1.Department of Physics and Optoelectronics, Taiyuan University of Technology, Taiyuan 030024, China 2.Key Laboratory of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China 3.Centre for Translational Atomaterials, Swinburne University of Technology, Victoria 3122, Australia
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 61575138), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11904255), the Key R & D Program of Shanxi Province, China (International Cooperation) (Grant No. 201903D421052), and the Applied Based Research Program of Shanxi Province (Youth Fund), China (Grant No. 201901D211070)
Received Date:18 May 2020
Accepted Date:12 July 2020
Available Online:03 January 2021
Published Online:20 January 2021
Abstract:Two-dimensional (2D) hexagonal boron nitride (hBN) possesses many unique properties such as high mechanical strength and excellent chemical and thermal stability. The 2D hBN exhibits a wide bandgap in the UV region and optically-stable ultra-bright quantum emitters that make hBN a promising nanophotonic platform for quantum computing and information processing, especially in the visible wavelength range. Therefore, it is greatly important to build up different nanophotonic devices with different functionalities based on this material platform to achieve the integrated photonic chips. Among the devices, the integratable optical asymmetric transmission devices are important elements for functional quantum computing chips. Since hBN is a dielectric material, photonic crystal (PhC) structure is the most suitable in principle and allows on-chip integration with other photonic devices. In this study, we theoretically design an asymmetric transmission device based on 2D hBN PhC heterostructures in the visible wavelength range for the first time. Due to the relatively low refractive index of 2D hBN material (n < 2.4), we design a free-standing hBN PhC heterostructure to maximize the light trapping in the structure and minimize the propagation loss. The asymmetric transmission device is composed of two square-lattice 2D PhC structures, namely PhC 1 and PhC 2. We use the plane wave expansion method (PWM) to calculate the iso-frequency contours (EFCs) of the PhC structures to study the light propagation inside of the PhCs, which will propagate along the gradient of direction of the EFCs. We design the PhC structure in the way that the incident light beams from different angles can be self-collimated along the Г-X direction of the PhC 2 and coupled out. On the other hand, the backward incident light is blocked by the bandgaps of PhC 2. In this way, asymmetric optical transmission is achieved with high forward transmittance and contrast ratio. In addition, we further finely tune the structural parameters, including the lattice constant and column radius of the PhCs to optimize the performance by using the finite difference time domain (FDTD) method. The resulting 2D hBN PhC heterostructure achieves an asymmetric transmission in a wavelength range of 610–684 nm with a peak forward transmittance of 0.65 at a wavelength of 652 nm. Meanwhile, the backward transmittance is controlled to be 0.04. As a result, the contrast ratio can reach up to 0.95. The working bandwidth of the hBN PhC is 74 nm (TF > 0.5). In addition, the designed asymmetric transmission device has a small size of 11 μm × 11 μm, thus it is suitable for on-chip integration. Our results open up possibilities for designing new nanophotonic devices based on 2D hBN material for quantum computing and information processing. The design principle can be generally used to design other photonic devices based on 2D hBN material. Keywords:asymmetric transmission/ two-dimensional hexagonal boron nitride/ photonic crystal/ heterostructure
首先采用平面波展开法计算TE偏振模式下PhC 1和PhC 2的能带图[33,34] (具体的方法说明见补充材料), 结果如图2所示. 图2(b)中阴影部分为禁带区域, 结构采用了定向带隙来阻挡反向入射光. 研究发现, hBN与空气的折射率差较小, 使得PhC 2的带隙宽度在可见光波段内随晶格常数a和半径r变化不大. 从图2(a)中可以看出, 异质结构中PhC 1在归一化频率0.79a/λ—0.84a/λ (对应476—506 nm)范围内存在水平方向(Γ-X方向)的定向带隙. PhC 2在归一化频率0.62a/λ—0.65a/λ(对应646—677 nm)范围内存在水平方向(Γ-X方向)的定向带隙. 因此, 对于正向光波从左侧入射到PhC 1中, 除了476—506 nm波段的光, 其余可见光均可以到达异质结构的界面处, 进而折射进入PhC 2中. 而对于反向入射的可见光波从结构右侧入射, 会在PhC 2的禁带646—677 nm波段内, 实现反向抑制, 无法传输到PhC 1中. 图 2 (a) PhC 1的能带图; (b) PhC 2的能带图, 阴影部分代表Γ-X方向禁止光波传输的频带 Figure2. (a) The band diagrams of the PhC 1; (b) the band diagrams of the PhC 2. The shaded area represents the frequency band in which light transmission is prohibited at the Γ-X direction.
为了进一步研究TE偏振光波在异质结构中的传输机制, 对于正向光波在PhC中的传播路径, 需要绘制PhC 1和PhC 2相应的等频率图(equal frequency contours, EFCs). 采用平面波展开方法计算可见光波段对应TE偏振模式下的PhC 1第二能带相应的等频图和PhC 2第五能带相应的等频图, 如图3所示. 光波在PhC中的传播方向取决于群速度vg的方向[34], 群速度vg是第n个能带的角频率ωn和波矢量k的函数: 图 3 (a) PhC 1中TE偏振模式下第二条能带对应的等频图; (b) PhC 2中TE偏振模式下第五条能带对应的等频图(红色和蓝色虚线表示670和630 nm对应的等频线). TE偏振的正向入射光 (c) 和反向入射光 (d) 在670 nm波长处的电场强度分布图; 正向入射光(e)和反向入射光(f)在630 nm波长处的电场强度分布图 Figure3. (a) The EFCs of the second band in PhC 1 for TE polarization; (b) the EFCs of the fifth band in PhC 2 for TE polarization (The red and blue dotted lines represent the EFCs corresponding to 670 and 630 nm). The electric field intensity distribution diagrams of forward incident light (c) and backward incident light (d) of TE polarization at the wavelength of 670 nm. The electric field intensity distribution diagrams of forward incident light (e) and backward incident light (f) of TE polarization at the wavelength of 630 nm
图 1 基于二维hBN PhC异质结构的光波非对称传输示意图, 右图为二维hBN材料的分子结构图
图 2 (a) PhC 1的能带图; (b) PhC 2的能带图, 阴影部分代表Γ-X方向禁止光波传输的频带
图 3 (a) PhC 1中TE偏振模式下第二条能带对应的等频图; (b) PhC 2中TE偏振模式下第五条能带对应的等频图(红色和蓝色虚线表示670和630 nm对应的等频线). TE偏振的正向入射光 (c) 和反向入射光 (d) 在670 nm波长处的电场强度分布图; 正向入射光(e)和反向入射光(f)在630 nm波长处的电场强度分布图
图 4 PhC 1取不同晶格常数 (a) 与不同柱子半径(b) 的透射率; 异质结构中PhC 2取不同的晶格常数(c) 与柱子半径(d) 的透射率
图 5 (a) 二维hBN PhC异质结构的透射光谱图; (b) 有限厚度为2000 nm时, 二维hBN PhC平板异质结构的透射光谱图