Novel nonreciprocal materials based on magnetic photonic crystals
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Novel nonreciprocal materials based on magnetic photonic crystals A. Figotin and I. Vitebskiy University of California at Irvine, Irvine, CA 92697-3875, U.S.A. ABSTRACT Magnetic photonic crystals are spatially periodic dielectric composites with at least one of the constitutive components being a magnetically polarized material. Magnetic polarization, either spontaneous or induced, is always associated with nonreciprocal circular birefringence (Faraday rotation), which can bring qualitatively new features to the electrodynamics of photonic crystals. If the geometry of the periodic array meets certain symmetry criterion, the electromagnetic properties of the composite appear similar to those of a hypothetical bianisotropic medium with gigantic linear magnetoelectric effect. In particular, such a photonic crystal can display sptrong spectral asymmetry, which implies that electromagnetic waves propagate from left to right significantly faster or slower than from right to left. The strong spectral asymmetry can result in the phenomenon of electromagnetic unidirectionality. A lossless unidirectional medium, being perfectly transmissive for electromagnetic wave of certain frequency, "freezes" the radiation of the same frequency propagating in the opposite direction. The frozen mode is a coherent Bloch wave with nearly zero group velocity and drastically enhanced amplitude. The phenomenon of electromagnetic unidirectionality is essentially nonreciprocal and unique to gyrotropic photonic crystals. Physical conditions for the phenomenon include (i) significant Faraday rotation in the magnetic component of the composite structure at the frequency range of interest and (ii) the proper spatial arangement of the constituents. Unidirectional photonic crystals can be very attractive for a variety of applications. ELECTROMAGNETICS OF NONRECIPROCAL PERIODIC MEDIA In spatially periodic media, such as photonic crystals, the electromagnetic eigenmodes can be represented in the Bloch form Ψ k ( r + a ) = Ψ k ( r ) exp ( ik ⋅ a ) ,
(1)
where k is the Bloch wave vector and a is a lattice translation. The correspondence ω(k) between the wave vector k and the frequency ω is referred to as the dispersion relation. In most cases, the dispersion relation is symmetric with respect to the wave vector ω( k ) = ω( − k ) .
(2)
Usually, the relation (2) can be viewed as a direct consequence of time reversal and/or space inversion symmetry of the periodic array. Indeed, let I and R denote the space inversion and time reversal operations, respectively. Since either operation reverses the direction of the Bloch wave vector Ik = − k , Rk = − k ,
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we can conclude that if R ∈ G and/or I ∈ G, then ω( k ) = ω( − k ) for any k ,
(3)
where G is the magnetic symmetry group of the periodic array. All non-magnetic media support time reversal symmetry. In addition, most of the homogeneous and periodic heterogeneous structures are centrosymmetric. As a consequence, the overwhelming majority of homogeneous materials, as well as periodic compo
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