Quadratic Electro-Optic Kerr Effect

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 

Electro-Optic Constants of Piezoelectric Single Crystals of CGG-Type 

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The T(3) rtjk gives the linear electro-optic (Pockels) effect, while the 7(4) ptjkl is responsible for the quadratic electro-optic (Kerr) effect qtjkl is the photoelastic tensor. 

Figure 11 shows the change in the refractive indices AWj and Ang as a function of an applied dc electric field for a PLZT (9.5/65/35) ceramic. The dc field was cycled from 0 to +1.1 MV.m+ down to -1.1 MV.m i, and back up to 0. Awj remained near zero while Afig decreased quadratically with the dc field, due to the electro-optic Kerr effect, until a minimum of -... 

The Kerr quadratic electro-optic effect Single-crystal BaTiO3 (T>TC)... 

In passive mode-locking, an additional element in the cavity can be a saturable absorber (e.g., an organic dye), which absorbs and thus attenuates low-intensity modes but transmits strong pulses. Kerr lens mode-locking exploits the optical Kerr63 or DC quadratic electro-optic effect here the refractive index is changed by An = (c/v) K E2, where E is the electric field and K is the Kerr constant. 

Photonics is playing an ever-increasing role in our modern information society. Photon is gradually replacing the electron, the elementary particle in electronics. Several hooks and reviews have appeared dealing with the theory of nonlinear optics and the structural characteristics and applications of nonlinear optical molecules and materials [1—18]. Tlie earliest nonlinear optical (NLO) effect discovered was the electro-optic (EO) effect. The linear EO coefficient defines the Pockel effect, discovered in 1906, while the quadratic (nonlinear) EO coefficient s,i relates to the Kerr effect, discovered 31 years later (1875). Truly, all-optical NLO effects were not discovered until the discovery of lasers. Second harmonic generation (SHG) was first observed in a single crystal of quartz by Franken et al. [1] in 1961. They frequency doubled the output of a ruby laser (694.3 nm) into the 383... 

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

There are two common types of electro-optic birefringent effects within the PLZT compositional phase diagram, i.e., (i) nonmemory quadratic (Kerr effect) and (ii) memory hnear (Pockel effect). The respective electro-optic coefficients for these effects are calculated by using the following relationships ... 

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. 

In Equation (14.7), the linear term vanishes and only the Kerr effect term survives. The electrooptic tensor for the Kerr effect varies with different molecular stmcture. For an isotropic Uquid, its quadratic electro-optic effect coefficients can be represented by the following matrix ... 

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. 

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. 

In non-polar, isotropic crystals or in glasses, there is no crystallographic direction distinguished and the linear electro-optic effect is absent. Nevertheless a static field may change the index by displacing ions with respect to their valence electrons. In this case the lowest non-vanishing coefficients are of the quadratic form, i.e. the refractive index changes proportionally to the square of the applied field Kerr 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. 

Whether or not the dependence is expressed in terms of E or P is a matter of choice it seems customary in the literature relating to single crystals to use the r coefficient for the linear Pockels effect and g for the quadratic Kerr effect. In the case of electro-optic ceramics r and R are most commonly used. 

Electro-absorption (EA) spectroscopy, where optical absorption is observed under the application of an electric field to the sample, is another method that can distinguish between localised and inter-band excitations. The electric field produces a Stark shift of allowed optical absorptions and renders forbidden transitions allowed by mixing the wavefunctions of the excited states. Excitons show a quadratic Stark (Kerr) effect with a spectral profile that is the first derivative of the absorption spectrum for localised (Frenkel) excitons and the second derivative for charge transfer excitons, i.e. 

The Kerr Effect in Polymer Solutions and Colloids.— Strong electro-optical birefringence is observed in colloidal systems and in macromolecular solutions." Numerous theoreticed papers" have been devoted to the quadratic optical birefringence exhibited by solutions of small macro-molecules in weak electric fields. O Konski et al. and others < - have shown that complete alignment of macromolecules in a static electric field does in fact take place in various macromolecular solutions, permitting the observation of the electric saturation of opticed birefrin nce." ... 

It follows from the preceding results that the electro-optical properties of molecules in degenerate electronic states should have unusual temperature dependence, which is absent in the case of nondegenerate states. Even for nondipolar degenerate electronic states (e.g., for states in which the reduced matrix elements of the dipole moment are zero) for certain relationships between the vibronic constant and the temperature, there may be a quadratic dependence of the Kerr effect on p, similar to that observed in the case of molecules that are simultaneously anisotropic polarizable and possess a proper dipole moment. The nonlinear dependence on p under consideration is due exclusively to the vibronic interaction that redetermines the vibronic spectrum and leads to different polarizability in different vibronic states. This dependence on p has to be distinguished from that which arises due to the nonzero value of the dipole moment in the initial ground electronic state (e.g., as in the case of the E term in molecules with D3h symmetry). The two sources of the... 

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. 

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 general, the distortions on the electronic wave function of liquid crystal molecules caused by an applied field do not cause appreciable change to its contribution to the refractive indices (see Chapter 10). However, the orientation of the molecules can be dramatically altered by the apphed field. This process alters the overall optical properties of the medium and is the principal mechanism used in liquid-crystal-based electro-optical devices. As noted in Section 6.2.2, the electrically induced orientational refractive index changes could be Pockel or Kerr effect. In this and the next sections, we shall focus on nematic liquid crystals in which the director axis reorientation is a Kerr-like effect that is, the process is quadratic in the applied field. 

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