Third-order NLO susceptibility

Table 4. Third order NLO susceptibilities and molecular second hyperpolarizabilities of simple catenane and rotaxane molecules as determined by the optical third harmonic generation technique...

It must be noted that the values reported in the literature vary over broad ranges. Therefore, the values listed here reflect only the general behavior of several classes of compounds. It can be seen in Table 3.5 that trans-polyacetylenes (PAs) and polydiacetylenes (PDAs) exhibit the largest third-order NLO susceptibilities. The x value of cis-PA (not shown) is more than an order of magnitude smaller than that of trans-PA. Derivatives of poly-p-phenylene, poly(phenyl-ene vinylene), and polythiophene also exhibit NLO activity, but to a much lesser extent than PAs and PDAs. As pointed out above, polysilanes also possess quite large x values. This is explained by the cr-conjugation of the silicon chain, which implies a pronounced delocalization of cr-electrons. A very large x value... 

The third order NLO susceptibility was determined by degenerate four wave mbdng using a pico second laser consisting of a mode-locked Quantel NdiYag laser that was frequency doubled to 532 nm It ould be noted that some values thus observed... 

Doping with active species (e.g., Au or Ag NPs, and CdSe or PbS QDs) can result in new NLO materials, such as those with significant third-order NLO susceptibility. The Z-scan method is used to characterize NLO effect in nanocomposite sol-gel films. Z-scan measures the nonlinear refiactive index and nonlinear absorption coefficient of a material [22]. The measurement setup is shown in Figure 22.3. A standard open-aperture Z-scan apparatus is used to measure the nonlinear extinction coefficients of materials, using a laser with a pulse duration of fs, ps, or at least ns as an excitation source, to avoid thermal effects. All the Z-scan measurements described in this chapter were carried out at room temperature. Sol-gel films doped with noble metal NPs (e.g., Au, Ag, and Cu) or QDs (e.g., CdS and PbS) have been investigated by Z-scan measurements [23,24]. 

Out of the large range of possible nonlinear optical effects, chemists are likely to encounter only a limited number of measurement techniques. These include both second- and third-order NLO characterization methods. A brief listing of the different types of measurements, the nonlinear susceptibility involved and the related molecular nonlinear polarizabilities is given here. 

Conjugated polymers satisfy these requirements and have thus emerged as the most widely studied materials for their susceptability. Some of the examples of conjugated polymers, that have been studied for their third order NLO properties, are polydiacetylenes, poly-p-phenylenevinylenes and polythiophenes. However, CVD has only been used in the case of poly-p-phenylenevinylenes (PPV) [section 3.4], although values have not been reported. An excellent review of third order nonlinear optical properties of PPV in general, can be found in literature. Recently, McElvain et al. ° reported the values of CVD polyazomethines to be... 

The third-order NLO effects are described by xi. i) susceptibility on macroscopic level and by second hyperpolarizability y tensor on microscopic one. In contrary to the second order NLO effects the third order effects are present in all molecules and in bulk materials. There exists also a similar relationship between die corresponding bulk susceptibilities and the molecular hyperpolarizabilities as in the... 

The polymers having delocalized r-electron in the main chain have been expected to possess extremely large third-order optical susceptibility.However, such an extended jr-electron conjugation generally rendered the polymers insoluble and infusible as well, which has seriously limited the fabrication of practical NLO devices. Recently, it was reported that the third-order nonlinear optical properties of poly(l,6-heptadiyne)s which were environmentally stable, soluble, and processable. The third-order optical nonlinearities of poly(l,6-heptadiyne)s bearing NLO active chomophores were evaluated for the first time. The third-order nonlinear susceptibility... 

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. 

The importance of the hyperpolarizability and susceptibility values relates to the fact that, provided these values are sufficiently large, a material exposed to a high-intensity laser beam exhibits nonlinear optical (NLO) properties. Remarkably, the optical properties of the material are altered by the light itself, although neither physical nor chemical alterations remain after the light is switched off. The quahty of nonlinear optical effects is cmciaUy determined by symmetry parameters. With respect to the electric field dependence of the vector P given by Eq. (3-4), second- and third-order NLO processes may be discriminated, depending on whether or determines the process. The discrimination between second- and third-order effects stems from the fact that second-order NLO processes are forbidden in centrosymmetric materials, a restriction that does not hold for third-order NLO processes. In the case of centrosymmetric materials, x is equal to zero, and the nonhnear dependence of the vector P is solely determined by Consequently, third-order NLO processes can occur with all materials, whereas second-order optical nonlinearity requires non-centrosymmetric materials. 

As with phthalocyanines, the third-order nonlinear optical susceptibility, of porphyrins can be manipulated by chemical substitution. The third-order NLO properties of several tetraphenylporphyrin compounds were first reported by Meloney et The was measured by the degenerate four-wave mixing (DFWM) technique from... 

The nonlinear optical (NLO) susceptibilities of bioengineered aromatic polymers synthesized by enzyme-catalyzed reactions are given in Tables 2, 3, and 4. Homopolymers and copolymers are synthesized by enzyme-catalyzed reactions from aromatic monomers such as phenols and aromatic amines and their alkyl-substituted derivatives. The third-order nonlinear optical measurements are carried out in solutions at a concentration of 1 mg/mL of the solvent. Unless otherwise indicated, most of the polymers are solubilized in a solvent mixture of dimethyl formamide and methanol (DMF-MeOH) or dimethyl sulfoxide and methanol (DMSO-MeOH), both in a 4 1 ratio. These solvent mixtures are selected on the basis of their optical properties at 532 nm (where all the NLO measurements reported here are carried out), such as low noise and optical absorption, and solubility of the bioengineered polymers in the solvent system selected. To reduce light scattering, the polymer solutions are filtered to remove undissolved materials, the polymer concentrations are corrected for the final x calculations, and x values are extrapolated to the pure sample based on the concentrations of NLO materials in the solvent used. Other details of the experimental setup and calculations used to determine third-order nonlinear susceptibilities were given earlier and described in earlier publications [5,6,9,17-19]. 

The NLO properties in the above-mentioned Pis are attributed to the NLO chromophores which are molecularly dispersed in or covalently bonded to thermally stable PI chains. Aromatic polyisoimides (Pil), isomers of PI, have conjugated structure along their main chains, and hence are supposed to show intrinsic third-order NLO properties. The third-order non-linear susceptibility, of several Pil films was estimated to be in the order of esu by third harmonic generation measurements (Table 13) with... 

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. 

Some of the first third order NLO studies of CPs were carried out on the poly(di-acetylenes) (P(DiAc)). One of the first such studies, on P(DiAc)-toluene sulfonate (PTS) single crystals, carried out by Sauteret et al. [502], revealed third order bulk NLO susceptibilities x fzzzz) polymer chain axis) of 1.6 X 10 ° esu at 2.62 pm and 8.5 X 10 ° esu at 1.89 pm. These values have as yet been exceeded only by one study, that of Drury on oriented Durham P(Ac) [503], in which a value for x zzzz> (Z= polymer chain axis) of 10 esu at 1.9 pm. However, this value of the susceptibility was inferred from THG data somewhat indirectly. Dennis et al. [504] reported off-resonant x xyyx values of 7 X 10 esu for solutions of various P(DiAc), extrapolated to pure substance and determined via DFWM at 532 nm. 

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