Pockels effect, electric field induced

The first observation of natural optical anisotropy was made in 1669 by Bartolinius in calcite crystals, in which light travels at different velocities depending on the direction of propagation relative to the crystal structure. The electrooptic effect, electric-field-induced anisotropy, was first observed in glass in 1875 by J. Kerr. Kerr found a nonlinear dependence of refractive index on applied electric field. The term Kerr effect is used to describe the quadratic electrooptic effect observed in isotropic materials. The linear electrooptic effect was first observed in quartz crystals in 1883 by W. Rontgen and A. Kundt. Pockels broadened the analysis of this relationship in quartz and other crystals, which led to the term Pockels effect to describe linear behavior. In the 1960s several developments... 

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. 

At time t = 0, a dc field is applied it produces an electric field-induced Pockels effect (EFIPE), which is solely due to a third-order effect Eq) in the case of the copolymer because the molecules are not oriented by the dc field alone at room temperature, but which also contains a part due to the rotation, in a polar manner, of free chromophores in the guest-host system (induced The value of x is measured from the modulations of ATR... 

P( P(-o> w,0) P(0 -fa>,w) Y( - Y(-2(i) (i>,tD,0) Y(-o) (i>,0,0) Second harmonic generation (SHG) Electrooptic Pockels effect Optical rectification Third harmonic generation DC electric-field-induced SHG Intensity-dependent refractive index Optical Kerr effect Coherent anti-Stokes Raman pSHG pEOPE pOR. yTHG. EFISH oj DC-SHG. JlDRI or. yOKE. yCARS... 

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, 2 > = > - - 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 + 0), or the quadratic electrooptic (Kerr) effect ( > = > - - 0 -I- 0). These electrooptic effects are discussed extensively in the article Electrooptical Applications (qv). EFISH is... 

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

Apart from purely electronic effects, an asymmetric nuclear relaxation in the electric field can also contribute to the first hyperpolarizability in processes that are partly induced by a static field, such as the Pockels effect [55, 56], and much attention is currently devoted to the study of the vibrational hyperpolarizability, can be deduced from experimental data in two different ways [57, 58], and a review of the theoretical calculations of p, is given in Refs. [59] and [60]. The numerical value of the static P is often similar to that of static electronic hyperpolarizabilities, and this was rationalized with a two-state valence-bond charge transfer model. Recent ab-initio computational tests have shown, however, that this model is not always adequate and that a direct correlation between static electronic and vibrational hyperpolarizabilities does not exist [61]. 

Several techniques have been developed for determining the second-order susceptibility [24]. Of practical importance are methods that may be employed for aligned polymeric systems containing polar moieties [4, 8]. Methods making use of the Pockels or linear electro-optic (EO) effect are based on the measurement of the variation in the refractive index of thin polymer films induced by an external electric field. In this way, values of the electro-optic coefficients rss and in are obtained, which are related to the corresponding values through Eq. (3.16). 

For our analysis, we shall assume an NLO polymer belonging to the tetragonal symmetry class 4 [15,71]. Uniaxial crystals possess EO properties by which a polarization and, hence, a birefringence can be induced when an electric field (E) is applied to the crystal (Pockels effect) [26,29]. The Pockels effect is a linear EO effect the induced birefringence is directly proportional to the first power of the applied electric field. Thus, uniaxial crystals exhibit anisotropic behavior. 

Noncentrosymmetric crystals show other properties in addition to frequency conversion, for instance the linear electro-optic or Pockels effect the linear change of the refractive index induced by an applied DC electric field. Furthermore, the point groups and allow for the existence of a permanent electric dipole moment. Indeed, crystals... 

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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