Optical-field-induced director reorientation

Optical field-induced director reorientation is responsible for the largest nonlinear optical susceptibility observed in liquid crystals, the largest in any known material. Although the process is slow, the nonlinearity is about 10 times greater than that of CS2. Because of its magnitude, the orientational nonlinearity of liquid crystals has been termed giant optical nonlinearity (GON). 

Liquid crystals are generally characterized by the strong correlation between molecules, which respond cooperatively to external perturbations. That strong molecular reorientation (or director reorientation) can be easily induced by a static electric or magnetic field is a well-known phenomenon. The same effect induced by optical fields was, however, only studied recently. " Unusually large nonlinear optical effects based on the optical-field-induced molecular reorientation have been observed in nematic liquid-crystal films under the illumination of one or more cw laser beams. In these cases, both the static and dynamical properties of this field-induced molecular motion are found to obey the Ericksen-Leslie continuum theory, which describe the collective molecular reorientation by the rotation of a director (average molecular orientation). 

The most widely utilized optical nonlinearity of liquid crystals is electric-field-induced director reorientation, which is used in display application. Although it is usually dealt with under the heading of electro-... 

Simplified Treatment of Optical Field-Induced Director Axis Reorientation... 

As one can see from the preceding discussions on optical field induced director axis reorientation in hquid crystals, the torque exerted by the optical field on the director axis is basically quadratic in the field amplitude. Except for its dispersion influence on the optical dielectric constant 8(co), the frequency of the electric field is basically not involved. Furthermore, if two or more fields are acting on the director axis, the resulting torque exerted on the director axis is simply proportional to the square amplitude of the total fields. Accordingly, it is possible to enhance the optical field induced effect by application of a low-frequency ac or dc electric field, much as the optically addressed liquid crystal spatial light modulator discussed in Chapter 6. In the latter, the responsible mechanism is the photoconduction generated by the incident optical field in the semicondnctor layer adjacent to the liquid crystals. 

A well-known nonlinear process taking place in the liquid state of anisotropic molecules is the optical-field induced birefringence (optical Kerr effect ). This nonlinearity results from the reorientation of the molecules in the electric field of a light beam. In the isotropic phase the optical field perturbs the orientational distribution of the molecules. In the perturbed state more molecules are aligned parallel to the electric field than perpendicularly to it and as a consequence the medium becomes birefringent. On the other hand in liquid crystals the orientational distribution of the molecules is inherently anisotropic. The optical field, just as a d.c. electric or magnetic field, induces a collective rotation of the molecules. This process can be described as a reorientation of the director. 

Although by far nematics are the most extensively used ones, other phases (smectic, cholesteric, etc.) of hquid crystals and mixed systems such as polymer-dispersed liquid crystals capable of field-induced reorientation have also been employed for electro-optical studies and applications. They are basically based on the same basic mechanism of field-induced director axis reorientation similar to nematic hquid crystals i.e., the response is Kerr like in that it is independent of the direction of the electric field. In general, nematic liquid crystal electro-optics devices switch at a rate of several terrs of hertz, corresponding to response times from a few to tens of microsecorrds. 

The sketch of the experimental set-up is shown in Figure 1. A Q-switched Nd-YAG laser, operating at 1.06 ixm and a pulse repetition 2-12.5 Hz was used to provide the fundamental (pump) beam. The peak power was 200-300 kW. The beam was focused with a 43 cm lens so that the power density on the sample placed in a thermostate was about 100-200 MW-cm. " For investigation the field-induced SHG, short pulses (tp = 20 fxs) of high voltage Up = 4kV) were provided by an electrical generator. The pulse duration was chosen from the condition Trelaxation time for dipolar (Debye) polarization, and T is the director reorientation time. Under such a condition, molecular dipoles are oriented by the field but the Fredericks transition does not take place. The sensitivity of our set-up was about 30 photons of the optical second harmonic per single laser pulse. The cell temperature was stabilized with an accuracy of 0.1° K. 

Field-induced reorientation of the director with attendant optical changes has recently been used in a novel application with the potential for large-area LCDs polymer dispersed LCs (PDLCs). A PDLC is a microemulsion of MLC dispersed in a conventional transparent polymer film. In the off state there is a mismatch between the refractive index of the MLC and that of the host polymer film. Hence the dispersion of MLC droplets scatters light very effectively, giving an optically opaque film (Fig. 5.14, left-hand side). On application of an external electric field (across a capacitor-like transparent coating of tin oxide on both sides of the polymer film), the director assumes the same orientation in all of the microdroplets. If the... 

The prediction [19] that a low power optical field can induce appreciable director reorientation just above the dc field induced Freedericksz transition has been verified experimentally [20,21] concurrently with experimental and theoretical work on optical reorientation [22-24]. Since then, it has become one of the most intensively studied nonlinear optical effects in liquid crystals [3]. The phenomenon originates from the tendency of the director to align parallel to the electric field of light due to the anisotropic molecular polarizability. The free energy density arising from the interaction of a plane electromagnetic wave and the liquid... 

In Chapters 6 and 7, we diseuss these field-induced nematic director axis reorientations in detail in the context of electro-optical switching and display applications. 

The preceding discussion and results apply to the case where an extraordinary wave laser is obliquely incident on the (homeotropic) sample (i.e., (3 0). For the case where a laser is perpendicularly incident on the sample (i.e., its optical electric field is normal to the director axis), there will be a critical optical field >, the so-called Freedericksz transition field [see Eq. (8.54)], below which molecular reorientation will not take place. Second, the tum-on time of the molecular reorientation depends on the field strength above Ep (i.e., on op-. ). For small E op the tum-on time can approach many minutes Studies with nanosecond and picosecond lasers" have shown that under this perpendicularly incident (i.e., (3=0) geometry, it is very difficult to induce molecular reorientation through the mechanism discussed previously. 

In this section, we discuss a mechanism for enhanced optical nonlinearity in which the photoinduced charges and fields occur within the liquid crystal. It is well known that dc field induced cmient flow in nematic liquid crystals, which possess anisotropic conductivities, could lead to nematic flows and director axis reorientation, and to the creation of a space-charge field. The charged carriers responsible for the electrical conduction come from impurities present in the otherwise purely dielectric nematic liquid crystal. If these impurities are photoionizable, an incident optical intensity [e g., an intensity grating created by the interference of two coherent optical beams (see Fig. 8.13)], it is possible, therefore, to create a space-charge... 

Holographic polymer dispersed liquid crystals (H-PDLCs) are obtained by photopolymerisation of a hquid crystal-prepolymer mixture in the interference field of two or more laser beams [14,15]. This induces phase separation in which hquid crystalline material predominantly congregates in dark regions of the optical interference pattern [16,17]. As a result, holographic gratings with extremely high refractive-index contrast are formed. In addition, the diffraction efficiency of these gratings is electrically switchable the apphcation of an electric field results in reorientation of the nematic director field within... 

The optical reorientation processes discussed up to now were qualitatively similar to the corresponding low-frequency field effects. As mentioned earlier this is not always the case. A breakdown of the analogy with static fields was first reported by Zolotko et al. who observed in a homeotropic layer a drastic increase of the Freedericksz threshold power for an o-ray as the angle of incidence was increased. Durbin et al. mentioned that in a planar cell Freedericksz transition cannot be induced by a light beam polarized perpendicularly to the director. From a simple analogy one would expect for these cases a threshold not deviating significantly... 

The reorienution of the director of a nematic liquid crystal induced by the field of a light wave is considered. An oblique (with respect to the director) extraordinary wave of low intensity yields the predicted and previously observed giant optical nonlinearity in a nematic liquid crystal. For normal incidence of the light wave on the cuvette with a homeotropic orientation of the nematic liquid crystal, the reorientation appears only at light intensities above a certain threshold, and the process itself is similar to the Fredericks transition. The spatial distribution of the director direction is calculated for intensities above and below threshold. Hysteresis of the Fredericks transition in a light field, which has no analog in the case of static fields, is predicted. 

In general, the distortions on the electronic wave function of liquid crystal molecules caused by an applied field do not cause appreciable change to its contribution to the refractive indices (see Chapter 10). However, the orientation of the molecules can be dramatically altered by the apphed field. This process alters the overall optical properties of the medium and is the principal mechanism used in liquid-crystal-based electro-optical devices. As noted in Section 6.2.2, the electrically induced orientational refractive index changes could be Pockel or Kerr effect. In this and the next sections, we shall focus on nematic liquid crystals in which the director axis reorientation is a Kerr-like effect that is, the process is quadratic in the applied field. 

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