Liquid crystals nonlinear studies

Srajer, G Fraden, S., and Meyer. R. B., Field-induced noncqulibrium periodic structures in nematic liquid crystals nonlinear study of the twist Frederiks transition, Phys. Rev. A, 39, 4828-4834 (1989). 

In the present volume we discuss a relatively new and rapidly developing branch of the field, namely nonlinear optical effects in liquid crystals. Optical studies have always played a significant role in liquid crystal science. Research of optical nonlinearities in liquid crystals began at the end of the sixties. Since then it became a powerful tool in the investigation of symmetry properties, interfacial phenomena or dynamic behaviour. Furthermore, several new aspects of nonlinear processes were demonstrated and studied extensively in liquid crystals. The subject covered in this book is therefore of importance both for liquid crystal research and for nonlinear optics itself. 

SAMs are generating attention for numerous potential uses ranging from chromatography [SO] to substrates for liquid crystal alignment [SI]. Most attention has been focused on future application as nonlinear optical devices [49] however, their use to control electron transfer at electrochemical surfaces has already been realized [S2], In addition, they provide ideal model surfaces for studies of protein adsorption [S3]. 

The unique properties of liquid crystals have also provided opportunity for study of novel nonlinear optical processes. An example involves the ability to modify the pitch of cholesteric liquid crystals. Because a pseudo-wave vector may be associated with the period of pitch, a number of interesting Umklapp type phasematching processes (processes in which wave vector conservation is relaxed to allow the vector addition to equal some combination of the material pseudo-wave vectors rather than zero) are possible in these pseudo-one-dimensional media. Shen and coworkers have investigated these employing optical third harmonic generation (5.) and four-wavemixing (6). 

Polymer-based photochromic systems have been studied extensively and are attractive in terms of practical applications because of their advantages of stability and processability. A number of reviews and articles dealing with various aspects of photochromic polymers and photoactive biomaterials have been published. 68 Chiral photochromic peptides are discussed in Chapter 13, and photochromic liquid crystals and polymers for holographic data storage and nonlinear optics have been reviewed. 69 Specific stereochemical effects in chiral photoresponsive polymers include ... 

As has already been seen these complexes have interesting properties in the fields of nonlinear optics and thin films. Indeed, it was the fact that such complexes were available from liquid-crystal projects that prompted our studies. The work with Rh(I) and Ir(I) complexes was... 

A number of fluids mentioned throughout the text that are of importance in physicochemical hydrodynamics do not behave in the Newtonian fashion outlined in Section 2.2. That is, the stress tensor is not a linear function of the rate of strain tensor. Such nonlinear fluids are termed non-Newtonian and the study of their behavior falls under the science of rheology, which deals with the study of the deformation and flow of matter. The materials encompassed by this broad subject cover a spectrum from Newtonian fluids at one end to elastic materials at the other with such fluids as tars, liquid crystals, and silly putty in between. Among the fluids we have discussed in the text that do not exhibit a Newtonian behavior are some polymeric liquids, some protein solutions, and suspensions. 

Owing to the various mechanisms for optical nonlinearities present in the ordered as well as isotropic phases of liquid crystals, almost all nonlinear optical phenomena have been observed. Some of these phenomena were studied for their novelty, others have been developed into diagnostic tools or practical devices. In accordance with the basic mechanism involved, these observed effects are grouped together under the following... 

Using liquid crystals with large anisotropies, and some ingenuous way of aligning the molecules (electrically or optically) to induce large second-order nonlinearity, it is likely that some of these novel studies could eventually result in practically competitive harmonic generators. 

In both the cases considered, an optical contrast of the patterns observed in isotropic liquids is very small. Certainly, the anisotropy of Uquid crystals brings new features in. For instance, the anisotropy of (helectric or diamagnetic susceptibility causes the Fredericks transition in nematics and wave like instabilities in cholesterics (see next Section), and the flexoelectric polarizaticm results in the field-controllable domain patterns. In turn, the anisotropy of electric conductivity is responsible for instability in the form of rolls to be discussed below. All these instabilities are not observed in the isotropic liquids and have an electric field threshold controlled by the corresponding parameters of anisotropy. In addition, due to the optical anisotropy, the contrast of the patterns that are driven by isotropic mechanisms , i.e. only indirectly dependent on anisotropy parameters, increases dramatically. Thanks to this, one can easily study specific features and mechanisms of different instability modes, both isotropic and anisotropic. The characteristic pattern formation is a special branch of physics dealing with a nonlinear response of dissipative media to external fields, and liquid crystals are suitable model objects for investigation of the relevant phenomena [39]. 

Optical harmonic generation is one of the earliest and most developed area in the field of nonlinear optics. Not surprisingly, investigations of nonlinear optical effects in liquid crystals started also with the study of harmonic generation. The aim of the first studies was to observe second harmonic generation (SHG) in cholesteric liquid crystals. 

Systematic research on optical reorientation in the nematic phase itself started around 1980 in at least four groups simultaneously (Zolotko et al. in Moscow and Budapest Zel dovich et al, in Moscow and Yerevan Durbin et al, in Berkeley Khoo et al, in Pennsylvania). Since then it became one of the most intensively studied nonlinear optical effects in liquid crystals. 

As demonstrated in this volume, the study of optical effects in liquid crystals is motivated by three main purposes. Firstly, it is used as a tool in the basic research of different liquid crystalline states. Secondly, in mesophases new types of optical nonlinearities occur or new aspects of nonlinear processes become apparent. The study of these effects contributes to the progress of nonlinear optics. Thirdly, liquid crystals are investigated from the point of view of applications in certain nonlinear optical devices. 

Laser-induced molecular reorientation is a common cause of optical nonlinearity in a fluid medium. In this respect, liquid crystals are often strongly nonlinear because of their large molecular anisotropy and strong correlation between molecules. The nonlinear optical properties of liquid crystals in the isotropic phase have already been studied quite extensively by a number of researchers in the past decade, This is, however, not true for liquid crystals in the mesophases. 

The nonlinear optical properties of nematic liquid crystals have recently been studied by various authors. It has been shown that an intensity-dependent refractive index is due to the optical reorientation of the molecules. 

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). 

Linear and nonlinear optical properties of liquid crystals in their mesophases have been studied in several contexts, in both fundamental and application-oriented pursuits. In the context of nonlinear optical processes, they have recently received considerable renewed interests as a result of the newly discovered extraordinarily large optical nonlinearity due to the laser-induced molecular reorientation, and a renewed effort explicitly at the large thermal index effect in liquid crystals. In the last few years, several groups [2]-[10] have looked at the optical nonlinearity in the mesophases of liquid crystals and the associated nonlinear processes. A brief review of some of these nonlinear optical processes and the fundamental mechanisms in both the liquid crystal and the isotropic phases has recently appeared [1]. In this paper, therefore, we will concentrate only on optical wave mixing processes that are relevant to this Special Issue. 

II. Thermal Nonlinearity The dependence of the refractive index of nematic liquid crystal on the temperature has occupied central importance in the study of the fundamental and applied properties of liquid crystals [11]. In this discussion, we will follow the literature [11], [14] and choose as the starting point of our analysis of the thermal nonlinearities the dielectric constants = nj and 2 = Depending on the levels of sophistication one desires, there are several possible forms of e and C2 in terms of molecular parameters (see, for example, De Jeu, [11]). In the simplest case, they are given by... 

In some nematics, e.g., PCB (4-cyano-4 -pentylbi-phenyl), the natural absorption is quite small at the second harmonics of the Nd YAG laser. To enhance the absorption constant and thus the nonlinearity, it is possible to dissolve some dyes that absorb at around 0.53 /xm, e.g., rhodamine 6G. Experiments have been conducted [13], [17] in nematic films with traces of dissolved dyes which showed that the required laser energies for several nonlinear processes based on the thermal effect were drastically reduced. A detailed study of the rise portion of the He-Ne diffraction also shows that the intramolecular relaxation processes that transfer the excitation from the dye to the liquid crystal take place probably at much shorter time scales than the laser pulse length, as the diffraction from a dyed sample has exactly the same rise time as the undyed sample. 

We have presented a discussion of the theories and experiments on laser-induced optica nonlinearities and some recently observed wave-mixing processes in nematic liquid crystals based on the phase grating induced by two laser pulses. These studies have demonstrated again the unique and interesting physical characteristics of liquid crystals that have attracted the attention of fundamental and applied researchers alike. It is also clear that some practically useful nonlinear optical devices could be constructed. The nematic phase is but one of the several mesophases of liquid crystal that possess these interesting nonlinearities. Cholesterics and smectics [4] and other hybrid forms of nematics [6] also possess large nonlinearities. We anticipate that many more effects will be observed in the near future. 

Huang JY, Superfine R, Shen YR (1990) Nonlinear spectroscopic study of coadsorbed liquid-crystal and surfactant monolayers Conformation and interaction. Phys Rev A 42 3660... 

Light-induced orientational nonlinearities and related effeets were extensively studied during the last two deeades. The results have been reviewed in [105]-[108j. Several parameters of liquid crystals can change due to the influence of the light field. At low light intensity, the effect could be due to the following processes ... 

---