Studying Focusing Properties of Graded Index Photonic Crystals Made of Material with Different Refractive Index
الموضوعات : فصلنامه نانوساختارهای اپتوالکترونیکیNasrin Miri 1 , Abdolrasoul Gharaati 2
1 - Physics Department, Payame Noor University, Tehran, Iran
2 - Physics Department, Payame Noor University, Tehran, Iran
الکلمات المفتاحية: effective refractive index, plane wave expansion, graded index photonic crystals, finite-difference time-domain,
ملخص المقالة :
In this paper we investigate focusing properties of graded index (GRIN) photonic crystal (PC) structures which are composed of different materials with different refractive indices. GRIN PC structure is constructed from air holes in dielectric background. The holes radii are varied in the normal direction to the propagation in such a way that a parabolic effective refractive index is produced. The focusing characteristic is studied relative to the refractive index variation of background material. While increasing refractive index of background material of the GRIN PC structure, the effective refractive index of the structure increases. With increasing effective refractive index, the focusing capability of the GRIN PC structure increase and outgoing wave at focal point will be more concentrated. The result shows that the designed GRIN PC structure work very well as a focusing lens. The finite-difference time-domain (FDTD) method was employed to compute field propagation through GRIN PC structure. Also, plane wave expansion (PWE) method has been carried out to extract the dispersion properties
[1] E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electronics, Phy. Rev. lett. 58 (1987) 2059.
[2] S. John, Strong localization of photons in certain disordered dielectric superlattices. Phy. Rev. Lett. 58(23) (1987) 2486.
[3] Lončar M, Vučković J, and Scherer A,. Methods for controlling positions of guided modes of photonic-crystal waveguides, J. Opt. Soc. Am. B 18 (2001)1362-1368.
[4] Kurt H, Citrin D S,. Photonic-crystal heterostructure waveguides, IEEE J. Quant. Electron. 43 (2007) 78-84.
[5] Zhou W D, Sabarinathan J, Bhattacharya P, Kochman B, Berg E, Yu P C, and Pang S,. Characteristics of a photonic bandgap single defect microcavity electroluminescent device, IEEE J. Quant. Electron. 37 (2001) 1153-1160.
[6] Luo C, Johnson S G, Joannopoulos J., Pendry J,. All-angle negative refraction without negative effective index. Phys. Rev. B. 65(20) (2002) 201104.
[7] Kosaka H, Kawashima T, Tomita A, Notomi M, Tamamura T, Sato T, et al. Superprism phenomena in photonic crystals. Phys. Rev. B. 58(16) (1998) R10096.
[8] Amet J, Baida F I, Burr G W , Bernal M P,. The superprism effect in lithium niobate photonic crystals for ultra-fast, ultra-compact electro-optical switching. PHOTONIC NANOSTRUCT. 6(1) (2008) 47-59.
[9] Kosaka H, Kawashima T, Tomita A, Notomi M, Tamamura T, Sato T, et al. Self-collimating phenomena in photonic crystals. Appl. Phys. Lett. 74(9) (1999) 1212-4.
[10] Kim T T, Lee S G, Park H Y, Kim J E, Kee C S,. Asymmetric Mach-Zehnder filter based on self-collimation phenomenon in two-dimensional photonic crystals. Opt. Express. 18(6) (2010) 5384-9.
[11] E. Centeno, D. Cassagne, Graded photonic crystals. Opt. Lett. 30 (2005) 2278-2280.
[12] E. Centeno, D. Cassagne, J. P.Albert, Mirage and superbending effect in two-dimensional graded photonic crystals. Phys. Rev. B. 73(23) (2006) 235119.
[13] Turduev M, Oner B, Giden I, and Kurt H,. Mode transformation using graded photonic crystals with axial asymmetry, J. Opt. Soc. Am. B 30 (2013) 1569-1579.
[14] Oner B B, Turduev M, Giden I H, and Kurt H,. Efficient mode converter design using asymmetric graded index photonic structures. Opt. lett. 38(2) (2013) 220-222.
[15] Kurt H, Oner B B, Turduev M, and Giden I H,. Modified Maxwell fish-eye approach for efficient coupler design by graded photonic crystals. Opt. express. 20(20) (2012) 22018-22033.
[16] Yilmaz D, Giden I H, Turduev M, and Kurt H,. Design of a Wavelength selective medium by graded index photonic crystals. IEEE J. Quant. Electron. 49(5) (2013) 477-484.
[17] Le Roux X, Caer C, Marris-Morini D, Izard N, Vivien L, and Cassan E,. Wavelength demultiplexer based on a two-dimensional graded photonic crystal. IEEE PHOTONIC TECH L. 23(15) (2011) 1094-1096.
[18] Turduev M, Giden I H, and Kurt H,. Design of flat lens-like graded index medium by photonic crystals: Exploring both low and high frequency regimes. Opt. Commun. 339 (2015) 22-33.
[19] H. Kurt, D. S. Citrin, Graded index photonic crystals. Opt. Express. 15(1240-1253), 3, (2007).
[20] H. Kurt, E. Colak, O. Cakmak, H. Caglayan, E. Ozbay, The focusing effect of graded index photonic crystals. Appl. Phys. Lett, 93(171108), (2008).
[21] Wang, H.W., & Chen, L.W. A cylindrical optical black hole using graded index photonic crystals. J. Appl. Phys. 109(103104), 10, (2011).
[22] E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, & J.M. Lourtioz, Graded photonic crystals curve the flow of light: An experimental demonstration by the mirage effect. Appl. Phys. Lett. 92(133501), 13, (2008).
[23] A. O. Cakmak, E. Colak, H. Caglayan, , H. Kurt, E. Ozbay, High efficiency of graded index photonic crystal as an input coupler. J. Appl. Phys. 105(103708), 10, (2009).
[24] M. Lu, B. K. Juluri, , S.C. S. Lin, B. Kiraly, T. Gao, T. J. Huang, Beam aperture modifier and beam deflector using gradient-index photonic crystals. J. Appl. Phys. 108(103505), 10, (2010).
[25] N. Yogesh, V. Subramanian, Spatial beam compression and effective beam injection using triangular gradient index profile photonic crystals. Prog. Electromagn. Res. 129 (2012) 51-67.
[26] M. Turduev, I. H. Giden, H. Kurt, Design of flat lens-like graded index medium by photonic crystals: Exploring both low and high frequency regimes. Opt. Commun. 339 (2015) 22-33.
[27] B. Vasić, R. Gajić, K. Hingerl, Graded photonic crystals for implementation of gradient refractive index media. Journal of Nanophotonics, 5(051806-051806-051807) (2011) 1.
[28] A. Taflove, , S. C. Hagness, Computational Electrodynamics: ''The Finite-Difference Time-Domain Method'' , 2nd Ed Artech House Publishers, 2005.
[29] Sukhoivanov, Igor A., and Igor V. Guryev. Photonic crystals: physics and practical modeling. Vol. 152. Springer, 2009.
[30] Gomez-Reino C, Perez MV, Bao C. Gradient-index optics: fundamentals and applications. Springer Science & Business Media, 2012.
[31] Notomi, á., Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap. Phys. Rev. B, (2000). 62(16) 10696.
[32] Aspnes, D. Local-field effects and effective-medium theory: A microscopic perspective. Am. J. Phys. (1982) 50(8).
[33] Sihvola, A.H., Electromagnetic mixing formulas and applications, pp. 39-84, the Institution of Electrical Engineers, London, United Kingdom (1999).
[34] Kirchner, A., K. Busch, and C. Soukoulis, Transport properties of random arrays of dielectric cylinders. Phys. Rev. B. 57(1) (1998) 277.
[35] Halevi, P., A. Krokhin, and J. Arriaga, Photonic crystal optics and homogenization of 2D periodic composites. Phys. Rev. lett. 1999. 82(4) (1999) 719.
