Vol. 48

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2014-08-07

The Electromagnetic Properties of the Generalized Cantor Stack in Spherical Multilayered Systems

By Gennadiy Burlak, Maricruz Najera Villeda, and Rene Santaolaya Salgado
Progress In Electromagnetics Research Letters, Vol. 48, 1-6, 2014
doi:10.2528/PIERL14061001

Abstract

By the transfer matrix approach we numerically study the electromagnetic properties (narrow peak positions) of the transmission spectra for microspheres coated by a multilayered stack with the generalized Cantor structure (fractal). As opposed to the standard Cantor system with removed γ/3 [γ=1] section we consider here the solid stack with Si/SiO2 layers at general γ value. In such a solid composition the SiO2 layers replace the empty Cantor sections and the parameter γ acquires meaning of a specific control parameter. At successive generations the central layers (in blocks of the spherical stack) acquire a progressive decreased width that leads to generation of the radially inhomogeneous defects. We show that the wave phase interference in such a fractal pattern leads to formation of very narrow electromagnetic transmittance resonances that can be used in modern optoelectronics.

Citation


Gennadiy Burlak, Maricruz Najera Villeda, and Rene Santaolaya Salgado, "The Electromagnetic Properties of the Generalized Cantor Stack in Spherical Multilayered Systems," Progress In Electromagnetics Research Letters, Vol. 48, 1-6, 2014.
doi:10.2528/PIERL14061001
http://www.jpier.org/PIERL/pier.php?paper=14061001

References


    1. Braginsky, V. B., M. L. Gorodetsky, and V. S. Ilchenko, "Quality-factor and nonlinear properties of optical whispering-gallery modes," Phys. Lett. A, Vol. 137, 393-399, 1989.
    doi:10.1016/0375-9601(89)90912-2

    2. Astratov, V., "Fundamentals and applications of microsphere resonator circuits in photonic microresonator research and applications," Springer Series in Optical Sciences, Vol. 156/2010, 423-457, 2010.
    doi:10.1007/978-1-4419-1744-7_17

    3. Stratton, A., Electromagnetic Theory, McGraw-Hill, New York, 1941.

    4. Brady, D., G. Papen, and J. E. Sipe, "Spherical distributed dielectric resonators," J. Opt. Soc. Am. B, Vol. 10, 644-651, 1993.
    doi:10.1364/JOSAB.10.000644

    5. Burlak, G., et al., "Electromagnetic oscillations in the multilayer spherical resonator," Opt. Commun., Vol. 180, 49-60, 2000.
    doi:10.1016/S0030-4018(00)00697-0

    6. Chan, C. T., et al., "Photonic band gaps from metallo-dielectric spheres," Physica B, Vol. 279, 150-159, 2000.
    doi:10.1016/S0921-4526(99)00705-X

    7. Miyazaki, H., et al., "Photonic band in two-dimensional lattices of micrometer-sized spheres mechanically arranged under a scanning electron microscope," J. Appl. Phys., Vol. 87, 7152-7159, 2000.
    doi:10.1063/1.372962

    8. Talebi, R., K. Abbasian, and A. Rostami, "Analytical modeling of quality factor for shell type microsphere resonators," Progress In Electromagnetics Research B, Vol. 30, 293-311, 2011.

    9. Astratov, V. N., A. Darafsheh, M. D. Kerr, K. W. Allen, and N. M. Fried, "Focusing microprobes based on integrated chains of microspheres," PIERS Online, Vol. 6, No. 8, 793-799, 2010.
    doi:10.2529/PIERS091220210416

    10. Astratov, V. N., S. P. Ashili, and A. M. Kapitonov, "Optical properties of mesoscopic systems of coupled microspheres," PIERS Online, Vol. 3, 278-280, 2007.
    doi:10.2529/PIERS060908001922

    11. Burlak, G., "Enhanced optical fields in a multilayered microsphere with quasiperiodic spherical stack," Phys. Scr., Vol. 76, 571-576, 2007.
    doi:10.1088/0031-8949/76/5/027

    12. Burlak, G. and A. D?az-de-Anda, "Optical fields in a multilayered microsphere with quasiperiodic spherical stack," Optics. Commun., Vol. 281, 181-189, 2008.
    doi:10.1016/j.optcom.2007.09.026

    13. Burlak, G., A. D′?az-de-Anda, and A. Zamudio-Lara, "The narrow transmission peaks and field confinement produced by defects in a multilayered microsphere," Optics Commun., Vol. 285, 1542-1549, 2012.
    doi:10.1016/j.optcom.2011.11.101

    14. Gouyet, J. F., Physics and Fractal Structures, Springer, Berlin, 1996.

    15. Zhong, Y. X. and Z. H. Wang, "Super narrow bandpass filter using fractal cantor structures," Int. J. Infrared. Milli., Vol. 25, 1315-1323, 2004.

    16. Burlak, G., The Classical and Quantum Dynamics of the Multispherical Nanostructures, Imperial College Press, 2004.

    17. Panofsky, W. and M. Phillips, Classical Electricity and Magnetism, 2nd Edition, Chapter 13, Addison-Wesley Publishing Company, Reading, MA, 1962.