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Transmission of light waves at the frequency near the edge of the band gap in two-dimensional square lattice photonic crystals is studied by using the plane wave expansion method (PWM) and finite difference in time domain (FDTD) method. It is found that, directional emission from two-dimensional photonic crystals can be realized if the effective refractive index is nearly zero. Moreover, the direction of the emitting beam is independent of the orientation of the crystal lattice, but dependent on the direction of the crystal surface. This is quite different from the self-collimation phenomenon in photonic crystals.
[1] Yablonvitch E 1987 Phys. Rev. Lett. 58 2059
[2] [3] John S 1987 Phys. Rev. Lett. 58 2486
[4] [5] Lezec H J, Degiron A, Devaux E, Linke R A, Martin-Moreno L, Garcia-Vidal F J, Ebbesen T W 2002 Science 297 820
[6] Gan L, Liu Y Z, Li J Y, Zhang Z B, Zhang D Z, Li Z Y 2009 Opt. Express 17 9962
[7] [8] Bulu I, Caglayan H, Ozbay E 2003 Appl. Phys. Lett. 83 3263
[9] [10] Moreno E, Garca-Vidal F J, Martn-Moreno L 2004 Phys. Rev. B 69 121402
[11] [12] [13] Kramper P, Agio M, Soukoulis C M, Birner A, Mller F, Wehrspohn R B, Gsele U, Sandoghdar V 2004 Phys. Rev. Lett. 92 113903
[14] Morrison S K, Kivshar Y S 2005 Appl. Phys. Lett. 86 081110
[15] [16] [17] Han K, Wang Z Y, Shen X P, Wu Q H, Tong X, Tang G, Wu Y X 2011 Acta Phys. Sin. 60 044212 (in Chinese)[韩奎, 王子煜, 沈晓鹏, 吴琼华, 童星, 唐刚, 吴玉喜 2011 60 044212]
[18] [19] Feng S, Ren C, Wang W Z, Wang Y Q 2012 Chin. Phys. B 21 114212
[20] Gan L, Qin F, Li Z Y 2012 Opt. Lett.37 2412
[21] [22] Liang W Y, Dong J W, Liang G Q, Wang H Z 2009 Appl. Phys. B 96 781
[23] [24] Cao Y J, Yun G H, Narsu 2011 Acta Phys. Sin. 60 077502 (in Chinese)[曹永军, 云国宏, 那日苏 2011 60 077502]
[25] [26] Zhu X F, Liu S C, Xu T, Wang T H, Cheng J C 2010 Chin. Phys. B 19 044301
[27] [28] [29] Veselago V G 1968 Sov. Phys. Usp. 10 509
[30] Notoni M 2000 Phys. Rev. B 62 10696
[31] [32] Foteinopoulou S, Soukoulis C M 2005 Phys. Rev. B 72 165112
[33] [34] [35] Sakoda K 2001 Optical Properties of Photonic Crystals (New York: Springer) p32
[36] [37] Zhang C X, Xu X S 2012 Chin. Phys. B 21 044213
[38] Taflove A, Hagness S C 2000 Computational Electrodynamics: The Finite-Difference Time-Domain Method (2nd Ed.) (Boston: Artech House) p179
[39] [40] [41] Lu S L, Wu X L, Ren X G, Mei Y C, Shen J, Huang Z X 2012 Acta Phys. Sin. 61 194701 (in Chinese)[鲁思龙, 吴先良, 任信钢, 梅诣偲, 沈晶, 黄志祥 2012 61 194701]
[42] Liang G H, L Q Z, Teng A P, Li Y J 2014 Chin. Phys. B 23 054103
[43] [44] [45] Zhang B 2005 Acta Phys. Sin. 54 5677 (in Chinese)[张波 2005 54 5677]
[46] Chigrin D N, Enoch S, Torres C M S, Tayeb G 2003 Opt. Express 11 1203
[47] -
[1] Yablonvitch E 1987 Phys. Rev. Lett. 58 2059
[2] [3] John S 1987 Phys. Rev. Lett. 58 2486
[4] [5] Lezec H J, Degiron A, Devaux E, Linke R A, Martin-Moreno L, Garcia-Vidal F J, Ebbesen T W 2002 Science 297 820
[6] Gan L, Liu Y Z, Li J Y, Zhang Z B, Zhang D Z, Li Z Y 2009 Opt. Express 17 9962
[7] [8] Bulu I, Caglayan H, Ozbay E 2003 Appl. Phys. Lett. 83 3263
[9] [10] Moreno E, Garca-Vidal F J, Martn-Moreno L 2004 Phys. Rev. B 69 121402
[11] [12] [13] Kramper P, Agio M, Soukoulis C M, Birner A, Mller F, Wehrspohn R B, Gsele U, Sandoghdar V 2004 Phys. Rev. Lett. 92 113903
[14] Morrison S K, Kivshar Y S 2005 Appl. Phys. Lett. 86 081110
[15] [16] [17] Han K, Wang Z Y, Shen X P, Wu Q H, Tong X, Tang G, Wu Y X 2011 Acta Phys. Sin. 60 044212 (in Chinese)[韩奎, 王子煜, 沈晓鹏, 吴琼华, 童星, 唐刚, 吴玉喜 2011 60 044212]
[18] [19] Feng S, Ren C, Wang W Z, Wang Y Q 2012 Chin. Phys. B 21 114212
[20] Gan L, Qin F, Li Z Y 2012 Opt. Lett.37 2412
[21] [22] Liang W Y, Dong J W, Liang G Q, Wang H Z 2009 Appl. Phys. B 96 781
[23] [24] Cao Y J, Yun G H, Narsu 2011 Acta Phys. Sin. 60 077502 (in Chinese)[曹永军, 云国宏, 那日苏 2011 60 077502]
[25] [26] Zhu X F, Liu S C, Xu T, Wang T H, Cheng J C 2010 Chin. Phys. B 19 044301
[27] [28] [29] Veselago V G 1968 Sov. Phys. Usp. 10 509
[30] Notoni M 2000 Phys. Rev. B 62 10696
[31] [32] Foteinopoulou S, Soukoulis C M 2005 Phys. Rev. B 72 165112
[33] [34] [35] Sakoda K 2001 Optical Properties of Photonic Crystals (New York: Springer) p32
[36] [37] Zhang C X, Xu X S 2012 Chin. Phys. B 21 044213
[38] Taflove A, Hagness S C 2000 Computational Electrodynamics: The Finite-Difference Time-Domain Method (2nd Ed.) (Boston: Artech House) p179
[39] [40] [41] Lu S L, Wu X L, Ren X G, Mei Y C, Shen J, Huang Z X 2012 Acta Phys. Sin. 61 194701 (in Chinese)[鲁思龙, 吴先良, 任信钢, 梅诣偲, 沈晶, 黄志祥 2012 61 194701]
[42] Liang G H, L Q Z, Teng A P, Li Y J 2014 Chin. Phys. B 23 054103
[43] [44] [45] Zhang B 2005 Acta Phys. Sin. 54 5677 (in Chinese)[张波 2005 54 5677]
[46] Chigrin D N, Enoch S, Torres C M S, Tayeb G 2003 Opt. Express 11 1203
[47]
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