搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

有耗色散光子晶体带隙结构的本征值分析新方法

王辉 沙威 黄志祥 吴先良 沈晶

引用本文:
Citation:

有耗色散光子晶体带隙结构的本征值分析新方法

王辉, 沙威, 黄志祥, 吴先良, 沈晶

A novel eigenvalue method for calculating the band structure of lossy and dispersive photonic crystals

Wang Hui, Sha Wei E. I., Huang Zhi-Xiang, Wu Xian-Liang, Shen Jing
PDF
导出引用
  • 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.
    • 基金项目: 国家自然科学基金(批准号:51277001,61101064,61301062)、教育部新世纪优秀人才支持计划(批准号:NCET-12-0596)、教育部博士学科点专项基金(批准号:20123401110009)、 安徽省杰出青年基金(批准号:1108085J01)和安徽省高校重点项目(批准号:KJ2012A103)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51277001, 61101064, 61301062), the Program for New Century Talents in University of Ministry of Education of China (Grant No. NCET-12-0596), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20123401110009), the Fund for Distinguished Young Scholars of Anhui Province, China (Grant No. 1108085J01), and the Key Program of the Higher Education Institutions of Anhui Province, China (Grant No. KJ2012A103).
    [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

  • [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

  • [1] 肖利, 雷天宇, 梁禺, 赵敏, 刘慧, 张斯淇, 李宏, 马季, 吴向尧. 二维函数光子晶体. 物理学报, 2016, 65(13): 134207. doi: 10.7498/aps.65.134207
    [2] 张亚妮. 低损耗低非线性高负色散光子晶体光纤的优化设计. 物理学报, 2012, 61(8): 084213. doi: 10.7498/aps.61.084213
    [3] 邓舒鹏, 李文萃, 黄文彬, 刘永刚, 彭增辉, 鲁兴海, 宣丽. 基于全息聚合物分散液晶的有机二维光子晶体激光器的研究. 物理学报, 2011, 60(8): 086103. doi: 10.7498/aps.60.086103
    [4] 姜凌红, 侯蓝田. 双零色散光子晶体光纤结构参数的变化对其性能的影响. 物理学报, 2010, 59(2): 1095-1100. doi: 10.7498/aps.59.1095
    [5] 高喜, 杨梓强, 侯钧, 亓丽梅, 兰峰, 史宗君, 李大治, 梁正. 具有变态光子带隙结构的相对论Cherenkov辐射源的研究. 物理学报, 2009, 58(2): 1105-1109. doi: 10.7498/aps.58.1105
    [6] 庄 飞, 沈建其, 叶 军. 调控电磁感应透明气体折射率实现可控光子带隙结构. 物理学报, 2007, 56(1): 541-545. doi: 10.7498/aps.56.541
    [7] 钟 凯, 张会云, 张玉萍, 李喜福, 王 鹏, 姚建铨. 基于六角结构二维光子晶体绝对带隙的优化设计研究. 物理学报, 2007, 56(12): 7029-7033. doi: 10.7498/aps.56.7029
    [8] 谭康伯, 梁昌洪. 有耗孤子的最小作用量原理及其在二维光子带隙结构中的应用. 物理学报, 2007, 56(5): 2704-2708. doi: 10.7498/aps.56.2704
    [9] 刘頔威, 刘盛纲. 二维单斜点阵光子晶体的第一布里渊区及带隙计算. 物理学报, 2007, 56(5): 2747-2750. doi: 10.7498/aps.56.2747
    [10] 顾建忠, 林水洋, 王 闯, 喻筱静, 孙晓玮. 基于补偿型微带谐振单元的一维光子带隙结构. 物理学报, 2006, 55(8): 4176-4180. doi: 10.7498/aps.55.4176
    [11] 曾 隽, 潘杰勇, 董建文, 汪河洲. 大小周期正方格子复合结构的光子带隙特性. 物理学报, 2006, 55(6): 2785-2788. doi: 10.7498/aps.55.2785
    [12] 郝保良, 刘濮鲲, 唐昌建. 二维非正交坐标斜方格金属光子带隙结构. 物理学报, 2006, 55(4): 1862-1867. doi: 10.7498/aps.55.1862
    [13] 潘杰勇, 梁冠全, 毛卫东, 汪河洲. 一类粗锐复合结构光子晶体的完全带隙研究. 物理学报, 2006, 55(2): 729-732. doi: 10.7498/aps.55.729
    [14] 关春颖, 苑立波. 六角蜂窝结构光子晶体异质结带隙特性研究. 物理学报, 2006, 55(3): 1244-1247. doi: 10.7498/aps.55.1244
    [15] 李 蓉, 程 阳, 崔丽彬, 朱 峰, 周 静, 刘大禾, 刘 守, 张向苏. 晶格数目对面心立方结构光子晶体带隙的影响. 物理学报, 2006, 55(1): 188-191. doi: 10.7498/aps.55.188
    [16] 林宝勤, 徐利军, 袁乃昌. 以各向异性介质为衬底的共面紧凑型光子带隙结构. 物理学报, 2005, 54(8): 3711-3715. doi: 10.7498/aps.54.3711
    [17] 车 明, 周云松, 王福合, 顾本源. 二维正方格子磁性光子晶体的带隙结构. 物理学报, 2005, 54(10): 4770-4775. doi: 10.7498/aps.54.4770
    [18] 李蓉, 任坤, 任晓斌, 周静, 刘大禾. 一维光子晶体带隙结构对不同偏振态的角度和波长响应. 物理学报, 2004, 53(8): 2520-2525. doi: 10.7498/aps.53.2520
    [19] 庄飞, 吴良, 何赛灵. 用线性变换方法计算二维正方晶胞正n边形直柱光子晶体的带隙结构. 物理学报, 2002, 51(12): 2865-2870. doi: 10.7498/aps.51.2865
    [20] 王辉, 李永平. 用特征矩阵法计算光子晶体的带隙结构. 物理学报, 2001, 50(11): 2172-2178. doi: 10.7498/aps.50.2172
计量
  • 文章访问数:  4677
  • PDF下载量:  502
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-04-18
  • 修回日期:  2014-05-16
  • 刊出日期:  2014-09-05

/

返回文章
返回