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Using the transfer matrix method, the tunable characteristics of the interface state generated by one-dimensional photonic structure with inversion symmetry are studied, and the samples are prepared by electron beam evaporation technology for experimental verification. According to the different inversion symmetry centers of unit cell, the inverted symmetric layered photonic structures are divided into two types i.e. PCI and PCII. The calculation results show that for the combined structure composed of PCI and PCII, there is an interface state at a characteristic frequency where the sum of the imaginary parts of the surface impedance of PCI and PCII is equal to zero, and this frequency of the interface state is independent of the number of unit cells. On this basis, if a PCI structure is added to form PCI + PCII + PCI photonic structure, two interface states will be generated in the same band gap, and changing the unit cell number in each or part of of individual PCI and PCII structures, the frequencies of two interface states can be regulated. The experimental results show that the regulation of interface state by controlling unit cell number is feasible, which provides a more flexible idea for designing the extremely narrow-band filters and multi-channel filters to meet different application requirements.
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Keywords:
- photonic bandgap material /
- transfer matrix /
- electron beam evaporation technology /
- filter /
- interface state
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图 1 由二元反转对称光子结构PCI和PCII构成的两种组合结构示意图 (a) PCI + PCII; (b) PCI + PCII + PCI
Figure 1. Schematic diagram of two combined structures composed of binary inversion symmetric photonic structures: (a) PCI + PCII; (b) PCI + PCII + PCI.
图 2 由PCI和PCII构成的组合结构 (a) 组合结构PCI + PCII的反射谱; (b) 组合结构PCI + PCII + PCI的反射谱; (c) 组合结构PCI + PCII的反射谱和表面阻抗虚部; (d) 组合结构PCI + PCII + PCI的反射谱和表面阻抗虚部
Figure 2. Combined structures composed of PCI and PCII: (a) Reflection spectrum of combined structure PCI + PCII; (b) reflection spectrum of combined structure PCI + PCII + PCI; (c) reflection spectra and imaginary part of surface impedance of combined structure PCI + PCII; (d) reflection spectrum and imaginary part of surface impedance of combined structure PCI + PCII + PCI.
图 3 组合结构PCI(N) + PCII(N) + PCI(N)随元胞数改变的计算结果 (a) 组合结构随元胞数N变化的光谱; (b) 两个界面态位置λ1, λ2随元胞数N改变的计算结果
Figure 3. Calculation results of combined structure PCI (N) + PCII (N) + PCI (N) with changing of the unit cell numbers N: (a) The spectra of the combined structure with the different N; (b) two interface states of the combined structures with different N.
图 4 组合结构PCI(N) + PCII(M) + PCI(N)随元胞数改变的计算结果 (a) 组合结构随PCII元胞数M变化的光谱(保持N = 3不变); (b) 保持M = 2N的条件不变, 组合结构的两个界面态λ1, λ2随元胞数N改变的计算结果
Figure 4. Calculation results of combined structures PCI (N ) + PCII (M ) + PCI (N ) with changing of the unit cell numbers M: (a) The spectra of the combined structures with different M (keep N = 3 unchanged); (b) keeping the condition of M = 2N unchanged, the two interface states of the composite structures with different N.
图 5 组合结构PCI + PCII的界面态λ0与组合结构PCI(N) + PCII(M) + PCI(N)(满足M = 2N)的第一个界面态λ1随元胞数N改变的计算结果
Figure 5. The interface state of combined structures PCI + PCII λ0 and the first interface state of combined structures PCI (N) + PCII (M) + PCI (N) (keep M = 2N) λ1 with different N.
图 6 制备的组合结构样品的反射光谱(N = 5) (a) PCI + PCII结构; (b) PCI + PCII + PCI结构
Figure 6. Reflection spectra of the fabricated samples (N = 5): (a) PCI + PCII; (b) PCI + PCII + PCI.
图 7 元胞数对界面态调控的实验测量结果 (a) 含不同元胞数N的组合结构PCI(N) + PCII(N) + PCI(N)的反射光谱测量结果; (b) 含不同元胞数M的组合结构PCI(N) + PCII(M) + PCI(N)的反射光谱测量结果(N = 3)
Figure 7. Experiment results of unit cell numbers regulation on the interface states: (a) Reflection spectrum of the fabricated structures PCI (N) + PCII (N) + PCI (N) with different N; (b) reflection spectrum of the fabricated structures PCI (N) + PCII (M) + PCI (N) with different M (keep N = 3).
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[1] 段雪珂, 任娟娟, 郝赫, 张淇, 龚旗煌, 古英 2019 68 144201
Google Scholar
Duan X K, Ren J J, Hao H, Zhang Q, Gong Q H, Gu Y 2019 Acta Phys. Sin. 68 144201
Google Scholar
[2] 李林, 程亚, 祝世宁 2021 物理 50 308
Google Scholar
Li L, Cheng Y, Zhu S N 2021 Physics 50 308
Google Scholar
[3] Zhang Y B, Liu H, Cheng H, Tian J G, Chen S Q 2020 Opto-Electron. Adv. 3 200002
Google Scholar
[4] 朱韵至 2020 博士学位论文 (南京: 南京大学)
Zhu Y Z 2020 Ph. D. Dissertation (Nanjing: Nanjing University) (in Chinese)
[5] Deng Z L, Tu Q A, Wang Y J, Wang Z Q, Shi T, Feng Z W, Qiao X C, Wang G P, Xiao S M, Li X P 2021 Adv. Mater. 33 2103472
Google Scholar
[6] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
Google Scholar
[7] John S 1987 Phys. Rev. Lett. 58 2486
Google Scholar
[8] 顾国昌, 李宏强, 陈洪涛, 陈鸿, 吴翔 2000 光学学报 20 728
Gu G C, Li H Q, Chen H T, Chen H, Wu X 2000 Acta Opt. Sin. 20 728
[9] 杜桂强, 刘念华 2004 53 1095
Google Scholar
Du G Q, Liu N H 2004 Acta Phys. Sin. 53 1095
Google Scholar
[10] Biswal A, Kumar R, Nayak C, Dhanalakshmi S 2021 Optik 234 166597
Google Scholar
[11] Liu X J, Ren M L, Pan Q, Zhang X R, Ma J, Wu X Y 2020 Physica E 126 114415
Google Scholar
[12] Taya S A, Doghmosh N, Upadhyay A 2021 Opt. Quantum Electron. 53 35
Google Scholar
[13] 张正仁, 隆正文, 袁玉群, 刁心峰 2010 59 587
Google Scholar
Zhang Z R, Long Z W, Yuan Y Q, Diao X F 2010 Acta Phys. Sin. 59 587
Google Scholar
[14] Xu X F, Huang J Y, Zhang H, Guo X Y, Mu S S, Liu Y Q, Zhai N 2021 Opt. Commun. 498 127262
Google Scholar
[15] Tan H Y, Zhou M J, Zhuge L J, Wu X M 2021 J. Phys. D: Appl. Phys. 54 085106
Google Scholar
[16] Kalozoumis P A, Theocharis G, Achilleos V, Félix S, Richoux O, Pagneux V 2018 Phys. Rev. A 98 023838
Google Scholar
[17] Xiao M, Zhang Z Q, Chan C T 2014 Phys. Rev. X 4 021017
Google Scholar
[18] 高慧芬, 周小芳, 黄学勤 2022 71 044301
Google Scholar
Gao H F, Zhou X F, Huang X Q 2022 Acta Phys. Sin. 71 044301
Google Scholar
[19] Liu Q, Sun J D, Sun Y D, Ren Z H, Liu C, Lv J W, Wang F M, Wang L Y, Liu W, Sun T, Chu P K 2020 Opt. Mater. 102 109800
Google Scholar
[20] Feng S, Ren C, Wang W Z, Wang Y Q 2013 Opt. Commun. 289 144
Google Scholar
[21] 刘博文, 胡明列, 宋有建, 柴路, 王清月 2008 中国激光 03 479
Google Scholar
Liu B W, Hu M L, Song Y J, Chai L, Wang Q Y 2008 Chin. J. Lasers 03 479
Google Scholar
[22] Zaghdoudi J, Kanzari M 2018 Optik 160 189
Google Scholar
[23] Elshahat S, Abood I, Esmail M S M, Ouyang Z B, Lu C C 2021 Nanomaterials-Basel 11 194
Google Scholar
[24] 高冬 2019 硕士学位论文 (青岛: 青岛科技大学)
Gao D 2019 M. S. Thesis (Qingdao: Qingdao University of science and technology) (in Chinese)
[25] 毛维涛, 李杨, 赵秋玲, 滕利华, 王霞 2020 中国激光 47 292
Mao W T, Li Y, Zhao Q L, Teng L H, Wang X 2020 Chin. J. Lasers 47 292
[26] Gao W S, Xiao M, Chan C T, Tam W Y 2015 Opt. Lett. 40 5259
Google Scholar
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