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A novel eigenvalue method is proposed to calculate the band structure of lossy and dispersive photonic crystal (PC). Using an idea from quantum transport problem, a standard linear eigenvalue equation rather than a nonlinear eigenvalue equation is obtained by a rigorous and artful transformation. And the physical parameters of lossy and dispersive PC are obtained by solving the linear eigenvalue equation using finite-difference frequency-domain (FDFD) method. Compared with other methods, the proposed method has great features, such as clear concept, simple calculation, less computing time and storage. A dielectric PC is simulated by the proposed method, and the results accord well with those from the traditional FDFD method, which verifies the validity of the proposed method. Moreover, the dispersion relation of the lossy and dispersive PC is calculated by the proposed method, and the surface plasmon frequency is obtained. Furthermore, the influence of loss on the dispersion relation and eigenmode field distribution is studied. The results provide some theoretical guidance for studying the lossy and dispersive PC.
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Keywords:
- photonic crystals with lossy and dispersive materials /
- band structure /
- linear eigenvalue equation
[1] Johu S 1987 Phys. Rev. Lett. 58 2486
[2] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[3] Winn J N, Fink S, Joannopoulos J D 1998 Opt. Lett. 23 1573
[4] Joannopoulos J D, Villeneuve P R, Fan S 1997 Nature 386 143
[5] Wang D, Xu S, Cao Y W, Qin F 2014 Acta Phys. Sin. 63 018401(in Chinese)[王冬, 徐莎, 曹延伟, 秦奋 2014 物理学报 63 018401]
[6] Huang Z X, Koschny T, Soukoulis C M 2012 Phys. Rev. Lett. 108 187402
[7] Painter O, Lee R K, Scherer A, Yariv A, O' Brien J D, Dapkus P D, Kim I 1999 Science 284 1819
[8] Noda S, Chutinan A, Imada M 2000 Nature 407 608
[9] Fan S H, Johnson S G, Joannopoulos J D, Manolatou C, Haus H A 2001 J. Opt. Soc. Am. B 18 162
[10] Yang H Y D 1996 IEEE Trans. Microwave Theory Tech. 44 2688
[11] Joannopoulos J D, Johnson S G, Winn J N, Meade R D 2008 Photonic Crystals: Molding the Flow of Light (New Jersey: Princeton University Press) pp10-12, 252-258
[12] Sakoda K 2001 Optical Properties of Photonic Crystal ser. Optical Sciences (New York: Springer Press) pp151-154, 13-21
[13] Jiang B, Zhang Y J, Wang Y F, Zheng W H 2012 J. Appl. Phys. 112 033112
[14] Davanco M, Urzhumov Y, Shvets G 2007 Opt. Express 15 9681
[15] Fietz C, Urzhumov Y, Shvets G 2011 Opt. Express 19 19027
[16] Ruhe A 1973 SIAM J. Numer. Anal. 10 674
[17] Shvets G, Urzhumov Y A 2004 Phys. Rev. Lett. 93 243902
[18] Guo S P, Wu F, Albin S, Rogowski R S 2004 Opt. Express 12 1741
[19] Raman A, Fan S H 2010 Phys. Rev. Lett. 104 087401
[20] Wang H, Wu B, Huang Z X, Wu X L 2014 Comput. Phys. Commun. 185 862
[21] Wang H, Huang Z X, Wu X L, Ren X G 2011 Chin. Phys. B 20 114701
[22] Qiu M, He S L 2000 J. Appl. Phys. 87 8268
[23] Luisier M, Schenk A, Fichtner W, Klimeck G 2006 Phys. Rev. B 74 205323
[24] Qiao P F, Sha W E I, Choy W C H, Chew W C 2011 Phys. Rev. A 83 043824
[25] Fung K H, Tang R C H, Chan C T 2011 Opt. Lett. 36 2206
[26] Huang X, Hang Z H, Zheng H, Chan C T 2011 Nature Mat. 10 582
[27] Sha W E I, Choy W C H, Chew W C 2010 Opt. Express 18 5993
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[1] Johu S 1987 Phys. Rev. Lett. 58 2486
[2] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[3] Winn J N, Fink S, Joannopoulos J D 1998 Opt. Lett. 23 1573
[4] Joannopoulos J D, Villeneuve P R, Fan S 1997 Nature 386 143
[5] Wang D, Xu S, Cao Y W, Qin F 2014 Acta Phys. Sin. 63 018401(in Chinese)[王冬, 徐莎, 曹延伟, 秦奋 2014 物理学报 63 018401]
[6] Huang Z X, Koschny T, Soukoulis C M 2012 Phys. Rev. Lett. 108 187402
[7] Painter O, Lee R K, Scherer A, Yariv A, O' Brien J D, Dapkus P D, Kim I 1999 Science 284 1819
[8] Noda S, Chutinan A, Imada M 2000 Nature 407 608
[9] Fan S H, Johnson S G, Joannopoulos J D, Manolatou C, Haus H A 2001 J. Opt. Soc. Am. B 18 162
[10] Yang H Y D 1996 IEEE Trans. Microwave Theory Tech. 44 2688
[11] Joannopoulos J D, Johnson S G, Winn J N, Meade R D 2008 Photonic Crystals: Molding the Flow of Light (New Jersey: Princeton University Press) pp10-12, 252-258
[12] Sakoda K 2001 Optical Properties of Photonic Crystal ser. Optical Sciences (New York: Springer Press) pp151-154, 13-21
[13] Jiang B, Zhang Y J, Wang Y F, Zheng W H 2012 J. Appl. Phys. 112 033112
[14] Davanco M, Urzhumov Y, Shvets G 2007 Opt. Express 15 9681
[15] Fietz C, Urzhumov Y, Shvets G 2011 Opt. Express 19 19027
[16] Ruhe A 1973 SIAM J. Numer. Anal. 10 674
[17] Shvets G, Urzhumov Y A 2004 Phys. Rev. Lett. 93 243902
[18] Guo S P, Wu F, Albin S, Rogowski R S 2004 Opt. Express 12 1741
[19] Raman A, Fan S H 2010 Phys. Rev. Lett. 104 087401
[20] Wang H, Wu B, Huang Z X, Wu X L 2014 Comput. Phys. Commun. 185 862
[21] Wang H, Huang Z X, Wu X L, Ren X G 2011 Chin. Phys. B 20 114701
[22] Qiu M, He S L 2000 J. Appl. Phys. 87 8268
[23] Luisier M, Schenk A, Fichtner W, Klimeck G 2006 Phys. Rev. B 74 205323
[24] Qiao P F, Sha W E I, Choy W C H, Chew W C 2011 Phys. Rev. A 83 043824
[25] Fung K H, Tang R C H, Chan C T 2011 Opt. Lett. 36 2206
[26] Huang X, Hang Z H, Zheng H, Chan C T 2011 Nature Mat. 10 582
[27] Sha W E I, Choy W C H, Chew W C 2010 Opt. Express 18 5993
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