volume | PIER Journals

Abstract

In this paper, the properties of anisotropic photonic band gaps (PBGs) in three-dimensional (3D) nomagnetized plasma photonic crystals (PPCs) composed of anisotropic dielectric (the uniaxial material) spheres immersed in uniform nomagnetized plasma background with various lattices including the diamond, face-centered-cubic (fcc), body-centered-cubic (bcc) and simple-cubic (sc) lattices, are theoretically investigated by the plane wave expansion (PWE) method. The equations for calculating the anisotropic PBGs in the first irreducible Brillouin zone are theoretically deduced. The anisotropic PBGs and a flatbands region can be obtained as the uniaxial material introduced into 3D PPCs. The PPCs with diamond lattices consisting of isotropic dielectric have the larger PBGs compared to PPCs doped by the uniaxial material since its low symmetry structure. Furthermore, the PPCs with fcc, bcc, sc lattices will not exhibit a complete PBG unless the uniaxial material is introduced. The influences of the ordinary-refractive index, extrordinary-refractive index, filling factor and plasma frequency external magnetic field on the properties of anisotropic PBGs for 3D PPCs with fcc, bcc, sc lattices are investigated in detail, respectively, and some corresponding physical explanations are also given. The numerical results show that the anisotropy can open partial band gaps in 3D PPCs with fcc, bcc, sc lattices, and the complete PBGs can be obtained compared to 3D PPCs doped by the conventional isotropic dielectric. It also is shown that the anisotropic PBGs can be tuned by the ordinary-refractive index, extrodinary-refractive index, filling factor and plasma frequency, respectively. The complete PBGs can be obtained by introducing the uniaxial material as 3D PPCs are with high-symmetry lattices. This also provides a way to design the tunable devices.

1. Yablonovitch, E., "Inhibited spontaneous emission of photons in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, 2059-2061, 1987.
doi:10.1103/PhysRevLett.58.2059

2. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett., Vol. 58, 2486-2489, 1987.
doi:10.1103/PhysRevLett.58.2486

3. Banerjee, A., "Enhanced refractometric optical sensing by using one-dimensional ternary photonic crystals," Progress In Electromagnetics Research, Vol. 89, 11-22, 2009.
doi:10.2528/PIER08112105

4. Jim, K. L., D. Y. Wang, C. W. Leung, C. L. Choy, and H. L. W. Chan, "One-dimensional tunable ferroelectric photonic crystals based on Ba0.7Sr0.3TiO3/MgO multilayer thin films," J. Appl. Phys., Vol. 103, 083107, 2008.
doi:10.1063/1.2907418

5. Tanabe, T., M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, "Low mode volume slotted photonic crystal single nanobeam cavity," Appl. Phys. Lett., Vol. 97, 151112, 2005.
doi:10.1063/1.2089185

6. Sirigiri, J. R., K. E. Kreischer, J. Machuzak, I. Mastovsky, M. A. Shapiro, and R. J. Temkin, "Photonic-band-gap resonator gyrotron," Phys. Rev. Lett., Vol. 86, 5628, 2001.
doi:10.1103/PhysRevLett.86.5628

7. Smirnova, E. I., A. S. Kesar, I. Mastovsky, M. A. Shapiro, and R. J. Temkin, "Demonstration of a 17 GHz, high-gradient accelerator with a photonic-band-gap structure," Phys. Rev. Lett., Vol. 95, 074801, 2005.
doi:10.1103/PhysRevLett.95.074801

8. Zhang, H. F., M. Li, and S. B. Liu, "Study periodic band gap structure of the magnetized plasma photonic crystals," Optelectron Lett., Vol. 5, 112-116, 2009.
doi:10.1007/s11801-009-8165-0

9. Zhang, H. F., S. B. Liu, X. K. Kong, B. R. Bian, and Y. Dai, "Omnidirectional photonic band gaps enlarged by Fibonacci quasi-periodic one-dimensional ternary superconductor photonic crystals," Solid State Commun., Vol. 152, 2113-2119, 2012.
doi:10.1016/j.ssc.2012.09.009

10. Kuzmiak, V. and A. A. Maradudin, "Distribution of electromagnetic field and group velocities in two-dimensional periodic systems with dissipative metallic components," Phy. Rev. B, Vol. 58, 7230-7251, 1998.
doi:10.1103/PhysRevB.58.7230

11. Hojo, H. and A. Mase, "Dispersion relation of electromagnetic waves in one dimensional plasma photonic crystals," Plasma Fusion Res., Vol. 80, 89-90, 2004.
doi:10.1585/jspf.80.89

12. Sakai, O. and K. Tachibana, "Plasma as metamaterial: A review," Plasma Sources Sci. Technol., Vol. 21, 013001, 2012.
doi:10.1088/0963-0252/21/1/013001

13. Ginzberg, V. L., The Propagation of Electromagnetic Waves in Plasmas, Pergamon, Pergamon, New York, 1970.

14. Qi, L. and Z. Yang, "Modified plane wave method analysis of dielectric plasma photonic crystal," Progress In Electromagnetics Research, Vol. 91, 319-332, 2009.
doi:10.2528/PIER09022605

15. Guo, B., "Photonic band gap structures of obliquely incident electromagnetic wave propagation in a one-dimension absorptive plasma photonic crystal," Phys. Plasmas, Vol. 16, 043508, 2009.
doi:10.1063/1.3116642

16. Li, C., S. Liu, X. Kong, H. Zhang, B. Bian, and X. Zhang, "A novel comb-like plasma photonic crystals filter in the presence of evanescent wave," IEEE Trans. Plasma Sci., Vol. 39, 1969-1973, 2011.
doi:10.1109/TPS.2011.2162653

17. Zhang, H. F., S. B. Liu, and X. K. Kong, "Enlarged the omnidirectional band gap in one-dimensional plasma photonic crystals with ternary Thue-Morse aperiodic structure," Physica B, Vol. 410, 244-250, 2013.
doi:10.1016/j.physb.2012.10.025

18. Zhang, H. F., S. B. Liu, X. K. Kong, L. Zhou, C. Z. Li, and B. R. Bian, "Enlarged omnidirectional photonic photonic band gap in heterostructure of plasma and dielectric photonic crystals," Optik, Vol. 124, 751-756, 2013.
doi:10.1016/j.ijleo.2012.01.025

19. Shiverhwari, L., "Zero permittivity band characteristics in one-dimensional plasma dielectric photonic crystals," Optik, Vol. 122, 1523-1526, 2011.
doi:10.1016/j.ijleo.2010.09.036

20. Sakaguchi, T., O. Sakai, and K. Tachibana, "Photonic bands in two-dimensional microplasma array II. Band gaps observed in millimeter and sub-terahertz ranges," J. Appl. Phys., Vol. 101, 073305, 2007.
doi:10.1063/1.2713940

21. Sakai, O., T. Sakaguchi, and K. Tachibana, "Photonic bands in two-dimensional mircoplasma array I. Theoretical derivation of band structure of electromagnetic waves," J. Appl. Phys., Vol. 101, 073304, 2007.
doi:10.1063/1.2713939

22. Fan, W. and L. Dong, "Tunable one-dimensional plasma photonic crystals in dielectric barrier discharge," Phys. Plasmas, Vol. 17, 073506, 2010.
doi:10.1063/1.3456520

23. Guo, B., "Photonic band gap structures of obliquely incident electromagnetic wave propagation in a one-dimension absorptive plasma photonic crystal," Phys. Plasmas, Vol. 16, 043508, 2009.
doi:10.1063/1.3116642

24. Liu, S. B., C. Q. Gu, J. J. Zhou, and N. C. Yuan, "FDTD simulation for magnetized plasma photonic crystals," Acta Physica Sinica, Vol. 55, 1283-1288, 2006.

25. Zhang, H. F., L. Ma, and S. B. Liu, "Defect mode properties of magnetized plasma photonic crystals," Acta Physica Sinica, Vol. 58, 01071-01075, 2009.

26. Zhang, H. F., S. B. Liu, X. K. Kong, L. Zou, C. Z. Li, and W. S. Qing, "Enhancement of omnidirectional photonic band gaps in one-dimensional dielectric plasma photonic crystals with a matching layer," Phys. Plasmas, Vol. 19, 022103, 2012.
doi:10.1063/1.3680628

27. Zhang, H. F., S. B. Liu, X. K. Kong, B. R. Bian, and Y. Dai, "Omnidirectional photonic band gap enlarged by one-dimensional ternary unmagnetized plasma photonic crystals based on a new Fibonacci quasiperiodic structure," Phys. Plasmas, Vol. 19, 122102, 2012.
doi:10.1063/1.4769128

28. Qi, L., Z. Yang, and T. Fu, "Defect modes in one-dimensional magnetized plasma photonic crystals with a dielectric defect layer," Phys. Plasmas, Vol. 19, 012509, 2012.
doi:10.1063/1.3677876

29. Zhang, H. F., S. B. Liu, and X. K. Kong, "Photonic band gaps in one-dimensional magnetized plasma photonic crystals with arbitrary declination," Phys. Plasmas, Vol. 19, 122103, 2012.
doi:10.1063/1.4766474

30. Hamidi, S. M., "Optical and magneto-optical properties of one-dimensional magnetized coupled resonator plasma photonic crystals," Phys. Plasmas, Vol. 19, 012503, 2012.
doi:10.1063/1.3677263

31. Mehdian, H., Z. Mohammadzahery, and A. Hasanbeigi, "Analysis of plasma-magnetic photonic crystals with a tunable band gap," Phys. Plasmas, Vol. 20, 043505, 2013.
doi:10.1063/1.4795306

32. Qi, L., "Photonic band structures of two-dimensional magnetized plasma photonic crystals," J. Appl. Phys., Vol. 111, 073301, 2012.
doi:10.1063/1.3699213

33. Zhang, H. F., X. K. Kong, and S. B. Liu, "Analysis of the properties of tunable prohibited band gaps for two-dimensional unmagnetized plasma photonic crystals under TM mode," Acta Physica Sinica, Vol. 60, 055209, 2011.

34. Zhang, H. F., S. B. Liu, and X. K. Kong, "Defect mode properties of two-dimensional unmagnetized plasma photonic crystals with line-defect under transverse magnetic mode," Acta Physica Sinica, Vol. 60, 025215, 2011.

35. Fu, T., Z. Yang, Z. Shi, F. Lan, D. Li, and X. Gao, "Dispersion properties of a 2D magnetized plasma metallic photonic crystals," Phys. Plasmas, Vol. 20, 023109, 2013.
doi:10.1063/1.4792264

36. Zhang, H. F., S. B. Liu, X. K. Kong, B. R. Bian, and Y. N. Guo, "Dispersion properties of two-dimensional plasma photonic crystals with periodically external magnetic field," Solid State Commun., Vol. 152, 1221-1229, 2012.
doi:10.1016/j.ssc.2012.04.055

37. Qi, L. and X. Zhang, "Band gap characteristics of plasma with periodically varying external magnetic field," Solid State Commun., Vol. 151, 1838-1841, 2011.
doi:10.1016/j.ssc.2011.08.012

38. Zhang, H. F., S. B. Liu, X. K. Kong, and B. R. Bian, "The characteristics of photonic band gaps for three-dimensional unmagnetized dielectric plasma photonic crystals with simple-cubic lattice," Optic Commun., Vol. 288, 82-90, 2013.
doi:10.1016/j.optcom.2012.09.078

39. Zhang, H. F., S. B. Liu, X. K. Kong, and B. R. Bian, "The properties of photonic band gaps for three-dimensional plasma photonic crystals in a diamond structure," Phys. Plasmas, Vol. 20, 042110, 2013.
doi:10.1063/1.4801043

40. Zhang, H. F., S. B. Liu, and X. K. Kong, "Dispersion properties of three-dimensional plasma photonic crystals in diamond lattice arrangement," J. Lightwave Technol., Vol. 17, 1694-1702, 2013.
doi:10.1109/JLT.2013.2256879

41. Zhang, H. F., S. B. Liu, and B. X. Li, "The properties of photonic band gaps for three-dimensional tunable photonic crystals with simple-cubic lattices doped by magnetized plasma," Optics & Laster Technology, Vol. 50, 93-102, 2013.
doi:10.1016/j.optlastec.2013.02.011

42. Zhang, H. F., S. B. Liu, H. Yang, and X. K. Kong, "Analysis of photonic band gap in dispersive properties of tunable three-dimensional photonic crystals doped by magnetized plasma," Phys. Plasmas, Vol. 20, 032118, 2013.
doi:10.1063/1.4798523

43. Li, Z. Y., J. Wang, and B. Y. Gu, "Creation of partial gaps in anisotropic photonic-band-gap structures," Phy. Rev. B, Vol. 58, 3721-3729, 1998.
doi:10.1103/PhysRevB.58.3721

44. Malkova, N., S. Kim, T. Dilazaro, and V. Gopalan, "Symmetrical analysis of complex two-dimensional hexagonal photonic crystals," Phys. Rev. B, Vol. 67, 125203, 2003.
doi:10.1103/PhysRevB.67.125203

45. Li, Z. Y., B. Y. Gu, and G. Y. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett., Vol. 81, 2574-2577, 1998.
doi:10.1103/PhysRevLett.81.2574

46. Li, Z. and L. Lin, "Photonic band structures solved by a plane-wave-based transfer-matrix method," Phys. Rev. E, Vol. 67, 056702, 2003.
doi:10.1103/PhysRevE.67.056702

47. Marrone, M., V. F. Rodriguez-Esquerre, and H. E. Hernandez-Figueroa, "Novel numerical method for the analysis of 2D photonic crystals: The cell method," Opt. Exp., Vol. 10, 1299-1304, 2002.
doi:10.1364/OE.10.001299

48. Jun, S., Y. S. Cho, and S. Im, "Moving least-square method for the band-structure calculation of 2D photonic crystals," Opt. Exp., Vol. 11, 541-551, 2003.
doi:10.1364/OE.11.000541

49. Chiang, P., C. Yu, and H. Chang, "Analysis of two-dimensional photonic crystals using a multidomain pseudospectral method," Phys. Rev. E, Vol. 75, 026703, 2003.
doi:10.1103/PhysRevE.75.026703

50. Lou, M., Q. H. Liu, and Z. Li, "Spectral element method for band structures of three-dimensional anisotropic photonic crystals," Phys. Rev. E, Vol. 80, 56702, 2012.

51. Zhang, H. F., S. B. Liu, X. K. Kong, L. Zhou, C. Z. Li, and B. R. Bo, "Comment on `photonic bands in two-dimensional microplasma array. I. Theoretical derivation of band structures of electromagnetic wave'," J. Appl. Phys., Vol. 110, 026104, 2011.
doi:10.1063/1.3605490

Prof. Hai Feng Zhang

Dr. Shaobin Liu

Dr. Xiang-Kun Kong