Spoof localized surface plasmons in corrugated ring ... - OSA Publishing

Spoof localized surface plasmons in corrugated ring structures excited by microstrip line Bao Jia Yang, Yong Jin Zhou,* and Qian Xun Xiao Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University, Shanghai 200072, China * [email protected]

Abstract: We have investigated the fundamental and high-order spoof localized surface plasmons (LSPs) modes in the proposed corrugated ring resonator printed on a thin dielectric substrate with or without ground plane. An efficient and ease-of-integration method to excite spoof LSPs in the textured ring resonator has been adopted to suppress unwanted high-order modes and enhance fundamental modes. A multi-band-pass filter has been proposed and numerically demonstrated. Experimental results at the microwave frequencies verify the high performances of the corrugated ring resonator and the filter, showing great agreements with the simulation results. We have also shown that the fabricated device is sensitive to the variation of the refraction index of materials under test, even when the material is as thin as paper. ©2015 Optical Society of America OCIS codes: (250.5403) Plasmonics; (160.3918) Metamaterials; (240.6680) Surface plasmons.

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

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Received 1 Jul 2015; revised 4 Aug 2015; accepted 4 Aug 2015; published 6 Aug 2015 10 Aug 2015 | Vol. 23, No. 16 | DOI:10.1364/OE.23.021434 | OPTICS EXPRESS 21434

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1. Introduction Localized surface plasmons (LSPs) on small metal particles have been of interest for increasing applications in the optical antenna [1,2], surface-enhanced Raman scattering [3,4], chemical and biological sensors [5,6], and photovoltaic [7], etc. In order to realize highly confined propagating surface electromagnetic (EM) waves at the microwave and terahertz (THz) frequencies, spoof (or designer) SPs on the textured metal surfaces were proposed and verified [8,9], paving the way to realize spoof (designer) plasmonic waveguides and components [10–16]. Conformal SPs (CSPs) waveguides based on ultrathin corrugated metal strips have been demonstrated [17], leading to various ultrathin microwave and THz plasmonic functional devices [18–25]. A pioneering study on spoof LSPs has been conducted to show that a two dimensional (2D) periodically textured metallic cylinder was able to support spoof LSPs [26]. It’s been shown that a periodically textured closed cavity can also support spoof LSPs [27]. Magnetic LSPs supported by cylindrical structures were then theoretically and experimentally explored [28]. Recently, the spoof LSPs on the ultrathin textured metallic disk were demonstrated experimentally at microwave frequencies [29]. Compared to long cylinders [26], it is easy to observe lower plasmonic resonances (dipole and quadrupole modes) on the ultrathin textured disk. High-order spoof LSPs in periodically corrugated metal particles were also theoretically and experimentally investigated, showing these modes resemble the optical whispering gallery modes sustained by dielectric resonators [30]. It has been illustrated that

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both electric and magnetic LSP resonances can be excited by the spoof SPs modes in an ultrathin plasmonic combined system and spoof SPs transmissions can be judiciously controlled by the LSP structures [31]. More recently, vertical transport of subwavelength localized surface EM modes has been achieved through near-field coupling of highly confined surface EM modes supported by spoof plasmonic resonators [32]. It has been demonstrated that both even mode (fundamental mode) and odd mode (high-order mode) of spoof SPs can be supported on a symmetric corrugated thin film [33]. As indicated in [29], however, the higher-order resonant even modes are difficult to excite by a plane wave, while the dipole resonance is very weak under the excitation of the monopole source. By incorporating an extra ground plane underneath, enhanced high-order even mode resonances of spoof LSPs on the ultrathin textured disk under the excitation of a monopole source have been experimentally demonstrated [34]. In this paper, we numerically investigate even modes and odd modes of spoof LSPs in the periodically corrugated ring resonator with or without ground plane. Although the monopole excitation is simple and broadband, it is not efficient and not easy to integrate with the planar devices. Here we propose an efficient and ease-of-integration method to excite spoof LSPs in the textured ring resonator. We have shown that unwanted high-order resonant modes have been suppressed and fundamental modes are enhanced with higher quality (Q) factors for plasmonic circuit design. A multiband band-pass filter based on the corrugated ring resonator is proposed and numerically investigated. Experimental results at the microwave frequencies show great agreements with the simulation results, which verify the high performances of the corrugated ring resonator and the multi-band-pass filter. We have also shown that the fabricated filter is sensitive to the variation of the dielectric constant of materials under test, even the material is as thin as paper. 2. Spoof LSPs on corrugated ring resonator The inset of Fig. 1(a) depicts the schematic configuration of the proposed ultrathin corrugated ring resonator printed on the dielectric substrate (Rogers RO4350) whose thickness d is 1.016 mm and relative dielectric constant is 3.48. The corrugated ring resonator is a closed corrugated metal strip with periodic array of grooves, where the number of the grooves is N = 40 and the radius r of the ring is 12 mm. The central strip width g of the corrugated strip is 1 mm. The groove height, period, and width of the metal corrugated strip are set to be h = 5 mm, p = 2π(r + g + h)/N = 2.82 mm, and a = 0.4p = 1.13 mm, respectively. The thickness of the metal is 18 μm. To excite spoof LSPs modes in the ring resonator, a plane wave with a magnetic field perpendicular to the structure surface is incident from the left to the right, as shown in the inset of Fig. 1(a). The calculated extinction cross section (ECS) spectrum is shown in Fig. 1(b), where seven extinction peaks marked by m1-m4 and M1-M3 can be observed. The resonance peaks m1-m4 correspond to the dipole, quadrupole, hexapole, and octopole even modes at frequencies 2.5, 4.24, 5.6, and 6.57 GHz, respectively. While the resonance peaks M1-M3 correspond to three odd modes at frequencies 7.96, 8.38, and 8.65 GHz. However, the resonances of high-order even modes are weak. An extra ground plane [34] whose thickness is 18 μm has been incorporated to enhance the high-order resonances, as shown in the inset of Fig. 1(b). In simulation, one monopole antenna is used as a near-field excitation source and the other as a probe. The near field response has been shown in Fig. 1(b). Except the odd modes marked by M1-M3, we can observe that there are more resonance peaks marked by m1-m8, which are located at frequencies 1.21, 2.36, 3.41, 4.37, 5.18, 5.86, 6.41, and 6.81 GHz, respectively. Comparing with Fig. 1(a), we can see that all the resonance even modes have red shifted and high-order even modes are enhanced. In order to verify the multipolar spoof LSPs resonant modes on the corrugated ring resonator, electric-field vertical (Ez) distributions on the plane 2 mm above the corrugated ring resonator without ground plane at the resonant frequencies are illustrated in Fig. 1(c). The field patterns at resonance modes m1-m4 are symmetric (i.e., the even mode), while the field patterns at resonance modes M1-M3 are anti-symmetric (i.e., the odd mode). Figure 1(d) demonstrates the Ez-field distributions on the plane 2 mm above the

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corrugated ring resonator with ground plane, where only the first four resonance even modes are shown. It can be seen that both even modes and odd modes are also supported on the structure with ground plane.

Fig. 1. (a) The calculated ECS spectrum for the proposed thin textured ring resonator printed on the dielectric substrate. The inset shows the schematic configuration of the structure under the excitation of a plane wave. (b) The near field response for the structure with ground plane. The inset shows the schematic configuration of the structure with ground under the excitation of a monopole source. The 2D electric-field distributions on the plane 2 mm above the ring resonator at the resonant frequencies marked by m1-m4 and M1-M3: (c) for the structure without ground; (d) for the structure with ground.

In order to reveal the nature of spoof LSPs in the corrugated ring structure, the dispersion relations of corresponding spoof SPs on the symmetric corrugated strips are calculated by use of the eigenmode solver of commercial software CST microwave studio (CST). Figure 2(a) shows the dispersion relation for the structure without ground plane, where p = 2π(r + g)/N = 2.04 mm and a = 0.4p = 0.81 mm. The dispersion curves for the structure with ground plane are plotted in Fig. 2(b), where the groove height h and the substrate thickness d change. Comparing with Fig. 2(a), the asymptotic frequencies of spoof SPs for both even and odd modes on the structure with ground plane decreases, hence all peaks below asymptotic frequencies red shift, as shown by Figs. 1(a) and 1(b). The spoof SPs wavelength at the resonant peaks marked by m1-m8 can be calculated by λ = 2π/β, where β is the plasmonic wave vector which can be obtained from the black solid line with squares in Fig. 2(b). The calculated results are λm1 = 76.76 mm, λm2 = 38.51 mm, λm3 = 25.90 mm, λm4 = 19.4 mm, λm5 = 15.64 mm, λm6 = 13.18 mm, λm7 = 11.42 mm, and λm8 = 10.28 mm. The circumference of the corrugated ring is estimated as L = 2π(r + g/2) = 78.54 mm. We have verified that the relation between the spoof SPs wavelengths for the corrugated strips and the circumference satisfy L ≈i × λmi, where i = 1, 2, …, 8. Hence it is shown that spoof LSPs on the textured ring structure are actually standing surface waves, which is in accordance with the conclusion in [29].

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Fig. 2. (a) Dispersion relations of spoof SPs on the symmetric corrugated strips without ground. The black dash line indicates the light line. The inset shows the unit cell of the symmetric corrugated strips without ground. (b) The change of dispersion curves for symmetric corrugated structure with ground with different groove heights and substrate thicknesses.

Here an efficient and ease-of-integration method is adopted to excite the spoof LSPs modes in the proposed corrugated ring resonator with ground plane and the schematic configuration is displayed in Fig. 3(a). The EM energies are fed by the microstrip line (see the black dashed line) whose thickness is 18 μm. In order to minimize the reflected waves from the end of the microstrip line, a metallic disk is connected to the end of the microstrip line to increase broadband coupling degree of EM energies [35]. There are too many multipolar even odds and odd modes which could be useless in the plasmonic circuit design. By properly designing the parameters of the microstrip line, unwanted high-order resonant modes can be suppressed [36]. The width ws of the 50-Ω microstrip line is 1.1 mm. We have studied how reflection coefficients S11 of the structure excited by the microstrip line are affected by the length l and the radius r1 with the help of CST. The calculated results are shown in Figs. 3(b) and 3(c). It can be seen that there exist many high order resonance modes with high insertion loss for l ≤ 12.75 or l ≥ 18.75 mm. High order resonance modes can also be observed for r1 = 1 or 3 mm. To suppress such unwanted high-order resonance modes, the length l of the microstrip line and the radius r1 of the metallic disk at the end of the microstrip line are set to be 15.57 mm and 2 mm, respectively. The S11 curves for the structure excited by the optimal microstrip line are shown in Fig. 3(d), where the black solid line and the red dash dot line correspond to the simulation results by use of CST and HFSS. HFSS is based on finite element method (FEM). We can see that the simulated resonant frequencies agree very well. However, there exist burrs in the S11 curve obtained by CST. That is because the ring resonator is a kind of strong resonance structure and the input signals cannot be completely attenuated to zero after 20 pulses duration. The fitting result of the CST simulation result using Origin (multiple peaks curve fitting method) is also plotted in Fig. 3(d) (see the blue short dash dot line), which agrees better to the result obtained by HFSS. Although the computing accuracy is high, FEM is a frequency domain method and time consuming since it is required that frequencies should be swept to obtain the broadband response spectra. However, the calculation time is short and 2D electric field distributions in the plane above the resonator can be easily observed by use of CST. Hence, CST is adopted and the simulation results are processed with the above fitting method in the following numerical calculations. From Fig. 3(d), we can observe that there are seven sharp resonant points marked by m1-m7, which are located at frequencies 1.21, 2.38, 3.48, 4.41, 5.25, 5.91, and 6.47 GHz, respectively. Comparing with the resonant frequencies 1.21, 2.36, 3.41, 4.37, 5.18, 5.86, and 6.41 GHz in Fig. 1(b), we can see that there are little deviations for structure under two different exciting sources. Furthermore, the fundamental resonance modes

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have been enhanced. For examples, Q factor of m1 resonance mode has been increased to 48.4, while it’s only 4.48 for the case under the excitation of a monopole. Q factor of m3 resonance mode has been changed from 11.4 to 69.6. When groove height h increases from 5 mm to 6 mm, the asymptotic frequency for spoof SPs decreases, shown in Fig. 2(b). We can clearly see that all the resonance nadirs below the asymptotic frequency have red shifted (dash line) in Fig. 3(d). When the thickness d of substrate is gradually changed from 0.508 mm to 1.524 mm, corresponding asymptotic frequencies of dispersion curves will increase. Blue shift of resonance nadirs can also be observed from S11 spectra with increasing thickness (dash dot dot line) in Fig. 3(d). In order to verify the multipolar spoof LSPs modes on the corrugated ring resonator, Fig. 3(e) illustrates the 2D Ez-field distributions on the plane 2 mm above the corrugated ring resonator at these resonant frequencies, which correspond to dipole, quadrupole, hexapole, octopole, decapole, dodecapole, and quattuordecpole modes, respectively. It can be seen that the fundamental resonance modes marked by m1-m7 can be clearly observed.

Fig. 3. (a) The schematic picture of the proposed corrugated ring resonator excited by a microstrip line. The change of S11 curves with (b) length l of the microstrip line, (c) radius r1 of metal disk at the end of the microstrip line. (d) The calculated S11 of the corrugated ring resonator by use of CST and HFSS. The blue short dash dot line is the fitting result from the CST simulation result using Origin multiple peaks curve fitting method. (e) 2D Ez-field distributions on the plane 2 mm above the corrugated ring resonator at the resonant frequencies m1-m7.

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To verify experimentally spoof LSPs on the corrugated ring resonator, we have fabricated the sample shown in the inset of Fig. 4(a). The fabricated sample is connected to Vector Network Analyzer (VNA, Agilent N5227A) to measure the reflection coefficients. Figure 4(a) demonstrates the whole experimental setup to measure the electric fields distributions in the plane above the ring resonator sample. The fabricated sample is pasted on the foam which is mounted to two computer-controlled linear translation stages, enabling a scanning area of 44 mm by 44 mm with a resolution of 1 mm. The coaxial detecting probe (SFT-50-1 cable) is fixed onto the stationary shelf. The inner conductor of the monopole probe is extended 1 mm to detect the z-component of the electric fields within the plane 2 mm above the sample. The measured and simulated reflection coefficients spectrums are shown in Fig. 4(b), where the black dash-dot-dot line and red solid line correspond to simulation and measurement S11 curves, respectively. The measured resonance nadirs at m1-m7 modes are located at 1.25, 2.45, 3.55, 4.55, 5.40, 6.07, and 6.65 GHz, respectively. Compared to the simulated resonant frequencies at 1.21, 2.38, 3.48, 4.41, 5.25, 5.91, and 6.47 GHz, there are little deviations. For further validations, the measured near electric-field distributions on the plane 2 mm above the fabricated sample at these measured resonant nadirs are illustrated in Fig. 4(c). Comparing Fig. 3(e) with Fig. 4(c), we have confirmed that the field patterns have good agreements between the simulations and measurements. The field patters at modes m1-m7 can be clearly observed.

Fig. 4. (a) The experimental setup. The inset is the photograph of the enlarged measurement arrangements including the fabricated sample, detecting probe and feeding cable. (b) The measured and simulated S11. (c) The measured 2D Ez-field distributions at the resonance frequencies located at 1.25, 2.45, 3.55, 4.55, 5.40, 6.07, and 6.65 GHz, respectively.

3. Multi-band-pass filter and sensor Based on the proposed plasmonic corrugated ring resonator, a multi-band-pass filter is proposed as shown in Fig. 5(a), where another microstrip line (Port 2) is added at the opposite position of Port 1 and all the other parameters are the same as those of the sample in Fig. 4(a). Since the cost of the multilayer printed circuit board (PCB) fabrication is high, the sample is actually assembled by two monolayers, as shown in Fig. 5(b). The top layer is a corrugated ring printed on the dielectric substrate, and the bottom layer consists of two microstrip lines printed on the substrate and a ground plane. The measured reflection coefficients and transmission coefficients are shown in Fig. 5(c) and Fig. 5(d), where the measured results show great agreements to the simulation results. The simulated pass-band central frequencies are 1.20, #244123 (C) 2015 OSA


2.38, 3.49, 4.43, 5.30, 5.91, and 6.49 GHz for the seven pass-bands, while the measured results correspond to 1.21, 2.40, 3.52, 4.51, 5.34, 6.02, and 6.58 GHz, respectively. Hence, there are little deviations between the simulation and measurement results. According to the measurement result (red solid line) in Fig. 5(d), it can be observed that the insertion loss is less than 3 dB for m1-m3 modes and it is less than 4 dB for m4 mode. Full width at half maximum (FWHM) for m1-m4 modes are 40, 117, 154, and 110 MHz from the measurements, and their relative bandwidths are 3.3%, 4.9%, 4.4%, and 2.4%, respectively. By incorporating specially designed band-pass filters [37] in the output branches, more plasmonic functional devices can be implemented, such as wavelength division demultiplexer.

Fig. 5. (a) The schematic picture of the proposed multi-band-pass filter. (b) The fabricated sample which is assembled by the top and bottom monolayer. The simulated and measured (c) reflection coefficients and (d) transmission coefficients.

Next we will show that the multi-band-pass filter based on the resonator is very sensitive to the variation of the refractive index (n) of the materials under test, indicating high sensitivity as a sensor. The detected dielectric material is put between the top layer and bottom layer as shown in the inset of Fig. 6(a), where the thickness of the detected sample is 0.5 mm in simulation. Figures 6(a) and 6(b) show the simulated S11 and S21 when the refractive index of the detected material changes from 1.62 to 1.87. We can observe that the resonant frequency shifts are from 1.34 GHz to 1.28 GHz for the dipole mode, from 2.63 GHz to 2.52 GHz for the quadrupole mode, from 3.81 GHz to 3.66 GHz for the hexapole mode, from 4.8 GHz to 4.63 GHz for octopole mode, from 5.68 GHz to 5.47 GHz for the decapole mode, and from 6.33 GHz to 6.11 GHz for the dodecapole mode. It means that we can obtain a 0.06 GHz (or 4.7%) shift in dipole resonance, a 0.11 GHz (or 4.4%) shift in quadrupole resonance, a 0.15 GHz (or 4.1%) shift in hexapole resonance, a 0.17 GHz (or 3.7%) shift in octopole resonance, a 0.21 GHz (or 3.8%) shift in decapole resonance, and 0.22 GHz (or 3.6%) shift in dodecapole

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resonance when the variation of the refractive index is 0.25 refraction index unit (RIU). The sensing apparatus is also sensitive even when the detected material is as thin as paper. A piece of paper is put between the top and bottom layer, as shown in Fig. 6(c). The measured reflection coefficients are plotted in Fig. 6(d) and obvious resonant frequencies shift can be observed. Comparing with the sensor proposed in [29], the proposed structure is highly integrated and easy to operate. Besides, its sensitivity is higher due to larger Q factors.

Fig. 6. (a) The change of calculated S11 with the refractive index (n) of the detected material. (b) The change of calculated S21 with n. (c) The schematic picture of measuring apparatus, where a piece of paper is put between top and bottom layer of the fabricated sample. (d) The measured S11 with or without paper.

4. Conclusion In summary, we have demonstrated spoof LSPs even and odd modes on the proposed ultrathin corrugated ring resonator with or without ground plane. Spoof LSPs in the corrugated ring resonator with ground plane can be efficiently excited by use of the microstrip line. We have showed that resonance even modes are obviously enhanced with much higher Q factors. A multiband band-pass filter is also proposed based on the resonator. Experimental results at the microwave frequencies have been conducted to verify these plasmonic devices, which show great agreements with the simulation results. We have also shown that the fabricated filter is very sensitive to the variation of the refraction index, even when the material under test is as thin as paper. By incorporating specially designed band-pass filters, more plasmonic functional devices can be implemented, such as wavelength division demultiplexer. Acknowledgments This work was supported in part by the National Natural Science Foundation of China under Grant No. 61307129, in part by Shanghai Municipal Science and Technology Commission under Grant No. 13ZR1454500, and in part by National High Technology Research and Development Program of China (863 Program) under Grant No. 2015AA016201.

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