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Since the discovery of optical activity in crystalline quartz in 1811, and then in liquids, gases, and liquid crystals, materials that effectively rotate the plane of polarization of a beam of light have continued to be of great interest in many disciplines including biology, chemistry, and physics. Quartz crystals were found to exist in two structural forms that are mirror images of each other. In right-handed (d-rotary) quartz, the silicon and oxygen atoms form a right-handed helix, and an observer looking along the axis toward a source of light sees a clockwise rotation of the vibration direction, whereas the left-handed (l-rotary) version produces anticlockwise rotation. Handedness of optically active substances is a critical issue in biology and chemistry; thus, sugar dextrose (d-glucose) is the most important carbohydrate in human metabolism, and in general the amino acids that form proteins are l-rotary. In many optical devices such as computer and TV displays, it is necessary to control or modify the reflectance spectrum and the polarization spectrum of a beam of light. An emerging industrial trend is to combine passive dielectric anisotropic films and active liquid crystal layers. Both can act as birefringent slabs with aligned microstructural columns or aligned cigar-shaped molecules, and both can behave as chiral materials with a helical structure and large rotary power. In this chapter we are concerned in particular with the optical properties of dielectric structurally chiral media. In 1959 the pioneering work of Young and Kowal prepared the way for fabrication of chiral media by vacuum deposition of dielectric material onto a rotating substrate. Such a medium is locally birefringent in form, with axes that twist steadily with distance into the medium. The effect on light is small except near the so-called circular Bragg resonance, where light that matches the handedness and pitch of the chiral structure is reflected strongly. Given that the material is handed and periodic, we refer to it as a chiral photonic medium. Other types of chiral media have been fabricated, including planar arrays of metallic and nonmetallic chiral structures, but they are not considered here. In practice, interfacial reflections change the handedness of a fraction of the light reflected from a chiral photonic medium, and then maximum reflectance occurs for slightly elliptical, rather than circular, light. Following such observations we speculate that elliptical Bragg resonators may be designed for any polarization, possibly as a composite material in which a chiral medium is threaded through a birefringent medium with fixed axes. With such optical applications in mind we survey the properties of several chiral architectures, including standard-chiral material, thickness-modulated chiral material, chiral material threaded through an isotropic medium and through a birefringent medium, and chiral material threaded through a second chiral material with the same or different pitch and handedness. Characterization is initially by polarization response maps and then by reflectance spectra calculated for the polarization of maximum response.
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