Analytical Investigation of TM Surface Waves in 1D Photonic Crystals Capped by a Self-Focusing Left-Handed Slab
الموضوعات : فصلنامه نانوساختارهای اپتوالکترونیکیKarim Milanchian 1 , Zahra eyni 2
1 - Department of Physics, Payame Noor University, PO BOX 19395-3697 Tehran, IRAN
2 - Department of Physics, Payame Noor University, PO BOX 19395-3697 Tehran, IRAN
الکلمات المفتاحية: Photonic Crystals, Nonlinear surface waves, Left-handed materials,
ملخص المقالة :
In this paper, the localized TM surface waves of a nonlinear self-focusing
left-handed slab sandwiched between a uniform medium and a one-dimensional
photonic crystal (1D PC) is analytically investigated. Our method is based on the first
integral of the nonlinear Maxwell's equations. For the TM surface waves, the presence
of two electric field components makes the analysis difficult. Therefore, we used the
uniaxial approximation for the nonlinear slab. The considered 1D PC can be a lefthanded
PC (made of alternate left-handed (LH) and right-handed material) or a usual
PC. In these structures, we find that the nonlinear LHM slab allows to control the
dispersion properties of p-polarized surface waves. It is shown that there are no surface
modes in the linear regime in the conventional PC and by increasing the intensity of
electromagnetic field to higher value, the surface modes are emerged. To confirm our
achievements, we also compared
[1] J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding
the Flow of Light, 2nd ed, Princeton University Press, New Jersey, 2008.
[2] E. Yablonovitch, Photonic band-gap structures, J. Opt. Soc. Am. B. 10 (1993)
283-295.
[3] P. Lodahl, A. Floris van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D.
Vanmaekelbergh, and W. L. Vos, Controlling the dynamics of spontaneous
emission from quantum dots by photonic crystals, Nature., 430 (2004) 654-657.
[4] Q. Gong and X. Hu, Photonic Crystals: Principles and Applications. CRC Press,
2013.
[5] Liyong Cui, Xiao Li, Jun Chen, Yongyin Cao, Guiqiang Du, and Jack Ng, Onedimensional
photonic crystals bound by light, Phys. Rev. A., 96 (2017) 023833.
[6] A. Yariv and P. Yeh, Optical Waves in Layered Media. Wiley, New York,
1988.
[7] A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky,
Surface states in photonic crystals, Phys. Usp., 53 (2010) 243–256.
[8] J. Polo, T. Mackay, and A. Lakhtakia, Electromagnetic Surface Waves: A
Modern Perspective, Waltham, MA: Elsevier, 2013.
[9] R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos,
Electromagnetic Bloch waves at the surface of a photonic crystal, Phys. Rev. B.,
44 (1991) 10961.
[10] P. Yeh, A. Yariv, and A. Y. Cho, Optical surface waves in periodic layered
media, Appl. Phys. Lett., 32 (1978) 104–105.
[11] M. J. Serpe, Y. Kang, and Q. M. Zhang, Photonic Materials for Sensing, Biosensing and Display Devices. Springer, 2016.
[12] A. Sinibaldi, R. Rizzo, G. Figliozzi, E. Descrovi, N. Danz, P. Munzert, A. Anopchenko, and F. Michelotti, A full ellipsometric approach to optical sensing with Bloch surface waves on photonic crystals, Opt. Express., 21 (2013) 23331–23344.
[13] Z. Eyni, A. Namdar, S. Roshan Entezar and H. Tajalli, Dispersion properties of nonlinear surface waves in one-dimensional photonic crystals with a nonlinear self-defocusing cap layer of left-handed metamaterial, J. Opt. Soc. Am. B., 27 (2010) 2116-2121.
[14] A. Namdar, S. Roshan Entezar, H. Tajalli and Z. eyni. Backward nonlinear surface Tamm states in left-handed metamaterials, Opt. Express., 16 (2008) 10543-10548.
[15] Z. Eyni, S. Roshan Entezar, A. Namdar, and H. Tajalli. Tamm states of a nonlinear slab sandwiched between a uniform medium and a one-dimensional photonic crystal, PIERL., 18 (2010) 115-124.
[16] S. Roshan Entezar A. Namdar, H. Tajalli and Z. eyni. Nonlinear surface waves in one-dimensional photonic crystals containing left-handed metamaterials. Phys. Rev. A., 78 (2008) 023816.
[17] R. A. Shelby, D. R. Smith, and S. Schultz. Experimental verification of a negative index of refraction, Science., 292 (2001) 77–79.
[18] U. K. Chettiar, A. V. Kildishev, H. K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm, Opt. Lett., 32 (2007) 1671–1673.
[19] A. Boltasseva and V. M. Shalaev, Fabrication of optical negative-index metamaterials: Recent advances and outlook, Metamaterials., 2 (2008) 1–17.
[20] V. K. Fedyanin and D. Mihalache, P-polarized surface polaritons in layered structures, Z. Phys. B-Condesed Matter., 47 (1982) 167-173.
[21] A. A. D. Boardman, A. A. Maradudin, G. I. stegman, T. Twardowski and E. M. Wright, Exact theory of nonlinear p-polarized optical waves, Phys. Rev. A., 35 (1987) 1159-1164.
[22] A. A. Zharov,, I. V. Shadrivov, and Y. S. Kivshar, Nonlinear properties of left-handed metamaterials, Phys. Rev. Lett., 91 (2003) 37401.
[23] Handbook of Mathematical Function, Dover, New York, 1972, 569-576.
[24] A. Namdar, I. V. Shadrivov, and Y. S. Kivshar, Excitation of backward Tamm states at an interface between a periodic photonic crystal and a left-handed metamaterial, Phys. Rev. A., 75 (2007) 053812.
