Photonic crystal, cholesteric

LC phase, while the later systems are based on chirality amplification mechanism. There are many types of chiral LC phases such as cholesteric (N ), chiral smectic (Sm ), blue phase (BP), and twist grain boundary (TGB) phase. Among them, N and SmC phases are the most studied due to their potential technological applications. BPs are also receiving increasing attention due to their interesting 3D cubic structures and potential applications as 3D photonic crystals. 

It should be noted that the appearance of the cholesteric phase of Reinitzer was different from the appearance of the classical cholesteric phase shown in Fig. 1.3b. The phase was opaque and had blue tint. It took a century to decipher its structure it appears to be a blue phase (see Chapter 4) with a structure of liquid lattice consisting exclusively of defects of an initially ideal helical structure. This phase is periodic and shows Bragg diffractiMi of light in all the three principal directions. Therefore, Reinitzer has discovered the first generic photonic crystal At present, a study of photonic crystals, mostly artificial, is one of the hot topics in physics [8]. 

In the helical structure, the optical ellipsoid of the smectic C phase rotates together with the tilt plane. Like in cholesterics, we can imagine that helical turns form a stuck of equidistant quasi-layers that results in optical Bragg reflections in the visible range. Therefore, like cholesterics, smectic C liquid crystals are onedimensional photonic crystals. However, in the case of SmC, the distance between the reflecting layers is equal to the full pitch Pq and not to the half-pitch as in cholesterics, because at each half-pitch the molecules in the SmC are tilted in opposite directions. Hence, we have a situation physically different from that in cholesterics. 

The concept of defects came about from crystallography. Defects are dismptions of ideal crystal lattice such as vacancies (point defects) or dislocations (linear defects). In numerous liquid crystalline phases, there is variety of defects and many of them are not observed in the solid crystals. A study of defects in liquid crystals is very important from both the academic and practical points of view [7,8]. Defects in liquid crystals are very useful for (i) identification of different phases by microscopic observation of the characteristic defects (ii) study of the elastic properties by observation of defect interactions (iii) understanding of the three-dimensional periodic structures (e.g., the blue phase in cholesterics) using a new concept of lattices of defects (iv) modelling of fundamental physical phenomena such as magnetic monopoles, interaction of quarks, etc. In the optical technology, defects usually play the detrimental role examples are defect walls in the twist nematic cells, shock instability in ferroelectric smectics, Grandjean disclinations in cholesteric cells used in dye microlasers, etc. However, more recently, defect structures find their applications in three-dimensional photonic crystals (e.g. blue phases), the bistable displays and smart memory cards. 

Emoto A, Uchida E, Fukuda T (2012) Optical and physical applications of photocontrollable materials azobenzene-containing and liquid crystalline polymers. Polymers 4 150-186 Ericson LM, Fan H, Peng HQ, Davis VA, Zhou W, Sulpizio J, Wang Y, Booker R, Vavro J, Guthy C et al (2004) Macroscopic, neat, single-walled carbon nanotube fibers. Science 305 1447-1450 Etchegoin P (2000) Blue phases of cholesteric liquid crystals as thermotropic photonic crystals. Phys Rev E 62 1435-1437... 

Etchegoin, P., 2000. Blue phases of cholesteric liquid crystals as thermotropic photonic crystals. Phys. Rev. E. 62 1435-1437. 

Cholesteric Liquid Crystal as a One-Dimensional Photonic Crystal... 

Chapters 1-5 cover the basic physics and optical properties of liquid crystals intended for beginning workers in liquid crystal related areas. Although the major focus is on nematics, we have included sufficient discussions on other mesophases of liquid crystals such as the smectics, ferroelectrics, and cholesterics to enable the readers to proceed to more advanced or specialized topics elsewhere. New sections have also been added. For example, in Chapter 4, a particularly important addition is a quantitative discussion of the optical properties and fundamentals of one-dimensional photonic crystal band stractures. Dispersion is added to fill in an important gap in most treatments of cholesteric liqrrid crystals. 

VI Kopp, B Fan, HKM Vithana, and AZ Genack, Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals, Opt. Lett., 23 1707-1709, 1998. 

U.A. Hrozhyk, S.V. Serak, N.V. Tabiryan, T.J. Bunning, Photoinduced isotropic state of cholesteric liquid crystals novel dynamic photonic materials. Adv. Mater. 19, 3244—3247 (2007)... 

Matsui T, Ozaki M, Yoshino K (2004) Tunable photonic defect modes in a cholesteric liquid crystal induced by optical deformation of helix. Phys Rev E 69 061715 Yoshida H, Lee CH, Fujii A, Ozaki M (2007) Tunable chiral photonic defect modes in locally polymerized cholesteric liquid crystals. Mol Cryst Liq Cryst 477 255... 

Liquid crystals have a history of more than 100 years. It is believed that the person who discovered liquid crystals is Friedrich Reinitzer, an Austrian botanist [7]. The liquid crystal phase observed by him in 1888 was a cholesteric phase. Since then, liquid crystals have come a long way and become a major branch of interdisciplinary sciences. Scientifically, liquid crystals are important because of the richness of structures and transitions. Technologically, they have won tremendous success in display and photonic applications [8-10]. 

Materials whose dielectric properties vary periodically in space are capable of localizing photons. Such photonic band gap materials, whose structure can be regarded as a distributed laser cavity, can also lase. Cholesteric liquid crystals can act as such lasers. In addition, cholesteric elastomers can allow the distributed cavity, and hence the lasing wavelength, to be tuned by mechanical strain. 

Schmidtke J, Stifle W (2003) Photonic defect modes in cholesteric liquid crystal films. Eur Phys J E Soft Matter 12 553-564... 

Cr=crystal Sm=smectic CrSmB = crystal smectic B N=nematic Ch=cholesteric I=isotropic fluorescence = steady state fluorescence SPC = time-resolved single photon counting CPF=circularly polarized fluorescence UV-vis = UV-visible absorption spectrophotometry DSC=differential scanning calorimetry OM = optical microscopy XRD = X-ray diffraction EPR=electron paramagnetic resonance NMR=nuclear magnetic resonance. 

As discussed in Chapter 5, chiral liquid crystals exhibit modulated groimd states and are therefore self-assembled PEG materials. The simplest of them is the cholesteric liquid crystal, which is a one-dimensional photonic band-gap material if the helical pitch is in the visible wavelength range. As illustrated in Chapter 5, such structure leads to selective reflection rendering a color to the material. The helical—and therefore the color—is sensitive to... 

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