Bragg reflection from cholesteric liquid crystals

Abstract

In this paper we discuss the optical reflective properties of single and multidomain cholesteric liquid crystals both experimentally and theoretically. The multidomain system has been prepared by dispersing a low concentration of polymer in a cholesteric liquid crystal. This results in a (passive) bistable colorful reflective display. Here we discuss the role of the polymer in altering the reflective properties in regard to their spectra and viewing characteristics. Theoretically we o6'er an application of the well known Berreman method [J. Opt. Soc. Am. 62, 502 (1972)] suitable for systems composed of an ensemble of uncorrelated domains, each of which is composed of the same dielectric anisotropy, however with its own local orientation. Using this technique the reflective properties of a cholesteric liquid crystal possessing a distribution in the orientation of the helix axes are simulated. We furthermore illustrate how a small fluctuation in the pitch from one domain to another significantly reduces any interference fringes. From these simulations we will show how experimentally by using a polymer network one may control the extent to which the orientation of the helix axes are distributed.PACS number(s): 61.30.v

Unusual coloration in scarabaeid beetles

“…In addition the green reflectance band has a full width at half maximum (FWHM) of almost double that of the red band. Since the spectral width of a cholesteric material is given by δλ = P o δn [9], with δn the birefringence, this is rather strange as it indicates that the two colour variations are based on materials with a large difference in birefringence. One would expect beetles of the same species to be constructed from identical materials with at best a small difference in the layer thickness.…”

“…Different expressions for other formulations of the same problem can be found in the literature [10,11]. Optimal reflection is obtained when the Bragg condition [2,9] is met:…”

“…The layer matrix L was calculated by a suitable series expansion (up to nine terms) of the exponent [9]. Azzam and Bashara [7] showed that the layer matrix can be used to calculate a 2 × 2 reflection matrix for a slab of anisotropic material sandwiched between semi-infinite ambient and substrate layers for plane polarized incident light.…”

Exhibition of circular Bragg phenomenon by hyperbolic, dielectric, structurally chiral materials

“…The stopband is best seen when the thickness of the SCM exceeds a certain number of helical pitches. 6,[9][10][11] When dissipation is small enough to be ignored, ̳ ε r ðzÞ is positive definite, and the variations of ε a;b;c with respect to the free-space wavelength λ 0 are also small enough to be ignored, the circular-polarization-sensitive stopband can be delineated as 4…”

“…In this problem, the half space z < 0 is vacuous while the half space z > 0 is occupied by the hyperbolic SCM, and a circularly polarized plane wave is obliquely incident on the interface z ¼ 0 from its vacuous side. As it is known that the circular Bragg phenomenon develops as the thickness of an SCM increases, 4,10 an SCM half space should conceptually deliver the best developed circular Bragg phenomenon. The underlying boundary-value problem is introduced briefly in Sec.…”