Abstract
We propose a method to synthesize several band-rejection filters by etching split-ring resonators (SRRs) on the transmission line for spoof surface plasmon polaritons (SPPs), which is made of double-side or single-side corrugated metal strips. From dispersion relations, the corrugated strips can support spoof SPP modes when the operating frequency is less than the cutoff frequency. The electric field component perpendicular to the strip surface of the SPP modes can excite the complementary SRRs (CSRRs), leading to resonant modes preventing the SPP propagation near the resonant frequencies. Using this principle, single-frequency rejection filters, double-frequency rejection filters and broad band-stop filters with bandwidth of 1.5âGHz have been designed and fabricated using the single- and/or double-side corrugated strips. Both measured results and numerical simulations demonstrate the excellent filtering characteristics of all design, which are in good agreements. The isolation of all filters can be less than â20âdB and even reach to â38âdB at rejection frequencies. The proposed rejection and stop-band filters give important potentials to develop integrated plasmonic functional devices and circuits at microwave and terahertz frequencies.
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Introduction
Propagating surface plasmon polaritons (SPPs) are tightly fettered on the interface of metal and dielectric at the optical frequency1, behaving good performance for SPP transmission in the direction parallel to the metal surface with exponential decay in the direction normal to the surface2,3. Many scientists have devoted to research SPPs for the advantage of strong local-field enhancement and breaking the diffraction limit as propagating surface waves4,5. The main reason for the formation of the optical SPPs is the manifestation of the metallic negative permittivity at those frequencies6. However, in virtue of perfect electric conductors of the metal at lower frequencies (far infrared, terahertz and microwave bands), the plasmonic waves cannot be efficiently confined to the metal7.
To overcome this limitation, the plasmonic metamaterials of corrugated metal structures was proposed to excite the so-called spoof SPP modes, which have similar dispersion relations and spatial confinements to SPPs in the optical region8. Since then, there have been periodic arrays enchased with slits, holes or blocks of one- or two-dimensional structures reported for propping spoof SPP modes up availably9,10,11,12. The hybrid circuits combining traditional transmission line and ultrathin corrugated metallic strips have made the conversion and transition between the spatial guided waves and spoof SPPs possible12,13,14. In the meantime, the wide-band filters15,16, band rejection filters17, radiating antennas18,19 and some active devices have been produced successfully based on spoof SPPs12,20 and it is evident that they will benefit to circuit integration and even system integration in view of the excellence of miniaturization and breaking the challenge of signal integrity12,14.
Split-ring resonators (SRRs) were originally put forward for their capability to the synthesis of metamaterials with negative effective permeability21,22,23. CSRRs are a kind of defected ground structures by etching SRR elements on the ground plane24,25,26. Regarded as a new type of metamaterial resonators, it has been shown that CSRRs have also negative permittivity27. Microstrip SRRs can be considered as the magnetic dipole resonators excited by axial magnetic field and microstrip CSRRs can relatively be considered as the electric dipole resonators excited by axial electric field28,29. For inhibiting signal propagation in the vicinity of their resonance frequency, both SRRs and CSRRs are widely used for the design of the miniature microwave devices such as filters, antennas and couplers29,30,31,32.
In this article, we propose several band-rejection filters through etching CSRR elements on the SPP structure. The spoof SPP waveguide makes use of double-side or single-side corrugated strips to produce tighter electromagnetic field confinement and smaller propagating wavelength. In order to connect the measured system, coplanar waveguide (CPW) is employed to feed the SPP structures. Two transition sections serve as a bridge between the SPP waveguide and CPW for smooth conversion. SRRs are etched on the metal part of the corrugated strips, coming into being CSRRs. The electric field component perpendicular to the surface of metal can excite CSRRs for inhibiting signal propagation in the vicinity of their resonance frequency. Numerical and experimental results are presented to confirm the good filtering performance of the whole structure. The design method makes the model structure simpler and more compact and the features of filtering SPP waves are significant for the follow-up developments of plasmonic integrated circuits and systems.
Results
The proposed band-rejection filter is illustrated in Fig. 1, containing the double-side corrugated strips, CSRRs, CPWs and two transition sections, in which the subfigures (bâe) correspond to parts AâD of the whole structure shown in Fig. 1(a), respectively. The designed filter circuit is printed on a thin and flexible dielectric film, F4B, whose relative permittivity is 2.65 (1â+â0.003âi) and thickness is 0.17 mm. The annealed copper (with electric conductivity Ïâ=â5.8âeâ+â007âS/m) is used as metal layers with thickness of 0.018âmm.
For facilitating the experiment with standard SMA connectors, at the end of the filter circuit shown in Fig. 1(b), we design two CPWs to feed the guided-wave energies or receive the spoof SPP signals. Parameters Hâ=â11âmm, gapâ=â0.24âmm and L1â=20âmm for CPWs are chosen to get 50âΩ input and output impedance. Figure 1(c) depicts a transition section between CPW and the double-side corrugated metallic strip with high efficiency, which has been demonstrated in ref. 13. The transition section containing gradient grooves and two flaring grounds symmetrical to horizontal axis are designed for impedance and momentum matching. The gradient grooves are linear, whose expression is f2(x). The starting and ending points of f2(x) respectively are the highest and the lowest points of the groove and thus the slope of f2(x) is L2/d, where dâ=â3.5âmm refers to the depth of groove and L2â=â50âmm. The curve of the flaring ground is an exponential function in which the x axis is assumed to be the central line of the double-side corrugated strip and the y axis is located at the left starting side of part B. In the formula, parameters L3â=â90âmm and w1â=â35âmm represent the length and width of the flaring ground and the degree of the bending curve f1(x) is câ=â0.07.
In the main transmission section, we adopt a typical configuration of spoof SPP waveguide, a double-side corrugated strip, whose unit cell is displayed in Fig. 1(d). The period of unit arrangement is pâ=â5.5âmm and the width of groove is aâ=â2 mm. The length of the whole structure is 342.5âmm. The basic principle of the composition of SRRs is two concentric regular polygons or circular ring with opposite splits. Since the symmetry of the double-side corrugation will result in the symmetrical plasmonic modes, SRRs with circular rings are chosen to reach the symmetrically coupling field. As shown in Fig. 1(e), circular SRRs are etched on the metal parts of the corrugated strips, in which the circular-ring center is located at the center of the metal between two grooves. For the integrity of the CSRR structure, the radius of outer ring r should be less than the length between the edge of the groove and the center of the unit cell , in case that SRR is too large to be etched on the metal part of corrugation. The ring width and split width are chosen as wâ=â0.35âmm and gâ=â0.15âmm, respectively.
The Eigen-mode solver of commercial software, the CST Microwave Studio, is applied to calculate the dispersion curves of the SPP waveguide, comprehending propagation characteristics. In the simulation course, the boundary conditions are periodic in the x axis and electric walls in both y and z axes and the distance between the boundary and unit cell is 50âmm in y and z axes. Figure 2 depicts the dispersion curves of single-side (blue lines) and double-side (red lines) SPP waveguide. We clearly observe that the curves of both modes exhibit SPP-like behaviors and the cutoff frequency of the double-side corrugation is slightly lower than that of the single-side corrugation with the same groove depth d. Furthermore, the dispersion curves of the spoof SPP waveguides deviate gradually from the dispersion curve of CPW marked in black line when the propagation vector k grows up and they asymptotically approach to the lower cutoff frequencies when increasing the groove depth. For spoof SPP waves, the incident energy will be totally reflected when the working frequency is higher than the cutoff frequency because of the physical intermodal coupling between the forward and backward modes around the cutoff frequency34. Meanwhile, it implies that both single- and double-side corrugated metallic strips support spoof SPP electromagnetic waves.
Using the CST Microwave Studio, we further employ the time-domain solver to simulate the transmission coefficients of the circular CSRRs with different sizes for better apprehending the rejection property. Because CSRRs are considered as electric dipole resonators excited by axial electric field, the boundary conditions are electric wall in the z axis and magnetic wall in the y axis for guaranteeing the same working environment of CSRRs. Two ports are placed on both ends of the structure with open boundary in the x axis. As shown in transmission coefficients in Fig. 3(a), we easily discover that there are three resonance frequencies 8.15, 9.15 and 10.41 GHz when we change the values of the radius as râ=â2.31, 2.2 and 1.9âmm in the range from 1 to 13âGHz. From Fig. 3(b), we clearly see the simulated relationship between resonant frequency of the circular CSRR and ring radius r. In other words, it is visualized and lucid to find that the resonance frequency of CSRR decreases with the increase of the ring radius r. Meanwhile, we notice that the CSRR etched on the corrugated metallic structure will reduce the energy transmission. To confirm the insulation of CSRRs, we compare the near-field distributions with râ=â2.31âmm at the resonant frequency 8.15âGHz and 9.5âGHz within the propagating band. In Fig. 3(c), we notice that the fields are mainly oscillated around the first CSRR, leading to terminated wave propagation at the resonant frequency. However, Fig. 3(d) depicts the near-field distributions propagating without attenuation at 9.5âGHz.
To study the operation performance of the SPP waveguide etched CSRRs, we fabricate a prototype illustrated in Fig. 4(a), where the enlarged inset shows the details of CSRRs. Five identical CSRRs with râ=â2.31âmm are etched in the center of the spoof SPP transmission line made of double-side corrugated strips. For measurement, two SMA connectors are welded on both ends of the fabricated sample and we use two 50âΩ coaxial lines to connect the standard SMA connectors with the Agilent Vector Network Analyzer (VNA, N5230C). From the dispersion curve of double-side mode with dâ=â3.5âmm in Fig. 2(a), we observe that the cutoff frequency of the spoof SPP waveguide adopted in this paper is 13.07âGHz, so that the incident energy will be totally reflected when the working frequency is higher than 13.07âGHz. Figure 4(b) illustrates the simulated and measured transmission coefficients S21, respectively, at the propagating frequencies from 1 to 12âGHz lower than the cutoff frequency 13.07âGHz. It is clearly observed that the measured results have a small discrepancy with the simulations, which is mainly caused by the machining tolerance, loss of the coaxial cable and influence of the test environment in the experiment. From the transmission coefficients, we note that S21 is less than â30âdB at 8.15âGHz and the maximum S21 can reach â0.5âdB within the â3âdB bandwidth. As shown in Fig. 3(a), the frequency 8.15âGHz is the resonant frequency with râ=â2.31âmm, so that it is proved that the electric field component perpendicular to the metal surface can excite CSRRs. Meanwhile, the simulation results confirm the excellent filtering characteristics such as small insertion loss, significant rejection, high transmission efficiency and great square ration. The measured results further confirm the practicability of the proposed structure.
Owing to the maneuverability of the CSRR resonant frequencies with different circular-ring radii, we fabricate a double-frequency rejection SPP waveguide by using two kinds of CSRRs. As shown in Fig. 5(a), there are five CSRRs with circle radius râ=â2.30âmm and other five CSRRs with circle radius râ=â1.95âmm. Such ten CSRRs are etched on the central metal part of the corrugated strip and the interval between the two kinds of CSRRs is three times of the structure period. From the S scattering parameters of CSRRs with different circle radii, we notice that the resonant frequency is higher when the radius diminish in size. It is obvious that for CSRRs, there are two different resonant frequencies when râ=â2.30âmm and r =â1.95âmm, respectively. As the simulated and measured results illustrated in Fig. 5(b), we confirm that the proposed structure provides the excellent rejections at 8.21âGHz and 10.04âGHz. The simulated transmission coefficients at both 8.21âGHz and 10.04âGHz are less than â30âdB. On the basis of the performance of the tunable resonant frequency of CSRR, it is convenient to fabricate the multiple-frequency rejection filters and integrated circuits.
Since CSRRs always work in narrow frequency band, a small amount of CSRRs cannot achieve a broadband-frequency rejection. In other words, several kinds of CSRRs with different sizes can realize multi-band filtering. By adjusting the size of the structure, the adjacent resonant frequency points are close to each other, so that the broadband filtering effect is reached. Therefore, we use a series of CSRRs with different circle radii to fabricate the broad band-stop filter, as shown in Fig. 6(a). By optimizing the size of circle ring, we choose twenty-five etched CSRRs including five CSRRs with circle radius râ=â2.32âmm, five CSRRs with circle radius râ=â2.25âmm, five CSRRs with circle radius râ=â2.19âmm, five CSRRs with circle radius râ=â2.13âmm and five CSRRs with circle radius râ=â2.07âmm. Each different kind of circular ring set is separated from the others by a unit period of corrugation. The filtering performance of the broad band-stop is authenticated through Fig. 6(b), illustrating the simulated and measured transmission coefficients. We note a remarkable stop band from 8.11âGHz to 9.61âGHz and the simulated S21 of the stop band is less than â20âdB. It is clearly clarified the property of frequency rejection in a broad band on the proposed SPP waveguide.
It has been confirmed that both single-side and double-side corrugate metallic strips can support the propagation of spoof SPPs33. Figure 7(c) displays the unit cell of the single-side SPP waveguide with the width hâ=â5.5âmm. The period of single-side unit arrangement is pâ=â5.5âmm and the width and depth of groove are aâ=â2.2âmm and dâ=â4.2âmm, respectively. Due to the asymmetry of the single-side corrugated strip, we choose two different gaps gap1â=â0.15âmm and gap2â=â0.2âmm to describe CPW, as illustrated in Fig. 7(b). The gradient grooves are linear, whose slop is L2/d where L2â=â45âmm, indicating the length of the gradient grooves. L3â=â80âmm represents the length of the flaring ground and the degree of the bending curve part of flaring ground is câ=â0.04. The length of whole structure is 337âmm and other parameters that are not specified are the same as those in the numerical mode shown in Fig. 1. In virtue of the asymmetric SPP waves resulting from the single-side corrugation and the size of SRR to be etched on the metal part of the waveguide, we adopt rectangular CSRRs which are not symmetric with the y axis for coupling the asymmetric SPP waves, in which the rectangular CSRRs have smaller relative sizes for achieving the compact structure. As illustrated in Fig. 7(d), the length and width of the outer rectangle are denoted as ll1â=â2.5âmm and ll2â=â5.0âmm, respectively and the size ll1âÃâll2 should be smaller than (p-a)âÃâh for integrity of the rectangular CSRRs. The rectangular CSRRs are located at the position of h1â=â0.2âmm away from the bottom. We use wâ=â0.3âmm and gâ=â0.2âmm to depict the ring width and split width, respectively.
In order to understand the performance of the rectangular CSRR, we firstly simulate the transmission coefficient of a single rectangular CSRR. Figure 7(e) depicts three transmission coefficients with three sizes ll1âÃâll2â=â3.0âÃâ5.0, ll1âÃâll2â=â2.5âÃâ5.0 and ll1âÃâll2â=â2.5âÃâ4.6âmm2. It is observed that the resonance frequencies 8.0, 8.79 and 9.32âGHz of rectangular CSRRs increase as the size decreases. Then, the simulation mode of the single-side waveguide etched with six rectangular SRRs is fabricated, as given in Fig. 7(a). From the simulated and measured S scattering parameters of the filter illustrated in Fig. 7(f), we note a conspicuous stop band at 8.74âGHz where the transmission coefficients are less than â30âdB. Because the cutoff frequency of the single-side SPP waveguides with dâ=â4.2âmm adopted in this paper is 11.66âGHz, as shown in Fig. 2, we choose the propagating frequencies from 1 to 11âGHz. The simulated results confirm that the single-side SPP waveguide etched with the rectangular SRRs also have the excellent filtering characteristics and this structure can play an important role to develop plasmonic integrated circuits.
Discussion
From both simulation and measurement results in shown in Figs 4(b), 5(b), 6(b) and 7(f), we find that the proposed structures have highly efficient filtering performance. Figure 8(aâd) illustrate the photographs of single-frequency double-side, double- frequency double-side, broadband double-side and single-frequency single-side structures, respectively. The insert in each photograph shows the detailed geometry for the convenient comprehension. Compared with previous rejection filters based on spoof SPP waveguide17, the rejection bandwidth has been increased for the broadband rejection filter and the isolation of rejection frequencies is improved significantly and even reaches to â38âdB for the single-frequency rejection filters. Increasing the numbers of CSRRs can increase the isolation, as shown in Fig. 9 for the comparison between four and six CSRRs. On the other hand, the proposed structures are so simple and compact that they do not take up extra space. Because the single-side and double-side structures are manageable alone, it is convenient to control the signal filtering of each branch for SPP integrated circuits and systems.
For obtaining the physical insight into the SPP waveguide etched with CSRRs, we study the near-field electric distributions of z-components on the xây plane, which is 4âmm above the dielectric substrate. As example, we chose the broadband double-side sample for near-field simulations and measurements. The field monitor for electric fields is set up at some frequencies and the simulated field distributions are illustrated in Fig. 10(aâc). At the frequency 8.6âGHz at the rejection band, we note that the electric-field distribution is interrupted at the location of CSRRs, as demonstrated in Fig. 10(b). Because the corrugated metallic strip generates the electric-field component perpendicular to the SPP waveguide, CSRRs can be excited to the resonant state at the resonant frequency.
However, at 7âGHz and 10 GHzâin the pass band, we observe that the SPP waves are propagating through the corrugated strip and CSRRs with very small loss, as shown in Fig. 10(a,c). We also notice that the transition sections can effectively realize the coupling and conversion between the spatial guide waves and spoof SPPs in the filtering circuit. Figure 10(dâf) depict the relevant results of the near-field electric distributions measured by a home-made near-field scanning system, which have very good agreements with the numerical simulations. Both the simulated and measured results intuitively provide a proof to corroborate the great filtering performance of the transmission device for the plasmonic integrated circuits at microwave frequencies.
Conclusion
By mean of the circular and rectangular SRRs etched on the SPP waveguides using double-side and single-side corrugated metallic strips, we have presented several novel compact band-rejection filters to develop highly efficient and controllable rejection-band plasmonic circuits. In virtue of the highly confined electromagnetic waves of SPPs and smooth conversion of the transition sections, the proposed filters have excellent transmission efficiency and low loss. Meanwhile, owing to the fact that the electric field component perpendicular to the metallic surface will excite CSRRs, there are some signal propagation rejections at special designed resonance frequencies. Based on this principle, we have designed the single-frequency rejection filters, double-frequency rejection filters and broadband rejection filters using single-side and double-side SPP waveguides. All such structures have been manufactured for experimentally verifying the marvelous capability. Both simulation and measurement results have demonstrated the highly efficient filtering performance. The proposed tunable band-rejection filters provide potentials to promote the development of plasmonic functional devices and integrated circuits in both microwave and terahertz frequencies.
Methods
Numerical simulations are performed by commercial software, the CST Microwave Studio, whose eigen-mode solver and time-domain solver are employed to calculate the dispersion relation and S parameters, respectively. A 0.17-mm thin and flexible dielectric film F4B with the relative permittivity 2.65 (1â+â0.003âi) is used to fabricate the experimental filters. The metal layers with thickness 0.018âmm are adopted as a kind of annealed copper (electric conductivity Ïâ=â5.8âeâ+â007âS/m). For experiments, we utilize Agilent Vector Network Analyzer (VNA, N5230C) to measure S parameters of the fabricated filters. A home-made near-field scanning system is used to measure the near electric-field distributions.
Additional Information
How to cite this article: Zhang, Q. et al. A series of compact rejection filters based on the interaction between spoof SPPs and CSRRs. Sci. Rep. 6, 28256; doi: 10.1038/srep28256 (2016).
References
Stewart, M. E. et al. Nanostructured plasmonic sensors. Chem. Rev. 108, 494â521 (2008).
Maier, S. A. Plasmonics: fundamentals and applications: fundamentals and applications. (Springer Science & Business Media, 2007).
Harvey, A. Periodic and guiding structures at microwave frequencies. IEEE T. Microw. Theory 8, 30â61 (1960).
Fang, N., Lee, H., Sun, C. & Zhang, X. Subâdiffraction-limited optical imaging with a silver superlens. Science. 308(5721), 534â537 (2005).
Barnes, W. L., Dereux, A. & Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 424, 824â830 (2003).
Tsakmakidis, Kosmas L., Boardman, Allan D. & Hess, Ortwin. âTrapped rainbowâ storage of light in metamaterials. Nature 450(7168), 397â401 (2007).
Kumar, G., Cui, A., Pandey, S. & Nahata, A. Planar terahertz waveguides based on complementary split ring resonators. Opt. Exp. 19, 1072â1080 (2011).
Pendry, J., Martin-Moreno, L. & Garcia-Vidal, F. Mimicking surface plasmons with structured surfaces. Science 305, 847â848 (2004).
Hibbins, A. P., Evans, B. R. & Sambles, J. R. Experimental verification of designer surface plasmons. Science 308, 670â672 (2005).
Martin-Cano, D. et al. Domino plasmons for subwavelength terahertz circuitry. Opt. Exp. 18, 754â764 (2010).
Shen, X. & Cui, T. J. Planar plasmonic metamaterial on a thin film with nearly zero thickness. Appl. Phys. Lett. 102, 211909 (2013).
Zhang, H. C. et al. Broadband amplification of spoof surface plasmon polaritons at microwave frequencies. Laser & Photon. Rev. 9, 83â90 (2015).
Ma, H. F., Shen, X., Cheng, Q., Jiang, W. X. & Cui, T. J. Broadband and highâefficiency conversion from guided waves to spoof surface plasmon polaritons. Laser & Photon. Rev. 8, 146â151 (2014).
Liao, Z., Zhao, J., Pan, B. C., Shen, X. P. & Cui, T. J. Broadband transition between microstrip line and conformal surface plasmon waveguide. Journal of Physics D: Appl. Phys. 47, 315103 (2014).
Yin, J. Y., Ren, J., Zhang, H. C., Pan, B. C. & Cui, T. J. Broadband Frequency-Selective Spoof Surface Plasmon Polaritons on Ultrathin Metallic Structure. Sci. Rep. 5, 8165, doi: 10.1038/srep08165 (2015).
Gao, X., Zhou, L., Liao, Z., Ma, H. F. & Cui, T. J. An ultra-wideband surface plasmonic filter in microwave frequency. Appl. Phys. Lett. 104, 191603 (2014).
Pan, B. C., Liao, Z., Zhao, J. & Cui, T. J. Controlling rejections of spoof surface plasmon polaritons using metamaterial particles. Opt. Exp. 22, 13940â13950 (2014).
Yin, J. Y., Zhang, H. C., Fan, Y. & Cui, T. J. Direct Radiations of Surface Plasmon Polariton Waves by Gradient Groove Depth and Flaring Metal Structure. IEEE Antenn. Wirel. Pr. 5 (2015).
Xu, J. J., Zhang, H. C., Zhang, Q. & Cui, T. J. Efficient conversion of surface-plasmon-like modes to spatial radiated modes. Appl. Phys. Lett. 106, 021102 (2015).
Zhang, H. C. et al. Second-Harmonic Generation of Spoof Surface Plasmon Polaritons Using Nonlinear Plasmonic Metamaterials. ACS Photonics, doi: 10.1021/ascphotonics. 5b00580 (2015).
Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from conductors and enhanced nonlinear phenomena. Microwave Theory and Techniques, IEEE Tran. on 47(11), 2075â2084 (1999).
Gay-Balmaz, P. & Martin, O. J. Electromagnetic resonances in individual and coupled split-ring resonators. Journal of applied physics 92(5), 2929â2936 (2002).
Shen, G. H. J. & Lancaster, M. J. Microstrip Filters For RF/Microwave Application. New York: Wiley (2001).
Kim, C. S., Park, J. S., Ahn, D. & Lim, J. B. A novel 1-D periodic defected ground structure for planar circuits. Microwave and Guided Wave Letters, IEEE 10(4), 131â133 (2000).
Abdel-Rahman, A., Verma, A. K., Boutejdar, A. & Omar, A. S. Compact stub type microstrip bandpass filter using defected ground plane. IEEE Microwave and wireless components Letters 14(4), 136â138 (2004).
Lim, J. S., Kim, C. S., Ahn, D., Jeong, Y. C. & Nam, S. Design of low-pass filters using defected ground structure. Microwave Theory and Techniques, IEEE Tran. on 53(8), 2539â2545 (2005).
Falcone, F., Lopetegi, T., Baena, J. D., Marqués, R., MartÃn, F. & Sorolla, M. Effective negative-& epsiv; stopband microstrip lines based on complementary split ring resonators. Microwave and wireless components letters, IEEE 14(6), 280â282 (2004).
GarcÃa-GarcÃa, J., MartÃn, F., Baena, J. D., Marques, R. & Jelinek, L. On the resonances and polarizabilities of split ring resonators. Journal of Applied Physics 98(3), 033103 (2005).
Bonache, J., Gil, M., Gil, I., Garcia-Garcia, J. & Martin, F. On the electrical characteristics of complementary metamaterial resonators. Microwave and Wireless Components Letters, IEEE 16(10), 543â545 (2006).
Abdel-Rahman, A., Ali, A. R., Amari, S. & Omar, A. S. Compact bandpass filters using defected ground structure (DGS) coupled resonators. IEEE MTT-S International Microwave Symposium Digest Vol. 1, pp. 1479â1482 (2005).
Bonache, Jordi. et al. Application of complementary splitâring resonators to the design of compact narrow bandâpass structures in microstrip technology. Microwave and Optical Technology Letters 46(5), 508â512 (2005).
Deng, J. Y., Yin, Y. Z., Ren, X. S. & Liu, Q. Z. Study on a dual-band notched aperture UWB antenna using resonant strip and CSRR. Journal of Electromagnetic Waves and Applications 23(5â6), 627â634 (2009).
Shen, X., Cui, T. J., Martin-Cano, D. & Garcia-Vidal, F. J. Conformal surface plasmons propagating on ultrathin and flexible films. Proceedings of the National Academy of Sciences 110(1), 40â45 (2013).
He, S., He, Y. & Jin, Y. Revealing the truth about âtrapped rainbowâ storage of light in metamaterials. Sci. Rep. 2 (2012).
Acknowledgements
This work was supported in part by the National Science Foundation of China (61302018, 61401089, 61571117 and 61501117), in part by the National Instrumentation Program (2013YQ200647) and in part by the 111 Project (111â2â05).
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Q.Z. provided ideas and optimized the waveguide model. Q.Z., H.C.Z., J.Y.J., B.C.P. and T.J.C. were responsible for scientific explanations and performing the measurements. Q.Z. and T.J.C. wrote the paper based on the input from all authors. All authors devoted to the discussions.
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Zhang, Q., Zhang, H., Yin, J. et al. A series of compact rejection filters based on the interaction between spoof SPPs and CSRRs. Sci Rep 6, 28256 (2016). https://doi.org/10.1038/srep28256
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DOI: https://doi.org/10.1038/srep28256
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