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Abstract
A novel planar terahertz (THz) plasmonic waveguide developed from coplanar stripline (CPS) is proposed for the first time to achieve strongly confined THz propagation performance based on the concept of spoof surface plasmon polaritons (SSPP). Guided-wave characteristics of the proposed plasmonic waveguide are theoretically investigated by eigen-mode simulation technique and finite-difference time-domain solutions. It is found that the waveguide propagation characteristics can be directly manipulated by designing the SSPP unit cells, which exhibit flexible tuning ability of the asymptotic frequency and strong THz field confinement. The idea has been validated through fabricated filter experiments in microwave frequency regime by scaling up the geometry size of the proposed structure. The measured results illustrate high performance of the ultra-wideband filter, in which the reflection coefficient is better than −10 dB from 3 to 13.1 GHz with the smallest and worst insertion losses of 2.2 dB and 5.6 dB, respectively. This work presents a new SSPP waveguide developed from CPS to realize the THz-wave propagation with strong field confinement, which may have promising potential applications in various integrated THz plasmonic devices.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Surface plasmon polaritons (SPPs) are surface electromagnetic (EM) waves propagating along the metal-dielectric interface, which have attracted increasing attentions due to their remarkable capability of guiding and localizing EM waves into subwavelength scales during the last decade [1–3]. The unique characteristics associated with SPPs have potential applications for designing ultra-compact photonic circuits, high-resolution imaging, and high sensitive biochemical sensors [4–6]. However, the effect of natural SPPs can only exist at the optical frequency.
Although the SPPs cannot be supported in the terahertz or microwave regime, recently by mimicking the SPPs dispersion characteristics, the concept of spoof SPPs (SSPP) was introduced to support the highly confined surface EM waves at lower frequencies. A series of SSPP waveguides were presented in recent years, such as tapered parallel plate structures, metal wires, two-dimensional holes, and one-dimensional grooves [7–14]. These designs provide efficient solutions to manipulate the SSPP propagation at THz or microwave frequencies. Many promising THz or microwave devices were developed from SSPP technology, such as guided wave-to-SSPPs transition, sensors, filters, antennas, splitters, and amplifiers [15–26].
Compared with microwave bands, THz regime, which demonstrates many unique properties including non-ionizing radiation, transparency to some materials, etc., is less known and explored. Recently, some THz SSPP-based designs were report [27–31]. Most of these designs were developed from microstrip, slotline or coplanar waveguide (CPW) [30, 31]. However, to the best of our knowledge, no work has been reported on the coplanar striplines (CPS)-based SSPP designs in THz regime.
The CPS is a balanced uniplanar transmission line with the advantages of compact size, ease of mounting lumped components in shunt configuration, and the uniplanar via-free characteristics [32]. The CPS technology has been widely applied to design many novel devices, such as filters, antennas, and phase shifters [33–35]. Therefore, by developing the SSPP designs from the CPS technology, the proposed designs cannot only inherit the advantages of CPS (i.e., compact size, ease of mounting, etc.), but also will feature the SSPP distinct performance including asymptotic cutoff frequency and low-pass filtering capability as well as the high field confinement.
In this paper, a novel THz SSPP waveguide is developed from CPS for the first time. Compared with the slotline-based SSPP waveguide displayed in [36], the proposed design shows tighter fields confinement and enhanced magnitude of electric fields. Meanwhile, compared with the two presented solutions to the radiation loss challenge of slotlines at terahertz frequencies (i.e., slotline wrapped in a homogeneous medium and slotline on a layered substrate), the proposed structure only consists of one-layer dielectric substrate, which highly reduces the fabrication complexity. In addition, since the CPS consists of only two striplines, the proposed THz SSPP waveguide occupies fewer area without vias than some other uniplanar transmission line technologies (e.g., CPW) [12], [14]. Our work exhibits an ultra-wideband lowpass filtering response whose bandwidth can be directly manipulated by tuning the dimensions of the proposed SSPP unit cells. To validate the proposed idea, the analysis of dispersion characteristics, S-parameters simulation, and the field distribution calculation are demonstrated. A similar CPS-based SSPP structure scaled down to the microwave frequency regime is fabricated and measured to verify the feasibility of the proposed waveguide. This design provides a new perspective for integrated THz circuits and devices and may have promising potential application in biochemical sensors, high-resolution imaging, and novel THz circuits (i.e., power dividers, frequency splitters, crossovers, etc.).
2. Analysis of the proposed terahertz SSPP unit cell
The proposed THz SSPP unit cell developed from CPS is shown in Fig. 1(a), which is periodically machined into a metal film on the bottom layer of dielectric substrate to form the SSPP waveguide. The proposed SSPP unit cell consists of the dual striplines (i.e., CPS) along the y direction and two stubs symmetrically loaded to the middle of the striplines along the x direction. It is characterized by the following parameters: widths of CPS and stubs (i.e., W and Wn), gap of the y-direction striplines S, length of stub Ln, and the lattice constant or period D (see Fig. 1(a)). To simplify the analysis, the metallic part is assumed to be perfect electric conductor (PEC) with the thickness of T1 = 100 nm, and the substrate is using polyimide with the relative dielectric constant (εr) of 2.9, loss tangent of 0.003, and the thickness of T2 = 20 µm.
Fig. 1 (a) Schematic configuration of the proposed SSPP unit cell. (b) The dispersion curves of the light line and the proposed SSPP unit cell shown in (a) with different dimensions. The default geometric parameters of Ln = 35 μm, Wn = 10 μm, W = 5 μm, D = 22.5 μm, and S = 2.5 μm are fixed for all curves except the parametric sweeping.
To obtain the dispersion curves, theoretical calculations and numerical eigen-mode simulations are carried out by the commercial software, CST Microwave Studio. The dispersion characteristics of THz SSPP unit cell are investigated by placing the proposed unit cell in an air box where the boundaries in the y direction should be set as the periodic boundary, and the other boundaries in the x and z directions are set as the PEC boundary. All eigen-frequencies are calculated when sweeping the phase difference between the two periodic boundaries from 0° to 180°. Hence, the dispersion relation of the fundamental mode is obtained as displayed in Fig. 1(b), where k denotes propagation constant in the y axis.
The dispersion characteristics of the proposed THz unit cell can be controlled by shaping its geometry dimensions. As can be seen in Fig. 1(b), the dispersion curves of the proposed structure significantly deviate from the light line, indicating strong confinement of THz wave on the surface. This deviation is more apparent as the length of stubs Ln increases or the width of the stubs Wn decreases while maintaining other dimensions unchanged. The asymptotic frequency or cutoff frequency shifts down from the value of 1.4 THz to 1.1 THz as the two parameters (Ln, Wn) are selected from (35 μm, 20 μm) to (45 μm, 10 μm), respectively, which implies flexible tuning ability for the confinement of surface wave.
To explore the metal loss effect on the proposed THz SSPP wave propagation, we calculated the propagation lengths for different metals of SSPP waveguides (PEC, gold, copper films) and made the comparisons in Fig. 2. As indicated, the propagation length is sensitive to the metal loss with different types (i.e., PEC, gold, and copper) and will decrease with the increase of operating frequency due to the increasing ohmic losses. However, once the metal type is fixed, we also can simply reduce the stub length Ln to increase the propagation length. Therefore, we could optimize the proposed SSPP waveguide to partially reduce the metallic loss effect on the SSPP propagation.
Fig. 2 Propagation lengths versus the operating frequency for different metals of SSPP structures (PEC, gold, and copper films). Other physical parameters are the same as those in Fig. 1.
3. Terahertz SSPP waveguide developed from the CPS
Based on the unit cell in Fig. 1(a), a THz SSPP waveguide with the input and output ports of CPS is constructed as shown in Fig. 3. It is composed of two parts: periodic array of the proposed SSPP unit cells with the same stub length, and the transition for the mode conversion from CPS to SSPP waveguide with their stub lengths Hn as follows, H1 = 1 μm, H2 = 7.5 μm, H3 = 14 μm, H4 = 21 μm, H5 = 27.5 μm, H6 = 34 μm, H7 = 40.5 μm. The other dimensions are set as D = 22.5 μm, S = 2.5 μm, W = 5 μm, Wn = 10 μm, and Ln = 45 μm. The transition part produces gradient momentum to match the momentum of the plasmonic waveguide to the CPS. Only bottom view of the structure is depicted here since no metallization but only dielectric exists on the top side of the SSPP waveguide.
Fig. 3 Schematic configuration of the proposed THz SSPP waveguide with the input and output ports of CPS.
The properties of the proposed SSPP waveguide are investigated by the frequency domain simulation, where the parameters of the dielectric substrate and the metallic parts are the same as those presented above. A waveguide port is assigned to the left-side of the proposed structure as a THz energy feeding, and the open boundaries are applied in all directions to mimic the real space instead of the periodic and PEC boundaries in the eigenmode simulations. To simplify and expedite the simulation, besides the transition parts, N periods of the SSPP unit cells are constructed in this design.
Figure 4 displays the simulated 2-D distributions of the z-component electric fields. As shown in Fig. 4(a) and (b), the observed frequencies are at 1 and 1.5 THz, respectively, where 1 THz is located in the passband, and 1.5 THz lies in the stopband. For comparison, both of these two electric field distributions have the same color bar in dB scaling. Clearly observed that when the operation frequency is at 1 THz, the guided waves are gradually transformed to SSPPs (or vice versa), and in the SSPP waveguide section, the SSPP wave are effectively supported. However, the fields at 1.5 THz vanish rapidly along the SSPP propagation direction in the observed plane, proving again that SSPP modes will be efficiently blocked beyond the cutoff frequency of the proposed plasmonic structure. Note that not only the surface EM waves at 1 THz but also the other signals whose operation frequencies are lower than cutoff frequency can efficiently propagate along the proposed THz SSPP waveguide.
Fig. 4 Simulated z-direction electric field distributions on the x-y plane 2 μm above the proposed THz SSPP waveguide at different frequencies: (a) 1 THz and (b) 1.5 THz.
To further obtain a clear insight into the SSPP propagation features of the proposed waveguide, the frequency responses of the proposed THz SSPP waveguide are also calculated (see Fig. 5), where the ultra-wideband lowpass filtering characteristics can be achieved. The bandwidth of such frequency response can be adjusted by tuning the length of the loading stubs Ln. As can be seen in Fig. 5(a), the edge of the lowpass filtering response decreases from 1.45 to 1.15 THz as Ln increases from 35 to 45 μm. Figure 5(b) is the simulated performance comparison between cases with different periods N. These cases have almost the same frequency response curve in the passband, which indicates that the length of the proposed SSPP waveguide is insensitive to the SSPP wave propagation. In other words, SSPP wave is capable of propagating on the proposed SSPP unit cells array with low loss, and the insertion loss of the proposed filter mainly results from other parts rather than the SSPP unit cells array.
Fig. 5 Simulated S-parameters of the proposed THz SSPP waveguide (a) with different lengths Ln (N = 9) and (b) with different periods N (Ln = 45 μm).
The confinement details can be seen from the distributions of electric field amplitudes (|E| = [|Ex|2 + |Ey|2 + |Ez|2]1/2) at 1 THz and 1.5 THz along the x direction, as illustrated in Fig. 6(a). In view of the main central peak, both of these two fields decay exponentially when keeping away from central point, showing that the SSPP modes are tightly confined on the surface of the proposed waveguide. In addition, two small side peaks symmetrically appear at about ± 50 μm along the x direction which is attributed by the loading stubs of the proposed SSPP unit cells. It is important to note that the intensity of the electric fields at 1.5 THz is significantly lower than that at 1 THz, manifesting the cutoff properties of the proposed SSPP structure. The insets of the Fig. 6(a) demonstrate the SSPP power flows on the cross-sectional cuts at different locations (i.e., y = 0 μm and 10 μm) along the y direction at 0.5 THz, and both of these two insets have the same color bar in dB scaling. It is obviously visualized that the EM fields both decay sharply along the two orthogonally lateral (x and z) directions, illustrating the typical features of the SSPP propagation.
Fig. 6 (a) Simulated amplitudes of electric fields distributions |E| along the x direction when y = 0 μm and z = 2 μm. (b) power intensity distributions along the y direction when x = 0 μm and z = 2 μm. The inset shows the power distribution of 0.5 THz on the x-z plane when y = 0 μm and y = 10 μm.
Additionally, Fig. 6(b) demonstrates the power intensity distributions along the y direction where the THz input signal is fed at the left-side of the proposed waveguide (y = −390 μm). The 1.5 THz signal (red line) shows strong fluctuation as y ≤ −150 μm, whereas it decreases sharply to a weaker flat line as y > −150 μm. For comparison, the 1 THz power distribution along the propagation direction is also calculated, where a stable and almost flat line with small ripples indicates efficient SSPP wave propagation with low loss. Obviously, the SSPP unit cells array functions as a filter which selectively suppresses the signals operating over the asymptotic cutoff frequency. We apply such feature to form the stopband for the lowpass filtering response of the proposed THz SSPP waveguide.
To prove the advantages of the proposed structure including fields confinement and the enhancement of the fields magnitude, the comparison of the cross-section electric field distributions |E| between the slotline-based waveguide in [36] and the proposed THz SSPP structure is carried out and illustrated in Fig. 7. To make the comparison fair, these two cases have the same settings on the substrate, metallic film, and the dimension of the gap (i.e., S). The proposed one (i.e, red line) demonstrates higher peak value than that of the slotline-based waveguide (i.e., blue line), which means that the magnitude of the electric fields has been enhanced by adopting the proposed design. In addition, the comparison of the field confinement ability is demonstrated in the inset of Fig. 7(b), where the same color bar in dB scaling is applied. The warm colors represent the stronger magnitudes of |E| while the cold colors denote weaker ones, the shiny color part in the inset indicates the area where the electric energy mainly concentrates. Since the area of the shiny color part for the proposed structure is smaller than that of the conventional slotline, the proposed one shows stronger fields confinement than that of the slotline.
Fig. 7 (a) Cross sections (blue planes) used for calculating and demonstrating the electric fields distribution. (b) Comparisons of the simulated amplitudes of electric fields distributions |E| between the slotline and the proposed structure at the frequency of 0.5 THz. The inset of (b) is the electric fields distributions on cross section of the slotline and the proposed structure where both plots have the same color bar in dB scaling.
4. Application of the proposed SSPP structure in microwave filters
Not only applied in THz band, the proposed SSPP waveguide can be also extended to the microwave regime. In the lower frequency microwave regime, the proposed idea and prototype are easily verified through prevalent printed circuit board (PCB) fabrication technique. Therefore, we herein scale up the dimensions of the proposed THz SSPP unit cell to scale down the frequency to microwave. A microwave bandpass filter (BPF) is designed and fabricated based on such SSPP waveguide, as displayed in Fig. 8. The top and bottom metallic layers (i.e., the red and yellow parts) are printed on the dielectric substrate (i.e., gray part) with the relative dielectric constant (εr) of 2.65, and thickness of 0.5 mm. The proposed BPF is composed of three parts: the microstrip to CPS transition feeds for facilitating measurement, the CPS to SSPP transition and the SSPP waveguide. The width of the microstrip feeding line can be determined by setting the characteristic impedance of 50-Ω. To improve the impedance transformation between the CPS and the microstrip line, a microstrip circular stub at the end of the microstrip line and a slot circular stub at the end of the slotline are employed in the transition design. The detailed dimensions can be found in the caption of Fig. 8. The CPS to SSPP transition section and the SSPP waveguide are designed by adopting the enlargement version structure of the proposed THz SSPP waveguide.
Fig. 8 (a) Schematic configuration of the proposed microwave BPF with input and output microstrip-CPS transitions for facilitating measurement. (b) Photographs of the fabricated microwave BPF (N = 9). The geometric parameters of Ln = 3.54 mm, Wn = 1 mm, W = 0.5 mm, D = 3.5 mm, H1 = 0.53 mm, H2 = 0.96 mm, H3 = 1.39 mm, H4 = 1.82 mm, H5 = 2.25 mm, H6 = 2.68 mm, H7 = 3.11 mm, R1 = 2 mm, R2 = 3 mm, R3 = 1.8 mm, R4 = 3 mm, and S = 0.1 mm are chosen.
The passband of the proposed microwave BPF is built due to the contributions of the periodic arrangement of the proposed SSPP unit cells and the microstrip-CPS transition sections. In other words, the SSPP unit cells array creates the high-frequency stopband by the intrinsic cutoff characteristics while the microstrip-CPS transition sections generate the low-frequency stopband by rejecting the low-frequency current. For demonstration, the proposed BPF shown in Fig. 8(a) is fabricated and tested. Measurements are performed by using an Agilent N5247A vector network analyzer to obtain the scattering parameters (S-parameters). Moreover, the dispersion curves of the light line and the proposed microwave SSPP unit cell are also calculated as seen in Fig. 9(a), which shows the cutoff frequency of the proposed structure is at 12.8 GHz. Figure 9(b) indicates the comparison of numerical calculation and experimental measurement results where the average insertion losses of about 4.2 dB and the return losses of over 10 dB can be observed in the frequency range of 3-13.1 GHz. Satisfactory agreement can be obtained which validates good performance of the proposed microwave BPF developed from the proposed THz SSPP waveguide. The minor mismatch is mainly caused by soldering imperfection. It is interesting to note that the high-frequency edge of the passband is about at 12.8 GHz which is consistent with the cutoff frequency in Fig. 9(a).
Fig. 9 (a) Dispersion curves of the SSPP unit cell and light line. (b) Simulated and measured S-parameters of the proposed microwave filter. (c) Simulated transmission coefficient with varied length of the proposed SSPP waveguide (i.e., number of SSPP unit cells N).
The relatively large insertion losses within the passband are mainly caused by the transition design rather than the proposed SSPP waveguide. Figure 9(c) shows the simulated insertion losses of the proposed microwave BPF with different lengths of the proposed SSPP waveguide (i.e., number of the SSPP unit cells N). Although the lengths of SSPP waveguide are increased from N = 7 to 11, the insertion losses almost keep constant, which means that the insertion losses are insensitive to the length of the proposed SSPP waveguide. Hence, the insertion losses of the proposed SSPP waveguide are very low, which also can be seen in the results of THz SSPP structure (i.e., Fig. 5).
5. Conclusion
In conclusion, a THz SSPP unit cell and corresponding CPS-based waveguide are designed and analyzed in this work. In order to implant the proposed idea to microwave regime, we scaled up the proposed THz SSPP waveguide structure to support SSPP propagation in the microwave regime. A microwave BPF based on the SSPP waveguide is designed with ultra-wideband filtering characteristics, whose simulation and measurement are in good agreement. Our design approach is not restricted to the specific frequency band we proposed, and it can be applied in any other frequency bands. To the best of our knowledge, it is the first time to propose this spoof plasmonic waveguide developed from CPS with strongly confined terahertz propagation. This work may pave the way for novel microwave and THz wave CPS-based plasmonic circuits.
Funding
National Natural Science Foundation of China (NSFC) (61601390); Shenzhen Science and Technology Innovation Project (JCYJ20170306141249935).
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