An ultra-narrow-band optical filter based on zero refractive index metamaterial

Zhou Xiao-Xia; Chen Ying; Cai Li

doi:10.7498/aps.72.20230394

Abstract

Owing to the photonic band gap effect and defect state effect, photonic metamaterials have received much attention in the design of narrow bandpass filters, which are the key devices of optical communication equipment such as wavelength division multiplexing devices. In this work, based on zero-index metamaterial (ZIM), a compact filter with both high peak transmission coefficient and ultra-narrow bandwidth is proposed. The photonic metamaterial with conical dispersion and Dirac-like point is achieved by optimizing the structure and material component parameters of dielectric rods with square lattice in air. It is demonstrated that a triply degenerate state can be realized at the Dirac-like point, which relates this metamaterial to a zero-index medium with effective permittivity and permeability equal to zero simultaneously. Electromagnetic (EM) wave can propagate without any phase delay at this frequency, and strong dispersion occurs in the adjacent frequency cone, leading to dramatic changes in optical properties. We introduce a ZIM into photonic metamaterial defect filter to compress the bandwidth to the realization of ultra-narrow bandpass filter. The ZIM is embedded into the resonant cavity of line defect filter, which is also composed of dielectric rods with square lattice in air. In order to increase the sensitivity of the phase change with frequency, the Dirac-like frequency is adjusted to match the resonant frequency of the filter. We study the transmission spectrum of the structure through the COMSOL Multiphysics simulation software, and find that the peak width at half-maximum of the filter decreases as the thickness of ZIM increases, and the peak transmittance is still high when bandwidth is greatly compressed. The zero phase delay inside the slab can be observed. Through field distribution analysis, the zero-phase delay and strong coupling characteristics of electromagnetic field are observed at peak frequency. The comparison with conventional photonic metamaterials filter is discussed. We believe that this work is helpful in investigating the realization of ultra-narrow bandpass filters.

Keywords:

Authors and contacts

1.
School of Electronic Information and Electrical Engineering, Changsha University, Changsha 410000, China
2.
Laboratory of Science and Technology on Integrated Logistics Support, College of Intelligence Science, National University of Defense Technology, Changsha 410073, China

Corresponding author: Cai Li, cailiyunnan@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51975575).

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References

[1]	陈鹤鸣, 孟晴 2011 60 014202 Google Scholar Chen H M, Meng Q 2011 Acta Phys. Sin. 60 014202 Google Scholar
[2]	Mao J D, Li J, Zhou C Y, Zhao H, Sheng H J 2013 Laser Phys. 23 026003 Google Scholar
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Cited By

图 1 滤波器结构示意图　(a)线缺陷滤波器; (b)线缺陷+零折射超构材料滤波器

Figure 1. Schematic diagram of the filter: (a) Structure of the filter with line defect; (b) structure of the filter with line defect and zero index metamaterial.

DownLoad: Full-Size Img PowerPoint

图 2 (a)零折射超构材料的光子能带结构; (b), (c)含零折射超构材料滤波器的传输特性

Figure 2. (a)The band structure of a metamaterial with zero refractive index; (b), (c) transmission characteristics of filter with zero index metamaterials.

DownLoad: Full-Size Img PowerPoint

图 3 (a)传输谱和(b)缺陷间隙L₁随零折射超构材料厚度的变化

Figure 3. The variations of (a) the transmission spectrum and (b) the width of the defect with the thickness of the zero index metamaterials.

DownLoad: Full-Size Img PowerPoint

图 4 (a), (b)类狄拉克点频率处滤波器中的波场分布; (c)类狄拉克点附近ZIM的等效参数; (d), (e)滤波器非零折射率透射峰O₂, O₃的波场分布

Figure 4. (a), (b) The field distribution in the filter near the Dirac-like point; (c) the effective permittivity and permeability of the ZIM as a function of frequency near the Dirac-like point; (d), (e) the field distribution in the filter at transmission peak O₂ and O₃ with nonzero refractive index.

DownLoad: Full-Size Img PowerPoint

图 5 (a)不含ZIM滤波器的传输谱随超构材料厚度的变化; (b)含ZIM滤波器的传输谱随ZIM厚度的变化

Figure 5. The variations of the transmission spectrum (a) with the thickness of PMs1 for the filter without ZIM and (b) with the thickness of ZIM for the filter with ZIM.

DownLoad: Full-Size Img PowerPoint

图 6 (a)有限厚度的线缺陷+零折射超构材料滤波器示意图; (b)考虑PMs1中介质柱损耗的滤波器传输谱; (c)考虑ZIM中材料损耗的滤波器传输谱

Figure 6. (a) Schematic diagram of the finite thickness filter with line defect and zero index metamaterial; (b), (c) transmission spectrum considering different material losses of dielectric columns in defects and in ZIM.

DownLoad: Full-Size Img PowerPoint

map

[1]	陈鹤鸣, 孟晴 2011 60 014202 Google Scholar Chen H M, Meng Q 2011 Acta Phys. Sin. 60 014202 Google Scholar
[2]	Mao J D, Li J, Zhou C Y, Zhao H, Sheng H J 2013 Laser Phys. 23 026003 Google Scholar
[3]	Meng X J, Li J S, Guo Y, Du H J, Liu Y D, Li S G, Guo H T, Bi W H 2021 J. Opt. Soc. Am. B. 38 1525 Google Scholar
[4]	Yablonovitch E 1987 Phys. Rev. Lett. 58 2059 Google Scholar
[5]	Wang F, Cheng Y Z, Wang X, Qi D, Luo H, Gong R Z 2018 Opt. Mater. 75 373 Google Scholar
[6]	John S 1987 Phys. Rev. Lett. 58 2486 Google Scholar
[7]	Fan S H, Villeneuve P R, Joannopoulos J D, Haus H A 1998 Opt. Express 3 4 Google Scholar
[8]	罗宇轩, 程用志, 陈浮, 罗辉, 李享成 2023 72 044101 Google Scholar Luo Y X, Cheng Y Z, Chen F, Luo H, Li X C 2023 Acta Phys. Sin. 72 044101 Google Scholar
[9]	Chen L, Liao D G, Guo X G, Zhao J Y, Zhu Y M, Zhuang S L 2019 Front. Inform. Technol. Elect. Eng. 20 591 Google Scholar
[10]	杨春云, 徐旭明, 叶涛, 缪路平 2011 60 017807 Google Scholar Yang C Y, Xu X M, Ye T, Miu L P 2011 Acta Phys. Sin. 60 017807 Google Scholar
[11]	陈颖, 王文跃, 于娜 2014 63 034205 Google Scholar Chen Y, Wang W Y, Yu N 2014 Acta Phys. Sin. 63 034205 Google Scholar
[12]	余建立, 沈宏君, 叶松, 洪求三 2012 光学学报 32 1106003 Google Scholar Yu J L, Shen H J, Ye S, Hong Q S 2012 Acta Opt. Sin. 32 1106003 Google Scholar
[13]	Dai Z X, Wang J L, Heng Y 2011 Opt. Express 19 3667 Google Scholar
[14]	Chen C, Li X C, Li H H, Xu K, Wu J, Lin J T 2007 Opt. Express 15 11278 Google Scholar
[15]	庄煜阳, 周雯, 季珂, 陈鹤鸣 2015 64 224202 Google Scholar Zhuang Y Y, Zhou W, Ji K, Chen H M 2015 Acta Phys. Sin. 64 224202 Google Scholar
[16]	Edwards B, Alù A, Young M, Silveirinha M, Engheta N 2008 Phys. Rev. Lett. 100 033903 Google Scholar
[17]	Huang X Q, Lai Y, Hang Z H, Zheng H H, Chan C T 2011 Nat. Mater. 10 582 Google Scholar
[18]	Cheng Q, Jiang W X, Cui T J 2012 Phys. Rev. Lett. 108 213903 Google Scholar
[19]	Vulis D I, Reshef O, Camayd-Munoz P, Mazur E 2019 Rep. Prog. Phys. 82 012001 Google Scholar
[20]	Li Y, Chan C T, Mazur E 2021 Light-Sci. Appl. 10 203 Google Scholar
[21]	Luo J, Lai Y 2022 Front. Phys. 10 845624 Google Scholar
[22]	Silveirinha M G, Engheta N 2006 Phys. Rev. Lett. 97 157403 Google Scholar
[23]	Silveirinha M G, Engheta N 2007 Phys. Rev. B 76 245109 Google Scholar
[24]	Enoch S, Tayeb G, Sabouroux P, Guerin N, Vincent P 2002 Phys. Rev. Lett. 89 213902 Google Scholar
[25]	Ma Y G, Wang P, Chen X, Ong C K 2009 Appl. Phys. Lett. 94 044107 Google Scholar
[26]	Edwards B, Alù, Silveirinha M G, Engheta N 2009 J. Appl. Phys. 105 044905 Google Scholar
[27]	Luo J, Xu P, Chen H Y, Hou B, Gao L, Lai Y 2012 Appl. Phys. Lett. 100 221903 Google Scholar
[28]	Alù A, Silveirinha M G, Salandrino A, Engheta N 2007 Phys. Rev. B 75 155410 Google Scholar
[29]	Nguyen V C, Chen L, Halterman K 2010 Phys. Rev. Lett. 105 233908 Google Scholar
[30]	Xu J M, Chen L, Zang X F, Cai B, Peng Y, Zhu Y M 2013 Appl. Phys. Lett. 103 161116 Google Scholar
[31]	Chan C T, Huang X, Liu F, Hang Z H 2012 PIER B 44 163 Google Scholar
[32]	Huang X Q, Chan C T 2015 Acta Phys. Sin. 64 0184208 (in Chinese) [黄学勤, 陈子亭 2015 64 184208 Google Scholar Huang X Q, Chan C T 2015 Acta Phys. Sin. 64 0184208 (in Chinese) Google Scholar
[33]	Wang L G, Wang Z G, Zhang J X, Zhu S Y 2009 Opt. Lett. 34 1510 Google Scholar
[34]	Wu Y, Li J, Zhang Z Q, Chan C T 2006 Phys. Rev. B 74 085111 Google Scholar
[35]	Jin J F, Liu S Y, Lin Z F, Chui S T 2011 Phys. Rev. B 84 115101 Google Scholar
[36]	Moitra P, Yang Y, Anderson Z, Kravchenko I I, Briggs D P, Valentine J 2013 Nat. Photon. 7 791

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