Abstract
The photon properties of two-dimensional periodic structures formed by infinite homogeneous dielectric cylinders packed in a square lattice have been investigated theoretically. Depending on the dielectric contrast between the cylinders and the surrounding medium, the photonic band structure, transmission spectra of crystals with a finite number of layers, and spectra of Mie scattering by an isolated cylinder have been calculated. The calculations have been performed for the TE polarization. The transformation of photonic stop-bands corresponding to Bragg and Mie resonances has been analyzed using the obtained data. The main effect consists in “castling” energy positions of the Bragg stop-bands and Mie stop-bands. For low-contrast photonic crystals, the low-frequency region of the energy spectrum is determined by Bragg stop-bands, and Mie stop-bands are located higher in energy. With an increase in the dielectric contrast, the energy of Mie stop-bands decreases, and they intersect the region of Bragg stop-bands weakly varying in the TE polarization and form the low-energy region of the spectrum.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Optical Properties of Photonic Structures: Interplay of Order and Disorder, Ed. by M. F. Limonov and R. M. De La Rue (CRC Press, Boca Raton, Florida, United States, 2012).
S. O’Brien and J. B. Pendry, J. Phys.: Condens. Matter 14, 4035 (2002).
K. Vynck, D. Felbacq, E. Centeno, A Cǎbuz, D. Cassagne, and B. Guizal, Phys. Rev. Lett. 102, 133 901 (2009).
E. Kallos, I. Chremmos, and V. Yannopapas, Phys. Rev. B: Condens. Matter 86, 245108 (2012).
Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, Mater. Today 12, 60 (2009).
E. A. Semouchkina, G. B. Semouchkin, M. Lanagan, and C. A. Randall, IEEE Trans. Microwave Theory Tech. 53, 1477 (2005).
M. Iwasaki, E. A. Semouchkina, G. B. Semouchkin, K. Z. Rajab, C. A. Randall, and M. T. Lanagan, Jpn. J. Appl. Phys. 45, 2835 (2006).
E. Semouchkina, Metamaterials: Classes, Properties and Applications (Nova Science, New York, 2010), pp. 137–164.
E. Semouchkina, Metamaterial (InTech, Rijeka, Croatia, 2012), pp. 91–112.
F. Chen, X. Wang, and E. Semouchkina, Microwave Opt. Technol. Lett. 54, 555 (2012).
A. Hosseinzadeh and E. Semouchkina, Microwave Opt. Technol. Lett. 55, 134 (2013).
V. M. Shalaev and A. K. Sarychev, Electrodynamics of Metamaterials (World Scientific, Singapore, 2007).
V. N. Astratov, V. N. Bogomolov, A. A. Kaplyanskii, A. V. Prokofiev, L. A. Samoilovich, S. M. Samoilovich, and Y. A. Vlasov, Nuovo Cimento Soc. Ital. Fis., D 17, 1349 (1995).
S. G. Romanov, T. Maka, C. M. Sotomayor Torres, M. Müller, R. Zentel, D. Cassagne, J. Manzanares-Martinez, and C. Jouanin, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 63, 056603 (2001).
A. V. Baryshev, A. V. Ankudinov, A. A. Kaplyanskii, V. A. Kosobukin, M. F. Limonov, K. B. Samusev, and D. E. Usvyat, Phys. Solid State 44(9), 1648 (2002).
A. V. Baryshev, A. A. Kaplyanskii, V. A. Kosobukin, M. F. Limonov, and A. P. Skvortsov, Phys. Solid State 46(7), 1331 (2004).
E. Palacios-Lidón, B. H. Juárez, E. Castillo-Martinez, and C. López, J. Appl. Phys. 97, 63502 (2005).
M. V. Rybin, A. V. Baryshev, M. Inoue, A. A. Kaplyanskii, V. A. Kosobukin, V. F. Limonov, A. K. Samusev, and A. V. Sel’kin, Photonics Nanostruct.: Fundam. Appl. 4, 146 (2006).
M. V. Rybin, K. B. Samusev, and M. F. Limonov, Photonics Nanostruct.: Fundam. Appl. 5, 119 (2007).
M. V. Rybin, K. B. Samusev, and M. F. Limonov, Phys. Solid State 49(12), 2280 (2007).
M. V. Rybin, A. V. Baryshev, A. B. Khanikaev, M. Inoue, K. B. Samusev, A. V. Sel’kin, G. Yushin, and M. F. Limonov, Phys. Rev. B: Condens. Matter 77, 205106 (2008).
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998).
M. F. Limonov, Y. E. Kitaev, A. V. Chugreev, V. P. Smirnov, Y. S. Grushko, S. G. Kolesnik, and S. N. Kolesnik, Phys. Rev. B: Condens. Matter 57, 7586 (1998).
P. Tronc, Y. Kitaev, G. Wang, M. Limonov, A. Panfilov, and G. Neu, Phys. Status Solidi B 216, 599 (1999).
Y. E. Kitaev, M. F. Limonov, A. G. Panfilov, R. A. Evarestov, and A. P. Mirgorodsky, Phys. Rev. B: Condens. Matter 49, 9933 (1994).
J. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University Press, Princeton, New Jersey, United States, 2008).
J. A. Stratton, Electromagnetic Theory (Wiley, New York, 2007).
A. V. Moroz, M. F. Limonov, M. V. Rybin, and K. B. Samusev, Phys. Solid State 53(6), 1105 (2011).
I. I. Shishkin, K. B. Samusev, M. V. Rybin, M. F. Limonov, Yu. S. Kivshar’, A. Gaidukeviichute, R. V. Kiyan, and B. N. Chichkov, JETP Lett. 95(9), 457 (2012).
K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).
R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, Phys. Rev. B: Condens. Matter 48, 8434 (1993).
D. S. Watkins, Fundamentals of Matrix Computations, 3rd ed. (Wiley, New York, 2010).
S. G. Johnson and J. D. Joannopoulos, Opt. Express 8, 173 (2001).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.V. Rybin, I.S. Sinev, K.B. Samusev, A. Hosseinzadeh, G.B. Semouchkin, E.A. Semouchkina, M.F. Limonov, 2014, published in Fizika Tverdogo Tela, 2014, Vol. 56, No. 3, pp. 567–572.
Rights and permissions
About this article
Cite this article
Rybin, M.V., Sinev, I.S., Samusev, K.B. et al. Photonic properties of two-dimensional high-contrast periodic structures: Numerical calculations. Phys. Solid State 56, 588–593 (2014). https://doi.org/10.1134/S1063783414030275
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063783414030275