非长波极限下二维光子晶体中横电模的等效介质理论

耿滔; 王岩; 王新; 董祥美

doi:10.7498/aps.64.154210

摘要

基于Mie散射理论, 推导、建立了适用于非长波极限的二维光子晶体中横电模的等效介质理论. 随后利用该理论探讨了二维光子晶体中横电模的负折射特性和零折射特性, 计算结果与相应的能带结构相符合, 验证了该理论在非长波极限条件下的适用性. 更进一步的是, 使用该理论能得到从能带结构中无法获取的额外信息.

关键词:

An effective medium theory of two-dimensional photonic crystal for TE mode beyond the long-wavelength limit has been established based on the Mie scattering theory. Först, the proposed theory has been used to study the negative-refractive-index photonic crystals for TE mode. This theory can be used to calculate the effective indices and the effective impedance, and to predict the position of the band gap. Results agree well with the band structures, especially when the equifrequency surface contours are almost circular. Then the proposed theory is used to study the zero-refractive-index photonic crystals for TE mode. It can be seen a triply-degenerate point at Γ point, forming a Dirac cone in the band structures. It has been called an “accidental-degeneracy-induced Dirac point”, where the effective index is zero and the effective impedance is 1. Results calculated using the proposed theory agree well with the band structures. This means that the theory can be used well beyond the long-wavelength limit. Furthermore, the additional impedance information, which cannot be obtained by band structures, can be derived from the proposed theory.

Keywords:

作者及机构信息

1.
上海市现代光学系统重点实验室, 教育部光学仪器与系统工程研究中心, 上海理工大学光电信息与计算机工程学院, 上海 200093

基金项目: 上海市青年科技启明星计划项目(批准号: 12QA1402300)、国家自然科学基金青年科学基金(批准号: 61008044)、上海市自然科学基金(批准号: 14ZR1428500)和上海市重点学科项目第三期项目(批准号: S30502)资助的课题.

Authors and contacts

1.
Shanghai Key Lab of Modern Optical System, Engineering Research Center of Optical Instrument and System, Ministry of Education, University of Shanghai for Science and Technology, Shanghai 200093, China

Funds: Project supported by the Shanghai Rising-Star Program, China (Grant No. 12QA1402300), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61008044), the Basic Research Program of Shanghai, China (Grant No. 14ZR1428500), and the Shanghai Leading Academic Discipline Project, China (Grant No. S30502).

参考文献

[1]	Jin L, Zhu Q Y, Fu Y Q 2013 Chin. Phys. B 22 094102
[2]	Li Y N, Gu P F, Zhang J L, Li M Y, Liu X 2006 Acta Phys. Sin. 55 4918 (in Chinese) [厉以宇, 顾培夫, 张锦龙, 李明宇, 刘旭 2006 55 4918]
[3]	Huang X, Lai L, Hang Z H, Zheng H, Chan Z T 2011 Nat. Mater. 10 582
[4]	Zhao H, Shen Y F, Zhang Z J 2014 Acta Phys. Sin. 63 174204 (in Chinese) [赵浩, 沈义峰, 张中杰 2014 63 174204]
[5]	Ginzburg P, Fortuño F J R, Wurtz G A, Dickson W, Murphy A, Morgan F, Pollard J R, Iorsh I, Atrashchenko A, Belov P A, Kivshar Y S, Nevet A, Ankonina G, Orenstein M, Zayats A V 2013 Opt. Express 21 14907
[6]	Li G J, Kang X L, Li Y P 2007 Acta Phys. Sin. 56 6403 (in Chinese) [李国俊, 康学亮, 李永平 2007 56 6403]
[7]	Jin L, Zhu Q Y, Fu Y Q, Yu W X 2013 Chin. Phys. B 22 104101
[8]	Kabashin A V, Evans P, Pastkovsky S, Hendren W, Wurtz G A, Atkinson R, Pollard R, Podolskiy V A, Zayats A V 2009 Nat. Mater. 8 867
[9]	Suchowski H, O’Brien K, Wong Z J, Salandrino A, Yin X, Zhang X 2013 Science 342 1223
[10]	Chui S T, Hu L 2002 Phys. Rev. B 65 144407
[11]	Sarychev A K, McPhedran R C, Shalaev V M 2001 Phys. Rev. B 64 079904
[12]	Koschny T, Economou E N, Smith D R, Vier D C, Soukoulis, C M 2005 Phys. Rev. B 71 245105
[13]	Wu Y, Li J, Zhang Z Q, Chan C T 2006 Phys. Rev. B 74 085111
[14]	Chern R L, Chen Y T 2009 Phys. Rev. B 80 075118
[15]	Jin J, Liu S, Lin Z, Chui S T 2009 Phys. Rev. B 80 115101
[16]	Bohren C F, Huffman D R 1983 Absorption and Scattering of Light by Small Particles (Canada: John Wiley & Sons, Inc) p195
[17]	Notomi M 2000 Phys. Rev. B 62 10696
[18]	Tang Z, Zhang H, Peng R, Ye Y, Shen L, Wen S, Fan D 2006 Phys. Rev. B 73 235103
[19]	Geng T, Liu T Y, zhuang S L 2007 Chin. Opt. Lett. 5 361

施引文献

[1]	Jin L, Zhu Q Y, Fu Y Q 2013 Chin. Phys. B 22 094102
[2]	Li Y N, Gu P F, Zhang J L, Li M Y, Liu X 2006 Acta Phys. Sin. 55 4918 (in Chinese) [厉以宇, 顾培夫, 张锦龙, 李明宇, 刘旭 2006 55 4918]
[3]	Huang X, Lai L, Hang Z H, Zheng H, Chan Z T 2011 Nat. Mater. 10 582
[4]	Zhao H, Shen Y F, Zhang Z J 2014 Acta Phys. Sin. 63 174204 (in Chinese) [赵浩, 沈义峰, 张中杰 2014 63 174204]
[5]	Ginzburg P, Fortuño F J R, Wurtz G A, Dickson W, Murphy A, Morgan F, Pollard J R, Iorsh I, Atrashchenko A, Belov P A, Kivshar Y S, Nevet A, Ankonina G, Orenstein M, Zayats A V 2013 Opt. Express 21 14907
[6]	Li G J, Kang X L, Li Y P 2007 Acta Phys. Sin. 56 6403 (in Chinese) [李国俊, 康学亮, 李永平 2007 56 6403]
[7]	Jin L, Zhu Q Y, Fu Y Q, Yu W X 2013 Chin. Phys. B 22 104101
[8]	Kabashin A V, Evans P, Pastkovsky S, Hendren W, Wurtz G A, Atkinson R, Pollard R, Podolskiy V A, Zayats A V 2009 Nat. Mater. 8 867
[9]	Suchowski H, O’Brien K, Wong Z J, Salandrino A, Yin X, Zhang X 2013 Science 342 1223
[10]	Chui S T, Hu L 2002 Phys. Rev. B 65 144407
[11]	Sarychev A K, McPhedran R C, Shalaev V M 2001 Phys. Rev. B 64 079904
[12]	Koschny T, Economou E N, Smith D R, Vier D C, Soukoulis, C M 2005 Phys. Rev. B 71 245105
[13]	Wu Y, Li J, Zhang Z Q, Chan C T 2006 Phys. Rev. B 74 085111
[14]	Chern R L, Chen Y T 2009 Phys. Rev. B 80 075118
[15]	Jin J, Liu S, Lin Z, Chui S T 2009 Phys. Rev. B 80 115101
[16]	Bohren C F, Huffman D R 1983 Absorption and Scattering of Light by Small Particles (Canada: John Wiley & Sons, Inc) p195
[17]	Notomi M 2000 Phys. Rev. B 62 10696
[18]	Tang Z, Zhang H, Peng R, Ye Y, Shen L, Wen S, Fan D 2006 Phys. Rev. B 73 235103
[19]	Geng T, Liu T Y, zhuang S L 2007 Chin. Opt. Lett. 5 361

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