Phase symmetry, optical properties

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

Chirality (or a lack of mirror symmetry) plays an important role in the LC field. Molecular chirality, due to one or more chiral carbon site(s), can lead to a reduction in the phase symmetry, and yield a large variety of novel mesophases that possess unique structures and optical properties. One important consequence of chirality is polar order when molecules contain lateral electric dipoles. Electric polarization is obtained in tilted smectic phases. The reduced symmetry in the phase yields an in-layer polarization and the tilt sense of each layer can change synclinically (chiral SmC ) or anticlinically (SmC)) to form a helical superstructure perpendicular to the layer planes. Hence helical distributions of the molecules in the superstructure can result in a ferro- (SmC ), antiferro- (SmC)), and ferri-electric phases. Other chiral subphases (e.g., Q) can also exist. In the SmC) phase, the directions of the tilt alternate from one layer to the next, and the in-plane spontaneous polarization reverses by 180° between two neighbouring layers. The structures of the C a and C phases are less certain. The ferrielectric C shows two interdigitated helices as in the SmC) phase, but here the molecules are rotated by an angle different from 180° w.r.t. the helix axis between two neighbouring layers. 

It is worth noting that the four-fold symmetry of hexadecapole moment is revealed only at the synchronous pumping and, what is important, at time moments when the hexadecapole moment is precisely aligned with one of its symmetry axis along the linear polarization of the field and the atomic coherence p 2, 2 in the M-system has its maximal value. The periodic change of the optical properties of atomic medium modulates the angle of tight polarization that leads to the FM NMOR resonances. If the time-dependent optical rotation is measured at the first harmonic of (.lm, a resonance is seen when Qm = k Ql which allows one to separate the NFS produced by different atomic PM. Indeed, in the experiment the in-phase and quadrature amplitudes of optical rotation,... 

The local symmetry of smectic A phase is the same as that of the nematics, be., its point group is D h, while the symmetry of the smectic C phase is ( b/, (a ( 2 symmetry axis plus a reflection plane perpendicular to the axis). In addition, both smectic phases exhibit a one-dimension translational order. Owing to the difference in symmetry, the smectic phases show different optical properties. The smectic A phase is optically uniaxial, but the smectic C phase is optically biaxial. 

In this liquid crystal phase, the molecules have non-symmetrical carbon atoms and thus lose mirror symmetry. Otherwise optically active molecules are doped into host nematogenic molecules to induce the chiral liquid crystals. The liquid crystals consisting of such molecules show a helical structure. The most important chiral liquid crystal is the cholesteric liquid crystals. As discussed in Section 1.2, the cholesteric liquid crystal was the first discovered liquid crystal and is an important member of the liquid crystal family. In some of the literature, it is denoted as the N phase, the chiral nematic liquid crystal. As a convention, the asterisk is used in the nomenclature of liquid crystals to mean the chiral phase. Cholesteric liquid crystals have beautiful and interesting optical properties, e.g., the selective reflection of circularly polarized light, significant optical rotation, circular dichroism, etc. 

The optical properti es of thin polycrystalline films are influenced by the extent of grain orientation, which is also manifested in the Raman band intensities for vibrational modes of different symmetry. Figure 9a illustrates the two strongest Raman active modes for the rutile phase of Ti02. The Eg assigned mode exhibits a vibrational frequency of 444 cm"l, while the frequency for the Aig mode is 608 cm l. A series of 0.6 micrometer thick rutile films with variable ordering in the grain structure was prepared by sputter deposition techniques. Refracti ve indices... 

If nematogenic groups are linked via short flexible spacers to the polymer backbone, the macroscopic properties of nematic polymers may deviate from conventional nematic systems, o i/ing to a disturbing effect of the polymer main chain. This is indicated e.g. by the absence of typical nematic textures and some anomalous optical properties The symmetry of the phase structure, how-... 

Like solid ferroelectrics, the ferroelectric liquid crystals, particularly the FLCPs, show a pyroelectric effect and a piezoelectric effect and are capable of switching polarization direction (dielectric hysteresis). Moreover, they can switch propagating or reflected polarized light. Finally, the polar symmetry of the phase leads to nonlinear optical properties of the FLCPs such as second-harmonic generation, the Pockels effect, and the Kerr effect. These physical properties of the ferroelectric LC polymers are discussed in the following sections. 

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. 

The identification of the appropriate order parameter for nematic liquid crystals is aided by a consideration of the observed structure and symmetry of the phase. As in any liquid, the molecules in the nematic phase have no translational order i.e., the centers of mass of the molecules are distributed at random throughout the volume of the liquid. Experiments of many varieties, however, do demonstrate that the nematic phase differs from ordinary liquids in that it is anisotropic. The symmetry, in fact, is cylindrical that is, there exists a unique axis along which the properties of the phase display one set of values, while another set of values is exhibited in all directions perpendicular to this axis. The symmetry axis is traditionally referred to as the director . The optical properties of nematics provide an example of how the cylindrical symmetry is manifest. For light passing parallel to the director, optical isotropy is observed, while for all directions perpendicular to the director, optical birefringence is observed. Rays polarized parallel to the director have a different index of refraction from those polarized perpendicular to the director. 

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