Third-order phenomena

Several measuring techniques giving evidence of third-order nonlinear behavior are listed in Table 3.1 [26, 27]. 

It is difficult to compare the third-order susceptibilities of systems examined using different measuring techniques. Since they are based on fundamentally different origins, they do not yield identical values. Different nonlinear 

Resonance occurs at wavelengths around that of the absorption band. Moreover, the strong frequency (wavelength) dependence of and the influence of repetition frequency and pulse duration of the laser on have to be taken into account. It is beyond the scope of this book to describe the various measuring 

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The arrival of practical fiber optic communication networks has strengthened the need for more-efficient devices which are capable of routing or modulating optical signals. Such devices often rely on nonlinear optical effects such as the Pockels and Kerr effects which are second- and third-order phenomena, respectively. These effects arise as a result of the electric-field expansion for the electric polarization in a nonlinear medium ... 

It will be seen that the second-order treatment leads to results which deviate more from the correct values than do those given by the first-order treatment alone. This is due in part to the fact that the second-order energy was derived without considerar-tion of the resonance phenomenon, and is probably in error for that reason. The third-order energy is also no doubt appreciable. It can be concluded from table 3 that the first-order perturbation calculation in problems of this type will usually lead to rather good results, and that in general the second-order term need not be evaluated. 

As the number of lattice sites increases, the electrons experience additional correlations, so the representable region shrinks. That is, if TZi is the representable region for a lattice with i = A sites, then TZ4 dTZ dTZ% TZw d . This phenomenon is accurately tracked by the third-order estimates, and Fig. 3 shows that convergence to the limiting case where A oo is rapid. 

Most of the studies devoted to the nonlinear optical properties of metal nanoparticles use the notation x (<>>) to refer to the susceptibility for the optical Kerr effect. Unless otherwise specified, we will also adopt this simplified designation in the following. Let us just recall that it corresponds, in fact, to an experimental situation where a unique plane wave, linearly polarized (or three plane waves with same polarization and frequency), generates the third-order nonlinear optical phenomenon in an isotropic medium at the same frequency, and that the susceptibility is a priori a complex quantity. 

The original Placzek theory of Raman scattering [30] was in terms of the linear, or first order microscopic polarizability, a (a second rank tensor), not the third order h3q)erpolarizability, y (a fourth rank tensor). The Dirac and Kramers-Heisenberg quantum theory for linear dispersion did account for Raman scattering. It turns out that this link of properties at third order to those at first order works well for the electronically nonresonant Raman processes, but it cannot hold rigorously for the fully (triply) resonant Raman spectroscopies. However, provided one discards the important line shaping phenomenon called pure dephasing , one can show how the third order susceptibility does reduce to the treatment based on the (linear) polarizability tensor [6, 27]. 

The models most often used to describe the response are first-, second-, and, very occasionally, third-order polynomials. The number of coefficients in a polynomial increases very rapidly with the number of variables and the degree of the model and the number of experiments needed increases at least as rapidly. Also a given model will describe the phenomenon that we are trying to model better over a restricted experimental domain than over a wide one. These three considerations imply certain conditions for using response surface modelling. 

The phenomenon of kinetics of small gas molecules by which the high-temperature hydrogen-oxygen reaction yields its most important simplification is the third-order kinetics of association reactions at familiar gas pressures. The proportionality of the rates of reactions... 

Among the third-order effects, of particular interest is the light intensity dependence of refractive index of the medium. This light control by light phenomenon, being an all-optical effect, provides the fastest photonic mechanism available. Another important application of photonics is derived from the intensity dependence of optical transmittance of materials. This phenomenon is the principle of optical power limiting used for sensor, human eye or electronic circuitry protection. The above two applications are the examples of the intensity dependent complex third-order optical susceptibility of a photonic medium. 

The two-photon absorption (TPA) phenomenon was proposed by Gbeppert-Mayer in 1931 [118] and experimentally first observed by Kaiser and Garrett [119]. TPA is one of the important third-order NLO features. When a molecule is exposed to an intense optical field such as from a pulse laser, it can absorb two photons simultaneously by involving a virtual intermediate state. Figure 49.9 schematically represent this process. If the two photons are of the same frequency, the process is called degenerate TPA if they are of different frequency, the process is a nondegenerate TPA [120]. 

The optical Kerr effect is a phenomenon of the optical field-induced birefringence and refers to the linear birefiingence induced by a linearly polarized optical field. The pump and probe beams are polarized 45 to each other in optical Kerr effect experiments. The probe beam may be composed of two orthogonal linearly polarized beams, and the polarization of one beam is parallel to that of the pump beam. According to third-order optical nonlinearity, the pump beam-induced linear birefringence is given by [46]. 

Beyond the linear regime, there is also growing interest in second- and third-order response " in all these fields. In particular the field of nonlinear optics has been investigated heavily, especially the phenomenon... 

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