Second-order nonlinear optical effect

Second-order NLO effects can be considered as the interaction of the polarizable electrons of the NLO material with two electric fields, fc] and E2, these fields potentially having different polarizations and potentially oscillating with frequencies coj and a 2, respectively. For example, consider the interaction of the material with two laser beams of different frequencies. The second-order term of Eq. (5) becomes 

In another special case, one of the fields in Eq. (7) is a d.c. electric field, E2, applied to the material, i.e. w2 = 0. The optical frequency polarization arising from the second-order susceptibility is 

the applied field, E2, changes the effective linear susceptibility (i.e. the dependence of the polarization on the light field, Eft. Since the linear susceptibility is related to the refractive index, the refractive index of the material is also changed by the applied field. This is known as the linear electrooptic (EO) or Pockels effect and can be used to modulate the polarization or phase of light by changing the applied voltage. 

SHG can also be used to determine (or the related quantity d33, which specifically relates to a mixing of fields of optical frequencies) for poled chromo- 

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Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

Heinz T F 1991 Second-order nonlinear optical effects at surfaces and interfaces Noniinear Surfaoe... 

Reider G A and Heinz T F 1995 Second-order nonlinear optical effects at surfaces and interfaces recent advances Photonio Probes of Surfaoes ed P Halevi (Amsterdam Elsevier) pp 413-78... 

Figure 9.3 Schematic illustration of second-order nonlinear optical effects, (a) Second-harmonic generation. Two light fields at frequency go are incident on medium with nonvanishing / 2. Nonlinear interaction with medium creates new field at frequency 2 go. (b) Frequency mixing. One light field at frequency GO and one at frequency go2 is incident on nonlinear medium. Nonlinear interaction with medium creates new field at frequency goi + go2. (c) electro-optic effect. Static electric field E (0) applied over nonlinear medium changes phase of an incoming light field.

In order to describe second-order nonlinear optical effects, it is not sufficient to treat (> and x<2) as a scalar quantity. Instead the second-order polarizability and susceptibility must be treated as a third-rank tensors 3p and Xp with 27 components and the dipole moment, polarization, and electric field as vectors. As such, the relations between the dipole moment (polarization) vector and the electric field vector can be defined as ... 

The coplanarity has endowed arylated TEEs with some of the highest known third-order optical nonlinearities and, in the case of acentricity, also very large second-order nonlinear optical effects. Furthermore, the strain-free planarity allows cis- and trans-arylated TEEs to interconvert upon photochemical excitation without competition from undesirable thermal isomerization. 

Because the coefficients a—y decrease as a > p > y, the effects arising from the higher terms are observed only at very high fields, typically those found in laser light. Let us concentrate here on materials giving rise to second-order nonlinear optical effects, i.e., those in which the p term is important. 

This has always been held to be true. However, in a limited number of examples, centric molecules do give rise to second-order nonlinear optical effects in the bulk. This is attributed to solid-state effects. See, for example. Ref (12). 

Yamada, S., Kawazu. M., Matsuo, T. Second-order nonlinear optical effects in stacked assemblies of ultrathin polymer films with amphiphilic ruthenium complex. J. Phys. Chem. 98, 3573-3574 (1994)... 

Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosymmetric media. Input waves at frequencies (o j and a 2, with corresponding wavevectors Aj(co j) and are approaching the interface from medium 1. Nonlinear...

Heinz T F 1991 Second-order nonlinear optical effects at surfaces and interfaces Nonlinear Surface Electromagnetic Phenomena ed H-E Ponath and G I Stegeman (Amsterdam North-Holland) pp 353-416... 

Choi, D.H. Wijekoon. W.M.K.P. Kim, H.M. Prasad, P.N. Second-order nonlinear optical effects in novel polymethacrylates containing a molecular-ionic chro-mophore in the side chain. Chem. Mater. 1994. 6 (2). 

Figure 14 Examples of functional polyions employed in ESA multilayers to study second-order nonlinear optical effects.

As is a third-rank tensor, it is effective only for noncentrosymmetric media. Therefore, the medium used for the second-order nonlinear optical effect must have a noncentrosymmetric ordering of the NLO dipoles, possibly by spontaneous ordering or by electric field poling (39). In contrast, order is not required for third-order nonlinear materials (e.g., conjugated polymers), but the of a given material is given by (40) ... 

Nitroaniline is the standard of comparison for nonlinear optical compounds. The molecule is noncentrosymmetric on the molecular level and has a high hyperpolarizability (P = 34.5 x 10" esu, Oudar and Chemla, 1977), but it crystallizes centrosymmetrically therefore, it does not show second-order nonlinear optical effects in the crystalline phase (Miyata et al., 1994). In contrast, 3-nitroaniline crystallizes in a noncentrosymmetric space group, but the P value is much lower (P = 6.0 X esu, Oudar and Chanla, 1977) than the value of 4-nitroaniline, because the charge transfer in the latter case (para-isomer) is much stronger. 

As a wide variety of second-order nonlinear optical effects exist, only a few examples will be mentioned here. 

In 2006, Bernard et al. also examined centrosymmetric boron cluster-containing molecules. Although these molecules did not show second-order nonlinear optical effects because of their cen-trosymmetry, they are interesting candidates for third-order TPA nonlinear processes. Centrosymmetric materials are more suitable for TPA applications in the visible range than noncentrosymmetric ones, because of their lower coloration (Wang et al., 2001). The presence of donor substituents at each arm of tripodal systems increases the TPA properties (Brunei et al., 2001). Bernard et al. desaibed, for the first time, branched octupolar systems with three dodecaborate units (Figure 13.16). 

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