太赫兹多维复用与折射率传感集成器件封面文章【增强内容出版】
Terahertz waves featuring broad bandwidths play an increasingly important role in next-generation communication systems. For both terahertz wired and wireless communications, terahertz waveguide integrated devices providing“on-line”signal processing functionalities are in vital demand. In the next-generation communication system, the multiplexing technology around the electromagnetic wave physical parameters such as terahertz radiation polarization, frequency, and phase is an effective solution to enhancing spectrum efficiency. Additionally, the future Internet of Everything information system should have a real-time monitoring function of communication environmental parameters (temperature, humidity, etc.). Given the above technical requirements of multidimensional multiplexing and environmental sensing, novel terahertz functional integrated devices for high-speed information transmission-manipulation-perception fusion should be studied urgently. Several terahertz silicon-based waveguide devices have been demonstrated, but the planar structure restricts the spatial degree of freedom for the devices, which means the devices can only be integrated in a 2D plane. Terahertz fiber-based devices are substrate-free to provide terahertz wave routing abilities along any spatial direction. Nevertheless, most of the reported terahertz fiber devices offer a single functionality, remaining a significant scope of multiple device integration. Thus, we propose a polarization-maintaining subwavelength fiber-based multidimensional multiplexing and sensing integrated device which is composed of fiber bends, a 50/50 Y-splitter, directional couplers, and Bragg gratings. The proposed fiber device provides (de)multiplexing in an additional direction that is orthogonal to the 2D space in contrast to the planar devices. Meanwhile, the device integrates multiple functionalities, including frequency- and polarization-(de)multiplexing, dispersion compensation, and surrounding refractive index sensing. In a nutshell, the integrated device provides exciting perspectives for boosting transmission capacity and developing communication-sensing integration of the next-generation communication systems.
The finite element analysis method and finite-difference time-domain model are employed in our study. First, the finite element analysis method is adopted to calculate the transmission parameters (fractional power in the core, loss, group velocity dispersion, etc.) of terahertz subwavelength fibers with different cross-sectional parameters to design polarization-maintaining fibers supporting low-loss and low-dispersion transmission. Then, S-shaped and 90° bending fibers are designed using Bessel curves. Furthermore, the finite-difference time-domain model is utilized to analyze the transmission characteristics of S-shaped and 90° bending fibers. Then, two S-shaped bending fibers with the same bending radius are utilized to form a Y-splitter. In the next step, we leverage the supermode theory as a theoretical guide and the finite element analysis method as a tool to calculate the required coupling length of the directional couplers. Additionally, the finite element analysis method is employed to investigate the effects of grating cell cross-section parameters, thickness, and number of cycles on grating performance (e.g., transmission and dispersion compensation), and thus accomplish the structural design of uniform gratings. Finally, the performance of the proposed terahertz devices including directional couplers, Y-splitter, uniform grating, and phase-shifted grating is simulated and analyzed using the time-domain finite difference method.
We present terahertz subwavelength rectangular fibers, bending fibers, Y-splitter, directional couplers, uniform grating, phase-shift grating, and multidimensional-multiplexing and refractive-index-sensing integrated devices. First, the subwavelength fiber supports low-loss (below 0.051 dB/mm) and high-birefringent (beyond 0.03) transmissions at a target bandwidth over 0.24-0.28 THz as shown in Fig. 2. Second, the transmission of S-shaped bending fibers with a bending radius of 10 mm is slightly higher than that of 90° bending fibers in the frequency range of 0.24-0.28 THz, whose transmission is higher than -1 dB at the operating frequency of 0.25 THz [Fig. 4(d)]. Thanks to the high transmission of x-bent S-shaped bends, a 50/50 Y-splitter can be readily designed using two bends with the same radius of 10 mm. Third, for the x-placed x-bent directional coupler, high transmission (above -3 dB) and high ER (above 7 dB) are obtained for both x-polarization and y-polarization modes when coupling lengths are in the range of 11.8-12.3 mm. Finally, the integrated device achieves simultaneously polarization and frequency (de)multiplexing, with high transmissions [drop port: -5.94 dB for 0.25 THz x-polarization with dispersion compensation; through port: -7.20 dB for 0.25 THz y-polarization, -2.02 dB for 0.27 THz x-polarization] and high ER (drop port: 15.16 dB; through port: 8.06 dB). Additionally, the device integrates fiber Bragg gratings, allowing both zero-GVD dispersion compensation and refractive-index sensing (sensitivity of 0.181 THz/RIU) abilities (Figs. 17 and 18).
We propose and analyze a terahertz multidimensional-multiplexing and sensing integrated device based on subwavelength birefringent fibers, composed of fiber bends, 50/50 Y-splitter, directional couplers, and Bragg gratings. First, a directional coupler with high transmission and high extinction ratio is designed by introducing a bent fiber to achieve polarization and frequency (de)multiplexing functions. Second, the uniform grating and phase-shift grating in the integrated device enable dispersion compensation and environmental refractive index sensing respectively. Terahertz subwavelength fiber devices feature dense integration in 3D space and efficient transmission, which provides novel design solutions for the integrated terahertz wave transmission-manipulation-sensing information system. Meanwhile, we also envision that many more components such as modulators and imaging devices will be further integrated on the terahertz fiber platform.
1 引言
为满足数据传输容量激增的需求，下一代无线通信系统的载波频率将不可避免地向具有超大带宽的太赫兹频段（0.1~10.0 THz）转移［1-5］。得益于高质量太赫兹信号源［6］和探测器［7］的发展，各种太赫兹无线和有线通信系统迅速涌现。最近，美国东北大学利用肖特基二极管技术在2.03 km距离内实现了2 Gbit/s的太赫兹无线通信［8］。同时，南洋理工大学展示了工作频率为340 GHz时基于硅拓扑光子波导的单通道160 Gbit/s通信链路［9］。无论是在无线还是有线通信系统中，提供信号处理和集成功能的太赫兹器件都至关重要［10-13］。
根据波导结构，太赫兹波导器件可分为光纤器件和硅基平面器件。对于长度一般为几厘米的片上互连来说，平面器件是非常理想的选择［14-16］。例如，华中科技大学提出了一种太赫兹硅基多维（解）复用器，该复用器由环形谐振器和偏振分束器-旋转器组成，可同时操纵偏振和频率，他们通过实验实现了0.38 THz频率处8 Gbit/s的数据传输速率［17］。然而，平面器件是在高电阻率晶圆上制成的，仅能够在二维（2D）平面集成，这限制了器件的空间自由度。对于长达数米的太赫兹通信链路来说，光纤器件是实现信号传输和“在线”操控（即在太赫兹波沿光纤器件传输的过程中进行操控）的关键技术［1，18］。基于太赫兹光纤的耦合器［19-20］、分束器［11，21］、色散补偿器［22］和滤波器［10，23］等可提供（解）复用、路由、多种信号传感功能。台湾大学提出了一种由两根方管形光纤组成的太赫兹漏模定向耦合器，由于中空结构之间的弱模式耦合，该耦合器需要10.8 cm的耦合长度［19］。蒙特利尔大学提出了一种基于光栅耦合器的频分复用器，能够对比特率高达6 Gbit/s的太赫兹信号进行（解）复用［24］。马尔堡大学利用3D打印机制造出了弯曲半径小于10 mm的Y型分束器，其额外的弯曲损耗可以忽略不计［21］。蒙特利尔大学还展示了一种基于金属空芯波导的色散补偿器，其在0.14 THz附近的负群速度色散（GVD）约为-25 ps·THz-1·mm-1［22］。北京交通大学设计并制作了基于太赫兹亚波长矩形聚合物光纤的光栅，该光栅可同时对两种偏振态进行滤波，并且阻带的消光比（ER）超过20.9 dB，半峰全宽（FWHM）约为21.1 GHz［10］。此外，北京交通大学提出了一种基于圆对称亚波长光纤的相移光栅，探索了其在折射率（RI）传感方面的潜力［25］。
然而，大多数已报道的太赫兹光纤器件只提供单一功能。对于丰富的太赫兹波应用领域，集成多种功能的光纤器件仍有很大的发展空间。本文提出了一种基于太赫兹亚波长光纤的多维复用与RI传感集成器件。该器件由两个定向耦合器、一个50/50 Y型分束器、一个均匀布拉格光栅和一个π相移布拉格光栅组成，可实现偏振-频率（解）复用、色散补偿以及环境RI传感功能。本文工作突破了硅基波导器件仅能在2D空间进行集成的限制，丰富了太赫兹波导器件在信息传输、处理等方面的应用。
2 集成器件结构及设计方法
本文提出的多维复用与RI传感集成器件结构如
图 1. 太赫兹多维复用与RI传感集成器件模型图及亚波长光纤传输性能仿真结果。（a）器件的3D结构；光纤中（b）x偏振态及（c）y偏振态在0.25 THz时芯子周围的归一化电场分布（箭头代表电矢量）
Fig. 1. Schematic diagram of multidimensional-multiplexing and RI sensing integrated device, and simulation results of subwavelength fiber transmission performance. (a) 3D structure of device; normalized electric field intensity of (b) x-polarized modes and (c) y-polarized modes for fiber at 0.25 THz (arrows represent electric vectors)
如
图 2. 亚波长光纤传输性能仿真结果。有无泡沫包层时光纤中x偏振态和y偏振态的（a）芯子中的有效折射率和双折射率、（b）功率束缚因子、（c）损耗以及（d）群速度色散（GVD）随频率的变化曲线
Fig. 2. Simulation results of subwavelength fiber transmission performance. (a) Effective RI and birefringence, (b) fractional power in core, (c) loss, and (d) GVD values of x-polarized and y-polarized states with and without foam cladding for fiber as functions of frequency
3 器件仿真及结果分析
3.1 弯曲光纤
弯曲光纤对于信号的路由以及耦合至关重要。在上述亚波长光纤的基础上，本文根据贝塞尔曲线提出了两种弯曲光纤：90°弯曲光纤和S型弯曲光纤。这两种光纤又可以分别设计成沿x轴或y轴弯曲的光纤，从而形成
图 3. 4种弯曲光纤的结构示意图。（a）x轴90°弯曲光纤；（b）x轴S型弯曲光纤；（c）y轴90°弯曲光纤；（d）y轴S型弯曲光纤
Fig. 3. Schematics of four types of bent fibers. (a) x-bent 90° fiber; (b) x-bent S-shaped fiber; (c) y-bent 90° fiber; (d) y-bent S-shaped fiber
图 4. 90°和S型弯曲光纤的传输率随弯曲半径以及频率的变化。（a）90°弯曲光纤和（b）S型弯曲光纤在0.25 THz频率处的传输率随弯曲半径的变化；（c）弯曲半径为10 mm的90°弯曲光纤和（d）S型弯曲光纤的传输率随频率的变化
Fig. 4. Transmission varying with bend radius and frequency for 90° and S-shaped bending fibers. Transmission of (a) 90° and (b) S-shaped bending fibers at 0.25 THz as a function of bending radius; transmission of (c) 90° and (d) S-shaped bending fibers with bending radius of 10 mm as a function of frequency
Y型分束器可使用两个弯曲半径均为10 mm的S型光纤组合而成，其结构如
图 5. Y型分束器结构图及分束性能仿真结果。（a）50/50 Y型分束器示意图，其中输入端口为P1，两个输出端口为P2和P3；（b）Y型分束器中x偏振态在0.25 THz频率处的功率分布；（c）从Y型分束器的两个输出端口P2和P3输出模式的传输率随频率的变化曲线；（d）Y型分束器中y偏振态在0.25 THz频率处的功率分布
Fig. 5. Structure diagram of Y-splitter and simulation results of beam splitting performance. (a) Schematic of 50/50 Y-splitter. Input port is P1, while two outputs are P2 and P3; (b) simulated power distribution of x-polarized state for the Y-splitter at 0.25 THz; (c) transmission of Y-splitter at P2 and P3 ports as a function of frequency; (d) simulated power distribution of y-polarized state for Y-splitter at 0.25 THz
3.2 定向耦合器
定向耦合器是设计频率和偏振（解）复用系统的关键部件，可用于同时处理频率和偏振信息。
图 6. 定向耦合器结构示意图以及两种正交偏振模式在其中的功率分布。（a）沿x轴放置的定向耦合器示意图（箭头曲线表示定向耦合器中x偏振态和y偏振态的传输路径，x轴表示亚波长光纤的放置方向）；（b）工作频率为0.25 THz时x偏振态和y偏振态在定向耦合器中的功率分布
Fig. 6. Schematic of directional coupler and power distributions of two orthogonal polarization modes. (a) Schematic of directional coupler placed along x-axis (arrow lines indicate propagation paths of both x-polarized and y-polarized states for directional coupler, x-axis represents placement direction for subwavelength fibers); (b) simulated power distributions of directional coupler for x-polarized and y-polarized states at 0.25 THz
得益于上述弯曲光纤的低弯曲损耗，首先设计了引入弯曲半径为10 mm的90°弯曲光纤的定向耦合器，以同时获取两种正交偏振模式。为了提高定向耦合器的耦合性能，将两个直光纤紧贴在一起。在此基础上，与弯曲光纤进行级联，根据光纤的两种弯曲方向和两种放置方向进行组合，设计了
图 7. 4种定向耦合器的结构示意图。（a）沿x轴放置x轴弯曲的定向耦合器；（b）沿y轴放置x轴弯曲的定向耦合器；（c）沿x轴放置y轴弯曲的定向耦合器；（d）沿y轴放置y轴弯曲的定向耦合器
Fig. 7. Schematics of four types of directional couplers. (a) x-placed x-bent directional coupler; (b) y-placed x-bent directional coupler; (c) x-placed y-bent directional coupler; (d) y-placed y-bent directional coupler
值得注意的是，传统的耦合模理论不再适用于引入亚波长弯曲光纤的定向耦合器，模式耦合不仅发生在相邻的两根直光纤上，也发生在弯曲光纤与直光纤之间的区域。因此，需要对每种定向耦合器的耦合长度进行手动调整，使其在工作频率处具备最佳的耦合性能。为了评估耦合器的性能，引入了ER的概念，其中x偏振态和y偏振态的ER［35-36］分别表示为
式中：
图 8. 4种定向耦合器在0.25 THz工作频率处的传输率和ER随耦合长度的变化曲线。（a）沿x轴放置x轴弯曲的定向耦合器；（b）沿y轴放置x轴弯曲的定向耦合器；（c）沿x轴放置y轴弯曲的定向耦合器；（d）沿y轴放置y轴弯曲的定向耦合器
Fig. 8. Transmissions and ER values for four directional couplers as functions of coupling length at operating frequency of 0.25 THz. (a) x-placed x-bent directional coupler; (b) y-placed x-bent directional coupler; (c) x-placed y-bent directional coupler; (d) y-placed y-bent directional coupler
调整完4种定向耦合器的耦合长度后，还需要分析0.24~0.28 THz工作频率范围内的频率响应。
图 9. 4种定向耦合器的传输率和ER随频率的变化。（a）沿x轴放置x轴弯曲的定向耦合器；（b）沿y轴放置x轴弯曲的定向耦合器；（c）沿x轴放置y轴弯曲的定向耦合器；（d）沿y轴放置y轴弯曲的定向耦合器
Fig. 9. Transmission and ER values for four directional couplers as functions of frequency. (a) x-placed x-bent directional coupler; (b) y-placed x-bent directional coupler; (c) x-placed y-bent directional coupler; (d) y-placed y-bent directional coupler
图 10. 0.25 THz频率处 x偏振态和y偏振态在沿x轴放置的x轴弯曲定向耦合器中xz平面上的功率分布。（a）x偏振态；（b）y偏振态
Fig. 10. Power distributions on xz-plane of x-polarized and y-polarized states at 0.25 THz for x-placed x-bent directional coupler. (a) x-polarized state; (b) y-polarized state
接下来对引入S型弯曲光纤的定向耦合器进行设计。沿x轴放置x轴弯曲和沿x轴放置y轴弯曲定向耦合器的结构如
图 11. 引入S型弯曲光纤的定向耦合器结构图。（a）沿x轴放置x轴弯曲定向耦合器；（b）沿x轴放置y轴弯曲定向耦合器
Fig. 11. Schematics of directional couplers consisting of S-shaped bending fibers. (a) x-placed x-bent directional coupler; (b) x-placed y-bent directional coupler
图 12. 两种定向耦合器的传输率和ER随频率的变化曲线。（a）沿x轴放置x轴弯曲的定向耦合器；（b）沿x轴放置y轴弯曲的定向耦合器
Fig. 12. Transmission and ER values of two directional couplers as functions of frequency. (a) x-placed x-bent directional coupler; (b) x-placed y-bent directional coupler
图 13. 在0.27 THz频率处沿x轴放置y轴弯曲定向耦合器中的功率分布。（a）x偏振态；（b）y偏振态
Fig. 13. Simulated power distributions at 0.27 THz for x-placed y-bent directional coupler. (a) x-polarized state; (b) y-polarized state
3.3 光纤光栅
太赫兹光纤布拉格光栅在构建信号处理和环境传感器件方面起着极为关键的作用。太赫兹光纤通道通常会在有线传输链路上引入信号色散（典型值为4 ps·THz-1·mm-1）［30］，为了补偿传输色散，本课题组利用微机械加工技术制作了均匀光栅［28］。本文以0.25 THz为目标频率，重新对均匀布拉格光栅进行设计，其仿真参数分别为：
图 14. 色散补偿器的结构和仿真结果。（a）色散补偿器的整体结构；（b）光栅单元在xz平面和yz平面上的截面参数；（c）色散补偿器的传输率和群速度色散随频率变化的曲线
Fig. 14. Structure and simulation results of dispersion compensator. (a) Schematic of dispersion compensator; (b) single grating unit cross-sections in xz-plane and yz-plane; (c) transmission and GVD values of dispersion compensator as functions of frequency
基于本课题组的前期工作［10］，本文设计了一种基于光纤相移光栅的传感器，用于对环境RI变化进行监测。值得注意的是，为了监测周围环境的RI变化，π相移光栅不能封装在泡沫包层内。如
图 15. 相移光栅的结构和仿真结果。（a）相移光栅的整体结构；（b）光栅单元在xz平面和yz平面上的截面参数；（c）相移光栅中y偏振态的传输率随频率变化的曲线
Fig. 15. Structure and simulation results of π-shifted grating. (a) Schematic of π-shifted grating; (b) single grating unit cross-sections in xz-plane and yz-plane; (c) transmission for y-polarized state of π-shifted grating as a function of frequency
3.4 多维复用与RI传感集成器件
本文研究了由矩形亚波长光纤、弯曲光纤、50/50 Y型分束器、定向耦合器、均匀光栅以及相移光栅组成的太赫兹多维复用与RI传感集成器件［
图 16. 不同偏振和不同频率的信号在多维复用与传感集成器件中的功率分布
Fig. 16. Simulated power distribution for modes propagating along multidimensional-multiplexing and sensing integrated device
图 17. 不同偏振信号的传输率和ER随频率的变化曲线。（a）中心频率为0.25 THz的x偏振态和y偏振态窄带信号在集成器件的下行端口和直通端口的传输率和ER随频率的变化曲线；（b）中心频率为0.27 THz的x偏振态窄带信号在集成器件直通端口的传输率随频率的变化曲线
Fig. 17. Transmission and ER values for signals with different polarizations as functions of frequency. (a) Transmission and ER values of x-polarized and y-polarized narrowband signals with a central frequency of 0.25 THz at drop port and through port for integrated device as functions of frequency; (b) transmission of x-polarized narrowband signal with central frequency of 0.27 THz at through port for integrated device as a function of frequency
图 18. 不同环境RI下相移光栅的传输谱以及中心频率随RI的变化。（a）相移光栅的传输谱；（b）传输谱中心频率随RI的变化曲线
Fig. 18. Transmission spectra of phase-shifted grating under different refractive indices and center frequency varying with RI. (a) Transmission spectra of phase-shifted grating; (b) central frequency of transmission spectrum as a function of RI
4 结论
本文提出了一种基于太赫兹亚波长双折射光纤的多维复用与RI传感集成器件。首先，通过引入弯曲光纤设计了高传输率和高ER的定向耦合器，实现了偏振和频率（解）复用功能。其次，利用集成器件中的均匀光栅和相移光栅分别实现了色散补偿和环境RI感知。太赫兹亚波长光纤器件具有3D空间集成、高效传输等方面的优势，为太赫兹波传输-操控-感知一体化信息系统提供了新颖的设计方案。此外，太赫兹光纤平台有望进一步集成信号调制、高分辨率成像等有源、无源功能器件，为太赫兹信息系统落地提供技术支撑。
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