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.
Maricruz Najera Villeda,
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
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
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.