The Proposed Strategies to Achieve All-Angle, Polarization Insensitive and Broad Band Self- Collimation in 2D Square Lattice Photonic Crystals

Subject Areas : Majlesi Journal of Telecommunication Devices

Mina  Noori ¹ ()
Mohammad  Soroosh ² ()
Hamed  Baghban ³ ()

Received: 2014-11-23 Accepted : 2014-12-03 Published : 2014-12-01

Keywords: en,

Abstract :

In this article, we investigated the possibility of achieving all- angle, polarization insensitive and broad band self- collimation simultaneously in a same structure, which is one of the most recently introduced urgent requirements in the field of optical integration. In order to fulfill these three attractive properties in 2D square array photonic crystals, different strategies are used and a comprehensive analysis using Plane Wave Expansion and Finite Difference Time Domain methods are done. Here, the main attempt was to save the structure’s simple geometry and not to complicate the basic structure. So in order to get all- angle self- collimation, we had to use relatively high index material (n=6) for hole type structure which shows less dependency on polarization. The optimized structure has a frequency range of 2.6%, supporting all-angle self- collimation for both polarizations achieved to the expense of small deviation of 30 in collimation direction from ideal case, although it will not cause any significant problem for small sized devices in the field of optical integration. 

References:

[1] S. E. D. N. Chigrin, C. M. S. Torres, and G. Tayeb, "Self-guiding in two- dimensional photonic crystals," Optics Express, vol. 11, pp. 1203-1211, 2003.

[2] M. I. R. E. Hamam, S. G. Johnson, J. D. Joannopoulos, M. Soljacic, , "Broadband super-collimation in a hybrid photonic crystal structure," Optics Express vol. 17, pp. 8109-8118, 2009.

[3] F. Shuai and W. Yi-Quan, "Light propagation properties of two-dimensional photonic crystal channel filters with elliptical micro-cavities," Chinese Physics B, vol. 20, p. 104207, 2011.

[4] S. S. D. W. Prather, A. Sharkawy, S. McBride, P. Zanzucchi, C. Chen, D. Pustai, S. Venkataraman, J.Murakowski, G. Schneider, "Dispersion engineering of photonic crystals," Proc. SPIE, vol. 5184, pp. 30- 40, 2003.

[5] D. Jovanovic, R. Gajic, and K. Hingerl, "Refraction and band isotropy in 2D square-like Archimedean photonic crystal lattices," Opt Express, vol. 16, pp. 4048-58, Mar 17, 2008.

[6] M. Notomi, "Theory of light propagation in strongly modulated photonic crystals:

Refractionlike behavior in the vicinity of the photonic band gap," PHYSICAL REVIEW B, vol. 62, pp. 10696- 10705, 2000.

[7] R. M. R. Gajic, F. Kuchar, and K. Hingerl, "All-angle left-handed negative refraction in Kagome and honeycomb lattice photonic crystals," Phys. Rev. B, vol. 73, pp. 165310-17, 2006.

[8] R. M. R. Gaji ć, F. Kuchar, Đ. Jovanović , K. Hingerl, "Negative refraction and left-handedness in 2D Archimedean lattice photonic crystals," Mater. Sci. Forum, vol. 555, pp. 83-88, 2007.

[9] M. M. L.J. Wu, T. Karle, T.F. Krauss, "Super-prism phenomena in planar photonic crystals," IEEE J. Quantum Electron, vol. 38, pp. 915-918, 2002.

[10] M. M. A. E. Akosman, H. Kurt, E. Ozbay, "Compact wavelength de-multiplexer design using slow light regime of photonic crystal waveguides," Optics Express, vol. 19, pp. 24129-24138, 2011.

[11] L. C. B. F. J. Lawrence, K. B. Dossou, C. M. de Sterke, "Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition," Appl. Phys. Lett, vol. 93, p. 131111, 2008.

[12] K. X. Z. H. Wu, H. J. Yang, P. Jiang, X.J.He, "All-angle self-collimation in two- dimentional rhombic- lattice photonic crystals," vol. 14, pp. IOP publishing, journal of optics, 2012.

[13] M. B. d. l. E. J. Lugo, R. Doti, R. Nava, J. Tague˜na, R. A. del, J. Faubert, "Multiband negative refraction in one-dimensional photonic crystals," Optics Express, vol. 17, pp. 3042-3051, 2009.

[14] A. K. T. M. Shih, M. Dahelm, G. Petrich, M. Soljaˇci´c, E. Ippen, L. Kolodziejski, K. Hall, M. Kesler, "Supercollimation in photonic crystals composed of silicon rods," Appl. Phys. Lett, vol. 93, p. 131111, 2008.

[15] R. C. F. Shuai, W. W. Zhong, W. Y. Quan, "Controlling the self-collimation characteristics of a near-infrared two-dimensional metallic photonic crystal," Chin. Phys. B, vol. 21, p. 114212, 2012.

[16] H. W. L. Jiang, X. Li, "Polarization-insensitive and broad-angle self-collimation in a two-dimensional photonic crystal with rectangular air holes," Applied Optics, vol. 52, pp. 6676-6684, 2013.

[17] T. B. W. W. Y. Liang, C. P. Yin, J. W. Dong, F. C. Leng, and H. Z. Wang, "Super-broadband non-diffraction guiding modes in photonic crystals with elliptical rods," J. Phys. D: Appl. Phys, vol. 43, p. 075103, 2010.

[18] S. G. L. M.W. Kim, T.T. Kim, J.E. Kim, H. Y. Park, C.S. Kee, "Experimental demonstration of bending and splitting of self-collimated beams in two-dimensional photonic crystals," Appl. Phys. Lett, vol. 90, pp. 1131211-3, 2007.

[19] M. M. L.J. Wu, T.F. Krauss, "Beam steering in planar-photonic crystals: from superprism to supercollimator," J. Lightwave Technol, vol. 21, pp. 561–566, 2003.

[20] T. K. H. Kosaka, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami "Self-collimating phenomena in photonic crystals," Appl. Phys. Lett, vol. 74, pp. 1212-1214, 1999.

[21] K. X. Q. Xu, H. Yang, "Optimize design super collimation in square lattice two-dimensional photonic crystals," Optik - International Journal for Light and Electron Optics, vol. 121, pp. 1573-1576, 2010.

[22] D. Gao, Z. Zhou, and D. S. Citrin, "Self-collimated waveguide bends and partial bandgap reflection of photonic crystals with parallelogram lattice," J Opt Soc Am A Opt Image Sci Vis, vol. 25, pp. 791-5, Mar 2008.

[23] C. C. D. W. Prather, S. Shi, B. Miao, D. M. Pustai, S. Venkataraman, A. S. Sharkawy, G. J. Schneider, and J. A. Murakowski, "Ultralow-loss photonic crystal waveguides based on the self-collimation effect," Photonic Crystal Materials and Devices II, SPIE, vol. 5360, p. 175, 2004.

[24] D. S. G. J. Hou, H. M. Wu, and Z. P. Zhou, "Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals," Optics Communications, vol. 282, pp. 3172-3176, 2009.

[25] X. J. C. Y. Xu, S. Lan, Q. Guo, W. Hu, L. J. Wu, "The all-angle self-collimating phenomenon in photonic crystals with rectangular symmetry," J. Opt. A, vol. 10, p. 085201, 2008.

[26] A. F. Matthews, "Experimental demonstration of self-collimation beaming and splitting in photonic crystals at microwave frequencies," Optics Communications, vol. 282, pp. 1789-1792, 2009.

[27] Y. Z. Y. Zhang, and B. Li, "Optical switches and logic gates based on self- collimated beams in two-dimensional photonic crystals," Optics Express, vol. 15, pp. 9287-9292, 2007.

[28] Z. W. G. Zheng, D. Zhao, W. Zhang, Y. Liu, "Wavelength- division- multiplexing system with photonic crystal self- collimation and co- directional coupling effect," Optik - International Journal for Light and Electron Optics, vol. 125, pp. 2638- 2641, 2014.

[29] H. W. Y. Wang, Q. Xue, W. Zheng, "Photonic crystal self- collimation sensor," Optics Express, vol. 20, pp. 12111-12118, 2012.

[30] H. L. X.-Y. Chen, Y.-S. Qiu, Y.-F. Wang, and B. Ni, "Tunable Photonic Crystal Mach-Zehnder Interferometer Based on Self-collimation Effect," Chinese Physics Letters, vol. 25, pp. 4307-4310, 2008.

[31] W. Zhang, J. Liu, W.-P. Huang, and W. Zhao, "Self-collimating photonic-crystal wave plates," Optics Letters, vol. 34, pp. 2676-2678, 2009/09/01 2009.

[32] R. Iliew, C. Etrich, T. Pertsch, F. Lederer, and K. Staliunas, "Subdiffractive all-photonic crystal Fabry-Perot resonators," Optics Letters, vol. 33, pp. 2695-2697, 2008.

[33] S. Xiao-Peng, H. Kui, Y. Fang, L. Hai-Peng, W. Zi-Yu, and Z. Qi, "New Configuration of Ring Resonator in Photonic Crystal Based on Self-Collimation," Chinese Physics Letters, vol. 25, p. 4288, 2008.

[34] A. P. K. X. S. Christina, "Design of optical logic gates using self- collimated beams in 2D photonic crystal," Photonic Sensors, vol. 2, pp. 173- 179, 2012.

[35] Y. F. H. W. P. Lin, H. L. Kuo, , "Design of optical nor logic gates using two dimension photonic crystals," American Journal of Modern Physics, vol. 2, pp. 144- 147, 2012.

[36] T. P. White, C. M. de Sterke, R. C. McPhedran, and L. C. Botten, "Highly efficient wide-angle transmission into uniform rod-type photonic crystals," Applied Physics Letters, vol. 87, pp. -, 2005.

[37] J. J. P. R. C. Rumpf, "Optimization of planar self-collimating photonic crystals," J. Opt. Soc. Am. A, vol. 30, pp. 1297-1304, 2013.

[38] S. G. L. J. M. Park, H.R. Park, M. H. Lee, "self- collimating photonic crystal antireflection structure for both TE and TM polarizations," Optics Express, vol. 18, pp. 13083-13093 2010.

[39] T. J. S. Y. C. Chuang, "Complex rhombus lattice photonic crystals for broadband all-angle self-collimation," J. Opt, vol. 12, p. 035102, 2010.

[40] Y. C. H. Zhang, L. Chen, H. Zhu, L. Qian, D. Fan, "Full-angle collimations of two-dimensionalphotonic crystals with ultrahigh-indexbackground materials," IOP publishing, Journal of Optics, vol. 12, pp. 045103-045108, 2010.

[41] X. J. C. Y. Xu, S.Lan, Q. F. Dai, Q. Guo, L. J. Wu, "Polarization-independent self-collimation based on pill-void photonic crystals with square symmetry," optics Express, vol. 17, pp. 4903-12, 2009.

[42] K. H. X.P. Shen, Y.F. Shen, H.P. Li, Z.W. Xiao, J. Zheng, "Self-collimation of unpolarized electromagnetic waves in 2D photonic crystals," Acta Phys. Sin, vol. 55, pp. 2760–2764, 2006.

[43] B. U. A. Cicek, "Polarization-independent waveguiding with annular photonic crystal," Optics Express, vol. 17, pp. 18381-18386, 2009.

[44] L. A. D. V. Zabelin, N. Le Thomas, R. Houdr´e, M. V. Kotlyar, L. O’Faolin, T. F. Krauss, , "Self- collimating photonic crystal polarization beam splitter," Opt. Lett vol. 32, pp. 530-532, 2007.

[45] I. H. G. M. Turduev, H. Kurt, "Modified annular photonic crystals with enhanced dispersion relations: polarization insensitive self- collimation and nanophotonic wire waveguide designs," J. Opt. Soc. Am. B, vol. 29, pp. 1589- 1598, 2012.

[46] H. W. L. Y. Jiang, X. Y. Li, "Study on the polarization-insensitive self-collimation behavior in two-dimensional all-solid photonic crystals," J Opt. Springer, vol. 43, pp. 108-116, 2014.

[47] S. G. J. Chiyan Luo, J. D. Joannopoulos, J. B. Pendry, "All-angle negative refraction without negative effective index," PHYSICAL REVIEW B, vol. 65, pp. 201104- 4, 2002.

[48] M. L. J. Witzens, and A. Scherer, "Self-collimation in planar photonic crystals," Ieee Journal Of Selected Topics In Quantum Electronics, vol. 8, pp. 1246-1257, 2002.

[49] Y. O. Y. Ogawa, Y. Iida, "Study on Self-Collimated Light-Focusing Device Using the 2-D Photonic Crystal With a Parallelogram Lattice," J. Lightwave Technol vol. 23, p. 4374, 2005.

[50] H. W. L. Jiang, X. Li, "Polarization- insensitive and broad- angle self- collimation in a two- dimentional photonic crystal with rectangular air holes," Applied optics, vol. 52, pp. 6676-6684, 2013.

[51] F. F. M. Ebnali-Heidari, A. Ebnali-Heidari, "self- collimation effect in two- dimensional photonic crystal based on optofluidic technology," Progress In Electromagnetics Research M, vol. 25, pp. 255–268, 2012.