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为计算有耗色散光子晶体的带隙结构，提出了新的本征值分析方法. 该方法借助于量子输运问题中的思想，在本征值方程的推导过程中进行了巧妙的变换，将复杂的非线性本征值问题转化为线性本征值问题；并利用频域有限差分（FDFD）方法直接求解线性本征值方程，最终得到有耗色散光子晶体结构的相关物理参数. 与其他方法相比，该方法的最大特点为概念清晰、计算简便，最终节省了计算时间及所需内存量. 利用该方法，对介质光子晶体结构进行模拟，结果与传统FDFD方法符合较好，从而验证了方法的有效性. 此外，利用所提方法计算了有耗色散光子晶体结构的色散曲线，得到了表面等离子波激发的区域，进一步讨论了损耗对其色散曲线及本征模场的影响. 相关结果对色散有耗光子晶体的研究具有一定的理论指导意义.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
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[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
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[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
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[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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