用于中红外波深度亚波长传输的石墨烯间隙等离激元波导

滕达; 王凯; 李哲; 曹清; 唐亚楠; 赵永哲; 刘子怡; 张韵雯; 郭荣珍

doi:doi:10.3788/AOS202040.0623002

光学学报, 2020, 40 (6): 0623002, 网络出版: 2020-03-06

用于中红外波深度亚波长传输的石墨烯间隙等离激元波导下载： 1274次

Graphene Gap Plasmonic Waveguide for Deep-Subwavelength Transmission of Mid-Infrared Waves

滕达 ^1,2,*王凯 ^3,**李哲 ⁴曹清 ⁴唐亚楠 ^1,***赵永哲 ¹刘子怡 ¹张韵雯 ¹郭荣珍 ¹

作者单位

¹ 郑州师范学院物理与电子工程学院, 河南郑州 450044

² 郑州师范学院物理与电子工程学院量子材料研究中心, 河南郑州 450044

³ 中国科学院上海技术物理研究所红外成像材料与探测器重点实验室, 上海 200083

⁴ 上海大学理学院, 上海 200444

图 & 表

图 1. 波导结构示意图

Fig. 1. Schematic of waveguide structure

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图 2. 基模能量分布。(a)归一化能量分布;(b)|S_z|沿y轴分布

Fig. 2. Normalized energy distribution of fundamental mode. (a) Normalized energy distribution; (b) |S_z| along y direction

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图 3. 石墨烯等离激元模式特性随频率的变化关系。(a)Re(n_eff)和L_P;(b) A_eff/A₀和F_M。相关参数为μ_c=0.5 eV, T=300 K, τ=0.5 ps, R=30 nm, ε₁=3, ε₂=1, W=200 nm, H=100 nm, D=20 nm

Fig. 3. Graphene plasmon modal properties with respect to frequency. (a) Re(n_eff) and L_P; (b) A_eff/A₀ and F_M. Here, we set μ_c=0.5 eV, T=300 K, τ=0.5 ps, R=30 nm, ε₁=3, ε₂=1, W= 200 nm, H=100 nm, and D=20 nm

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图 4. 模式传输特性随半径R和间距D的变化关系。(a) Re(n_eff)和L_P随半径R的变化曲线,D=20 nm;(b) A_eff/A₀和F_M随半径R的变化曲线,D=20 nm;(c) Re(n_eff)和L_P随间距D的变化曲线,R=30 nm;(d) A_eff/A₀和F_M随间距D的变化曲线,R=30 nm

Fig. 4. Modal transmission properties with respect to R and D. (a) Re(n_eff) and L_P versus R when D=20 nm; (b) A_eff/A₀ and F_M versus R when D=20 nm; (c) Re(n_eff) and L_P versus D when R= 30 nm; (d) A_eff/A₀ and F_M versus D when R= 30 nm

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图 5. 模式传输特性随纳米线介电常数和石墨烯化学势的变化。(a) Re(n_eff)和L_P随纳米线介电常数ε₁的变化曲线,μ_c=0.5 eV;(b) A_eff/A₀和F_M随纳米线介电常数ε₁的变化曲线,μ_c=0.5 eV;(c) Re(n_eff)和L_P随石墨烯化学势μ_c的变化曲线,ε₁=2;(d) A_eff/A₀和F_M随石墨烯化学势μ_c的变化曲线,ε₁=2

Fig. 5. Modal transmission properties with respect to nanowire permittivity and chemical potential of graphene. (a) Re(n_eff) and L_P as functions of ε₁ when μ_c=0.5 eV; (b) A_eff/A₀ and F_M as functions of ε₁ when μ_c=0.5 eV; (c) Re(n_eff) and L_P as functions of μ_c when ε₁=2; (d)

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表 1矩形介质材料介电常数对石墨烯等离激元模式的影响

Table1. Impact of permittivity of rectangular dielectric on graphene plasmon mode

Value of permittivity	Effective mode index n_eff	Mode area A_eff /m²
2	37.062+0.278i	1.832×10^-15
4	48.950+0.441i	1.616×10^-15
6	63.776+0.626i	1.213×10^-15
8	79.689+0.811i	0.959×10^-15

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滕达, 王凯, 李哲, 曹清, 唐亚楠, 赵永哲, 刘子怡, 张韵雯, 郭荣珍. 用于中红外波深度亚波长传输的石墨烯间隙等离激元波导[J]. 光学学报, 2020, 40(6): 0623002. Da Teng, Kai Wang, Zhe Li, Qing Cao, Yanan Tang, Yongzhe Zhao, Ziyi Liu, Yunwen Zhang, Rongzhen Guo. Graphene Gap Plasmonic Waveguide for Deep-Subwavelength Transmission of Mid-Infrared Waves[J]. Acta Optica Sinica, 2020, 40(6): 0623002.

用于中红外波深度亚波长传输的石墨烯间隙等离激元波导下载： 1274次

图 1. 波导结构示意图

Fig. 1. Schematic of waveguide structure

图 2. 基模能量分布。(a)归一化能量分布;(b)|S_z|沿y轴分布

Fig. 2. Normalized energy distribution of fundamental mode. (a) Normalized energy distribution; (b) |S_z| along y direction

图 3. 石墨烯等离激元模式特性随频率的变化关系。(a)Re(n_eff)和L_P;(b) A_eff/A₀和F_M。相关参数为μ_c=0.5 eV, T=300 K, τ=0.5 ps, R=30 nm, ε₁=3, ε₂=1, W=200 nm, H=100 nm, D=20 nm

Fig. 3. Graphene plasmon modal properties with respect to frequency. (a) Re(n_eff) and L_P; (b) A_eff/A₀ and F_M. Here, we set μ_c=0.5 eV, T=300 K, τ=0.5 ps, R=30 nm, ε₁=3, ε₂=1, W= 200 nm, H=100 nm, and D=20 nm

图 4. 模式传输特性随半径R和间距D的变化关系。(a) Re(n_eff)和L_P随半径R的变化曲线,D=20 nm;(b) A_eff/A₀和F_M随半径R的变化曲线,D=20 nm;(c) Re(n_eff)和L_P随间距D的变化曲线,R=30 nm;(d) A_eff/A₀和F_M随间距D的变化曲线,R=30 nm

Fig. 4. Modal transmission properties with respect to R and D. (a) Re(n_eff) and L_P versus R when D=20 nm; (b) A_eff/A₀ and F_M versus R when D=20 nm; (c) Re(n_eff) and L_P versus D when R= 30 nm; (d) A_eff/A₀ and F_M versus D when R= 30 nm

Fig. 5. Modal transmission properties with respect to nanowire permittivity and chemical potential of graphene. (a) Re(n_eff) and L_P as functions of ε₁ when μ_c=0.5 eV; (b) A_eff/A₀ and F_M as functions of ε₁ when μ_c=0.5 eV; (c) Re(n_eff) and L_P as functions of μ_c when ε₁=2; (d)

表 1矩形介质材料介电常数对石墨烯等离激元模式的影响

Table1. Impact of permittivity of rectangular dielectric on graphene plasmon mode

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图 1. 波导结构示意图

Fig. 1. Schematic of waveguide structure

图 2. 基模能量分布。(a)归一化能量分布;(b)|Sz|沿y轴分布

Fig. 2. Normalized energy distribution of fundamental mode. (a) Normalized energy distribution; (b) |Sz| along y direction

图 3. 石墨烯等离激元模式特性随频率的变化关系。(a)Re(neff)和LP;(b) Aeff/A0和FM。相关参数为μc=0.5 eV, T=300 K, τ=0.5 ps, R=30 nm, ε1=3, ε2=1, W=200 nm, H=100 nm, D=20 nm

Fig. 3. Graphene plasmon modal properties with respect to frequency. (a) Re(neff) and LP; (b) Aeff/A0 and FM. Here, we set μc=0.5 eV, T=300 K, τ=0.5 ps, R=30 nm, ε1=3, ε2=1, W= 200 nm, H=100 nm, and D=20 nm

图 4. 模式传输特性随半径R和间距D的变化关系。(a) Re(neff)和LP随半径R的变化曲线,D=20 nm;(b) Aeff/A0和FM随半径R的变化曲线,D=20 nm;(c) Re(neff)和LP随间距D的变化曲线,R=30 nm;(d) Aeff/A0和FM随间距D的变化曲线,R=30 nm

Fig. 4. Modal transmission properties with respect to R and D. (a) Re(neff) and LP versus R when D=20 nm; (b) Aeff/A0 and FM versus R when D=20 nm; (c) Re(neff) and LP versus D when R= 30 nm; (d) Aeff/A0 and FM versus D when R= 30 nm

Fig. 5. Modal transmission properties with respect to nanowire permittivity and chemical potential of graphene. (a) Re(neff) and LP as functions of ε1 when μc=0.5 eV; (b) Aeff/A0 and FM as functions of ε1 when μc=0.5 eV; (c) Re(neff) and LP as functions of μc when ε1=2; (d)

表 1矩形介质材料介电常数对石墨烯等离激元模式的影响

Table1. Impact of permittivity of rectangular dielectric on graphene plasmon mode

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图 2. 基模能量分布。(a)归一化能量分布;(b)|S_z|沿y轴分布

Fig. 2. Normalized energy distribution of fundamental mode. (a) Normalized energy distribution; (b) |S_z| along y direction

图 3. 石墨烯等离激元模式特性随频率的变化关系。(a)Re(n_eff)和L_P;(b) A_eff/A₀和F_M。相关参数为μ_c=0.5 eV, T=300 K, τ=0.5 ps, R=30 nm, ε₁=3, ε₂=1, W=200 nm, H=100 nm, D=20 nm

Fig. 3. Graphene plasmon modal properties with respect to frequency. (a) Re(n_eff) and L_P; (b) A_eff/A₀ and F_M. Here, we set μ_c=0.5 eV, T=300 K, τ=0.5 ps, R=30 nm, ε₁=3, ε₂=1, W= 200 nm, H=100 nm, and D=20 nm

图 4. 模式传输特性随半径R和间距D的变化关系。(a) Re(n_eff)和L_P随半径R的变化曲线,D=20 nm;(b) A_eff/A₀和F_M随半径R的变化曲线,D=20 nm;(c) Re(n_eff)和L_P随间距D的变化曲线,R=30 nm;(d) A_eff/A₀和F_M随间距D的变化曲线,R=30 nm

Fig. 4. Modal transmission properties with respect to R and D. (a) Re(n_eff) and L_P versus R when D=20 nm; (b) A_eff/A₀ and F_M versus R when D=20 nm; (c) Re(n_eff) and L_P versus D when R= 30 nm; (d) A_eff/A₀ and F_M versus D when R= 30 nm

Fig. 5. Modal transmission properties with respect to nanowire permittivity and chemical potential of graphene. (a) Re(n_eff) and L_P as functions of ε₁ when μ_c=0.5 eV; (b) A_eff/A₀ and F_M as functions of ε₁ when μ_c=0.5 eV; (c) Re(n_eff) and L_P as functions of μ_c when ε₁=2; (d)