Optical Freedericksz field

A. J. Karn, S. M. Arakelian, Y. R. Shen and H. L. Ong, "Observation of Magnetic-field-induced First-order Optical Freedericksz Transition in... 

The dynamics of reorientation in static fields was studied by Pieranski et o/. Durbin et investigated the dynamic behaviour of the optical Freedericksz... 

In 1990, Janossy showed that a small amount of dye added to a nematic liquid crystal dramatically reduces the threshold intensity of the optical Freedericksz transition [68]. Subsequently, it was demonstrated that the underlying process is an optically driven Brownian ratchet mechanism [69-71]. Here, energy, but not momentum, from the radiation field causes unidirectional continuous rotation of dye molecules in the nematic, exerting a torque on the director that exceeds the direct optical torque by orders of magnitude. Similar mechanisms could, in principle, be realized in LCEs. Whether such processes are viable in overcoming the orienting effect of the network is not clear the viability of such Brownian motor processes in LCEs is an intriguing open problem. 

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. 

Figure 12.7 shows a numerical simulation for an input beam power of 3.9 mW and a beam waist of 3 pm (the laser used is the 514.5 nm fine of an Ar laser). In the absence of the external bias (0q=O), the linearly polarized electric field of tire input light is perpendicrrlar to the director axis. Since its intensity is below the optical Freedericksz threshold value (cf. Chapter 8), it cannot create director axis reorientation that is, there is no self-action effect. The focused beam thus diffracts freely in X and as it propagates along z (Fig. 12.7a). When the external voltage above the Freedericksz threshold is applied, the director axis is reoriented (for the numerical simulation, the angle is assumed to be 45°). In this above Freedericksz condition, the ophcal field will reorient the director axis without threshold, and initiate the self-guiding process leading to the formation of a spatial soliton—a beam that maintains its beam waist over marty Rayleigh lengths (see Fig. 12.7b).

Due to their large optical anisotropies, liquid crystals (LCs) have a large optical nonlinearity which is the result of molecular reorientation (Freedericksz transition) in an external field which exceeds the critical field [1], The high external field inhibits the application of LCs, and decreasing the threshold as low as possible is a difficult task [2], LCs doped with a small amount of absorbing dyes that could decrease the needed optical field intensity have been reported [3]. The basic assumption is that the anomalous reorientation of the director results from the interaction between the excited dye molecules and the host. However, this sample would easily degrade under the influence of laser radiation. 

Molecular Alignment in A.C. Electric and Static Magnetic Fields Parallel to Each Other. Freedericksz and Zwetkoff (7) have investigated the ordering in the anisotropic liquid phase of p-azoxyanisole using optical... 

Fig. 3.4.3. (a) The usual experimental configuration for the optical observation of the Freedericksz effect. Li t is incident normal to the film. However, for reasons discussed in the text, this arrangement is unsuitable for observing a twist deformation, b) Oblique configuration which enables the optical detection of a twist deformation. The magnetic field is perjjendicular to the plane of the paper... 

J. J. Wu, G. S. Oug et ah, Obseriuition of Optical Field Induced First-Order Electric Freedericksz Transition and Electric Bistability in a parallel Aligned Nematic Liquid-Crystal film, Appl. Phys. Lett. (1988) 152... 

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... 

Optical-Field-Induced Birefringence and Freedericksz Transition in a Nematic Liquid Crystal... 

Optical-field—induced birefringence in nematic 4-cyano-4 -pentylbiphenyl was measured with cw pump and probe beams, and the optical-field-induced Freedericksz transition was observed for the first time. The results are in quantitative agreement with the theoretical prediction. 

The dynamic behavior of the optical-field-in-duced Freedericksz transition is also analogous to the dc case. The initial response of the induced molecular reorientation to the laser switch-on and the long-time response to the laser switch-off are both exponential with relaxation times Tqjj and Toff, respectively. 

To observe the optical-field-induced Freedericksz transition, the angle of incidence of the pump beam was set at 0°. The observed birefringence versus pump intensity at Tffj - T = 9.2 K is shown in Fig. 1. It exhibits a threshold intensity at 155 W/cm. According to Eq. (5),... 

As is shown in Fig. 5, the experimentally observed threshold field dependence on wo/d also follows the theoretical prediction. For E46, a 100-Axm sample has a Freedericksz transition field intensity of 200 W/cm (using the values = 0.3, K lO" , d = 0.01 cm, and n no 1.5). For large values of Wo/d (for example, wo/d > 5), the observed threshold field approaches this value. However, as the incident laser beam size decreases to a value comparable with the thickness d or less, the threshold optical intensities increase dramatically. At wq d, the threshold intensity increases by almost an order of magnitude. In general, the experimentally observed relative increase of the threshold field is slightly larger than the theoretical value, probably because of a systematic difference between the experimental observation of the onset of reorientation (by the appearance of the self-focusing effect on the exit Ar+ laser beam) and also... 

Observation of optical field induced first-order electric Freedericksz transition and electric bistability in a parallel aligned nematic liquid-crystal film... 

Optical field induced first-order electric Freedericksz transition and electric bistability in a homogeneously aligned nematic film is first observed. It is experimentally demonstrated that an applied optical field can transform the electric Freedericksz transition from second order to first order. The molecular reorientation as a function of electric field is then characterized by a hysteresis loop which exhibits the electric bistability. The results are in good agreement with theoretical predictions. 

Recently, particular attention has been devoted to the first-order Freedericksz transition (FT), molecular reorientation, and bistability in nematic liquid crystals (NLC s). In the last few years, Ong has shown that all of the electric and magnetic FT s and most of the optical FT s in a nonconducting homogeneous or homeotropic NLC are second-order transitions. However, applying a suitable static field, the second-order optical FT can be converted to first order in all existing NLC s. Similarly, applying a suitable optical field, the second-order electric or magnetic FT can also be converted to first order ... 

The optical-field-induced Freedericksz transition for a twist deformation by a normally incident laser beam in a planar-aligned nematic liquid crystal is studied. The Euler equation for the molecular director and the equations describing the evolution of the beam polarization in the birefringent medium are solved simultaneously in the small-perturbation limit. The stability of the undistorted state is investigated. An alternate series of stable and unstable bifurcations is found. This phenomenon has no analog in the Freedericksz transition induced by dc electric and magnetic external fields. 

When a light beam linearly polarized in the x-y plane with the elastic field directed at an angle to they axis is normally incident on the SmC layer, there is an additional term in the total free energy density of the system due to the optical field. For the discussion of the optical-field-induced Freedericksz transition, the total free energy density F (erg/cm ) can be written as... 

S. D. Durbin, S. M. Arakelian et al.. Optical-Field-Induced Birefringence and Freedericksz Transition in a Nematic Liquid Crystal, Phys. Rev. Lett. (1981) 107... 

From the point of view of physics, LCs are partially oriented fluids that exhibit anisotropic optical, dielectric, magnetic, and mechanical properties. The most important property of LCs is the reorganization of their supramolecular structures on external stimuli such as electric and magnetic fields, temperatnre, and mechanical stress, which lead to changes in their optical properties. In particular, electric tiled-induced control of optical properties of LCs (electro-optical effects based on the Freedericksz transition ) is at the heart of the multi-billion dollar liquid crystal display (LCD) industry. Most current LCD technologies rely on nematic " and to a lesser extent on ferroelectric LCs, while the recently discovered bent-core and orthoconic LCs still require significant investment into fundamental research and development. These and other applications and technologies continne to drive the search for new liquid crystal materials, and provide impetus to continue fundamental studies on new, often exotic, classes of compounds. 

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... 

Before giving analytical expressions for the director deformations in Freedericksz cells, we will summarize the magnetic and electrical methods. The advantage of electro-optical measurements is that the cell thickness does not enter the equations and is therefore ruled out as an error source. Furthermore, the electric field can always be considered strictly perpendicular to the sample plane. On the other hand, in the electric method conductivity effects can influence the measurements and exact knowledge of and is required to extract the second elastic constant from the birefringence or capacitance characteristics. Moreover, the electric measurement is restricted... 

Deuling HJ, Helfrich W (1974) Hysteresis in the deformation of nematic liquid crystal layers with homeotropic orientation. Appl Phys Lett 25 129-130 Durbin SD, Arakelian SM, Shen YR (1981) Optical-field-induced birefringence and Freedericksz transition in a nematic liquid crystal. Phys Rev Lett 47(19) 1411-1414 Freedericksz V, Zolina V (1933) Forces causing the orientation of an anisotropic liquid. Trans Faraday Soc 29 919-930... 

Shi J (2002) Criteria for the first order Freedericksz transitimrs. Liq Cryst 29(1) 121-125 Shi J, Yue H (2000) Surface- and optical-field-induced Freedericksz transitions and hysteresis in a nematic cell. Phys Rev E 62(l) 689-698... 

Yihnaz S, Melik H, Angay F, Emek M, Yildirim A (2008) Optical properties of aligned nematic liquid crystals in electric field. J Mod Phys 2 248-255 Zakhlevnykh AN (2004) Threshold magnetic fields and Freedericksz transition in a ferronematic. J Magn Magn Mater 269 238-244... 

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