volume | PIER Journals

Abstract

The dispersion characteristics of woodpile three-dimensional (3D) function photonic crystals (PCs) composed of plasma and function dielectric elements are theoretically investigated by a modified plane wave expansion method, respectively, and the formulas to obtain the dispersion diagrams are given. Only two cases are considered, which are the presence and absence of the external magnetic field. The external magnetic field is vertical to the wave vector, which means that only the magneto-optic Voiget effect is considered. For the proposed PCs, the function dielectric square columns are inserted into the plasma background with face-centered-tetragonal symmetry according to the woodpile lattices. The relationships between the parameters of such PCs and the features of the photonic band gaps (PBGs) for the extraordinary mode and electromagnetic wave are studied under two different cases. The calculated results show that the dispersion characteristics of the proposed PCs can be tailored by adjusting those parameters. If the extrinsic magnetic field does not exist, larger PBG can be found in the present PCs than 3D dielectric-air PCs, 3D function dielectric PCs and 3D plasma-dielectric PCs with the same lattices. If there is an external magnetic field, the narrower PBG for the extraordinary mode can be obtained than the 3D function dielectric PCs and 3D plasma-dielectric PCs with the same lattices. The computed results also show us a approach to realize the reconfigurable devices based on the PCs.

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

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

3. Joannopoulos, J. J., R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, New Jersey, 1995.

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

5. Ginzburg, V. L., The Propagation of Electromagnetic Waves in Plasmas, Pergamon, Oxford, New York, 1970.

6. 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

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

8. Zhang, H. F. and S. B. Liu, "Magneto-optical faraday effects in dispersive properties and unusual surface plasmon modes in the three-dimensional magnetized plasma photonic crystals," IEEE Photonics J., Vol. 6, 5300112, 2014.

9. Guo, B., "Photonic band gap structures of obliquely incident electromagnetic wave propagation in a one-dimension absorptive plasma photonic crystal," Phys. Plasmas, Vol. 16, 042508, 2009.
doi:10.1063/1.3116642

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

11. Zhang, H. F., "Investigations on the two-dimensional aperiodic plasma photonic crystals with fractal Fibonacci sequence," AIP Adv., Vol. 7, 2059-2549, 2017.

12. Shiveshwari, L., "Zero permittivity band characteristics in one-dimensional plasma dielectric photonic crystal," Optik, Vol. 122, 1523, 2011.
doi:10.1016/j.ijleo.2010.09.036

13. Dehnavi, Z. N., H. R. Askari, M. Malekshahi, and D. Dorranian, "Investigation of tunable omnidirectional band gap in 1D magnetized full plasma photonic crystals," Phys. Plasmas, Vol. 24, 093517, 2017.
doi:10.1063/1.5004695

14. 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

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

16. Zhang, H. F., S. B. Liu, and Y. C. Jiang, "The properties of photonic band gap and surface plasmon modes in the three-dimensional magnetized photonic crystals as the mixed polarized modes considered," Journal of Plasma Physics, Vol. 81, 90581020, 2015.
doi:10.1017/S0022377814001238

17. Ardakani, A. G., "Nonreciprocal electromagnetic wave propagation in one-dimensional ternary magnetized plasma photonic crystals," J. Opt. Soc. Am. B, Vol. 31, 332, 2014.
doi:10.1364/JOSAB.31.000332

18. Mehdian, Z. Mohammadzahery, and A. Hasanbeigi, "The effect of magnetic field on bistability in 1D photonic crystal doped by magnetized plasma and coupled nonlinear defects," Phys. Plasmas, Vol. 21, 012101, 2014.
doi:10.1063/1.4858897

19. Zhang, H. F., S. B. Liu, J. P. Zhen, and Y. J. Tang, "The right circular polarized waves in the three-dimensional anisotropic dispersive photonic crystals consisting of the magnetized plasma and uniaxial material as the Faraday effects considered," Phys. Plasmas, Vol. 21, No. 3, 032127, 2014.
doi:10.1063/1.4869729

20. Zhang, H. F. and S. B. Liu, "The properties of surface plasmon modes and switching gap for extraordinary mode in the three-dimensional magnetized plasma photonic crystals based on the Vogit effects," IEEE Journal of Quantum Electronics, Vol. 50, No. 7, 518-588, 2014.

21. 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

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

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

24. Zhang, H. F., S. Liu, and X.-K. Kong, "Properties of anisotropic photonic band gaps in three-dimensional plasma photonic crystals containing the uniaxial material with different lattices," Progress In Electromagnetics Research, Vol. 141, 267-289, 2013.
doi:10.2528/PIER13051703

25. 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. 31, 1694, 2013.
doi:10.1109/JLT.2013.2256879

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

27. Ho, K. M., C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, "Photonic band gaps in three dimensions: New layer-by-layer periodic structures," Solid State Commun., Vol. 89, 413-416, 1994.
doi:10.1016/0038-1098(94)90202-X

28. Kopperschmidt, P., "Tetragonal photonic woodpile structures," Appl. Phys. B, Vol. 76, 729-734, 2003.
doi:10.1007/s00340-003-1169-8

29. Fan, S. H., P. R. Villeneuve, and J. D. Joannopoulos, "Theoretical investigation of fabrication-related disorder on the properties of photonic crystals," J. Appl. Phys., Vol. 78, 1415-1418, 1995.
doi:10.1063/1.360298

30. Zhang, H. F., S. B. Liu, and X. K. Kong, "Investigation of anisotropic photonic band gaps in three-dimensional magnetized plasma photonic crystals containing the uniaxial material," Phys. Plasmas, Vol. 20, 092105, 2013.
doi:10.1063/1.4820771

31. Zhang, H. F., S. B. Liu, and Y. C. Jiang, "Tunable all-angle negative refraction and photonic band gaps in two-dimensional plasma photonic crystals with square-like Archimedean lattices," Phys. Plasmas, Vol. 21, 092104, 2014.
doi:10.1063/1.4894213

32. Maksymov, I. S., L. F. Marsal, M. A. Ustyantsev, and J. Pallarès, "Band structure calculation in two-dimensional Kerr-nonlinear photonic crystals," Opt. Commun., Vol. 248, 469-477, 2005.
doi:10.1016/j.optcom.2004.12.022

33. Azuma, H., "Quantum computation with Kerr-nonlinear photonic crystals," Journal of Physics D: Applied Physics, Vol. 41, 369-374, 2012.

34. Youssefi, B., M. K. Moravvej-Farshi, and N. Granpayeh, "Two bit all-optical analog-to-digital converter based on nonlinear Kerr effect in 2D photonic crystals," Opt. Commun., Vol. 285, 3228-3233, 2012.
doi:10.1016/j.optcom.2012.02.081

35. Zhang, H. F., "Three-dimensional function photonic crystals," Physica B, Vol. 525, 104-113, 2017.

36. Liu, X. J., Y. Liang, J. Ma, S. Q. Zhang, H. Li, X. Y. Wu, and Y. H. Wu, "Two-dimensional function photonic crystals," Physic E, Vol. 85, 227-237, 2017.
doi:10.1016/j.physe.2016.09.002

37. Wu, X. Y., S. Q. Zhang, B. J. Zhang, X. J. Liu, J. Wang, H. Li, N. Ba, X. G. Yin, and J. W. Li, "The effect of defect layer on transmissivity and light field distribution in general function photonic crystals," Physica E, Vol. 53, 1, 2013.
doi:10.1016/j.physe.2013.03.020

38. Fan, S., P. R. Villeneuve, and J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B, Vol. 54, 11245-11251, 1996.
doi:10.1103/PhysRevB.54.11245

39. McIntosh, K. A., L. J. Mahoney, K. M. Molvar, O. B. McMahon, S. Verghese, M. Rothschild, and E. R. Brown, "Three-dimensional metallodielectric photonic crystals exhibiting resonant infrared stop bands," Appl. Phys. Lett., Vol. 70, 2937, 1997.
doi:10.1063/1.118749

40. Li, J., G. Sun, and C. T. Chan, "Optical properties of photonic crystals composed of metal-coated spheres," Phys. Rev. B, Vol. 73, 075117, 2006.
doi:10.1103/PhysRevB.73.075117

41. Feng, L., M. H. Lu, V. Lomakin, and Y. Fainman, "Plasmonic photonic crystals with complete bandgap for surface plasmon polariton waves," Appl. Phys. Lett., Vol. 93, 231105, 2008.
doi:10.1063/1.3043581

42. Tserkezis, C., "Effective parameters for periodic photonic structures of resonant elements," J. Phys. Condens Matter, Vol. 21, 155404, 2009.
doi:10.1088/0953-8984/21/15/155404

43. Tserkezis, C., N. Stefanou, G. Gantzounis, and N. Papanikolaou, "Understanding artificial optical magnetism of periodic metal-dielectric-metal layered structures," Phys. Rev. B, Vol. 84, 115455, 2011.
doi:10.1103/PhysRevB.84.115455

44. Park, D. J., C. Zhang, J. C. Ku, Y. Zhou, G. C. Schatz, and C. A. Mirkin, "Plasmonic photonic crystals realized through DNA-programmable assembly," Proc. Ntnl. Acad. Sci., Vol. 112, 977, 2015.
doi:10.1073/pnas.1422649112

45. Dobson, D. C., J. Gopalakrishnan, and J. E. Pasciak, "An efficient method for band structure calculations in 3D photonic crystals," Journal of Computational Physics, Vol. 161, 668-679, 2000.
doi:10.1006/jcph.2000.6521

46. Zhang, H. F., G. W. Ding, H. M. Li, and S. B. Liu, "Complete photonic band gaps and tunable self-collimation in the two-dimensional plasma photonic crystals with a new structure," Phys. Plasmas, Vol. 22, 022105, 2015.
doi:10.1063/1.4906886

47. Ho, K. M., C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett., Vol. 65, 3152, 1990.
doi:10.1103/PhysRevLett.65.3152

48. Li, L., "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A, Vol. 13, 1870, 1996.
doi:10.1364/JOSAA.13.001870

Prof. Hai Feng Zhang

Dr. Hao Zhang