Effective properties of a periodic chiral arrangement of identical biaxially dielectric plates
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I. INTRODUCTION AND PRELIMINARIES Layered anisotropic media are employed in a wide variety of situations: as optical filters, compensators, and electro-optic modulators, for example. This is because anisotropic media are birefringent; i.e., to every direction of wave propagation there exist two possible plane waves which travel at different phase velocities. The differential phase between these two waves can then be utilized with profit.1"3 It is observed here that this anisotropy can be purely geometric in origin. Thus, in 1964 Rumsey4 proposed the construction of artificial gyromagnetic media by stacking up ferrite ply-boards, the ferrite fibers in alternate layers being similarly oriented; such a laminar composite would behave as a homogeneous anisotropic medium above some minimum frequency. Whether or not the anisotropy is synthetically contrived is, therefore, unimportant. Birefringence, however, is by no means the exclusive property of anisotropic media; there are isotropic media which exhibit circular birefringence.5 Because circular birefringence in naturally occurring substances generally manifests itself at optical frequencies, it is also termed optical activity. Only circularly-polarized plane waves can propagate in optically active (chiral) media.5 Again, it is the geometric conformation of the component molecules which is responsible for optical activity. As such, it too can be replicated at the lower frequencies by constructing artificial media which consist of chiral microstructures embedded in dielectric host materials. Theoretical analyses6'7 of the properties of these media suggest considerable promise for their eventual utility. The marriage of Rumsey's proposal with circular birefringence leads to an interesting class of laminar composites. These composites can be constructed of plates which are intrinsically anisotropic. But the optic axes of successive plates lie on a right- or a left-handed spiral; J. Mater. Res., Vol. 4, No. 6, Nov/Dec 1989
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hence, the laminar composite possesses form chirality in addition to intrinsic anisotropy. The authors have recently obtained8 the plane wave reflection and transmission characteristics of a handed (chiral) arrangement of uniaxial dielectric plates. A structurally chiral slab was constructed by stacking up a certain number of identical uniaxial plates, the consecutive optic axes describing either a right- or a left-handed spiral. It was reported in Ref. 8 that, while the co-polarized reflection and transmission characteristics are unaffected by the handedness of the arrangement, the cross-polarized characteristics are greatly influenced by the handedness. In the present paper, analysis is made of the electromagnetic field in a periodic chiral arrangement of identical biaxial plates, the consecutive optic axes again describing either a right- or a left-handed spiral, as shown in Fig. 1. The periodic ensemble extends over the range z e {—°°, °°}, while the plates lie parallel to the z = 0 plane. The o
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