Optical properties of cholesteric liquid crystals

As mentioned in Chapter 1, cholesteric liquid crystals have a helical structure. The helical structure results in unique optical properties, such as selective reflection, circular dichroism, drastic optical activity, and electro-optic effects. 

A sheet of cholesteric liquid crystals is sandwiched between two glass plates separated by a gap of tens microns. The cholesteric liquid crystals on two glass plates are homogeneously aligned to form the planar texture. The cell displays a bright color. The color varies according to the view angle and temperature. This is an important characteristic of cholesteric liquid crystals—selective reflection. 

The effect of the selective reflection doesn t result from the interference of a thin film, but from the Bragg-like reflection. 

Assume a to be the lattice gap of a crystal, usually a few A. When an incident X-ray impacts the sample, the well-known Bragg reflection occurs. 

The natural pitch P of cholesteric liquid crystals is in general in the order of 102 nm, comparable with the visible band of light. The Bragg reflection from cholesteric liquid crystal occurs at the wavelength 

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These unique optical properties of cholesteric liquid crystals have been investigated... 

The optical properties of cholesteric liquid crystals are very specific and are determined by the pitch and arrangement of the axis of the helix and the polarization of the incident light. In an external field changes occur both in the direction of the axis of the helix (texture transitions) and in its pitch (untwisting of the helix). Before considering these field variations let us give a brief account of the optical properties of cholesteric liquid crystals in the absence of a field. Comprehensive reviews of the topics have been given recently in [1, 2]. 

The optical properties of cholesteric liquid crystals have been studied extensively [23, 24]. Light propagation in helical cholesterics is governed by the spatially periodic relative dielectric tensor, whose eigenvalues are C and i for the electric field parallel and perpendicular to the director n. It can be written as... 

Optical Properties of Cholesteric Liquid-Crystal Films... 

C. W. Oseen, Arkiv Mat. Astron. Fysik 1928, 21A,l. This paper, like the earlier papers on the continuum theory, is written in German, a language that Oseen stoped using from 1933. References to Oseen s work are nowadays almost uniquely given to his article in English in Trans. Faraday Soc. 1933, 29, 883. While it is true that Eq. (1) is stated there, the article essentially contains the first comprehensive theory of the optical properties of cholesteric liquid crystals. 

A detailed treatment of the optical properties of cholesteric liquid crystals for obliquely incident light beams involves extensive numerical calculations and is outside the scope of this chapter. However, much of the physics underlying the observed optical behavior of these spiral structures can be understood by considering the more restricted case in which the wave vector of the incident light is everywhere normal to the local director, i.e., k 2. The development presented below parallels closely that of de Vries however, the approach is somewhat different. ... 

See, for example, D. W. Berreman and T. J. Scheffer, Reflection and Transmission by Single-Domain Cholesteric Liquid Crystal Films Theory and Verification, Mol. Cryst. and Liquid Cryst, 11, p. 395 (1970) R. Dreher and G. Meier, Optical Properties of Cholesteric Liquid Crystals, Phys. Rev., A8, p. 1616(1973). 

The approach presented in this chapter follows that contained in some unpublished lecture notes of P. S. Pershan on the optical properties of cholesteric liquid crystals. 

STRUCTURE AND OPTICAL PROPERTIES OF CHOLESTERIC LIQUID CRYSTALS... 

In this section, we investigate the optical properties of cholesteric liquid crystals that exhibit magneto-optic activityin the presence of an external static magnetic field ... 

Note -. In the above definition of right and left circularly polarized light, we adopt the convention frequently used in optics, that is, from the point of view of an observer looking at the light head on. For R, the observer will see a clockwise rotation of the electric field vector, while for L, the observer will see a counterclockwise rotation of the electric field vector. This is also the convention used in Chapter 4 when we discussed circularly polarized fight in the context of the optical properties of cholesteric liquid crystals. 

Electronic displays make use of the fact that the orientation of the molecules in liquid crystals changes in the presence of an electric field. This reorientation causes a change in their optical properties, making them opaque or transparent, and hence forming a pattern on a screen. Cholesteric liquid crystals are also of interest because the helical structure unwinds slightly as the temperature is changed. Because the twist of the helical structure affects the optical properties of the liquid crystal, these... 

The pitch P is the most important parameter of cholesteric liquid crystals. The physical properties of cholesteric liquid crystals are associated with P, such as selective reflection, optical rotation dispersion, circular dichroism, etc. The helical pitch is sensitive to the temperature and external field, for example, electric and magnetic field, chemical environment, pressure or radiation, etc. 

The cholesteric liquid crystal state consists of either all left-handed helices or all right-handed helices. The physical difference between these two states is manifested in their optical activities. See, for example, H. de Vries, Rotatory Power and Other Optical Properties of Certain Liquid Crystals, Acta. Cryst, 4, p. 219(1951). 

The cholesteric mesophase is thus very widespread both in natural and in synthetic polymer systems. The capacity of synthetic polymers to retain the properties of cholesteric liquid crystals, primarily the selective reflection of circularly polarized light, in the glassy and highly elastic state, makes them promising materials for creating different optical film elements (selective filters, polaroids, reflectors, heat indicators, etc.). 

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). 

Several unique optical properties arise from helical structures of cholesteric liquid crystals. 

Other equally remarkable optical properties are associated with the selective reflection. At normal incidence, the reflected light is circularly polarized one circular component is totally reflected, while the other passes through unchanged. Also, quite contrary to what is found in normal substances, the reflected wave has the same sense of circular polarization as that of the incident wave. This is an important difference between the nature of the optical rotation of normal substances and of cholesteric liquid crystals. While the more familiar cases of optical rotation have their origin in the selective absorption of one circularly polarized component of the light, the form optical rotation of the twisted structure in cholesteric liquid crystals originates in the selective reflection of one circularly polarized component of the light. 

Electro-Optic Properties of Polymer Stabilized Liquid Crystals. Polymer networks have been used to stabilize many of the liquid crystal display states in various types of displays quite advantageously. In this section, we present some recent work on correlating the material properties of the liquid crystal/polymer network composite to the electro-optic properties of the flat-panel displays specifically cholesteric texture displays (75) and simple nematic birefringent type displays (7(5). 

Cholesteric liquid crystals (CLCs) show very distinctly that molecular structure and external fields have a profound effect on cooperative behavior and phase structure (see also Chapters 2 and 3). CLCs possess a supermolecular periodic helical structure due to the chirality of molecules. The spatial periodicity (helical pitch) of cholesterics can be of the same order of magnitude as the wavelength of visible light. If so, a visible Bragg reflection occurs. On the other hand, the helix pitch is very sensitive to the influence of external conditions. A combination of these properties leads to the unique optical properties of cholesterics which are of both scientific and practical interest. 

The existence or nonexistence of mirror symmetry plays an important role in nature. The lack of mirror symmetry, called chirality, can be found in systems of all length scales, from elementary particles to macroscopic systems. Due to the collective behavior of the molecules in liquid crystals, molecular chirality has a particularly remarkable influence on the macroscopic physical properties of these systems. Probably, even the flrst observations of thermotropic liquid crystals by Planer (1861) and Reinitzer (1888) were due to the conspicuous selective reflection of the helical structure that occurs in chiral liquid crystals. Many physical properties of liquid crystals depend on chirality, e.g., certain linear and nonlinear optical properties, the occurrence of ferro-, ferri-, antiferro- and piezo-electric behavior, the electroclinic effect, and even the appearance of new phases. In addition, the majority of optical applications of liquid crystals is due to chiral structures, namely the ther-mochromic effect of cholesteric liquid crystals, the rotation of the plane of polarization in twisted nematic liquid crystal displays, and the ferroelectric and antiferroelectric switching of smectic liquid crystals. 

Introduction to the Optical Properties of Cholesteric and Chiral Nematic Liquid Crystals... 

Cholesteric mesophases in polymers were limited to these systems alone for a long time. However, due to the greatly increased scientific and practical interest in low-molecular-weight liquid crystals and cholesterics in particular at the end of the 1960s, studies began to be conducted on obtaining new types of thermotropic and lyotropic LC polymer cholesterics. These studies were stimulated by the unique optical properties of cholesterics, which permit widely... 

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