Electric Pockels effect

A second type of behavior existing in the PLZT s is the linear (Pockels) effect which is generally found in high coercive field, tetragonal materials (composition 3), This effect is so named because of the linear relationship between An and electric field. The truly linear, nonhysteretic character of this effect has been found to be intrinsic to the material and not due to domain reorientation processes which occur in the quadratic and memory materials. The linear materials possess permanent remanent polarization however, in this case the material is switched to its saturation remanence, and it remains in that state. Optical information is extracted from the ceramic by the action of an electric field which causes linear changes in the birefringence, but in no case is there polarization reversal in the material. 

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. 

The basis of NLO-effects arising from susceptibilities of second order, is the interaction of three electric fields with a material. The practical implementation of optical devices requires strong, coherent and monochromatic radiation and hence, laser technology. Not all of the interacting fields need to be optical fields, however. In devices that make use of the Pockels effect, an externally applied electric field is used to alter reversibly the refractive index of a material. In a second harmonic generation (SHG) process two photons of circular frequency w can be transformed into one photon of frequency Iw. SHG is the NLO effect used most for the evaluation of /3-tensor elements in solution. 

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]. 

Figure 8. The Pockels effect leads to a change in the refractive index of an electro-optic material due to the application of a static electric field. This can be used to build a Mach-Zehnder intensity modulator, for example, which will have an optical transmission dependent on the electric field applied to the Pockels material.

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... 

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. 

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... 

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)]. 

Technical applications based on the Pockels effect require systems that are non-centrosymmetric on a macroscopic level. This relates particularly to polymeric systems containing physically admixed or chemically incorporated components with permanent dipoles. In such cases, macroscopic second-order nonlinearity can be accomplished by poling, i.e. by aligning the permanent dipole moments of the components with the aid of an external electric field that is applied at temperatures in the vicinity of the polymer s glass transition temperature, Tg. The order thus obtained is frozen-in by cooling to a low temperature T Tg. The refractive... 

The second-order NLO properties are of interest for a variety of NLO processes [1-3]. One of the most relevant is the SHG, originated by the mixing of three waves two incident waves with frequency co interact with the molecule or the bulk material with NLO properties, defined by a given value of the quadratic hyperpolarizability, fi, or of the second-order electrical susceptibility, respectively, to produce a new electrical wave, named SH, of frequency 2co. Another important second-order NLO process is the electrooptic Pockels effect which requires the presence of an external d.c. electric field, E(0), in addition to the optical E co) electrical field. This effect produces a change in the refractive index of a material proportional to the applied electric field, and can be exploited in devices such as optical switches and modulators [1-3]. 

Quadratic Response (3rd rank tensors) (1) electric field effects Linear electrooptic (Pockels) effect, three-wave mixing, SHG. (2) radiation/magnetic field Faraday Effect. 

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