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ANALYTIC EXPRESSION FOR THE EFFECTIVE PLASMA FREQUENCY IN ONE-DIMENSIONAL METALLIC-DIELECTRIC PHOTONIC CRYSTAL

By J. Manzanares-Martinez

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Abstract:
In this work, an analytic expression to define the effective plasma frequency of an one-dimensional periodic system containing alternating dielectric and metallic slabs is proposed. Such metallic elements are considered to have a Drude dielectric function. The effective plasma frequency is obtained as a simple average of the constitutive materials, and its cutoff frequency for the propagating modes is compared with band structure calculations. We also explore the role of absorption in the transparency frequency cutoff.

Citation:
J. Manzanares-Martinez, "Analytic Expression for the Effective Plasma Frequency in One-Dimensional Metallic-Dielectric Photonic Crystal," Progress In Electromagnetics Research M, Vol. 13, 189-202, 2010.
doi:10.2528/PIERM10061905

References:
1. Sievenpiper, D. F., M. E. Sickmiller, and E. Yablonovitch, "3D wire mesh photonic crystals," Phys. Rev. Lett., Vol. 76, No. 14, 2480-2483, 1996.
doi:10.1103/PhysRevLett.76.2480

2. Pendry, J. B., A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett., Vol. 76, No. 25, 4773-4776, 1996.
doi:10.1103/PhysRevLett.76.4773

3. Raether, H., Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer, Berlin, 1988.

4. Kreibig, U. and M. Vollmer, Optical Properties of Metal Clusters, Springer, Berlin, 1995.

5. Low, K. L., M. Z. MatJarfi, and S. A. Khan, "Effective plasma frequency for two-dimensional metallic photonic crystals," Progress In Electromagnetics Research M, Vol. 12, 67-79, 2010.
doi:10.2528/PIERM10031505

6. Jiang, T., L. Shen, X. Zhang, and L. X. Ran, "High-order modes of spoof surface plasmon polaritons on periodically corrugated metal surfaces ," Progress In Electromagnetics Research M, Vol. 8, 91-102, 2009.
doi:10.2528/PIERM09062901

7. Soto-Puebla, D., M. Xiao, and F. Ramos-Mendieta, "Optical properties of a dielectric-metallic superlattice: The complex photonic bands," Phys. Lett. A, Vol. 326, 273-280, 2004.
doi:10.1016/j.physleta.2004.03.070

8. Kong, F., K. Li, H. Huang, B. I. Wu, and J. A. Kong, "Analysis of the surface magnetoplasmon modes in the semiconductor slit waveguide at terahertz frequencies," Progress In Electromagnetics Research, Vol. 82, 257-270, 2008.
doi:10.2528/PIER08031224

9. Apostol, M. and G. Vaman, "Plasmons and diffraction of an electromagnetic plane wave by a metallic sphere," Progress In Electromagnetics Research, Vol. 98, 97-118, 2009.
doi:10.2528/PIER09100103

10. Srivastava, S. K. and S. P. Ojha, "Photonic band gaps in one-dimensional metallic star waveguide structure," Progress In Electromagnetics Research, Vol. 84, 349-362, 2008.
doi:10.2528/PIER08080501

11. Pokrovsky, A. L. and A. L. Efros, "Electrodynamics of metallic photonic crystals and the problem of left-handed materials," Phys. Rev. Lett., Vol. 89, No. 9, 093901-093904, 2002.
doi:10.1103/PhysRevLett.89.093901

12. Maslovski, S. I., S. A. Tetryakov, and P. A. Belov, "Wire media with negative effective permittivity: A quasi-static model," Microwave Opt. Technol. Lett., Vol. 35, No. 1, 47-51, 2002.
doi:10.1002/mop.10512

13. Markos, P. and C. M. Soukoulis, "Absorption losses in periodic arrays of thin metallic wires," Opt. Lett., Vol. 28, 846-848, 2003.
doi:10.1364/OL.28.000846

14. Tretyakov, S., Analytical Modeling in Applied Electromagnetics, Artech-House Publishing, New-York, 2004.

15. Pendry, J. B., A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter, Vol. 10, No. 22, 4785-4809, 1998.
doi:10.1088/0953-8984/10/22/007

16. Smith, D. R., D. C. Vier, W. Padilla, C. S. Nemat-Nasse, and S. Shultz, "Loop-wire medium for investigating plasmons at microwave frequencies," Appl. Phys. Lett., Vol. 75, 1425-1427, 1999.
doi:10.1063/1.124714

17. Sigalas, M. M., C. T. Chan, K. M. Ho, and C. M. Soukoulis, "Metallic photonic band-gap materials," Phys. Rev. B, Vol. 52, No. 16, 11744-11751, 1995.
doi:10.1103/PhysRevB.52.11744

18. Brand, S., R. A. Abram, and M. A. Kaliteevski, "Complex photonic band structure and effective plasma frequency of a two-dimensional array of metal rods," Phys. Rev. B, Vol. 75, No. 3, 035102-035109, 2007.
doi:10.1103/PhysRevB.75.035102

19. Sarychev, A. K. and V. M. Shalaev, "Electromagnetic field fluctuations and optical nonlinearities in metal-dielectric composites," Phys. Rep., Vol. 335, 275-371, 2000.
doi:10.1016/S0370-1573(99)00118-0

20. Pimenov, A. and A. Loidl, "Experimental demonstration of artificial dielectrics with a high index of refraction," Phys. Rev. B, Vol. 74, No. 19, 193102-193105, 2006.
doi:10.1103/PhysRevB.74.193102

21. Pimenov, A., M. Biberacher, D. Ivannikov, A. Loidl, A. A. Mukhin, Y. G. Goncharov, and A. M. Balbashov, "Scaling of terahertz conductivity at the metal-insulator transition in doped manganites ," Phys. Rev. B, Vol. 73, No. 22, 220407-220410, 2006.
doi:10.1103/PhysRevB.73.220407

22. Pimenov, A. and A. Loidl, "Conductivity and permittivity of two-dimensional metallic photonic crystals," Phys. Rev. Lett., Vol. 96, No. 6, 063903-063906, 2006.
doi:10.1103/PhysRevLett.96.063903

23. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 282, 77-79, 2001.
doi:10.1126/science.1058847

24. Ward, A. J., J. B. Pendry, and W. J. Stewart, "Photonic dispersion surfaces," J. Phys.: Condens. Matter, Vol. 7, 2217-2224, 1995.
doi:10.1088/0953-8984/7/10/027

25. Scalora, M., M. J. Bloemer, A. S. Pethel, J. P. Dowling, C. M. Bowden, and A. S. Manka, "Transparent, metallo-dielectric, one-dimensional, photonic band-gap structure," J. Appl. Phys., Vol. 83, No. 5, 2377-2383, 1998.
doi:10.1063/1.366996

26. Bloemer, M. J. and M. Scalora, "Transmissive properties of Ag/MgF2 photonic band gaps," Appl. Phys. Lett., Vol. 72, No. 14, 1676-1678, 1998.
doi:10.1063/1.121150

27. Feng, S., J. M. Elson, and P. L. Overfelt, "Transparent photonic band in metallodielectric nanostructures," Phys. Rev. B, Vol. 72, No. 8, 085117-085122, 2005.
doi:10.1103/PhysRevB.72.085117

28. Xu, X., Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, "Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals ," Appl. Phys. Lett., Vol. 86, 09112-09114, 2005.

29. Jackson, J. D., Classical Electrodynamics, Wiley, New York, 1999.

30. Yeh, P., A. Yariv, and C. H. Hong, "Electromagnetic propagation in periodic startified media. I. General theory," J. Opt. Soc. A, Vol. 67, No. 4, 423-438, 1977.
doi:10.1364/JOSA.67.000423

31. Bergmair, M., M. Huber, and K. Hingerl, "Band structure, Wiener bounds, and coupled surface plasmons in one dimensional photonic crystals," Appl. Phys. Lett., Vol. 89, 081907-081909, 2006.
doi:10.1063/1.2338546


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