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2005-11-16
2D Magnetic Photonic Crystals with Square Lattice-Group Theoretical Standpoint
By
Progress In Electromagnetics Research, Vol. 58, 71-100, 2006
Abstract
We consider possible magnetic symmetries of two-dimensional 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.
Citation
Victor A. Dmitriev, "2D Magnetic Photonic Crystals with Square Lattice-Group Theoretical Standpoint," Progress In Electromagnetics Research, Vol. 58, 71-100, 2006.
doi:10.2528/PIER05061701
References

1. Bouckaert, L. P., R. Smoluchowski, and E. Wigner, "Theory of Brillouin zones and symmetry properties of wave functions in crystals," Phys. Rev., Vol. 50, 58-67, 1936.
doi:10.1103/PhysRev.50.58

2. Bradley, C. J. and A. P. Cracknell, The Mathematical Theory of Symmetry in Solids, Clarendon, 1972.

3. Ohtaka, K. and Y. Tanabe, "Photonic bands using vector spherical waves. III. Group-theoretical treatment," J. Phys. Soc. Jpn., Vol. 65, 2670-2684, 1996.
doi:10.1143/JPSJ.65.2670

4. Sakoda, K., "Symmetry, degeneracy and uncoupled modes in two-dimensional photonic lattices," Phys. Rev. B, Vol. 52, 7982-7986, 1995.
doi:10.1103/PhysRevB.52.7982

5. Lyubchanskii, I. L., N. N. Dadoenkova, M. I. Lyubchanskii, E. A. Shapovalov, and Th. Rasing, "Magnetic photonic crystals," J. Phys. D: Appl. Phys., Vol. 36, 277, 2003.
doi:10.1088/0022-3727/36/18/R01

6. Dmitriev, V., "Tunable and nonreciprocal photonic band- gap materials: group-theoretical approach," Proc. of the 10th Conference on Complex Media and Metamaterials, 20-24, 2004.

7. Altman, C. and K. Suchy, Reciprocity, Spatial Mapping and Time Reversal in Electromagnetics, 1991.

8. Fushchich, W. I. and A. G. Nikitin, Symmetries of Maxwell's Equations, D. Reidel Publishing Company, 1987.

9. Kushwaha, M. and G. Martinez, "Magnetic-field-dependent band gaps in two-dimensional photonic crystals," Phys. Rev. B, Vol. 65, 2002.
doi:10.1103/PhysRevB.65.153202

10. Xu, C., X. Hu, Y. Li, X. Liu, R. Fu, and J. Zi, "Semiconductor-based tunable photonic crystals by means of an external magnetic field," Phys. Rev. B, Vol. 68, 193201, 2003.
doi:10.1103/PhysRevB.68.193201

11. Zhou, Y.-S., B.-Y. Gu, and F.-H. Wang, "Photonic-band-gap structures and guide modes in two-dimensional magnetic photonic crystal heterostructures," Eur. Phys. J. B, Vol. 37, 293-299, 2004.
doi:10.1140/epjb/e2004-00059-3

12. Figotin, A., Yu. A. Godin, and I. Vitebsky, "Two-dimensional tunable photonic crystals," Phys. Rev. B, Vol. 57, 2841-2848, 1998.
doi:10.1103/PhysRevB.57.2841

13. Barybin, A. A. and V. A. Dmitriev, Modern Electrodynamics and Coupled-Mode theory: Application to Guided-Wave Optics, Rinton Press, 2002.

14. Kocinski, P., "Application of the irreducible part of the Brillouin zone to band-structure calculations in ferromagnetic crystals," J. Phys.: Condens. Matter, Vol. 5, 4519-4526, 1993.
doi:10.1088/0953-8984/5/26/022

15. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystals, Princeton University Press, 1995.

16. Gurevich, A. and G. Melkov, Magnetization Oscillations and Waves, CRC, 1996.

17. Dimmock, J. O. and R. G. Wheeler, "Symmetry properties of wave functions in magnetic crystals," Phys. Rev., Vol. 127, 391-404, 1962.
doi:10.1103/PhysRev.127.391

18. Dmitriev, V., "Comments on 'Properties of and generalized full-wave transmission line models for hybrid (bi)(an)isotropic waveguides' by Frank Olyslager," IEEE Trans. Microwave Theory Tech., Vol. MTT-47, 655-657, 1999.
doi:10.1109/22.763172

19. Baum, C. E. and N. H. Kritikos (eds.), Electromagnetic Symmetry, Taylor & Francis, 1995.

20. Figotin, A. and I. Vitebsky, "Electromagnetic unidirectionality in magnetic crystals," Phys. Rev. D, Vol. 67, 1655210, 2003.

21. Nishizawa, H. and T. Nakayama, "Magneto-optic anisotropy effect on photonic band structure," J. Phys. Soc. Jpn., Vol. 66, 613-617, 1997.
doi:10.1143/JPSJ.66.613

22. Belov, P. A., S. A. Tretyakov, and A. J. Viitanen, "Nonreciprocal microwave band-gap structures," Phys. Rev. E, Vol. 66, 016608, 2002.
doi:10.1103/PhysRevE.66.016608

23. Sakoda, K., Optical Properties of Photonic Crystals, Springer Verlag, 2001.

24. Potton, R. J., "Reciprocity in optics," Rep. Prog. Phys., Vol. 67, 717-754, 2004.
doi:10.1088/0034-4885/67/5/R03

25. Jalali, A. A. and A. T. Friberg, "Faraday rotation in two-dimensional magneto-optic photonic crystal," Optics Communications, Vol. 253, 145-150, 2005.
doi:10.1016/j.optcom.2005.04.064

26. Dimmock, J. O. and R. G. Wheeler, "Irreducible representations of magnetic groups," J. Phys. Chem. Solids, Vol. 23, 729-741, 1962.
doi:10.1016/0022-3697(62)90531-0