School of Physics & Electronic Engineering, Taishan University, Tai’an 271021, China
Proceedings of the Nature Research Society, Volume 1, Article Number 01005, 2017
Published Online: 13 October 2017 (Article)
Split-ring-resonators (SRRs) are one of the most common unit cell designs for metamaterials. Though extensively studied and well understood, such devices are often used as narrow-band filters due to SRRs' sharp resonance to electromagnetic wave. In this work, based on the idea of patterning metal SRRs on both sides of a dielectric substrate while rotating patterns on one side 90o to the other, we show that simple circular SRR can be a building block for broadband filters in terahertz (THz) range. The design principle is detailed with simulation results, showing that such fabricated devices essentially equates to two narrow-band filters on both sides of the substrate connected in series. By changing the unit cell from single SRR to double SRR, we effectively expanded the stop band width of the broadband filter. Devices were created on two types of substrates, 1 mm thick quartz and 100 µm thick polyethylene terephthalate (PET), demonstrating the ease and wide applicability of the fabrication process, while a bandwidth of as large as 1.40 THz has been achieved.
Metamaterials with many unique optical properties [1-5] are made of periodically arranged sub-wavelength metallic structures that are able to couple to external electromagnetic (EM) waves. One of such structures is the commonly used split-ring-resonators (SRR) [6-8]. Due to their simplicity and the close resemblance of their first order resonance to a conventional inductor-capacitor (LC) circuit , both single and double SRRs (DSRRs) have been extensively studied and understood as how to tune the resonant frequency by changing structural designs [9-10], the coupling effect between the SRRs [11-13] and so on. Moreover, tunability brought about by microelectromechanical systems (MEMS) technologies  and the flexibility of the devices enabled by using flexible substrates  have extended their applications even further.
The SRR-based metamaterials are known to have sharp and narrow resonances that are polarization-dependent [7,16]. While such narrow resonances are good for optical applications like filters, sensors and detectors, there is an increasing demand for broadband filters with easier fabrication process to give wide margins for manufacturing parameters and allow multi-frequency operations . Most of previous efforts have shunned SRRs for such applications and turned to isotropic patterns like metal patch [17,18], cross patterns [19,20] and closed rings [20,21] instead, especially when designing polarization-insensitive devices. These designs relied on closely stacked metal layers with very thin dielectric layers sandwiched in between. As a result, the control of dielectric layer thickness  and perfect alignment of each layer [18,20] are of critical importance to device performance. Han et al. pioneered the exploration of SRR-based broadband metamaterials . Their work cascaded multiple layers of SRRs of gradually changing sizes, and merged the resonances of these layers that lie at gradually shifting frequencies to form a broadband. While innovating, such a method still suffers from high transmission loss due to multiple dielectric layers. The need for creating SRRs of different sizes also complicates the fabrication process. Lastly, the inherent polarization-sensitive characteristics of the SRR structures are not avoided in their design.
In our previous work , we reported a method to design and fabricate broadband filter in terahertz (THz) frequency range using specially designed SRRs as the unit cell. The obtained stop band width was 0.42 THz. In this work, we show that this method works with the best studied circular SRRs as well, and by changing the unit cell from single SRR to double SRR, a bandwidth as large as 1.40 THz can be readily achieved, further giving light to the following advantages of the method. Firstly, we got rid of the stacking strategy of previous designs and used only one dielectric layer to minimize transmission loss. Secondly, for one device, SRRs of a fixed shape and dimensions is used. Thus the fabrication cost is lowered due to fewer masks required. Thirdly, our method poses little requirement on the material and thickness of the dielectric layer, as well as alignment accuracy in lithography step, further simplifying the fabrication process. Fourthly, the bandwidth of our device can be easily designed and tuned, owing to the well-studied design rules for determining the resonant frequencies of narrow-band SRR devices. Lastly, while enjoying the benefits of using SRRs, our device is still polarization-insensitive which allows wide range of applications.
The design principle is to fabricate SRR patterns on both sides of a thick (comparable or larger than operating wavelength) substrate, but rotates the pattern on one side 90o with respect to the other . It is worth pointing out that similar designs are common in chiral metamaterials [24-27], but the design logics are completely different. For chiral metamaterials, it is essential that a thin substrate (much smaller than the operating wavelength) is used for the SRRs on the two sides to couple. For example, a 2.5 mm substrate is used for chiral metamaterial operating around 10 GHz ; a gap of 600 nm is required for operations with wavelength around 20 μm . For the method proposed in this paper, a thick substrate is emphasized to purposely de-couple SRRs on both sides.
Figure 1 show such a device illuminated by a normally incident THz light and its unit cell. The period of each unit cell is 114 μm. The SRR geometry dimensions, outer diameter (a), inner diameter (b) and gap width (d) are 100 μm, 76 μm and 12 μm, respectively. For the ease of description, we define a randomly polarized incidence as ɵ-polarized, where ɵ is the angle between the incident polarization and the line joining the center of the SRR and the midpoint of its gap, as illustrated in Figure 1 (b). Therefore, an x-polarized incidence will be 90o-polarized for the front layer and 0o-polarized for the back layer; and a y-polarized light vice versa. For the double-layered device, polarization is defined with respect to the front layer. The transmission spectra for 0o- and 90o-polarized incidence were calculated using Lumerical finite-difference time-domain (FDTD) simulation for both a single-layered device and a double-layered one. The structures used in simulation consist of a 50 μm-thick quartz substrate with 500 nm-thick aluminum (Al) SRR patterns. The single-layered device has only the front layer SRRs. The simulation results are presented in Figure 2.
Figure 1. (a) Illustration of the designed double-layered device. (b) Zoomed-in view of the unit cell outlined by a dashed square in (a), with dimension parameters and polarization angle labeled.
Figure 2. Simulated transmission spectra for both single-layered and double-layered devices with 0o and 90o incident polarization angle.
Our simulation results on the single-layered device agree well with the well-studied transmission spectrum of SRR devices , and it shows the characteristics of polarization-sensitive narrow band bandstop filter because it resonates to the incident EM wave at specific frequency depending on the incident polarization. In this case, the resonant dip falls at 0.80 THz and 1.10 THz for a 0o- and a 90o-polarized incidence, respectively. As the substrate thickness of the double-layered device is greater than the attenuation length of the resonant electromagnetic modes [28,29], there is no near-field coupling between the two layers of SRRs. As was pointed out in our previous work , when a y-polarized THz wave is incident from the front of the device, it effectively passes two filters connected in series. The front layer SRRs will firstly filter out the frequency at 0.80 THz due to 0o-polarization incidence, and the back layer will then filter out the frequency at 1.10 THz as it sees a 90o-polarization incidence. The transmission spectrum of such a device is therefore a superposition of the two layers. As both filters do not have sharp transition between the passband and stopband and these two resonant frequencies are close enough as compared to the 3 dB bandwidth of each filter, the combinational result of these two serial filters generates a broadband bandstop spectrum. Since the two layers of SRRs are identical, an x-polarized light is filtered just the same, but in a reverse order. Therefore, such a device becomes polarization-insensitive . The broadband filtering works for any randomly polarized light, as the polarization azimuth can all be decomposed into x- and y-direction.
For a better observation of the serial filtering effect, a commercial FDTD solver, CST Microwave StudioTM was used to simulate the surface currents at the two resonances for single-layered device and at 0.80, 0.95 and 1.10 THz, corresponding to the beginning, midpoint and end of the broadband, for the double-layered device. The simulation results are shown in Figure 3. It is clear that in a single-layered device, for a 0o-polarized incidence, the resonance at 0.80 THz excites symmetric current at the two sides of the SRR; while for a 90o-polarized incidence, the resonance at 1.10 THz excites non-symmetric current flow across the gap and at the side opposite to the gap in the SRR. In double-layered device, for a 0o-polarized incidence, the front layer resonates at 0.80 THz, just like a single-layered device, independent from the back layer. At this frequency, the light was almost all filtered after passing the first layer, therefore, there is no current excited in the back layer. Gradually, as the frequency increases and deviates away from the resonant frequency of the front layer and approaches that of the back layer as it sees a 90o-polarized incidence, the current excited in the back SRR gets intensified. At 1.10 THz, the current in the back layer flows in the exact same fashion as that in a single-layered device excited by a 90o-polarized EM wave, confirming that there is no coupling between the front and the back layer. In the frequency range between 0.80 and 1.10 THz, the two filters at the front and the back are complementary to each other and form a stopband together. Similarly, for a 90o-polarized incidence, lower frequencies were filtered out together by both filters while higher frequencies were stopped fully before the first layer.
Figure 3. Plots of surface current distribution at the resonant frequency for single-layered device when illuminated by (a) 0o- and (b) 90o-polarized incidence, as well as (c) in the stopband at 0.80, 0.95 and 1.10 THz for double-layered device. The solid (on the front layer) and dashed (on the back layer) arrows indicate current directions in the resonating SRR.
Ultra broadband filters
In order to improve the bandwidth of such double-layered filters, DSRRs are used as unit cells in each layer (Figure 4 (a)). It is modified from the previous design by adding in a smaller concentric SRR whose gap is located oppositely. The outer diameter (a), inner diameter (b) and the gap width (d) of the inner SRR are 60, 40 and 12 μm, respectively. Figure 4 (b) shows the simulated transmission spectra for single-layered device whose unit cell consists of the big or small SRR, as well as the designed DSRR, respectively. The substrate used in simulation is again 50 μm- thick quartz. It is evident that our design combines the resonances of the two individual SRRs , and resonant frequencies showed no significant shift due to appropriately chosen spacing between the two rings . In this way, we obtained alternating resonances at neighbouring frequencies for 0o- and 90o-polarized incidence, which is essential in designing ultra-broadband filters.
Figure 4. (a) Illustration of the unit cell of an ultra-broadband filter. (b) Simulated transmission spectrum of single-layered devices with different unit cells at 0o- and 90o-polarized incidence, shown in black and red lines, respectively. The right column shows the corresponding unit cell.
As was discussed previously, each layer of the double-layered devices resonates to the external EM wave independently. Therefore, in actual fabrication of the device, substrate thickness and alignment of the unit cells are no longer an issue. We fabricated the DSRR single-layered and double-layered device on two types of substrates, 1 mm-thick quartz and 100 μm-thick PET with conventional optical lithography and lift-off processes. The microscopic images of such devices are shown in Figure 5. Misalignment of the unit cells can be easily seen in the PET device, as both sides of the thin and transparent device are focused simultaneously. The EM responses of the devices were characterized using terahertz time domain spectroscopy (THz-TDS, TeraView TPS 3000) in transmission mode. The measured transmission spectra were normalized to that of a plain quartz or PET with no metal patterns, and presented in Figure 6. The experimental results agreed well with the simulation on single-layered devices, while confirmed that a broad transmission stopband exists for double-layered devices regardless of incident polarization. The transmission level stays below 0.18 from 0.60 to 1.75 THz for quartz device, and from 0.60 to 2.0 THz for PET device. Moreover, quartz device showed more fluctuation in the spectrum due to more closely located Fabry–Pérot resonances as a result of increased substrate thickness.
Figure 5. Microscopic images of the devices fabricated on (a) 1 mm-thick quartz and (b) 100 μm-thick PET, respectively. The scale bars on both images are 100 μm.
Figure 6. Measured transmission spectra of single- and double-layered devices on (a) 1 mm-thick quartz substrate and (b) 100 μm-thick PET substrate with 0o- and 90o- incident polarization. The inserts are microscopic images of the devices respectively. The scale bars on both images are 100 μm.
In conclusion, we have demonstrated a simple and effective way to design and fabricate SRR-based polarization-insensitive ultra broadband filters in THz range. Such miniaturized and low-cost bandstop filters are achieved by patterning identical metal SRRs on both sides of a substrate and have one layer rotated 90o with respect to the other. We show that the patterns on both layers are not coupled, and thus substrate thickness and misalignment are not critical issues in fabrication. The resulting spectrum of such a device is therefore a superposition of that of each layer. Our theory was verified by simulation as well as experiments on quartz and PET substrates with different thickness. Finally, using DSRR as the building unit for such a device, we achieved a broadband as large as 1.40 THz. Being easily scalable in principle, such a method can find applications in other frequency ranges as well. This work therefore opens a new door to design strategies for broadband bandstop filters.
This work was supported by the National Natural Science Foundation of China (No. 61605139), the Natural Science Foundation of Shandong Province (No. ZR2016FQ15) and the Science and Technology Planning Project of Higher Education of Shandong Province (No. J16LJ10).
The authors declare no competing financial interest.
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