太赫兹导模谐振滤波器的自动化设计方法研究

Automated Design Study of Guided-Mode Resonance Filters Working at Terahertz Frequencies

太赫兹窄带滤波器是太赫兹波段无线通信、高分辨光谱分析和被动式安检成像等技术设备中不可或缺的功能器件,而介质光栅中的导模谐振(GMR)效应是实现高品质因数太赫兹窄带滤波器的重要方法。目前,常使用严格耦合波分析法(RCWA)描述光栅的辐射特性并结合粒子群算法(PSO)优化结构参数来设计导模谐振滤波器(GMRF)。然而,该方法的建模过程复杂并且不能设计广义的超材料光栅。本文提出一种新的自动化设计方法,使用电磁仿真软件CST和PSO相结合设计导模谐振滤波器,采用含有惩罚项的目标函数对滤波器参数进行优化。运用该设计方法分别设计了中心频率位于0.65 THz的一维矩形光栅带阻滤波器和中心频率位于0.6 THz的二维偏振无关的超材料导模谐振滤波器,并通过光刻和反应离子刻蚀加工所设计的高阻硅光栅,分别测量了光栅在TE偏振态下的正入射光谱和入射角为4°、8°的斜入射光谱,谐振的分布和变化规律与仿真结果一致,验证了设计方案的有效性。该研究为太赫兹波段导模谐振器件的研究提供了新的设计方法,并由此推动太赫兹无线通信、光谱分析和被动成像的发展。

Objective Terahertz narrowband filters are indispensable functional devices for terahertz wireless communication,high-resolution spectroscopy,and passive security imaging techniques;the guided-mode resonance(GMR)effect in dielectric grating is a promising route for realizing these narrowband filters.The combination of the particle-swarm optimization(PSO)algorithm and rigorous coupled-wave analysis(RCWA)is a widely used method for devising GMR filters.However,Maxwell equations are usually hard to establish and solve when dealing with more complicated gratings,especially for metasurface gratings.This study proposes a novel automated design method that uses the PSO algorithm to invoke the commercial software,CST,to calculate dielectric grating transmission.By adding a"penalty"item in the fitness function,we design a silicon grating with a GMR at 0.65THz and a polarization-independent metasurface grating with a GMR at 0.6THz.The proposed automated design method provides a novel approach for investigating terahertz GMR devices,which may greatly promote the development of terahertz communication,spectroscopy,and passive imaging.Methods Silicon is almost lossless and nondispersive in a terahertz band,making it suitable for narrowband filters.In this study,we set the refractive index of silicon to 3.45,which has been widely used in previous studies.We aimed to design a silicon grating that worked at 0.65THz and avoided absorption from water vapor.The whole design process was completed using MATLAB,where the PSO algorithm was easy to implement and converge.The whole design process began from program initialization and setting the parameters,in which the binary-coded PSO was used conveniently control the parameters’resolution.The fitness function adopted herein comprised two parts:the rootmean-square error between the objective and the calculated transmittance and the penalty item used to limit the central frequency.We used the same PSO frame to invoke an RCWA code and the commercial software CST for calculating the grating transmissions(Table 1).The results proved that our method outperforms the RCWA method regarding the design with complicated structures.To experimentally verify our design concept,the designed silicon grating was fabricated using photolithography and deep-reactive ion etching,followed by the measurements with a home-built 8F terahertz time domain spectroscopy system(Fig.6)at incident angles of 0°,4°,and 8°.Results and Discussions In the case of a transverse electric(TE)-polarized incident wave,the result obtained from the method using the CST is similar to that obtained by the method using the RCWA.For a transverse magnetic(TM)polarization incident wave,the silicon grating designed by the CST shows a much higher quality factor[Fig.3(b)].Moreover,our method can be used to handle more complicated structures,such as metasurface gratings[Fig.4(a)].The penalty item in the fitness function limits the central frequency of the metasurface grating at 0.6THz.Although an additional resonance is located at the higher frequency side,the high-Qresonance satisfies the design requirement.The monitored electric field distribution[Fig.4(d)]shows nodes and antinodes,which are typical standing wave characteristics,proving that the obtained resonance belongs to the GMR.The fabricated grating sample(Fig.5)shows an obvious resonance at 0.69THz under the TE polarization,which slightly deviates from the expected resonance at 0.65THz.The simulated results illustrate that the resonance of the proposed silicon grating blue-shifts with a decreasing periodicity and an increasing grating height(Fig.8),which may contribute to the resonance shifts.Changing the incident angles in the measurement splits the resonance at 0.69THz owing to the broken symmetry of the phase matching condition(Fig.9),which is consistent with the simulation and proves the GMR attribute of the 0.69THz resonance.Conclusions In this study,we propose an automated design method for devising terahertz GMR filters.The parameters of a silicon grating working at 0.65THz and a more complicated metasurface grating working at 0.6THz are obtained by invoking CST under the PSO framework.The simulated electric field distributions verify the GMR feature of the resonances realized in the gratings.More importantly,compared with the traditional method using the RCWA,our method can achieve high quality factor resonance and handle complex structures.The fabricated silicon grating is experimentally measured to prove our simulation results with 5GHz spectral resolution.The grating sample shows an obvious resonance at 0.69THz with 28 GHz linewidth under the normal incident wave.The GMR attribute of this resonance is well proven by the transmittances at the incident angles of 0°,4°,and 8°and the simulation results show a splitting behavior caused by the angle dependence of the GMR.This automated design method may promote the research on terahertz narrowband filters.