Reflection of cholesteric liquid crystals

The reflected light is also right-handed circularly polarized and has the amphtude r. The fields is 

The refractive index n depends on the eigenmode. The eigenmodes with left-handed circular polarization are rii and the eigenmodes with linear polarization are ri2. From Equations (2.127) and (2.128), we know that within and near the reflection band Im2I i. 

Note that the local frame is the same as the lab frame at the bottom and top surface of the Ch film because the film has m pitch. From these two equations we can get 

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W. Elser, R. D. Ennulat, Selective Reflection of Cholesteric Liquid Crystals, m Advances in Liquid Crystals, Vol. 2 (Ed. G. H. Brown) Academic Press, New York, 1976,73. 

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. 

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 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... 

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 reflective wavelength of cholesteric liquid crystals varies according to temperature. Such an effect has been made useful in thermography. It has been applied in the diagnosis of cancers by displaying the skin temperature distribution. It has also been applied to test faults in integrated circuits. The applications also include thermometers and temperature warning indicators and non-destructive detection. 

M. Mitov, N. Dessaud, Going beyond the reflectance limit of cholesteric liquid crystals. Nat. Mater. 5, 361-364 (2006)... 

U.A. Hrozhyk, S.V. Serak, N.V. Tabiryan, T.J. Bmming, Phototunable reflection notches of cholesteric liquid crystals. J. Appl. Phys. 104, 063102(1-7) (2008)... 

L.E. Hajido, A.C. Erigen, Theory of light reflection by cholesteric liquid crystals possessing a pitch gradient. J. Opt. Soc. Am. 69, 1017-1023 (1979)... 

Kent Display is a pioneer of cholesteric liquid crystal displays (ChLCDs) in which the director of the liquid crystal twists around a helical axis [3]. The remarkable property is that the cholesteric material reflects light of certain wavelengths depending on the pitch over which the director rotates. When an electric held is applied. 

Figure 2.16. Samples for demonstration of the Bragg reflection from cholesteric liquid crystal.

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. 

Outside the reflection band, cholesteric liquid crystals exhibit an extremely strong optical rotatory power which can amount to values as large as 20.000° or 50 complete rotations per millimeter. The sign of the rotatory power is different below and above the reflection band. 

Small concentrations of guest molecules may induce dramatic changes in the pitch of cholesteric liquid crystals. The corresponding (reflection) color response may be exploited in analytical chemistry as described in Section 6. 

As the intermolecular dispersion forces that maintain the molecules in the cholesteric structure are relatively small, a low additional amount of energy suffices to change the helix pitch. The pitch depends particularly on temperature. In some cases the dependence is so pronounced that typically a temperature rise of less than 3°C is adequate to change the color of reflected light from red over the entire visible spectrum to blue. The use of cholesteric liquid crystals in thermographic applications is based on this property (see also first part of this book). 

The dramatic variation of liquid crystalline properties with respect to temperature has resulted in the widespread use of cholesteric (chiral nematic) liquid crystals for thermography. The property that has been exploited most in liquid crystal thermography is the critical temperature dependence of the selective reflection from cholesteric liquid crystals, though other temperature dependent properties of mesophases have been utilized (e.g. the birefringence of nematic systems and selective reflection from other chiral phases). The helicoidal structure of cholesteric materials results in the selective reflection of visible light within a band of wavelengths of width AX, centered at a wavelength Xq, such that ... 

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 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.). 

Thermotropic cholesterics have several practical applications, some of which are very widespread. Most of the liquid crystal displays produced use either the twisted nematic (see Figure 7.3) or the supertwisted nematic electrooptical effects.6 The liquid crystal materials used in these cells contain a chiral component (effectively a cholesteric phase) which determines the twisting direction. Cholesteric LCs can also be used for storage displays utilizing the dynamic scattering mode.7 Short-pitch cholesterics with temperature-dependent selective reflection in the visible region show different colors at different temperatures and are used for popular digital thermometers.8... 

Organic materials with large optical rotations include cholesteric liquid crystals, molecules and polymers with chiral jt-conjugated systems, especially [n]helicenes [21, 31, 139]. The most important factor contributing to their large optical rotations is anomalous optical rotatory dispersion (ORD), which is associated with the presence of absorption (or reflection) with large rotational strength (Fig. 15.30). 

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