Solvable Model of Two-Dimensional Magnetophotonic Crystal (original) (raw)
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Two-dimensional magnetophotonic crystal: Exactly solvable model
Physical Review B, 2005
We present an analytical treatment of a two-dimensional ͑2D͒ magnetophotonic crystal ͑MPC͒ with a square lattice constructed from two infinite arrays of magnetoactive dielectric sheets at right angles, in the limit of very small sheet thickness and very high dielectric constant. Alteration of band structure by an external magnetic field is studied. Two different geometries are examined: the Faraday geometry-magnetic field parallel to the plane of 2D MPC-and the Voigt ͑Cotton-Mutton͒ geometry-magnetic field orthogonal to the plane of 2D MPC. In the case of Faraday geometry, we show that the optical activity reduces the symmetry of the system and removes degeneracy in the photonic band structure. Also, despite the weakness of magnetooptic activity, the dispersion ͑k͒ near band edges is strongly sensitive to external magnetic influence. In the vicinity of degeneracy, electromagnetic modes exhibit bistable behavior and discontinuously change their dispersion ͑k͒ when external magnetic field is applied. In the Voigt geometry s and p polarizations remain independent of each other, and only the band structure for s-polarized light is insignificantly altered.
Unidirectional band gaps in uniformly magnetized two-dimensional magnetophotonic crystals
Physical Review B, 2009
By exploiting the concepts of magnetic group theory we show how unidirectional behavior can be obtained in two-dimensional magneto-photonic crystals (MOPhC) with uniform magnetization. This group theory approach generalizes all previous investigations of one-way MOPhCs including those based on the use of antiparallel magnetic domains in the elementary crystal cell. Here, the theoretical approach is illustrated for one MOPhC example where unidirectional behavior is obtained by appropriately lowering the geometrical symmetry of the elementary motifs. One-way transmission is numerically demonstrated for a photonic crystal slice.
Journal of the Optical Society of America B, 2007
An analytical formulation for the band structure and Bloch modes in elliptically birefringent magnetophotonic crystals is presented. The model incorporates both the effects of gyrotropy and linear birefringence generally present in magneto-optic thin-film devices. Full analytical expressions are obtained for the dispersion relation and Bloch modes in a layered-stack photonic crystal, and their properties are analyzed. It is shown that other models recently discussed in the literature are contained as special limiting cases of the formulation presented herein.
Journal of Physics D: Applied Physics, 2006
When the constitutive materials of photonic crystals (PCs) are magnetic, or even only a defect introduced in PCs is magnetic, the resultant PCs exhibit very unique optical and magneto-optical properties. The strong photon confinement in the vicinity of magnetic defects results in large enhancement in linear and nonlinear magneto-optical responses of the media. Novel functions, such as band Faraday effect, magnetic super-prism effect and non-reciprocal or magnetically controllable photonic band structure, are predicted to occur theoretically. All the unique features of the media arise from the existence of magnetization in media, and hence they are called magnetophotonic crystals providing the spin-dependent nature in PCs.
Magnetooptical properties of two dimensional photonic crystals
The European Physical Journal B - Condensed Matter, 2004
Magnetooptical properties of the materials with periodically modulated dielectric constantphotonic crystals (or band-gap materials) have been examined with relation to their possible applications for the control of electromagnetic radiation in the integrated optics devices. For this investigation we propose the original theoretical approach based on the perturbation theory. Magnetooptical Faraday and Voigt effects have been studied near extremum points of photonic bands where their significant enhancement takes place. On the grounds of the elaborated theory some experimental results are discussed. Experimentally obtained Faraday rotation angle frequency dependence shows good agreement with our theoretical predictions.
Effect of a magnetic field on a two-dimensional metallic photonic crystal
Physical Review A, 2012
We study the effect of a static magnetic field on the band structure of a two-dimensional metallic photonic crystal (MPC). The band structure of the MPC has been calculated using the transfer matrix method. It is found that the position of the photonic band gap and the band edges of the MPC depends on the polarization of the incident light and intensity of the applied magnetic field. In our calculations we consider linearly polarized light as well as right-and left-circularly polarized light. In the case of right-circularly polarized light it is found that as the intensity of the magnetic field increases the width of the band gap of the crystal decreases. At a certain magnetic field strength the band gap disappears altogether. In other words there is a transition from a metallic photonic band gap material to a transparent dielectric material. This is an interesting effect which is similar to the metal-insulator transition that occurs in semiconductors. On the other hand, for left-circularly and linear polarized light the band edges shift to the higher energy and the band gap increases in the presence of a magnetic field. This implies that the MPC switches from a transparent state to reflecting states due to the application of the magnetic field. This is an interesting effect which might be used to make photonic switches.
2D Magnetic Photonic Crystals with Square Lattice-Group Theoretical Standpoint
Progress In Electromagnetics Research, 2006
We consider possible magnetic symmetries of twodimensional square lattices with circular ferrite rods magnetized by a uniform dc magnetic field. These structures can be used as tunable and nonreciprocal photonic crystals. Classification of eigenmodes in such crystals is defined on the basis of magnetic group theory and the theory of (co)representations. Some general electromagnetic properties of the magnetic crystals such as change in the basic domain of the Brillouin zone, change of symmetry in limiting cases, bidirectionality and nonreciprocity, symmetry relations for the waves and lifting of eigenwave degeneracies by dc magnetic field are also discussed.
Journal of the Optical Society of America B, 2008
An analysis is presented of wave-vector dispersion in elliptically birefringent stratified magneto-optic media having one-dimensional periodicity. It is found that local normal-mode polarization-state differences between adjacent layers lead to mode coupling and impact the wave-vector dispersion and the character of the Bloch states of the system. This coupling produces extra terms in the dispersion relation not present in uniform circularly birefringent magneto-optic stratified media. Normal mode coupling lifts the degeneracy at frequency band cross-over points under certain conditions and induces a magnetization-dependent optical band gap. This study examines the conditions for band gap formation in the system. It shows that such a frequency-split can be characterized by a simple coupling parameter that depends on the relation between polarization states of local normal modes in adjacent layers. The character of the Bloch states and conditions for maximizing the strength of the band splitting in these systems are analyzed.
Magnetic Photonic Crystals as Artificial Magnetoelectrics
Magnetoelectric Interaction Phenomena in Crystals, 2004
Magnetic photonic crystals are spatially periodic dielectric composites with at least one of the constitutive components being a magnetically polarized material. We show that the electrodynamic properties of magnetic photonic crystals with proper configuration correspond to those of hypothetical media with huge linear magnetoelectric effect. In particular, such composites can display strong asymmetry ω(k) ≠ ω(−k) of the electromagnetic dispersion relation, which can result in a number of interesting phenomena, including the electromagnetic unidirectionality. A unidirectional medium, being perfectly transmissive for electromagnetic wave of certain frequency, freezes the radiation of the same frequency propagating in the opposite direction in the form of a coherent standing wave with zero group velocity. At microwave frequencies, unidirectional photonic crystals can be made of common ferro-or ferrimagnetic materials alternated with anisotropic dielectric layers.