Electro-optic and nonlinear optical phenomena

Electro-optic (EO) phenomena are related to the interaction of an electric field with an optical process. The classical electro-optic effects, the Pockels and the Kerr effect, discovered in 1893 and 1875 with quartz and carbon disulfide, respectively, refer to the induction of birefringence in certain materials under the influence of an external electric field. Application of an electric field to the sample causes a change in the refractive index. In the case of the Pockels effect. An is linearly proportional to E, the strength of the applied electric field [see Eq. (3-1)]. Hence, it is also called the linear electro-optic effect In contrast. An is proportional to E in the case of the Kerr effect [see Eq. (3-2)]. 

Linear electro-optical effect — Pockels effect An = rE Quadratic electro-optical effect — Kerr effect An = q2E  

It should be emphasized that the Kerr effect refers to a quadratic, i.e. a nonlinear dependence of the refractive index on the strength of the externally ap- 

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I 3 Electro-optic and nonlinear optical phenomena ble 3.4 Commercially available NLO polymers [41]. 

The electrical characterization of polar media is crucial to investigate their suitability for ferroelectric memories, piezo- or pyroelectric devices and many other ferroelectric applications (see Chapter 3). Optical characterization of polar media is fundamental to investigate their ser-vicability for electro-optic devices or applications in the field of nonlinear optics (see Chapter 4). Additionally there are intentions to characterize polar media with a combination of both, electrical and optical methods, such as to understand ferroelectric phenomena that are influenced by the action of light. 

The dielectric tensor describes the linear response of a material to an electric field. In many experiments, and particularly in optical rheometry, anisotropy in is the object of measurement. This anisotropy is manifested as birefringence and dichroism, two quantities that will be discussed in detail in Chapter 2. The nonlinear terms are responsible for such effects as second harmonic generation, electro-optic activity, and frequency tripling. These phenomena occur when certain criteria are met in the material properties, and at high values of field strength. 

Electro-optic and magneto-optic phenomena contain terms of nonlinear optics effects (see Eqs. (4.32), (4.33), (4.36), and (4.39)). On the other hand, acousto-optic effects which arise from a periodical density fluctuation of the medium, analogous to the Brillouin scattering phenomenon, do not contain terms of nonlinear optics, as a general rule.5) The perturbation of light propagation by sonic waves differs from that induced by electric and magnetic fields. As the electric susceptibility, xe, is a function of the density of the medium, it will be influenced by the periodical density fluctuation induced in a medium by sound waves. 

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. 

Particular nonlinear optical phenomena arise also when static electric or magnetic fields are applied. The molecular states and selection rules are thereby modified, leading, for instance, to higher-order, nonlinear-optical variants of the linear (Pockels) and quadratic (Kerr) electro-optical effect, or of the linear (Faraday) and quadratic (Cotton-Mouton) magneto-optical effect. 

Liquid crystals possess wonderful light-scattering abilities, linear or nonlinear. As a result, studies of their nonlinear optical responses have been vigorously pursued in various contexts. As in the case of electro-opties, it would require a treatise to summarize all the work done to date, as almost all eonceivable nonlinear optical phenomena have been observed in liquid crystals in all their mesophases. Some of these phenomena were studied for their novelty others have been developed into diagnostic tools or practical devices. In this chapter, we limit our attention here to only exemplary studies whieh are fundamentally interesting and/or practically important. 

In conclusion, liquid crystals are complex and are wonderful electro-optical and nonlinear optical materials. Many novel, interesting, and useful materials (with negative, zero or positive refractive indices), processes, phenomena, and devices are awaiting our further exploration. ... 

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