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We propose a two-dimensional photonic crystal structure with low rotational symmetry and investigate its band structure characteristics over the whole first Brillouin zone by the plane wave expand method. The physical mechanism of broadband all-angle self-collimation effect and the influence of aspect ratio on the bandwidth are clarified. Furthermore, we obtain the existence criterion for self-collimation modes covering almost the whole fourth band for TE polarization. Especially, there exist two wide flat regions spanning over the first Brillouin zone which exhibit unique properties: one dimension corresponds to broad band from 0.47 to 0.53 (2πc/a), while the other corresponds to all incident angles of 0°–90°. Based on the above unique properties, the broadband all-angle self-collimation propagation with a bandwidth of 187 nm around 1550 nm is demonstrated by the finite-difference time-domain method.
[1] Kosaka H, Kawashima T, Tomita A, Notomi M, Tamamura T, Sato T, Kawakami S 1999 Appl. Phys. Lett. 74 1212
[2] Witzens J, Loncar M, Scherer A 2002 IEEE J. Sel. Top. Quantum Electron. 8 1246
[3] Fan C Z, Wang J Q, He J N, Ding P, Liang E J 2013 Chin. Phys. B 22 074211
[4] Zhang H F, Liu S B, Li B X 2014 Ann. Phys. 347 110
[5] Liu H, Liu D, Zhao H, Gao Y H 2013 Acta Phys. Sin. 62 194208 (in Chinese) [刘会, 刘丹, 赵恒, 高义华 2013 62 194208]
[6] Yue Q Y, Kong F M, Li K, Zhao J 2012 Acta Phys. Sin. 61 208502 (in Chinese) [岳庆炀, 孔凡敏, 李康, 赵佳 2012 61 208502]
[7] Wang X, Gao W S, Hung J, Tam W Y 2014 Appl. Opt. 53 2425
[8] Liang W Y, Chen W H, Yin M, Yin C P 2014 J. Opt. 16 065101
[9] Li W, Zhang X, Lin X, Jiang X 2014 Opt. Lett. 39 4486
[10] Liang W Y, Liu X M, Yin M 2013 J. Phys. D: Appl. Phys. 46 495109
[11] Jin L, Zhu Q Y, Fu Y Q 2013 Chin. Phys. B 22 094102
[12] Jia T, Baba M, Suzuki M, Ganeev R A, Kuroda H, Qiu J, Wang X, Li R, Xu Z 2008 Opt. Express 16 1874
[13] Zhang X, Chen Y H 2012 J. Opt. Soc. Am. B 29 2704
[14] Lawrence F J, de Sterke C M, Botten L C, McPhedran R C, Dossou K B 2013 Adv. Opt. Photon. 5 385
[15] Park J M, Lee S G, Park H Y, Kim J E 2008 Opt. Express 16 20354
[16] Jiang L Y, Wu H, Li X Y 2014 J. Opt. 43 108
[17] Chigrin D N, Enoch S, Sotomayor Torres C M, Tayeb G 2003 Opt. Express 11 1203
[18] Xu Y, Chen X J, Lan S, Guo Q, Hu W, Wu L J 2008 J. Opt. A: Pure Appl. Opt. 10 085201
[19] Wu Z H, Xie K, Yang H J, Jiang P, He X J 2012 J. Opt. 14 015002
[20] Gan L, Qin F, Li Z Y 2012 Opt. Lett. 37 2412
[21] Aghadjani M, Shahabadi M 2013 J. Opt. Soc. Am. B 30 3140
[22] Zhao D, Zhou C, Gong Q, Jiang X 2008 J. Phys. D: Appl. Phys. 41 115108
[23] Wang Y, Wang H, Xue Q, Zheng W 2012 Opt. Express 20 12111
[24] Cheng L F, Ren C, Wang P, Feng S 2014 Acta Phys. Sin. 63 154213 (in Chinese) [程立锋, 任承, 王萍, 冯帅 2014 63 154213]
[25] Johnson S G, Joannopoulos J D 2001 Opt. Express 8 173
[26] Joannopoulos J D, Jonhson S G, Winn J N, Meade R D 2008 Photonic Crystals: Molding the Flow of Light (2nd Ed.) (Princeton NJ: Princeton University Press
[27] Foteinopoulou S, Soukoulis C M 2003 Phys. Rev. B 67 235107
[28] Hsieh M L, Lan Y S 2008 J. Vac. Sci. Technol. B 26 914
[29] Taflove A, Hagness S C 2000 Computational Electrodynamics: The Finite-Difference Time-Domain Method (2nd Ed.) (Boston, MA: Artech House) chapter 3
[30] Witzens J, Hochberg M, Baehr-Jones T, Scherer A 2004 Phsy. Rev. E 69 046609
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[1] Kosaka H, Kawashima T, Tomita A, Notomi M, Tamamura T, Sato T, Kawakami S 1999 Appl. Phys. Lett. 74 1212
[2] Witzens J, Loncar M, Scherer A 2002 IEEE J. Sel. Top. Quantum Electron. 8 1246
[3] Fan C Z, Wang J Q, He J N, Ding P, Liang E J 2013 Chin. Phys. B 22 074211
[4] Zhang H F, Liu S B, Li B X 2014 Ann. Phys. 347 110
[5] Liu H, Liu D, Zhao H, Gao Y H 2013 Acta Phys. Sin. 62 194208 (in Chinese) [刘会, 刘丹, 赵恒, 高义华 2013 62 194208]
[6] Yue Q Y, Kong F M, Li K, Zhao J 2012 Acta Phys. Sin. 61 208502 (in Chinese) [岳庆炀, 孔凡敏, 李康, 赵佳 2012 61 208502]
[7] Wang X, Gao W S, Hung J, Tam W Y 2014 Appl. Opt. 53 2425
[8] Liang W Y, Chen W H, Yin M, Yin C P 2014 J. Opt. 16 065101
[9] Li W, Zhang X, Lin X, Jiang X 2014 Opt. Lett. 39 4486
[10] Liang W Y, Liu X M, Yin M 2013 J. Phys. D: Appl. Phys. 46 495109
[11] Jin L, Zhu Q Y, Fu Y Q 2013 Chin. Phys. B 22 094102
[12] Jia T, Baba M, Suzuki M, Ganeev R A, Kuroda H, Qiu J, Wang X, Li R, Xu Z 2008 Opt. Express 16 1874
[13] Zhang X, Chen Y H 2012 J. Opt. Soc. Am. B 29 2704
[14] Lawrence F J, de Sterke C M, Botten L C, McPhedran R C, Dossou K B 2013 Adv. Opt. Photon. 5 385
[15] Park J M, Lee S G, Park H Y, Kim J E 2008 Opt. Express 16 20354
[16] Jiang L Y, Wu H, Li X Y 2014 J. Opt. 43 108
[17] Chigrin D N, Enoch S, Sotomayor Torres C M, Tayeb G 2003 Opt. Express 11 1203
[18] Xu Y, Chen X J, Lan S, Guo Q, Hu W, Wu L J 2008 J. Opt. A: Pure Appl. Opt. 10 085201
[19] Wu Z H, Xie K, Yang H J, Jiang P, He X J 2012 J. Opt. 14 015002
[20] Gan L, Qin F, Li Z Y 2012 Opt. Lett. 37 2412
[21] Aghadjani M, Shahabadi M 2013 J. Opt. Soc. Am. B 30 3140
[22] Zhao D, Zhou C, Gong Q, Jiang X 2008 J. Phys. D: Appl. Phys. 41 115108
[23] Wang Y, Wang H, Xue Q, Zheng W 2012 Opt. Express 20 12111
[24] Cheng L F, Ren C, Wang P, Feng S 2014 Acta Phys. Sin. 63 154213 (in Chinese) [程立锋, 任承, 王萍, 冯帅 2014 63 154213]
[25] Johnson S G, Joannopoulos J D 2001 Opt. Express 8 173
[26] Joannopoulos J D, Jonhson S G, Winn J N, Meade R D 2008 Photonic Crystals: Molding the Flow of Light (2nd Ed.) (Princeton NJ: Princeton University Press
[27] Foteinopoulou S, Soukoulis C M 2003 Phys. Rev. B 67 235107
[28] Hsieh M L, Lan Y S 2008 J. Vac. Sci. Technol. B 26 914
[29] Taflove A, Hagness S C 2000 Computational Electrodynamics: The Finite-Difference Time-Domain Method (2nd Ed.) (Boston, MA: Artech House) chapter 3
[30] Witzens J, Hochberg M, Baehr-Jones T, Scherer A 2004 Phsy. Rev. E 69 046609
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