Effect of an anisotropic photoalignment layer and microgrooves on nematic liquid-crystal (LC) alignment was quantitatively examined using azobenzene polymer thin film with surface relief grating (SRG) of about 1 μm pitch. The SRG with various modulation depths was treated with polarized light irradiation to align molecules at 45° from the groove. Nematic LC molecules, 4′-n-pentyl-4-cyanobiphenyl, orient to the photoaligned direction on the SRG being shallower than 200 nm. The orientation rather sharply deviates from the photoaligned direction toward the groove direction with increasing grating depth into the deeper region than 200 nm and finally becomes parallel to the grooves on the SRG of 400 nm deep. This behavior is successfully simulated by the consideration of anisotropic surface interaction and an elastic energy of LCs.
We have investigated the molecular orientation of a liquid crystal (LC), pentylcyanobiphenyl (5CB), evaporated on a rubbed polymer by means of polarized ultraviolet absorption spectroscopy and surface second-harmonic generation. The results unambiguously reveal that the in-plane anisotropy is diminishingly small before the molecules form a monolayer, although films thicker than one monolayer have a finite in-plane anisotropy. This drastic change indicates that LC molecules on rubbed surfaces do not align well without the influence of the intermolecular interaction of LCs. Actually we confirmed that nonliquid-crystalline butylcyanobipheny (4CB) exhibits no orientation on the rubbed polymer surface regardless of thickness.
A novel method for understanding the alignment mechanism was motivated by the texture observation of a nematic liquid crystal (LC) contacted with a photoaligned layer after rubbing. Reorientation of director occurs by subsequent photoalignment to different direction from that forced by rubbing. Moreover, it was found by polarized absorption spectra that the preferential average main chain axis over whole the alignment layer does not change, indicating that the orientation change by photoalignment occurs only at very top surfaces. This experiment without changing surface morphology indicates that the alignment priority for the nematic LC is mainly governed by the anisotropic short-range intermolecular interaction between alignment films and LC molecules and the effect of microgrooves plays a minor role.
hducible representations of Brauer algebras are consmeted by using the induced representation and the linear equation method. As examples, some matrix representations of Brauer algebras Df(n) with f < 5 are presented. IntroductionBrauer algebras [I, 21 D f ( n ) , which are similar to the group algebra of the symmetric group S ' related to the decomposition of f-rank tensors of the general linear group GL(n), are the centralizer algebras of the orthogonal group O(n) or the symplectic group Sp(2m) when n = -2m. Using the complementary relation or the so-called Schur-Weyl duality relation between SJ and U@), one can obtain the knowledge of the representation theory of U(n), such as basis vectors, coupling and recoupling coefiicients from the symmetric group Sf [5-8]. The Brauer algebras D,(n) play a similar role for other classical Lie groups. More precisely, if G is the orthogonal group O ( n ) or the sympletic group Sp(Zm), the corresponding centralizer algebra Bf(G) are quotients of Brauer's D f ( n ) and Df(-2m), respectively [2, 41. On the other hand, the Brauer algebras D,(n) are a special case of Birman-Wenzl algebras [3]. The Birman-Wenzl algebras Cf(q, r ) appear in connection with the Kauffman link invariant and quantum groups of types B, C, D [4]. The Birman-Wenzl algebras Cf(q. T ) are a special realization of braid group. Unitary braid representations play an important role in the study of subfactors and in quantum field theory [15.16]. If the parameters q and r are not roots of unity, representations of C f ( q , r ) vary continuously with q and r . Thus one can obtain the information about the representations of C / ( q , r )from those of D,(n) for n > f -1 or non-integer n.In this paper, we will outline a method for constructing irreducible representations of Df(n). In section 2, we will briefly review the definitions and some important properties of D,(n). In section 3, we will outline an induced representation method for constructing irreps of D+). As examples, some orthogonal matrix representations of D,(n) will be derived by using the linear equation method (LEM) [W. The results will be presented in section 4. The technique developed in this paper can also be extended to the Birman-Wenzl algebra Cf(q, r ) case by using the results of Hecke algebra representations proposed previously 16-81.
The helical structures in ferroelectric liquid crystals can be utilized to realize a special phase matching for second-harmonic generation (SHG) when two counter fundamental waves propagate along the helical axis and the wavelength of SHG is near the photonic (selective reflection) band edge. On the basis of the exact theory [Drevensek-Olenik and Copic, Phys. Rev. E 56, 581 (1997)], a simple analytical description is derived and some characteristic features of the special phase matching are shown. (1) Special phase matching is definitely achieved under particular combinations of polarization. (2) The SH spectrum is related to a subsidiary oscillating structure in the selective reflection spectrum. The maximum SH intensity is realized at the first dip of the oscillation near one of the edges in the selective reflection band. (3) The thickness (d) dependence of the maximum SH intensity is d4 in thick cells, while it is d2 for conventional phase matching. (4) The linewidth for the SH peak is d(-3) dependent, which is much narrower than in conventional phase matching.
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