Third-order nonlinear process

It is evident from Table 7.1 that the shorter the effective pulse duration, the higher the nonlinear signal intensity. This is even more the case for third-order processes... 

The two important consequences of the third-order optical nonlinearities represented by x are third-harmonic generation and intensity dependence of the refractive index. Third-harmonic generation (THG) describes the process in which an incident photon field of frequency (oj) generates, through nonlinear polarization in the medium, a coherent optical field at 3a>. Through x interaction, the refractive index of the nonlinear medium is given as n = nQ+n I where n describes intensity dependence of the refractive index ana I is the instantaneous intensity of the laser pulse. There is no symmetry restriction on the third-order processes which can occur in all media including air. 

Thus, the ratio is dependent on experimental parameters such as the optical path length, sample number density, and the phase matching conditions for the intermediate third-order processes, as well as the ratio of the third-and fifth-order response functions. The ratio of the response functions is directly related to the magnitude of the nonlinearity in the system, which is reflected by the magnitude of the potential anharmonicity, g(3), and the nonlinearity in the polarizability, a,2>. For example, let us consider only the NP contribution to the direct fifth-order response [Equation (21)]. For simplicity we will consider a system represented by a single mode, in other words the response is isotropic. If we express the third-order response functions in term of the coordinate [Equation (17)] and ignore all higher order terms,... 

Fig. 16.9 (a) Concept of higher photon confinement at the tip apex by a nonlinear optical process. Efficiency of a first-order process such as spontaneous Raman or fluorescence directly reflects the field distribution at the tip apex while the efficiency of a second-order process such as SHG or SFG and a third-order process such as CARS shows further confinement due to the nonlinear response of the material, (b) Energy diagram of CARS process... 

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. 

From the above discussion, it is apparent that amorphous polymeric or glassy structures are more suitable as media for third-order nonlinear optical processes. Interest recently has shifted considerably to the third-order processes because they provide mechanisms for all-optical switching and all-optical signal processing. 

All these nonlinear techniques represent coherent third-order processes analogous to saturation spectroscopy, polarization spectroscopy, or two-photon absorption (Chap. 2), because the magnitude of the nonlinear signal is proportional to the third power of the involved fleld amplitudes (3.18a-3.18c). 

Therefore, a nonresonant third-order process can be overcome by a resonantly enhanced higher order process. Strong two-photon excitation or absorption saturation at 2ct), would generate strong fifth or higher order nonlinearities. Therefore, a careful characterization of a nonlinear optical response necessitates the investigation of the possible roles of higher order nonlinearities enhanced by multiphoton resonances or saturation processes. 

Cascading. In most cases, the distinction between second- and third-order nonlinearities is evident from the different phenomena each produce. That distinction blurs, however, when one considers the cascading of second-order effects to produce third-order nonlinear phenomena (51). In a cascaded process, the nonlinear optical field generated as a second-order response at one place combines anew with the incident field in a subsequent second-order process. Figure 2 shows a schematic of this effect at the molecular level where second-order effects in noncentrosymmetric molecules combine to yield a third-order response that may be difficult to separate from a pure third-order process. This form of cascading is complicated by the near-field relationships that appear in the interaction between molecules, but analysis of cascaded phenomena is of interest, because it provides a way to explore local fields and the correlations between orientations of dipoles in a centros5nnmetric material (52). 

Combination with Static Fieids. A common technique, useful for optoelectronic devices, is to combine a monochromatic optical field with a DC or quasistatic field. This combination can lead to refractive index and absorption changes (linear or quadratic electrooptic effects and electroabsorption), or to electric-field induced second-harmonic generation (EFISH or DC-SHG, 2o) = co + co + 0) in a quasi-third-order process. In EFISH, the DC field orients the molecular dipole moments to enable or enhance the second-harmonic response of the material to the applied laser frequency. The combination of a DC field component with a single optical field is referred to as the linear electrooptic (Pockels) effect (co = co -I- 0), or the quadratic electrooptic (Kerr) effect ( = -I- 0 -I- 0). EFISH is discussed in this article, however, for the important role that it has played in the characterization of nonlinear optical materials for other applications. 

In an effort to identify materials appropriate for the appHcation of third-order optical nonlinearity, several figures of merit (EOM) have been defined (1—r5,r51—r53). Parallel all-optical (Kerr effect) switching and processing involve the focusing of many images onto a nonlinear slab where the transmissive... 

Frequency-dependent polarizability a and second hyperpolarizability y corresponding to various third-order nonlinear optical processes have been... 

Frequency degenerate 2PA is a third order, y° nonlinear optical process whereby two photons of equal energy are simultaneously absorbed to raise a system into an excited state of energy equal to that of the sum of the two photons. The propagation... 

---