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 0.65 THz and a polarization-independent metasurface grating with a GMR at 0.6 THz. 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 0.65 THz 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 root-mean-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 0.6 THz. Although an additional resonance is located at the higher frequency side, the high-Q resonance 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 0.69 THz under the TE polarization, which slightly deviates from the expected resonance at 0.65 THz. 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 0.69 THz 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 0.69 THz resonance.

Conclusions In this study, we propose an automated design method for devising terahertz GMR filters. The parameters of a silicon grating working at 0.65 THz and a more complicated metasurface grating working at 0.6 THz 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 5 GHz spectral resolution. The grating sample shows an obvious resonance at 0.69 THz 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.