Pockels electro-optic effect

Figure 9. Conventional model of photorefraction in crystals iron impurity forms defect states of variable valence within the forbidden band gap of a lithium niobate crystal. Optical excitation of the divalent state leads to creation of a mobile electron in the conduction band. This is able to move and recombines with a trivalent iron impurity at another location which becomes divalent. The displacement of charge leads to an electric field and the Pockels electro-optic effect leads to local modification of the refractive index.

According to the Pockels electro-optic effect, a birefringence in an optical medium is established by an applied electric held. The birefringence is proportional to the electric held, in contrast to the Kerr effect where the birefringence is quadrahc to the held. 

The proportionality constants a and (> are the linear polarizability and the second-order polarizability (or first hyperpolarizability), and x(1) and x<2) are the first- and second-order susceptibility. The quadratic terms (> and x<2) are related by x(2) = (V/(P) and are responsible for second-order nonlinear optical (NLO) effects such as frequency doubling (or second-harmonic generation), frequency mixing, and the electro-optic effect (or Pockels effect). These effects are schematically illustrated in Figure 9.3. In the remainder of this chapter, we will primarily focus on the process of second-harmonic generation (SHG). 

Pockel cells use the linear electro optic effect in crystals to turn the plane of polarization when an external electric field is applied. A detailed description with references is given in... 

Historically, the earliest nonlinear optical (NLO) effect discovered was the electro-optic effect. The linear electro-optic (EO) coefficient rij defines the Pockels effect, discovered in 1906, while the quadratic EO coefficient sijki relates to the Kerr effect, discovered even earlier (1875). True, all-optical NLO effects were not discovered until the advent of the laser. 

This is called the linear electro-optic effect, also called the Pockels effect . 

In 1875 John Kerr carried out experiments on glass and detected electric-field-induced optical anisotropy. A quadratic dependence of n on E0 is now known as the Kerr effect. In 1883 both Wilhelm Rontgen and August Kundt independently reported a linear electro-optic effect in quartz which was analysed by Pockels in 1893. The linear electro-optical effect is termed the Pockels effect. 

X quantifies all second-order NLO effects such as SHG, electro-optic effect (Pockel) and frequency mixing, x is representative of third-order NLO effects such as THG, optical Kerr effect and two-photon absorption (TEA). The real part of 7 describes the nonlinear refractive index and its imaginary part the two-photon cross section (<72). 

Isotropic media can be made birefringent by application of an electric field. This phenomenon is an electro-optic effect.5 There are in fact several electro-optic effects the Pockels effect, the electro-optic Kerr effect, the Stark effect in atoms and molecules, the Franz-Keldysh effect in semiconductors, etc. (see Table 4.6). We will limit our discussion in this section to the Pockels effect and the electro-optic Kerr effect. 

The other electro-optic effect only occurs in the 20 piezoelectric crystal classes (no center of symmetry). This effect is known as the Pockels effect. The optical impermeability changes linearly with the static field... 

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 ... 

Ceramic PLZT has a number of structures, depending upon composition, and can show both the Pockels (linear) electro-optic effect in the ferroelectric rhombohedral and tetragonal phases and the Kerr (quadratic) effect in the cubic paraelectric state. Because of the ceramic nature of the material, the non-cubic phases show no birefringence in the as-prepared state and must be poled to become useful electro-optically (Section 6.4.1). PMN-PT and PZN-PT are relaxor ferroelectrics. These have an isotropic structure in the absence of an electric field, but this is easily altered in an applied electric field to give a birefringent electro-optic material. All of these phases, with optimised compositions, have much higher electro-optic coefficients than LiNb03 and are actively studied for device application. 

X0>( linear electro-optical effect (Pockels-effect) Light-modulation... 

The first term in Equation (14.6) is related to initial refractive indices of the medium at three primary directions, n, Uy, n. The second term refers to the linear electro-optic effect, which is known as the Pockels effect, and the third term refers to the quadratic electro-optic effect, known as the Kerr effect. Here, and Sjj are electro-optic tensors for the linear and quadratic electro-optic effects, respectively. The second-order Kerr effect is small as compared to the first-order linear effect, so it is usually neglected in the presence of linear effect. However, in crystals with centro-symmetric point groups, the linear effect vanishes and then the Kerr effect becomes dominant. 

Orientational Enhancement Effect. In addition to a strictly electronic and linear (Pockels) electro-optic response given by the first term on the right side of equation 1, the quasi-one-dimensional nonlinear optical chromophores incorporated into the pol5uner for their electro-optic response often exhibit large differences in the polarizability parallel versus perpendicular to the chromophore long axis (36,39-42). This so-called polarization anisotropjf (Aa a y -, where... 

This effect is even less pronounced than the linear Pockels effect in crystals. In contrast to the linear electro-optic effect that is confined to crystals lacking a center... 

Narasimhamurty, T. S. (1981). Kerr quadratic electro-optic effect Pockels phenomenological theory, in Photoelastic and Electro-Optic Properties of CrystalsAnonymous, pp. 359-362, Plenum Press, New York. 

So, d22 coefficient corresponds to and d to d a . The linear electro-optic effect or Pockels effect (Fig. 2.1) can be defined as a rotation or deformation of... 

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. 

In a motor-driven self-nuUing ellipsometer, the dc feedback currents are used to drive servomotors instead of being passed through the Faraday cell. As an alternative to the polarizer modulation described above, crystals with electro-optic effect (e.g., Pockels effect) can be used to modulate the relative phase retardation by an electric ac field. Independent modulations of polarizer... 

Linear Electro-Optic Effect (Pockels Effect) and Electro-Optic Modulators [19,20]... 

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