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利用一维光子晶体和二维等离子体光子晶体构建了一种基于束缚态的可调窄带滤波器, 滤波器的工作频率位于两个光子晶体的共同禁带内. 使用COMSOL Multiphysics有限元仿真软件研究了一维光子晶体的几何参数和等离子体参数对滤波器性能的影响. 研究发现两个禁带的中心频率和深度越接近, 则滤波器的峰值透射率越大, 且中心频率占主导作用. 另一方面, 滤波器的工作频率与等离子体密度成正比, 与碰撞频率成反比. 滤波器品质因子和峰值透射率随等离子体密度的增大先增大后减小, 随碰撞频率的增加而减小. 最后, 随着等离子体碰撞频率的增加, 峰值透射率和品质因子没有发生显著下降, 这表明滤波器对等离子体损耗有一定抵抗力. 我们相信这项工作有助于一些新型等离子体光子晶体滤波器的研究.Photonic crystals are widely used in a class of narrow-band frequency selective filter due to their excellent ability to control electromagnetic waves, in which the working frequency depends on the structural parameters of the point defect resonant cavity of the photonic crystal, and the introduction of some dispersive media into the cavity makes the filter adjustable. In general, this kind of cavity-filter is very sensitive to the parameter disturbance of the cavity, and the quality factor of the filter can be reduced significantly by material loss. On the other hand, some studies have shown that there may be bound states at the interface between two different photonic crystals, and the bound state is often accompanied by narrow band and high transmittance, which implies that a narrow-band filter based on bound states is feasible. Importantly, filters based on bound states may be resistant to material loss to some degree. In this paper, a bound state related tunable narrow-band filter composed of a one-dimensional photonic crystal and a two-dimensional plasma photonic crystal is proposed, and the working frequency of the filter is located in the common band gap of the two photonic crystals. The COMSOL Multiphysics finite element simulation software is used to study the influences of geometric parameters of the one-dimensional photonic crystal and plasma parameters on the performance of the filter. It is found that the closer to each other the center frequencies and depths of the two different forbidden bands are, the greater the peak transmittance of the filter, in which the center frequency dominates, will be. On the other hand, the working frequency of the filter is directly proportional to plasma density and inversely proportional to collision frequency. The quality factor of the filter first increases and then decreases with the increase of plasma density, and decreases with the increase of collision frequency. The peak transmittance of the filter first increases and then decreases with the increase of plasma density, and decreases with the increase of plasma collision frequency. Finally, with the increase of collision frequency, both the peak transmittance and the quality factor decrease slightly, which indicates that the filter has a certain resistance to plasma loss. We believe that this work is helpful in investigating some new plasmonic photonic crystal filters.
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Keywords:
- plasma /
- photonic crystal /
- tunable filter /
- bound state
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图 1 滤波器示意图, 下图展示了两种光子晶体的原胞
Fig. 1. Schematic diagram of the filter. The figure below shows the unit cells of two photonic crystals.
图 2 随等离子体密度增加, 2D PPC的1阶带隙经历了从关闭到再打开的过程
Fig. 2. As the plasma density increases, the first-order band gap of 2D PPC undergoes a process from closing to reopening
图 3 (a)
$ {n}_{\rm{e}}=0 $ 时两种光子晶体的能带图; (b)${n}_{\rm{e}}=6\times {10}^{11}\;{\rm{c}\rm{m}}^{-3}$ 时两种光子晶体的能带图; (c)$ {n}_{\rm{e}}=0 $ 和${n}_{\rm{e}} =6\;\times $ $ {10}^{11}\;{\rm{c}\rm{m}}^{-3}$ 时滤波器的透射谱; (d) 电场强度沿模型边界的线分布, 其中, 插图表示滤波器中的电场分布Fig. 3. (a) Band structure of two different PCs with
$ {n}_{\rm{e}}=0 $ ; (b) band structure of two different PCs with${n}_{\rm{e}}=6\times {10}^{11}\;{\rm{c}\rm{m}}^{-3}$ ; (c) trans-mission spectrum of the filter when$ {n}_{\rm{e}}=0 $ and${n}_{\rm{e}}=6\times {10}^{11}\;{\rm{c}\rm{m}}^{-3}$ ; (d) the intensity of electric field along the line of the model boundary, where the inset shows the electric field distribution in the filter.
图 4 (a)滤波器透射谱与
$ {N}_{1} $ 的关系; (b) 滤波器透射谱与d的关系Fig. 4. (a) The relationship between the transmission spectrum of the filter and
$ {N}_{1} $ ; (b) the relationship between the transmission spectrum of the filter and d.
图 5 (a)禁带匹配度与
$ {N}_{1} $ 的关系; (b)禁带匹配度与$ d $ 的关系Fig. 5. (a) The relationship between the band gap matching degree and
$ {N}_{1} $ ; (b) the relationship between the band gap matching degree and$ d $ .
图 6 (a) 滤波器透射谱与
$ {n}_{\rm{e}} $ 的关系, 点线表示滤波器的中心频率随$ {n}_{\rm{e}} $ 的变化; (b) 滤波器峰值透射率以及品质因子与$ {n}_{\rm{e}} $ 的关系Fig. 6. (a) The relationship between the transmission spectrum of the filter and
$ {n}_{\rm{e}} $ , while the dotted line shows the evolution of the center frequency of the filter with$ {n}_{\rm{e}} $ ; (b) the relationship between the peak transmittance of the filter as well as the quality factor and$ {n}_{\rm{e}} $ 
图 7 (a) 滤波器透射谱与
$ {\nu }_{\rm{e}} $ 的关系, 点线表示滤波器的中心频率随$ {\nu }_{\rm{e}} $ 的变化; (b) 滤波器峰值透射率以及品质因子与$ {\nu }_{\rm{e}} $ 的关系Fig. 7. (a) The relationship between the transmission spectrum of the filter and
$ {\nu }_{\rm{e}} $ , while the dotted line shows the evolution of the center frequency of the filter with$ {\nu }_{\rm{e}} $ ; (b) the relationship between the peak transmittance of the filter as well as the quality factor and$ {\nu }_{\rm{e}} $ . -
[1] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
Google Scholar
[2] John S 1987 Phys. Rev. Lett. 58 2486
Google Scholar
[3] Russell P 2003 Science 299 358
Google Scholar
[4] Fan S H, Villeneuve P R, Joannopoulos J D, Haus H A 1998 Opt. Express 3 4
Google Scholar
[5] Dinu M, Willet R L, Baldwin K, Pfeiffer L N, West K W 2003 Appl. Phys. Lett. 83 4471
Google Scholar
[6] Serier C, Cheype C, Chantalat R, Thevenot M, Monediere T, Reineix A, Jecko B 2001 Microw. Opt. Technol. Lett. 29 312
Google Scholar
[7] Xu J M, Chen L, Zang X F, Cai B, Peng Y, Zhu Y M 2013 Appl. Phys. Lett. 103 161116
Google Scholar
[8] 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
[9] Belyaev B A, Khodenkov S A, Shabanov V F 2016 Dokl. Phys. 61 155
Google Scholar
[10] Karakilinc O O, Dinleyici M S 2015 Microw. Opt. Technol. Lett. 57 1806
Google Scholar
[11] Upadhyay M, Awasthi S K, Shiveshwari L, Srivastava P, Ojha P 2015 J. Supercond. Nov. Magn. 28 2275
Google Scholar
[12] Wang C C, Chen L W 2010 Physica B 405 1210
Google Scholar
[13] Zhang H, Guo P, Chen P, Chang S J, Yuan J H 2009 J. Opt. Soc. Am. B-Opt. Phys. 26 101
Google Scholar
[14] Suthar B, Bhargava A 2012 IEEE Photonics Technol. Lett. 24 338
Google Scholar
[15] Wang B, Cappelli M A 2015 Appl. Phys. Lett. 107 171107
Google Scholar
[16] John D J, Steven G J, Joshua N W, Robert D M 2008 Photonic Crystals Molding the Flow of Light (2nd Ed.) (New Jersey: Princeton University Press)
[17] Xiao M, Zhang Z Q, Chan C T 2014 Phys. Rev. X 4 021017
Google Scholar
[18] Sakai O, Tachibana K 2012 Plasma Sources Sci. Technol. 21 013001
Google Scholar
[19] Shi X, Xue C H, Jiang H T, Chen H 2016 Opt. Express 24 18580
Google Scholar
[20] Ling L, John D J, Marin S 2014 Nat. Photonics 8 821
Google Scholar
[21] Tan H Y, Zhou M J, Zhuge L J, Wu X M 2019 Phys. Plasmas 26 052107
Google Scholar
[22] Tan H Y, Zhou M J, Zhuge L J, Wu X M 2021 J. Phys. D-Appl. Phys. 54 085106
Google Scholar
[23] 章海锋, 刘少斌, 孔祥鲲 2011 物理学报 60 055209
Google Scholar
Zhang H F, Liu S B, Kong X K 2011 Acta Phys. Sin. 60 055209
Google Scholar
[24] Kong X K, Liu S B, Zhang H F, Li C Z 2010 Phys. Plasmas 17 103506
Google Scholar
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