Electro-optical constants

Uchiki, H., and T. Kobayashi. 1988. New determination of electro-optic constants and relevant nonlinear susceptibilities and its application to doped polymer. / Appl Phys 64 2625-2629. 

Here, the first term is referred to as the first-order electro-optic effect (Pochels effect), and the second term is referred to as the second-order electro-optic effect (Kerr effect). The coefficients rij/, and Ry/, are ternary and quaternary tensor quantities known as the Pochels constant (first-order electro-optic constant) and Kerr constant (second-order electro-optic constant), respectively. As Table 7.1.3 shows, a second-order electro-optic effect is present in materials, including isotropic materials such as glass, whereas first-order electro-optic effects are only observed in piezoelectric crystals. In Table 7.1.3, electro-optic effects are present in crystals belonging to point groups. 

Measuring F therefore allows An to be determined, and the electro-optic constants and Rc can then be found from Eq. 10. 

Table 4.1-149 Electro-optical constants of zinc compounds. Under the influence of an electric field, the refractive index changes in accordance to the nonlinearity of the dielectric polarization (Pockels effect). Crystals with hexagonal symmetry have three electro-optical constants rsi, 733, 751 crystals with cubic symmetry have only one electro-optical constant 741...

Crystal Electro-optical constant (10- cm/V) X (nm) Temperature (K) Remarks... 

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

Electrical resistivity see Resistivity Electro-optic constants, 12-165 to 178 Electrochemical Series, 8-20 to 29 Electrode potential... 

UCHIKI H. and KOBAYASHI T., (1988). "New Determination of Electro-Optic Constants and Relevant Nonlinear Susceptibilities and its Application to Doped Polymer" J. Appl. Phys., 64, 2625-2629. 

In the previous sections, we have seen how computer simulations have contributed to our understanding of the microscopic structure of liquid crystals. By applying periodic boundary conditions preferably at constant pressure, a bulk fluid can be simulated free from any surface interactions. However, the surface properties of liquid crystals are significant in technological applications such as electro-optic displays. Liquid crystals also show a number of interesting features at surfaces which are not seen in the bulk phase and are of fundamental interest. In this final section, we describe recent simulations designed to study the interfacial properties of liquid crystals at various types of interface. First, however, it is appropriate to introduce some necessary terminology. 

Photoelectrochemical techniques have been utilized to determine the minority (electron) diffusion length (L) and other electrical parameters of p-ZnTe [125] and p-type Cdi-jcZnjcTe alloys [126]. In the latter case, the results for a series of single crystals with free carrier concentration in the range 10 " -10 cm (L = 2-4 xm, constant Urbach s parameter at ca. 125 eV ) were considered encouraging for the production of optical and electro-optical devices based on heterojunctions of these alloys. 

The proportionality constants a and (> are the linear polarizability and the second-order polarizability (or first hyperpolarizability), and x(1) and x<2) are the first- and second-order susceptibility. The quadratic terms (> and x<2) are related by x(2) = (V/(P) and are responsible for second-order nonlinear optical (NLO) effects such as frequency doubling (or second-harmonic generation), frequency mixing, and the electro-optic effect (or Pockels effect). These effects are schematically illustrated in Figure 9.3. In the remainder of this chapter, we will primarily focus on the process of second-harmonic generation (SHG). 

The interest in efficient optical frequency doubling has stimulated a search for new nonlinear materials. Kurtz 316) has reported a systematic approach for finding nonlinear crystalline solids, based on the use of the anharmonic oscillator model in conjunction with Miller s rule to estimate the SHG and electro optic coefficients of a material. This empirical rule states that the ratio of the nonlinear optical susceptibility to the product of the linear susceptibilities is a parameter which is nearly constant for a wide variety of inorganic solids. Using this empirical fact, one can arrive at an expression for the nonlinear coefficients that involves only the linear susceptibilities and known material constants. 

Group theory can tell us which elements of K are non-zero and about equalities between non-zero elements, but numerical factors (like /2 in the first row of K) are simply a matter of how the Kiq are defined in terms of the constants K, K, K, and Kq, this being usually done in a way that reduces the number of numerical factors. In LiNb03 the electro-optic coefficient r33 is more than three times r13, which gives rise to a relatively large difference in refractive index in directions along and normal to the optic (z) axis, thus making this material particularly useftd in device applications. 

In anisotropic materials, the electronic bonds may have different polarizabilities for different directions (you may think of different, orientation-dependent spring constants for the electronic harmonic oscillator). Remembering that only the E-vector of the light interacts with the electrons, we may use polarized light to test the polarizability of the material in different directions, lno is one of the most important electro-optic materials and we use it as an example. The common notations are shown in Figure 4.7. If the E-vector is in plane with the surface of the crystal, the wave is called a te wave. In this example, the te wave would experience the ordinary index na of LiNbOs (nG 2.20). If we rotate the polarization by 90°, the E-ve ctor will be vertical to the surface and the wave is called tm. In lno, it will experience the extraordinary index ne 2.29. Therefore these two differently polarized waves will propagate with different phase velocities v c/n. In the example of Figure 4.7, the te mode is faster than the tm mode. 

This ellipsoid is tilted with respect to the x, y, z-axes and the parameters By are a function of the electric field E. In order to couple the six constants By to the three components of E, 18 coefficients are needed. They are arranged in the form of a 3 x 6 matrix, which is sometimes called the electro-optic tensor ... 

Assessing thermal and photochemical stability is important. Thermal stability can be readily measured by measuring properties such as second harmonic generation as a function of heating at a constant rate (e.g., 4-10 °C/min) [121]. The temperature at which second-order optical nonlinearity is first observed to decrease is taken as defining the thermal stability of the material [2,3,5,63,63]. It is important to understand that the loss of second-order nonlinear optical activity measured in such experiments is not due to chemical decomposition of the electro-optic material but rather is due to relaxation of poling-induced acentric... 

A detailed consideration of more advanced theoretical treatments clarifies the role played by the polymer dielectric constant. In the absence of intermo-lecular electrostatic interactions, one would desire the lowest possible dielectric constant, e.g., PMMA would be a better host matrix than polycarbonate. This is because the dielectric constant of the polymer host would act to attenuate the poling field felt by the chromophores. On the other hand, in the presence of intermolecular electrostatic interactions, optimum electro-optic activity will be achieved for polymer hosts of intermediate dielectric constant. The dielectric constant of the host acts not only to attenuate the externally applied poling field, but also fields associated with intermolecular electrostatic interactions. 

The constants ryk and fyk are the Pockels electro-optic coefficients, and Rijkl and gyki the Kerr coefficients. They are related as follows ... 

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. 

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