The Electrooptic Effect

The changes in refractive index produced by an electric field E are given by 

Combination of Eqs. (25), (26), (36), and (37) yields the relations between the electrooptic coefficients and the molecular parameters 

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However, its was found possible to infer all four microscopic tensor coefficients from macroscopic crystalline values and this impossibility could be related to the molecular unit anisotropy. It can be shown that the molecular unit anisotropy imposes structural relations between coefficients of macroscopic nonlinearities, in addition to the usual relations resulting from crystal symmetry. Such additional relations appear for crystal point group 2,ra and 3. For the monoclinic point group 2, this relation has been tested in the case of MAP crystals, and excellent agreement has been found, triten taking into account crystal structure data (24), and nonlinear optical measurements on single crystal (19). This approach has been extended to the electrooptic tensor (4) and should lead to similar relations, trtten the electrooptic effect is primarily of electronic origin. 

Electrooptic materials. The dependence of refractive index on the electric field or the lattice polarization is referred to as the electrooptic effect ... 

Electrooptic Measurements. The final characterization method to be discussed is the measurement of the electrooptic coefficient. The electrooptic effect is derived from... 

It should be noted that although /3 at a given frequency is different for different NLO phenomena, both tend to the same zero-frequency limit, /30. Figure 11.3 compares the predictions of the two-level model for the frequency dispersion of the electrooptic effect with that for frequency doubling. While dispersion effects complicate comparison of the intrinsic nonlinearity of various chromophores... 

Fig. 11.3 Variation of fl for frequency doubling (solid lines) and the electrooptic effect (dotted line) with incident light frequency, m, according to the two-level Eqs. (17) and (18), respectively. /J0 is the static hyperpolarizability and a>ge is the transition energy from the ground state to the excited state responsible for / . Note that for frequency doubling there is an additional resonance seen when...

By the HTOF technique, an interference pattern from two ps or ns laser pulses creates a sinusoidal distribution of carriers. Under the influence of an applied field, the carriers separate. As the charge separation proceeds, a space-charge field is created that can be probed with a cw laser through the electrooptic effect. The space-charge field reaches a maximum when the carriers have drifted to a position of anticoincidence with the immobile distribution of carriers of opposite polarity. Further drift causes a decrease of the space-charge field until coincidence is reached again. The diffraction efficiency versus time shows oscillatory behavior. From the time tmax that corresponds to the first maximum, the mobility can be derived from the relationship... 

The electrooptic effect is defined through the optical indicatrix, or the refractive index ellipsoid, which can be written in its principal axes x = 1, y = 2, and z = 3 in the form... 

Knowledge of the electrooptic behavior of the FLCPs is of the utmost importance for display device applications. One relevant parameter in this respect is the response time. As for the spontaneous polarization, the determination of the response time requires a uniformly aligned sample. The test cell is placed between crossed polarizers so that one tilt direction is parallel to the direction of one polarizer. The electrooptic effect is achieved by applying an external electric field across the cell, which switches the side chains from one tilt direction to the other as the field is reversed. A photodiode measures the attenuation of a laser beam when the cell is switched between the two states. Generally, the electrooptical response time is defined as the time corresponding to a change in the light intensity from 10 to 90% when the polarity of the applied field is reversed ( 10-9o)-... 

If a nematic liquid crystal has negligible conductivity the results of Sections 11.2.1-11.2.5 for the Frederiks transition induced by a magnetic field may be directly applied to the electric field case. To this effect, it suffices to substitute H by E and all components of magnetic susceptibility tensor Xij hy correspondent components of dielectric permittivity tensor s,y. From the practical point of view the electrooptical effects are much more important and further on we discuss the optical response of nematics to the electric field. 

Most of the electrooptic effects are based on light scattering or on light absorption by polarizers or by dissolved dyes. Electrooptic effects which belong to the second group are tunable birefringence, the twisted nematic effect and the guest-host effect. 

The electrooptic effect is the effect in which a change in the refractive index of a crystal is produced by an electric field ... 

Much of what has been said above concerning the electrooptic effect also applies mutatis mutandis to the piezooptic effect (variation of refractive index by external mechanical stress). Due to unavoidable dispersion piezooptic coefficients measured by optical techniques can hardly be related to the low-frequency regime for which the definitions of Sect. 6.3 are intended. Determining these constants quasistatically or at sufficiently low frequencies would involve the measurement of permittivity under mechanical stress. Investigations of this type have been made by the group around Newnham and Cross (Uchino et al. (1980), Rittenmyer et al. (1983), Meng and Cross (1985)). 

The surface flexoelectric energy, which is found from (4.2) and (4.3). Attaining the minimum of the nematic free energy, (4.5) or (4.6), it is possible to derive the equilibrium director distribution in a static case. To find the response times, we have to solve the equations of nematodynamics in the electric field. The corresponding analysis shows that the director reorientation is always accompanied by the macroscopic flow, the so-called backflow [5]. (The only exclusion is the pure twist rotation of the director [1].) Backflow considerably affects the characteristic times of the electrooptical effects in uniform structures, especially in the case of strong deformations of the initial director orientation [3, 5]. 

The intensities J(A) in the on- and off-states are averaged with the function of the sensitivity of the human eye t/(A) and the energy distribution of the illumination source H X) over the visible spectrum (380-780 nm). The electrooptic effect in the twist cell placed between parallel and crossed po-laroids is called, in [98], the normally black and normally white mode, in accordance with the appearance of the twist cell in the off state. Contrast ratios in the white mode are considerably higher than in the black mode, as the luminance in the on state for a normally white mode could be very small and limited only by the quality of polaroids and orientation. 

Prom the point of view of the application the electrooptical effect in blue phases may become of interest for relatively low-voltage and relatively fast light modulators [101]. A beautiful color switching in the submillisecond range has been demonstrated on blue phases in [102]. 

The switching time in the electrooptical effects in FLCs is defined by the rotational viscosity which characterizes the energy dissipation in the director reorientation process [6, 10, 31-34]. According to the FLC symmetry, two viscosity coefficients should be taken into account, and 7, which determine the corresponding response rates with respect to the director angles 9 and p (Fig. 7.5). The relevant dynamic equations take the form [4, 20]... 

The theoretical and experimental results on physical properties of liquid crystals were reviewed by de Gennes [15], Chandrasekhar [16], de Jeu [17], Sonin [18], Belyakov and Sonin [19], Vertogen and de Jeu [20], and others. The electrooptical effects were discussed by Kapustin [21], Pikin [22], and Blinov [23]. Recent results on liquid crystalline materials and their application in devices can be found in [24-26, 29]. 

In this book the authors present a complete and readily understood treatment of virtually all known phenomena occurring in liquid crystals under the influence of an electric field. In the first three chapters (Chapters 1-3) bulk and surface properties of liquid crystalline materials are discussed. The next two chapters (4, 5) are devoted to consideration of the electrooptical effects due to the formation of uniform and spatially modulated structures in nematics. In Chapters 6 and 7 the electrooptical properties of the cholesteric and smectic mesophases are presented, including a discussion of ferroelectric materials. Major emphasis is given to explaining the qualitative aspects of the phenomena and to portraying their physical basis. The prospects for the practical application of electrooptical effects are also discussed (Chapter 8). 

Poly(phenylenevinylene) has been considered for many different applications due to its importance in nanoscale electronic devices. One such application is the search for efficient light emitting diodes. This property is the result of the electrooptical effect and constitutes an important area of modern research in theory as well as experiment. The efficiency of the nonradiative... 

The electrooptic effect is simply the change in an optical property, namely refractive index, with an applied field. Changes in refractive indices are relatively small, on the order of 10 however, this is sufficient to modulate the phase or intensity of transmitted light. A half-wavelength change in phase is sufficient to modulate polarized light from 0 to 100 percent transmission. 

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... 

Application of field causes a distortion of ABy in the optical indicatrix. The electrooptic effect can be described in terms of the dependence of the relative impermeability ABy... 

The viscosity parameters associated with the electrooptic effect, and the increased torque that can be exerted on the liquid crystal by an applied electric field due to the spontaneous polarization, result in an electrooptic effect that can be several orders of magnitude faster than in nematics. Switch-... 

How to produce analog gray levels in an SSFLC display is perhaps not so evident, because the electrooptic effect offers two optical states, hence it is digital. Nevertheless, the shape of the hysteresis curve reveals that there must be small domains with a slightly varying threshold, in some analogy with the common ferromagnetic case. Normally, however, the flank of the curve is not sufficiently smeared out to be controlled and to... 

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