摘要
二维拓扑光子绝缘体中格点的对称性作为一个设计的自由度还未被探索。在此研究中通过使用对称性较低的椭圆形格点来研究格点对称性对于能谷光子禁带的影响。通过改变椭圆形格点的长轴方向能够改变能谷光子禁带的中心波长及宽度,并将具有不同禁带宽度及中心波长的全电介质能谷光子晶体结构以镜面对称的方式组合实现全电介质光子拓扑绝缘体波导结构,实现了抗散射鲁棒单向光传输。该研究拓展了能谷光子晶体设计的自由度,为全电介质能谷光子晶体设计提供了新的可能性。
2.太原理工大学 新型传感器与智能控制教育部重点实验室,山西 太原 030024;
光子拓扑绝缘体的反向散射抑制且缺陷免疫的边界输运特性、自旋轨道选择传输特性、高维度的光场调控等特性使得拓扑光子学在近年来引起了广泛关注。拓扑绝缘体这个概念最早是在电子系统中提到的,电子在拓扑绝缘体系统中有自旋性质可以沿边缘单向传播。随后研究者将拓扑绝缘体引入到光学中,实现了宽带单向传输、抗散射传输等功
二维光子拓扑绝缘体中光学类量子霍尔系统常通过引入磁场打破时间反演对称性,产生单向传输的边界态;光学类量子自旋霍尔系统可以通过光子晶体晶格结构设计实现能带翻转,导致能带上出现非平庸的拓扑结构,从而实现二维的量子自旋霍尔效
本研究结构设计的全电介质能谷光子晶体结构如

图1 (a)基于椭圆形格点的全电介质能谷光子晶体结构示意图。硅和二氧化硅分别使用是灰色和蓝色表示。波导从左边进入,沿着具有谷霍尔效应的光子晶体波导(红色)的带结构从右边输出,(b)椭圆光子晶体VPC‖+晶胞结构示意图,(c)VPC‖和VPC‖+的TE模式的能带结构图,(d)为VPC⊥和VPC⊥+的TE模式的能带结构图,(e)显示了VPC‖+在介质柱中心放置左旋圆偏振(LCP)和右旋圆偏振(RCP)光源后的电场强度分布图,图中显示LCP光沿K方向传输,以及RCP光沿K’方向传输,(f)显示了VPC⊥+在介质柱中心放置LCP和RCP光源后的电场强度分布图,图中LCP光沿K方向传输,以及RCP沿K’方向传输。图中K与K’的方向使用白色箭头表示
Fig.1 (a) Schematic diagram of all-dielectric valley photonic crystal structure based on elliptical lattice. Silicon and silicon dioxide are gray and blue, respectively. The incident light enters from the left waveguide, propagates along the valley photonic crystal waveguide (red) with valley Hall effect, and exits from the right waveguide, (b) Schematic diagram of unit cell structure of the valley photonic crystal VPC‖+ , (c) Photonic band structure of TE mode of VPC‖ and VPC‖+ , (d) Photonic band structure of TE mode of VPC⊥ and VPC⊥+, (e) The electric field intensity distributions of left-handed circular polarized (LCP) and right-handed circular polarized (RCP) light sources in the center of the dielectric column in VPC‖+ , where LCP light propagates along the K direction, while RCP light propagates along the K’ direction, (f) The electric field intensity distributions of left-handed circular polarized (LCP) and right-handed circular polarized (RCP) light sources in the center of the dielectric column in VPC⊥+ , where LCP light propagates along the K direction, while RCP light propagates along the K’ direction. The directions of K and K’ in the figure are indicated by white arrows.
谷耦合打开了一个完整的禁带,阻止光子在特定禁带范围内进入光子晶体中,但特定偏振态的光波(包括LCP和RCP)可以沿着VPC‖+和VPC‖+的边界以不同的方向传播(LCP和RCP的传输方向相反,如

图2 (a)显示了VPC‖+和VPC‖-构成的超晶胞结构图,上下两边分别为四个周期的VPC‖+和VPC‖+,(b)为VPC‖+和VPC‖- 构成超晶胞结构的能带图,(c)为VPC‖+和VPC‖-结构交界面中心分别放置LCP、RCP电场图,(d)显示了VPC⊥+和VPC⊥-构成的超晶胞结构图,上下两边分别为四个周期的VPC⊥+和VPC⊥-,(d)为VPC⊥+和VPC⊥-构成超晶胞结构的能带图,(f)为VPC⊥+和VPC⊥-结构交界面中心分别放置LCP、RCP电场图,(g)为VPC‖+和VPC‖-结构组合结构正向和反向透射率,以及其透射对比度,(h)为VPC⊥+和VPC⊥-组合结构的正向和反向透射率,以及其透射对比度
Fig. 2 (a) The supercell structure composed of VPC‖+ and VPC‖-. The upper and lower sides are four periods of VPC‖+ and VPC‖-, (b) The photonic band diagram of the supercell structure composed of VPC‖+ and VPC‖-, (c) The electric field intensity distributions of LCP and RCP light sources placed at the center of the supercell structure (the interface between VPC‖+ and VPC‖-), respectively, (d) The supercell structure composed of VPC⊥+ and VPC⊥-. The upper and lower sides are four periods of VPC⊥+ and VPC⊥-, (e) The photonic band diagram of the supercell structure composed of VPC⊥+ and VPC⊥-, (f) The electric field intensity distributions of LCP and RCP light sources placed at the center of the supercell structure (the interface between VPC⊥+ and VPC⊥-), respectively, (g) Plots of forward and backward transmittance of the structure composed of VPC‖+ and VPC‖-, and the contrast ratio, (h) Plots of forward and backward transmittance of the structure composed of VPC⊥+ and VPC⊥-, and the contrast ratio
为了证明谷霍尔拓扑结构的鲁棒传输特性,本研究设计了由VPC‖+及VPC‖-,以及VPC⊥+及VPC⊥-所构成的直线型、Ω型边界态波导的传播,并研究了直线型波导中存在缺陷的情况。其结构设计如

图3 (a)VPC‖+和VPC‖-构成的Ω型拓扑光波导,以及光沿Ω型光波导传输的电场强度图,(b)VPC‖+和VPC‖-构成的直线型拓扑光波导,以及光沿着直线型拓扑光波导传输的电场强度图,(c)由VPC‖+和VPC‖-构成的具有点缺陷的直线型拓扑光波导,以及光沿着直线型带有点缺陷的光波导传输的电场图,其中点缺陷位置使用矩形框标出,(d)VPC⊥+和VPC⊥-构成的Ω型拓扑光波导,以及光沿Ω型光波导传输的电场强度图,(e)VPC⊥+和VPC⊥-构成的直线型拓扑光波导,以及光沿着直线型拓扑光波导传输的电场强度图,(f)由VPC⊥+和VPC⊥-构成的具有缺陷的直线型拓扑光波导,以及光沿着直线型带有点缺陷的光波导传输的电场图,其中点缺陷位置使用矩形框标出,(g)VPC‖+和VPC‖-构成的拓扑光波导的透射率曲线,红色和蓝色分别代表Ω型和直线型波导,黑色表示点缺陷波导,灰色区域表示禁带光波段,(h)VPC⊥+和VPC⊥-构成的拓扑光波导的透射率曲线,红色和蓝色分别代表Ω型和直线型波导,黑色表示点缺陷波导,灰色区域表示禁带光波段,(i)为VPC‖+和VPC‖-构成的Ω型波导与VPC⊥+和VPC⊥-构成的Ω型波导的透射率曲线,以方便比较。
Fig. 3 (a) An Ω-shape topological optical waveguide composed of VPC‖+ and VPC‖-, and the electric field intensity distributions of light propagating along the Ω-shape optical waveguide, (b) A straight topological optical waveguide composed of VPC‖+ and VPC‖-, and the electric field intensity distributions along the straight topological optical waveguide, (c) A straight topological optical waveguide with a point defect, and the electric field intensity distributions of light propagating along the defective waveguide, (d) An Ω-shape topological optical waveguide composed of VPC⊥+ and VPC⊥-, and the electric field intensity distributions of light propagating along the Ω-shape optical waveguide, (e) A straight topological optical waveguide composed of VPC⊥+ and VPC⊥-, and the electric field intensity distributions along the straight topological optical waveguide, (f) A straight topological optical waveguide with a point defect, and the electric field intensity distributions of light propagating along the defective waveguide. The point defects are marked by the rectangle, (g) Plots of the forward transmittance of the topological optical waveguide composed of VPC‖+ and VPC‖-. Ω-shape (red), straight waveguide (blue) and defective waveguide (black). The gray area represents the wavelength region of the photonic bandgap, (h) Plots of the forward transmittance of the topological optical waveguide composed of VPC⊥+ and VPC⊥-. Ω-shape (red), straight waveguide (blue) and defective waveguide (black). The gray area represents the wavelength region of the photonic bandgap, (i) Forward transmittance plots of the Ω-shaped waveguide composed of VPC‖+ and VPC‖- and composed of VPC⊥+ and VPC⊥-, respectively, for comparison.
传播的透射率光谱图展示在
本研究提出了全介电质能谷光子晶体结构设计,通过使用对称性较低的椭圆形格点结构,研究了格点长轴的不同取向对于光子晶体禁带中心波长及宽度以及光波导工作带宽的影响。本研究展示了,椭圆形格点的长轴取向主要影响了光子晶体的禁带中心位置及禁带宽度,因此影响了最终设计的结构的工作波长范围。同时,本研究发现不同长轴取向的椭圆格点的光子晶体结构均能实现良好的单向光传输性能,基本不受结构缺陷的影响。本研究所展示的全介电质能谷光子晶体的禁带宽度达到了150 nm,该设计从结构对称性的角度给光子拓扑绝缘体的设计提出新的思路。本研究设计的结构对于加工过程的要求的宽容度较高,在加工过程引入的误差及缺陷将不会对该结构的单向光传输特性造成明显影响。因此,该设计具有实验加工的可能性及应用前景。
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