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Unidirectional wave propagation in nonreciprocal photonic crystalsUsually, the electromagnetic dispersion relation w(k) of homogeneous or periodic heterogeneous media displays the fundamental property w(k) = w(k) of spectral symmetry withrespect to the direction of quasimomentum k. This relation is a direct consequence of the time reversal and/orspace inversion symmetry. If neither of the symmetries applies, the medium can supportspectral asymmetry, w (k) =\ w (k), which implies that plane waves propagate in one direction faster or slower than inthe opposite direction. In homogeneous media with linear magnetoelectric effect such a phenomenon has been knownfor decades. The problem with magnetoelectric crystals though is an extremely small degree of electromagnetic spectral asymmetry (0.0001 or less). This problem does not exist in magnetic photonic crystals, which are periodic arrays of ferromagnetic and other dielectric components [1]. Indeed, the presence of a ferromagnetic constituent can eliminate the time reversal from the macroscopic symmetry group of the periodic array. On theother hand, the space inversion can always be removed by proper choice of the geometry of the periodicstructure, even if each individual constituent is a centrosymmetric material. It does not mean, of course, that such aperiodic array will display any static magnetoelectric effect. But dynamically, it can behave like anartificial magnetoelectric medium with arbitrarily strong electromagnetic spectral asymmetry, unachievable inhomogeneous media. Strong spectral asymmetry can result in the phenomenon of electromagnetic unidirectionality[2]. A unidirectional periodic medium, being perfectly transparent for plane electromagnetic wavepropagating in a certain direction, "freezes" the radiation of the same frequency propagating in the oppositedirection. At the frequency of the frozen mode, the electromagnetic radiation incident on the surface of aunidirectional photonic slab can pass inside the periodic medium with little or even no reflectance, where it gets trapped inthe form of a coherent frozen mode with huge amplitude and zero group velocity.
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