Refractive index electro-optic effects

Changes in the refractive index by the electro-optic effect lead to phase encoding of the incident light distribution... 

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 . 

The linear electro-optic effect (see Chapter 4) transfers the periodically modulated space-charge field into a refractive index grating ... 

When investigating the polar structure by photo-induced light scattering we assume that the largest contribution to the initial optical noise is due to diffraction of the pump beam on optical inhomogeneities located at boundaries of ferroelectric domains [9], Figure 9.12 illustrates this concept schematically. Internal electric fields Ei (random fields) yield local perturbations 5n of the index of refraction via the linear electro-optic effect 5n = - n rssEi. 

Figure 9.12 Seed scattering at refractive index modulations induced by localized internal random fields via the electro-optic effect. The internal fields are also responsible for the formation of a rich ferroelectric domain structure. Here, a periodic sequence of domains with lengths A d is shown. Note, that the grating period of the refractive index modulation As is equal to the lengths of the ferroelectric domains.

The manifestation of the presence of polar nanodomains in strong rls in terms of the electro-optic effect was first demonstrated by Burns and Dacol [3] in measurements of the T dependence of the refractive index, n. For a normal ABO3 fe crystal, starting in the high-temperature PE phase, n decreases linearly with decreasing T down to Tc at which point n deviates from linearity. The deviation is proportional to the square of the polarization and... 

However, the linear response of a dielectric to an applied field is an approximation the actual response is non-linear and is of the form indicated in Fig. 8.6. The electro-optic effect has its origins in this non-linearity, and the very large electric fields associated with high-intensity laser light lead to the non-linear optics technology discussed briefly in Section 8.1.4. Clearly the permittivity measured for small increments in field depends on the biasing field E0, from which it follows that the refractive index also depends on E0. The dependence can be expressed by the following polynomial ... 

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. 

The electro-optic effect leads to the modification of the refractive index of a suitable material when an electric field is applied (Figure 8). The electro-optic effect must be present in a photorefractive material, so that the space charge electric field pattern due the relocated charges will lead to a patterned refractive index in the material this is a hologram. 

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.

The linear electro-optic effect arises from the ability of a material medium to change its refractive index under the action of an external electric field. This variation is proportional to the external field strength... 

Electro-optic effects refer to the changes in the refractive index of a material induced by the application of an external electric field, which modulates their optical properties [61, 62], Application of an applied external field induces in an optically isotropic material, like liquids, isotropic thin films, an optical birefringence. The size of this effect is represented by a coefficient B, called Kerr constant. The electric field induced refractive index difference is given by... 

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). 

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. 

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)]. 

Electro-optic effects describe a change in optical properties arising from an applied electric field. This can include changes in colour or optical absorption, characteristic of electrochromic materials (Section 9.6), or a change in refractive index. In perovskites, it is this latter effect that is important. These crystals have been used in electro-optic devices to modulate the phase, the amplitude or the polarisation of a light beam traversing the medium and so function as shutters and other components in optical/electronic circuits. 

The electro-optic effect comes about in the following way. When a static or slowly varying electric field is applied to a solid, it causes a displacement of the atom cores and electrons and hence alters the refractive index of the solid. The change is given by... 

Figure 10.13 shows experimental setup for the optical characteristic measurement of PMNT ceramics [133]. The size of PMN-PT ceramic sample was 5 mm X 2 mm x 1 mm for length x width x thickness. Ti/Pt/Au layers were sputtered on both surfaces of the ceramics as electrodes. Two collimators were used to collimate the incident beam and receive the transmission beam. The output beam was detected by using an optical spectrometer and phase demodulation. Because the PMN-PT electro-optic ceramics have a large refractive index, i.e., n = 2.465, the ceramic samples could be considered as a Fabry-Perot (FP) resonator, which can be used to measure the electric hysteresis and thermo-optic coefficient. The applied voltage generated a transverse electro-optic effect for the transmission light beam. 

The material has to simultaneously possess photoconductivity and electro-optical effect to have photorefractive properties. Typical candidate materials have low glass transition temperature, frequently reduced by the plasticizer. Diffraction efficiency is improved by addition of the plasticizer because chromophore groups have higher rotational mobility and increase their contribution of birefringence to the total refractive index modulation. ... 

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