and non-trivial dependence on the intermolecular distance, and, to understand the physical origin of this complex and interesting behavior we shall discuss several approximated results. 

The second-order NLO properties are of interest for a variety of NLO processes [1-3]. One of the most relevant is the SHG, originated by the mixing of three waves two incident waves with frequency co interact with the molecule or the bulk material with NLO properties, defined by a given value of the quadratic hyperpolarizability, fi, or of the second-order electrical susceptibility, respectively, to produce a new electrical wave, named SH, of frequency 2co. Another important second-order NLO process is the electrooptic Pockels effect which requires the presence of an external d.c. electric field, E(0), in addition to the optical E co) electrical field. This effect produces a change in the refractive index of a material proportional to the applied electric field, and can be exploited in devices such as optical switches and modulators [1-3]. 

In organic molecules, the high hyperpolarizabilities result from high transition dipole strengths originating from tt — tt transitions. Previous calculations for cyclic phosphazenes have shown that the dominant optical characteristics are n — 7T electronic transitions, which have notoriously weak transition strengths, and a large [46]. The common characteristics of the linear and cyclic phospho-... 

The nonlinear optical properties of polydiacetylenes are subject of an increasing interest in last years (1-4). This is due to the fact that polydiacetylenes are a one-dimensionnal system of higly polarizable conjugated tt elections The polarization depends strongly on electron delocalization length Moreover, the electronic origin of hyperpolarizability implies short response times On the other hand, the wave dispersed measurements of molecular hyperpolarizabilities yield information about forbidden electronic transitions In fact the bulk polarization can be developped in external electric field power series ... 

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. 

The fastest optical nonlinearity originates from the electronic response. To lowest order, )f = pP)/eo and = py)leQ, where P and /are molecular hyperpolarizabilities. As in the case of nonlinear susceptibilities, hyperpolarizabilities describe a variety of processes. Optical harmonic generation will be considered separately. 

In the hybrid materials based on the SiC nanoparticles and host polymer matrixes, the origin of the EO behaviour is intimately connected to the hyperpolarizabilities intrinsically involved in the SiC and depends on the interactions at the host-guest interfaces. The intrinsic effect originates from the nanocrystallite bulk in agreement with the EO behavior of 3C-SiC thin films (Vonsovici et al. 2000). The effect of the surrounding polymer on the nanocrystal nonlinear optical behavior was evaluated by numerical methods. In this case the molecular dynamic technique was first used to build the relevant architectures, which combine SiC nanocrystals and the polymers. In a second step, the EO parameters were computed and exhaustive comparison with experimental results was achieved and underlines the strength of the developed theoretical and numerical approaches. 

On the other hand, the HRS method allows measurements on nonpolar and/or ionic molecules. In HRS experiments, the first hyperpolarizability is derived from the intensity of the scattered light at optical frequency 2a> on incidence of a laser pulse at co. Contrary to EFISHG, the HRS signal originates from incoherent fluctuations of individual molecular scatterers that do not exhibit specific phase relations with respect to the others. 

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