Effective electro-optic coefficient

Determination of material parameters gain factor T, effective electro-optic coefficient (( reff) and effective trap density AAir... 

The effective electro-optic coefficient, r, of a material is related to chromophore number density, N, chromophore molecular first hyperpolarizability, P, and acentric order parameter, , by... 

The sign and magnitude of the effective electro-optic coefficient Yeff depends on the symmetry class of the ciystal and the direction of the electric field. 

The scattering pattern contains additional information about the scattering process itself as well as for the determination of material parameters. We will demonstrate in the following, that both the angular dependence of the holographic gain and the product of the effective linear electro-optic coefficient with the electron-hole competition factor as well as the effective trap density can be determined from the spatial distribution of the scattering pattern as a function of temperature [7],... 

A complete description of the electro-optic effect for single crystals necessitates full account being taken of the tensorial character of the electro-optic coefficients. The complexity is reduced with increasing symmetry of the crystal structure when an increasing number of tensor components are zero and others are simply interrelated. The main interest here is confined to polycrystalline ceramics with a bias field applied, when the symmetry is high and equivalent to oomm (6 mm) and so the number of tensor components is a minimum. However, the approach to the description of their electro-optic properties is formally identical with that for the more complex lower-symmetry crystals where up to a maximum of 36 independent tensor components may be required to describe their electro-optic properties fully. The methods are illustrated below with reference to single-crystal BaTi03 and a polycrystalline electro-optic ceramic. 

It has been established experimentally that the origin of the electro-optic effect in organic materials is largely electronic. This implies that the linear electro-optic coefficient can be estimated from the second harmonic coefficient. By properly accounting for the dispersion (using a two level model), the electronic contribution to the electro-optic coefficient is calculated to be r5 3 - 2.4 0.6 x 10 m/V at X-O.S m. Measured values of the electro-optic coefficient are in agreement within experimental uncertainty. These values compare favorably with that of GaAs (r4i - 1.2 x 10 m/V). 

In the literature however, other related parameters, besides x are often used to describe the macroscopic second-order NLO properties of materials. The SHG nonlinear coefficient d and the linear electro-optic coefficient r are the parameters commonly used for second-harmonic generation and the Pockels effect respectively [3, 5]. They are related to x according to Eqs. (4) and (5). 

The DPNA chromophore has a small dipole moment, less than 4 D, as calculated using the partial charges on the atoms assigned by the force-field. It would be difficult to see the concentration effect of the roll-off of the electro-optic coefficient with that small of a dipole moment. 

Figure 10. Concentration effect of ezFTC chromophores in PMMA for the parameters corresponding to a value p = 5.65, = 1 kV/pm, 7" = 600K. The linear increase in the electro-optic coefficient with an increase in concentration corresponds to the poling field-dipole interaction energy overwhelming the inter-chromophore interactions. Solid line is a linear fit to the data (circles)...

Ferroelectric lithium niobate (LiNbOs) has been of considerable interest because of its nonlinear optical properties. Conversion of infrared into visible radiation in LiNb03 crystals has been observed (Midwinter and Warner, 1967 Arutyunyan and Mkrtchyan, 1975). Electro-optic coefficients of LiNbOs have been determined for a wide range of frequencies ranging from the visible (Smakula and Claspy, 1967) to the millimeter-wave portion of the spectrum (Vinogradov et al., 1970). Other nonlinear optical properties such as photovoltaic effects (Kratzig and Kurz, 1977) and optically induced refractive index changes (Ashkin et al., 1966 Chen, 1969) have also been observed. 

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). 

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. 

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 ... 

In the external electric field the uniaxial crystal becomes biaxial. In addition to the natural birefringence of the uniaxial crystal, a field-induced birefringence is generated, which is approximately proportional to the field strength E [4.56]. The changes of no or n by the electric field depend on the symmetry of the crystal, the direction of the applied field, and on the magnitude of the electro-optic coefficients. For the KDP crystal only one electro-optic coefficient < 35 = —10.7 x 10 [ni/V] (see Sect. 5.8.1) is effective if the field is applied parallel to the optical axis. 

FIGURE 7.1.5 Birefringence induced by the electro-optic effect and the electric field, (a) Linear electro-optic effect. Linear electro-optic coefficient gradient, (b) Quadratic electro-optic effect. Coefficient of is proportional to (Rn — Rn) value. 

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