High-order modes of spoof surface plasmonic wave transmission on thin metal film structure Xiaoyong Liu, Yijun Feng,* Bo Zhu, Junming Zhao, and Tian Jiang, Department of Electronic Engineering, School of Electronic Science and Engineering, Nanjing Univeristy, Nanjing, 210093, China * [email protected]
Abstract: Recently, conformal surface plasmon (CSP) structure has been successfully proposed that could support spoof surface plasmon polaritons (SPPs) on corrugated metallic strip with ultrathin thickness [Proc. Natl. Acad. Sci. U.S.A. 110, 40-45 (2013)]. Such concept provides a flexible, conformal, and ultrathin wave-guiding element, very promising for application of plasmonic devices, and circuits in the frequency ranging from microwave to mid-infrared. In this work, we investigated the dispersions and field patterns of high-order modes of spoof SPPs along CSP structure of thin metal film with corrugated edge of periodic array of grooves, and carried out direct measurement on the transmission spectrum of multi-band of surface wave propagation at microwave frequency. It is found that the mode number and mode bands are mainly determined by the depth of the grooves, providing a way to control the multi-band transmission spectrum. We have also experimentally verified the high-order mode spoof SPPs propagation on curved CSP structure with acceptable bending loss. The multi-band propagation of spoof surface wave is believed to be applicable for further design of novel planar devices such as filters, resonators, and couplers, and the concept can be extended to terahertz frequency range. ©2013 Optical Society of America OCIS codes: (130.2790) Subwavelength structures; (240.6680) Guided waves; (300.6495) Surface plasmons.
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#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31155
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1. Introduction Surface plasmon polaritons (SPPs) are surface electromagnetic (EM) waves propagating along the dielectric-metal interface at optical frequencies [1-2]. They are highly localized along the interface, and become evanescent in the direction perpendicular to the interface with their field magnitude exponentially decaying in both the metal and the dielectric sides. The strong field confinement to sub-wavelength scale and consequent field enhancement at the dielectric-metal interface could lead to the overcome of the diffraction limit [3], and miniaturized optical integrated circuits and devices with scales smaller than the light wavelength [4-6]. Unlike in the optical frequency band, at far-infrared, terahertz, or microwave band metals resemble a perfect electric conductor (PEC) since their plasmon frequencies are usually lie in the ultraviolet region, thus do not support the SPP waves. Recently, alternative ideas have been proposed and demonstrated that plasmonic metamaterials consisting of metal surface textured with subwavelength-scale corrugations or dimples could support SPP-like surface waves. These structures are somewhat similar to the classical corrugated surface structures studied in the microwave frequency [7-9]. With these so-called “spoof” or “designer” SPPs, the surface plasmon frequency and SPP-like dispersion relation could be tailored by the plasmonic metamaterial geometry well down to the terahertz, or microwave region [10-26]. #197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31156
Different textured metal surfaces with either one-dimensional (1D) grooves, or twodimensional (2D) holes or domino chains could be engineered to support highly confined surface EM waves, however, all these plasmonic metamaterials are non-planar and rely on three-dimensional (3D) structures of sub-wavelength scaled geometry on metal surfaces, making them not convenient to be fabricated and integrated with other existing terahertz or microwave circuitry. More recently, a much improved planar plasmonic metamaterial has been proposed to support spoof SPPs on corrugated metallic strip with ultrathin thickness [2729]. Such concept, called as the conformal surface plasmon (CSP), even allows the highly confined propagation of microwave or terahertz wave on bent, twisted or folded routes, paving the way of developing versatile surface-wave integrated devices or circuits at low frequencies, especially at terahertz region. The CSP concept requires more extensive and in-depth exploration. Up to now, only the fundamental surface mode has been studied and the spoof SPPs performance has been verified through near-field mapping of the EM field distributions at fixed frequency. The textured metal structures usually support high-order mode spoof SPPs propagation [30-31], therefore this feature need to be studied within the CSP concept. Another important issue is the direct measurement of the transmission spectrum and the dispersion relation, which requires careful consideration of the effective coupling of the EM wave into and out of the CSP structure. In this paper, we will address these issues through both theoretical analysis and experimental exploration of the surface wave propagation on thin metal film structure. We investigate the high-order modes of spoof SPPs along thin metal film with corrugated edge of periodic array of grooves, and carry out direct measurements of the transmission spectra of both the fundamental and the high-order mode surface wave propagation at microwave frequency. We also test the bending loss for 90 degree curved CSP structure and verify the effective multiband spoof SPPs propagation along curved geometry. 2. Mode analysis Let us consider the typical CSP structure of a periodic array of edge grooves with depth h, width a, lattices constant d, etched on a perfectly conducting metallic strip of thickness t, as illustrated in the inset of Fig. 1. The dispersion relation of this CSP structure is analyzed numerically by the eigen-mode solver of the commercial full-wave software, CST Microwave studio. For operating in the microwave frequency, the parameters h, d, a, w are set as 22 mm, 8 mm, 3 mm, and 4.5 mm, respectively. The dispersion curves are displayed in Fig. 1 with varied thickness t of the metal strip to study its effect on the dispersion relation. To study the high-order modes in the CSP structure, a large groove depth h was chosen. Unlike the previous study presented in [27-29], where only the fundamental mode of spoof SPPs has been analyzed, we obtain dispersion curves with multi-branches at different frequency bands exhibiting typical SPP-like behavior in Fig. 1. Each branch of the dispersion curves for different thickness t approaches the light line at low frequency and reaches a horizontal asymptotic frequency limit at the edge of the first Brillouin zone. Such result indicates that not only the fundamental mode but also the high-order modes of spoof SPPs can be supported by the CSP structure for the chosen groove depth. Similar to the previous study [27-29], the modal dispersions are rather insensitive to the thickness of the metallic strip. When t = ∞, the structure becomes a one-dimensional groove array, whose dispersion relation (indicated by black lines in Fig. 1) can be approximated by the following equation neglecting diffraction effects [9],
a (1) where, β is the modal wave vector, and k0 = 2π / λ . As t decreases from infinite, the dispersion curve for each mode slightly deviates to lower frequency, indicating a stronger confinement of surface wave on the metallic strip, but is insensitive to further reduction of the thickness to ultrathin scale (from t = 10 mm to t = 0.035 mm). Since the ultrathin strip of the CSP structure can not be supported by itself, we also analyze the more practical case where an
β 2 − k02 = k0 tan ( k0 h ) , d
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31157
ultrathin strip of metallic groove array is placed on a dielectric substrate (a commercial printed circuit board (PCB)) with a relative permittivity of 2.55 and a thickness of 0.5 mm. The effect of the dielectric substrate can be considered as an increase of the effective permittivity of the medium where the spoof SPPs propagate, therefore, the dispersion curves will make further deviation from light line to lower frequency, as indicated by the simulation result in Fig. 1 (red lines). However, the feature of supporting multi-mode spoof SPPs propagation is unchanged.
Fig. 1. Dispersion curves for both the fundamental and high-order modes of the CSP structure with different thickness of the metallic strip.
As indicated in the dispersion curves of Fig. 1, the fundamental mode could start from zero frequency and cut off at the horizontal asymptotic frequency, while each high-order mode locates in a certain frequency band from the frequency of the intersection of the dispersion curve with the light line to its asymptotic frequency at the edge of the first Brillouin zone. It is remarked that all the bands do not overlap with each other leaving a bandgap between them; therefore, single mode propagation is always guaranteed by proper selection of the operation frequency, which is quite different from that in a conventional dielectric or metal waveguide. From the numerical calculations, we found that the mode bands are much more dependent on the depth of the edge groove than other geometric parameters. To visualize this, we consider a realistic CSP structure with ultrathin corrugated copper film (t = 0.035 mm) printed on a dielectric PCB with relative permittivity of εr = 2.55. We fix the parameters d, a, w as 8 mm, 3 mm, and 4.5 mm, respectively, while change the groove depth h from 5 to 30 mm. The transmission spectrum is calculated for a 170 mm long corrugated strip with different groove depth. In the calculation, we include both the input and output coupling ports that will be used in the real measurement (details can be found in the next section), where standard SMA connectors are utilized for the input and output of microwave signal and a section of co-planar waveguide (CPW) is employed to couple between the SMA connector and the CSP strip. As illustrated in Fig. 2, when the groove depth is about 5 mm, only the fundamental mode is supported, with a cutoff at about 9 GHz. The transmission increases with the operation frequency due to a more confined surface wave established along the CPS structure as a result of the increasing deviation of the dispersion curve from the light line. When the groove depth increases, the first or the second high-order mode manifests itself within a certain frequency band, respectively. As the groove depth increases, each mode band shifts to lower frequency and the transmission efficiency increases.
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31158
Fig. 2. Transmission spectrum of a long CSP structure as a function of the groove depth.
Both the fundamental and the high-order modes have a sharp cutoff frequency which decreases with the increase of the groove depth. An approximate estimation of the cutoff frequency of each band can be inferred from Eq. (1). Although Eq. (1) is obtained from a onedimensional structure of groove array, it can be employed roughly for the CPS structure with thin metallic strip, since the dispersion curves do not change much with the thickness of the metallic strip. However, for the CPS structure in Fig. 2, the effect of the dielectric substrate should be considered. The corrugated metallic film on the PCB substrate can be treated as an array of vertically aligned coplanar strip line, thus the effective permittivity can be estimated by [32]
ε r − 1 K ( k ′ ) K ( k1 ) (2) , 2 K ( k ) K ( k1′ ) where, K denotes the complete elliptic integral of the first kind, and k = a / d , k ′ = 1 − k 2 , k1 = sinh (π a / 4t ) / sinh (π d / 4t ) , k1′ = 1 − k12 , respectively. Therefore the cutoff frequency can be estimated from the following modified dispersion relation by replacing k0 with ε eff k0 in Eq. (1): a (3) β 2 − ε eff k02 = ε eff k0 tan ε eff k0 h . d As indicated by the dashed line in Fig. 2, the estimated cutoff frequency of each band set an upper limit, and the small deviation from the calculated transmission spectrum can be attributed to the finite thickness of the strip not considered in Eq. (1). This rough estimation of the cutoff frequency could be useful in designing the multi-transmission bands in the CSP structure. Similar to the previous analysis of high-order spoof SPP modes in one-dimensional structure of groove array in [30], let us consider the condition for high-order modes supported by the ultrathin CSP structure through the dispersion relation Eq. (3). If there appears a highorder mode spoof SPPs, its band begins at the intersection of its dispersion curve with the light line, at which β = ε eff k0 . From Eq. (2) and (3), we can obtain the frequency corresponds to the intersections by πc (4) , ωc = N ε eff h
ε eff = 1 +
(
)
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31159
where, N is a positive integer denoting the order of the mode and c the light speed in free space. The fundamental mode do not have a cutoff, which corresponds to the order of N = 0. For a high-order mode with N ≥ 1, the band exist between the intersection of dispersion curve with the light line and the asymptotic frequency at the edge of the first Brillouin zone, that is th N π / h ≤ β ≤ π / d . Therefore, the condition for the appearance of the N order mode becomes h > Nd . The simulation illustrated in Fig. 2 roughly agrees with this condition as the first (N = 1) or second (N = 2) high-order mode appears when the groove depth is larger than 8 mm or 16 mm, respectively. For a given groove depth, the supported spoof SPP mode number is estimated by 1 + int(h / d ) . It is also evident in Fig. 2 that the transmission efficiency of the fundamental propagation mode can achieve almost 95%, especially near the cutoff frequency for a case with a larger groove depth. This is due to the good impedance match of the CPW to the CSP strip for larger groove depth at low frequencies. However, for the first or the second high-order mode, the total transmission efficiency drops to 60% or 35% (peak value), respectively. This is due to the increase of the impedance mismatch between the CPW and the CSP strip as the increase of the operation frequency, and a portion of the input energy has been reflected indicated by the calculation of the reflection coefficient of the input port (not shown).
Fig. 3. Dispersion curves (a), and the transmission spectrum (b) calculated from a 170 mm long thin metallic corrugated strip on a PCB substrate with h, d, a, w fixed as 15 mm, 8 mm, 3 mm, and 4.5 mm, respectively. The open circles indicate the calculated time-averaged power density ratio of two cross-sections near the input and output edges.
Figure 3 also compares the calculated dispersion curve with the transmission spectrum for a particular value of the groove depth h = 15 mm. Both the fundamental (mode 0) and the first high-order mode (mode 1) are supported by the CSP structure. Within the frequency band of mode 0 and mode 1 determined by the dispersion curve transmission peaks are obtained which confirms a propagating spoof SPP wave along the CSP structure. The peak transmission efficiency is about 90% or 50% for the fundamental mode or the first high-order mode respectively, due to the impedance mismatch in the coupling structure of input and output ports, especially at higher frequency. It is noted that the transmission does not go to zero at the band-gap between mode 0 and mode 1 or the frequencies beyond the cutoff of the mode 1, which is due to the small radiation energy that coupled to the output port. To verify the net power propagation efficiency along the CSP strip excluding the influences of the coupling sections, we choose two cross-sections about 20 mm away form the input and the output edges of the corrugated thin film strip, and calculated the ratio of time-averaged power density (i.e., the Poynting vector, S = 0.5Re E × H∗ ) across the two planes. The result is
shown in Fig. 3, which demonstrates a propagation efficiency of almost 100% for the
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31160
fundamental mode and 95% for the first high-order mode along a 130 mm CSP strip (about five free-space wavelengths at the center frequency of the first high-order mode). This indicates that the CSP structure could support well confined fundamental mode as well as the high-order modes of spoof SPP wave propagating with high efficiency and low radiation loss.
Fig. 4. The simulated electric field distributions for (a) the fundamental mode, (b) the first high-order mode, and (c) the second high-order mode, at 2.4 GHz, 7.7 GHz and 13.3 GHz, respectively. The left, middle, and right columns indicate the z component of the electric field evaluated at the top of strip in the x-y plane, the electric field amplitude at the y-z plane that cuts the metal strip symmetrically, and in the cross-section perpendicular to the strip, respectively.
Fig. 5. The simulated magnetic field distributions for (a) the fundamental mode, (b) the first high-order mode, and (c) the second high-order mode, at 2.4 GHz, 7.7 GHz and 13.3 GHz, respectively. The upper or lower row indicates the magnetic field distribution in the crosssections perpendicular to the strip in y-z, or z-x plane, respectively.
To illustrate the EM fields of spoof SPP modes in the CSP structure, we calculate the electric and magnetic field distribution in a corrugated copper strip on a PCB substrate with h, d, a, w fixed as 22 mm, 8 mm, 3 mm, and 4.5 mm, respectively. To analyze the first three modes (N = 0, 1, and 2), we demonstrate the field distribution in Fig. 4 and Fig. 5 at operation frequency of 2.4 GHz, 7.7 GHz and 13.3 GHz, which correspond to the fundamental, the first and the second high-order modes, respectively. As demonstrated in Fig. 4 and Fig. 5, both the fundamental and the high-order modes have tightly confined field patterns to the metal strip illustrating typical features of SPP modes with little scattering loss. For the fundamental mode the EM fields distribute mostly inside the metallic slot with a maximum magnitude near the open end and decreased value in the slot, while for the high-order modes the EM fields #197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31161
distribute inside the metallic slot as well, but exhibit N minima and the maximum magnitude moves into the slot. This can be understood by viewing the groove in the structure as a short section of coplanar strip which behaves as a resonator with one end shorted and the other end open to the air. Thus, each band of the spoof SPPs can correspond to a resonant state of the coplanar strip. The spoof SPP wave propagation in the CSP structure is consequently supported by the stimulating and coupling of the resonant state of each groove with EM field distribution similar to that described in Fig. 4 and Fig. 5. 3. Experimental results To verify the multi-mode spoof SPP wave propagation in the CSP structure, several samples of ultrathin metallic corrugated strip have been fabricated by standard PCB technique and experimentally tested at microwave frequency (shown in Fig. 6). To carry out direct measurements of the transmission spectrum of multi-mode propagation, we employ SMA connectors to input and output microwave signal and measure the transmission through an Agilent N5244A vector network analyzer. To couple the SMA connectors to the single conductor CSP structure, a section of CPW (w0 = 1 mm, and s = 0.8 mm) with a characteristic impedance of about 100 Ω is used by directly connecting the center strip of the CPW to the CSP strip, as shown schematically in Fig. 6(a). The parameters of the fabricated samples are optimized to achieve proper impedance matching between the CPW and the CSP strip, especially at low frequency (not possible to get a wideband impedance match with this simple CPW), and the resulted optimal parameters are the same as described in Fig. 2 with varied groove depth.
Fig. 6. (a) The schematics of the proposed CSP structure with input and output CPW sections, and (b) the photograph of the fabricated sample with SMA connectors.
Samples with different groove depth have been tested to verify the supporting of different mode spoof SPP wave propagation. Fig. 7 displays one result for a sample with groove depth of h = 22 mm, which could theoretically support 3 modes, inferred from the calculated dispersion curves. The measured results shown in Fig. 7 clearly verified the propagation of the fundamental mode (mode 0) and the high-order modes (mode 1, and mode 2 for N = 1, and 2). The measured transmission could achieve a peak value of 85% for the fundamental mode due to good impedance match, while 50% or 30% for the first or the second high-order mode, respectively. The transmission bands for different modes agree with the calculated dispersion curves roughly well. Within the bands, the transmission increases with the frequency and achieves a peak value near the cutoff frequency defined by the asymptotic frequency of dispersion curves, due to that more confined surface wave is established with lower radiation loss. We believe the transmission for high-order modes could be enhanced by carefully design of the coupling of the input and output ports to the CSP strip with more complicated wideband CPW transition sections.
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31162
Fig. 7. (a) Calculated dispersion curves, and (b) the calculated and measured transmission spectrum from a 170 mm long thin metallic corrugated strip on a PCB substrate with h, d, a, w fixed as 22 mm, 8 mm, 3 mm, and 4.5 mm, respectively, supporting three modes of spoof SPP wave propagation.
Fig. 8. Simulated (solid lines) and measured (dashed lines) transmission spectrum for the CSP structures with different groove periodicity or width. (h = 22 mm, and w = 4.5 mm)
The band property is mainly determined by the groove depth; however, we also study the influences by other geometrical parameters. Fig. 8 displays the transmission spectrum for CSP structures with different periodicity d or width a of the groove. It is found that neither the periodicity nor the width of the groove has obvious effect on the band property. The highly confined EM wave and the ultrathin nature of the metallic film and dielectric substrate of the CSP structure enable it to be easily bended to propagate the spoof SPP wave along curved surface. To test the CSP modes propagation along curved surface, we investigate the surface wave transmission property of a 90 degree vertical bend structure as shown schematically in Fig. 9(a). It is found from the simulated EM field distribution (Figs. 9(c) and 9(d)) that well confined spoof SPPs of both the fundamental and the high-order modes could be established along the bended CSP structure. The bending of the structure does not influence the EM field patterns of the fundamental and high-order modes. No obvious decrease of the field amplitude is observed in the high-order mode propagation (Fig. 9(d)) which indicates a low bending lose even at higher operation frequency. The bending radius is
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31163
70 mm, which is about half the wavelength at the peak frequency of the fundamental mode, or twice the wavelength at the peak frequency of the first high-order mode.
Fig. 9. The schematics (a) and the photograph of a fabricated sample (b) of a 90 degree bend of the CSP structure. (c) and (d) illustrate the simulated electric field component perpendicular to the surface distributed along the bended metal strip at frequency of 2.5 GHz (the fundamental mode), and 7.8 GHz (the first high-order mode), respectively. (with a = 3 mm, h = 22 mm, d = 8 mm, and w = 4.5 mm)
Direct measurement of the transmission of the spoof SPP modes has been carried out through input and output coupling ports at the two ends of the 90 degree bend as shown in Fig. 9(b). Fig. 10 compares the transmission results between a bended and a straight CSP structure. The measurements agree with the simulation results well. For the fundamental mode, similar transmission spectrum has been obtained for the bend and unbend structures with same peak transmission of about 85%, same transmission bandwidth, and same cutoff frequency, indicating no obvious influence from the bending of the structure. While for the high-order mode, the bending of the structure has a slight influence. It does not change the cutoff frequency, but induces a shrink of the transmission band. This can be explained by the bending that enable the less confined surface wave at lower frequencies to radiate in the highorder mode band. There is also a slight decrease of the peak transmission of about 10% (from 52% to 47%) due to the bending loss. However, the experimental result clearly indicates that both fundamental and high-order modes can be supported to propagate with acceptable low bending loss on curved structure with bending radius comparable with the wavelength.
Fig. 10. Comparison of the simulated and measured transmission through the 90° bend (with a radius of 70 mm) and straight CSP structures with same length. (a = 5 mm，h = 22 mm，d = 8 mm，w = 4.5 mm)
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31164
4. Conclusions
In conclusion, we have analyzed the high-order mode transmission of spoof SPPs along the thin CSP structure composed of corrugated metal strip with periodic array of edge grooves on a thin dielectric substrate in the microwave frequency range. It shows that well confined surface wave of both the fundamental and high-order modes can be supported by the CSP structure, and the mode number is mainly determined by the depth of the grooves. Direct measurement of the transmission spectrum has been carried out on fabricated samples, which verifies the theoretical analysis and the numerical simulations. Furthermore, high-order mode of spoof SPPs propagation with acceptable bending loss is confirmed on curved structure due to the ultra-thin nature of the CSP structure. The multi-band propagation with pre-determined band property can be utilized to design novel functional devices such as filters, resonators, and couplers. We also believe that the multi-band transmission characteristic can be easily scaled to terahertz frequency and may find applications in developing planar surface plasmonic devices and circuitry in both microwave and terahertz domain. Acknowledgments
This work is partially supported by the National Nature Science Foundation of China (61371034, 61101011, 60990322, 60990320), the Key Grant Project of Ministry of Education of China (313029), the Ph.D. Programs Foundation of Ministry of Education of China (20100091110036, 20120091110032), and partially supported by Jiangsu Key Laboratory of Advanced Techniques for Manipulating Electromagnetic Waves.
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31165
Abstract: Recently, conformal surface plasmon (CSP) structure has been successfully proposed that could support spoof surface plasmon polaritons (SPPs) on corrugated metallic strip with ultrathin thickness [Proc. Natl. Acad. Sci. U.S.A. 110, 40-45 (2013)]. Such concept provides a flexible, conformal, and ultrathin wave-guiding element, very promising for application of plasmonic devices, and circuits in the frequency ranging from microwave to mid-infrared. In this work, we investigated the dispersions and field patterns of high-order modes of spoof SPPs along CSP structure of thin metal film with corrugated edge of periodic array of grooves, and carried out direct measurement on the transmission spectrum of multi-band of surface wave propagation at microwave frequency. It is found that the mode number and mode bands are mainly determined by the depth of the grooves, providing a way to control the multi-band transmission spectrum. We have also experimentally verified the high-order mode spoof SPPs propagation on curved CSP structure with acceptable bending loss. The multi-band propagation of spoof surface wave is believed to be applicable for further design of novel planar devices such as filters, resonators, and couplers, and the concept can be extended to terahertz frequency range. ©2013 Optical Society of America OCIS codes: (130.2790) Subwavelength structures; (240.6680) Guided waves; (300.6495) Surface plasmons.
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#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31155
14. A. P. Hibbins, E. Hendry, M. J. Lockyear, and J. R. Sambles, “Prism coupling to 'designer' surface plasmons,” Opt. Express 16, 20441-20447 (2008). 15. L. F. Shen, X. D. Chen, and T. J. Yang, “Terahertz surface plasmon polaritons on periodically corrugated metal surfaces,” Opt. Express 16, 3326–3333 (2008). 16. A. I. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and J. F. Garcia-Vidal, “Guiding terahertz waves along subwavelength channels,” Phys. Rev. B 79, 233104 (2009). 17. D. Martin-Cano, M. L. Nesterov, A. I. Fernandez-Dominguez, F. J. Garcia-Vidal, L. Martin-Moreno, and E. Moreno, “Domino plasmons for subwavelength terahertz circuitry,” Opt. Express 18, 754-764 (2010). 18. E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78, 235426 (2008). 19. W. S. Zhao, O. M. Eldaiki, R. X. Yang, and Z. L. Lu, “Deep subwavelength waveguiding and focusing based on designer surface plasmons,” Opt. Express 18, 21498-21503 (2010). 20. N. Talebi and M. Shahabadi, “Spoof surface plasmons propagating along a periodically corrugated coaxial waveguide,” J. Phys. D Appl. Phys. 43, 135302 (2010). 21. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernandez-Dominguez, L. Martin-Moreno, and F. J. Garcia-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics 2, 175-179 (2008). 22. Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett. 99, 111904 (2011). 23. Y. G. Ma, L. Lan, S. M. Zhong, and C. K. Ong, “Experimental demonstration of subwavelength domino plasmon devices for compact high-frequency circuit,” Opt. Express 19, 21189-21198 (2011). 24. W. Zhu, A. Agrawal, and A. Nahata, “Planar plasmonic terahertz guided-wave devices,” Opt. Express 16, 6216-6226 (2008). 25. Y. J. Zhou, Q. Jiang, and T. J. Cui, “Multidirectional surface-wave splitters,” Appl. Phys. Lett. 98, 221901 (2011). 26. E. M. G. Brock, E. Hendry, and A. P. Hibbins, “Subwavelength lateral confinement of microwave surface waves,” Appl. Phys. Lett. 99, 051108 (2011). 27. X. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A. 110, 40-45 (2013). 28. X. Gao, J. H. Shi, X. P Shen, H. F. Ma, W. X. Jiang, L. M. Li, and T. J. Cui, “Ultrathin dual-band surface plasmonic polariton waveguide and frequency splitter in microwave frequencies,” Appl. Phys. Lett. 102, 151912 (2013). 29. X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett. 102, 211909 (2013). 30. T. Jiang, L. Shen, X. Zhang, and L. Ran, “High-order modes of spoof surface Plasmon polaritons on periodically corrugated metal surfaces,” Progress in Electromagnetics Research M 8, 91-102 (2009). 31. X. Zhang, L. Shen, and L. Ran, “Low-frequency surface plasmon polaritons propagating along a metal film with periodic cut-through slits in symmetric or asymmetric environments,” J. Appl. Phys. 105, 013704 (2009). 32. B. C. Wadell, Transmission Line Design Handbook (Artech House, Norwood, MA 1991).
1. Introduction Surface plasmon polaritons (SPPs) are surface electromagnetic (EM) waves propagating along the dielectric-metal interface at optical frequencies [1-2]. They are highly localized along the interface, and become evanescent in the direction perpendicular to the interface with their field magnitude exponentially decaying in both the metal and the dielectric sides. The strong field confinement to sub-wavelength scale and consequent field enhancement at the dielectric-metal interface could lead to the overcome of the diffraction limit [3], and miniaturized optical integrated circuits and devices with scales smaller than the light wavelength [4-6]. Unlike in the optical frequency band, at far-infrared, terahertz, or microwave band metals resemble a perfect electric conductor (PEC) since their plasmon frequencies are usually lie in the ultraviolet region, thus do not support the SPP waves. Recently, alternative ideas have been proposed and demonstrated that plasmonic metamaterials consisting of metal surface textured with subwavelength-scale corrugations or dimples could support SPP-like surface waves. These structures are somewhat similar to the classical corrugated surface structures studied in the microwave frequency [7-9]. With these so-called “spoof” or “designer” SPPs, the surface plasmon frequency and SPP-like dispersion relation could be tailored by the plasmonic metamaterial geometry well down to the terahertz, or microwave region [10-26]. #197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31156
Different textured metal surfaces with either one-dimensional (1D) grooves, or twodimensional (2D) holes or domino chains could be engineered to support highly confined surface EM waves, however, all these plasmonic metamaterials are non-planar and rely on three-dimensional (3D) structures of sub-wavelength scaled geometry on metal surfaces, making them not convenient to be fabricated and integrated with other existing terahertz or microwave circuitry. More recently, a much improved planar plasmonic metamaterial has been proposed to support spoof SPPs on corrugated metallic strip with ultrathin thickness [2729]. Such concept, called as the conformal surface plasmon (CSP), even allows the highly confined propagation of microwave or terahertz wave on bent, twisted or folded routes, paving the way of developing versatile surface-wave integrated devices or circuits at low frequencies, especially at terahertz region. The CSP concept requires more extensive and in-depth exploration. Up to now, only the fundamental surface mode has been studied and the spoof SPPs performance has been verified through near-field mapping of the EM field distributions at fixed frequency. The textured metal structures usually support high-order mode spoof SPPs propagation [30-31], therefore this feature need to be studied within the CSP concept. Another important issue is the direct measurement of the transmission spectrum and the dispersion relation, which requires careful consideration of the effective coupling of the EM wave into and out of the CSP structure. In this paper, we will address these issues through both theoretical analysis and experimental exploration of the surface wave propagation on thin metal film structure. We investigate the high-order modes of spoof SPPs along thin metal film with corrugated edge of periodic array of grooves, and carry out direct measurements of the transmission spectra of both the fundamental and the high-order mode surface wave propagation at microwave frequency. We also test the bending loss for 90 degree curved CSP structure and verify the effective multiband spoof SPPs propagation along curved geometry. 2. Mode analysis Let us consider the typical CSP structure of a periodic array of edge grooves with depth h, width a, lattices constant d, etched on a perfectly conducting metallic strip of thickness t, as illustrated in the inset of Fig. 1. The dispersion relation of this CSP structure is analyzed numerically by the eigen-mode solver of the commercial full-wave software, CST Microwave studio. For operating in the microwave frequency, the parameters h, d, a, w are set as 22 mm, 8 mm, 3 mm, and 4.5 mm, respectively. The dispersion curves are displayed in Fig. 1 with varied thickness t of the metal strip to study its effect on the dispersion relation. To study the high-order modes in the CSP structure, a large groove depth h was chosen. Unlike the previous study presented in [27-29], where only the fundamental mode of spoof SPPs has been analyzed, we obtain dispersion curves with multi-branches at different frequency bands exhibiting typical SPP-like behavior in Fig. 1. Each branch of the dispersion curves for different thickness t approaches the light line at low frequency and reaches a horizontal asymptotic frequency limit at the edge of the first Brillouin zone. Such result indicates that not only the fundamental mode but also the high-order modes of spoof SPPs can be supported by the CSP structure for the chosen groove depth. Similar to the previous study [27-29], the modal dispersions are rather insensitive to the thickness of the metallic strip. When t = ∞, the structure becomes a one-dimensional groove array, whose dispersion relation (indicated by black lines in Fig. 1) can be approximated by the following equation neglecting diffraction effects [9],
a (1) where, β is the modal wave vector, and k0 = 2π / λ . As t decreases from infinite, the dispersion curve for each mode slightly deviates to lower frequency, indicating a stronger confinement of surface wave on the metallic strip, but is insensitive to further reduction of the thickness to ultrathin scale (from t = 10 mm to t = 0.035 mm). Since the ultrathin strip of the CSP structure can not be supported by itself, we also analyze the more practical case where an
β 2 − k02 = k0 tan ( k0 h ) , d
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31157
ultrathin strip of metallic groove array is placed on a dielectric substrate (a commercial printed circuit board (PCB)) with a relative permittivity of 2.55 and a thickness of 0.5 mm. The effect of the dielectric substrate can be considered as an increase of the effective permittivity of the medium where the spoof SPPs propagate, therefore, the dispersion curves will make further deviation from light line to lower frequency, as indicated by the simulation result in Fig. 1 (red lines). However, the feature of supporting multi-mode spoof SPPs propagation is unchanged.
Fig. 1. Dispersion curves for both the fundamental and high-order modes of the CSP structure with different thickness of the metallic strip.
As indicated in the dispersion curves of Fig. 1, the fundamental mode could start from zero frequency and cut off at the horizontal asymptotic frequency, while each high-order mode locates in a certain frequency band from the frequency of the intersection of the dispersion curve with the light line to its asymptotic frequency at the edge of the first Brillouin zone. It is remarked that all the bands do not overlap with each other leaving a bandgap between them; therefore, single mode propagation is always guaranteed by proper selection of the operation frequency, which is quite different from that in a conventional dielectric or metal waveguide. From the numerical calculations, we found that the mode bands are much more dependent on the depth of the edge groove than other geometric parameters. To visualize this, we consider a realistic CSP structure with ultrathin corrugated copper film (t = 0.035 mm) printed on a dielectric PCB with relative permittivity of εr = 2.55. We fix the parameters d, a, w as 8 mm, 3 mm, and 4.5 mm, respectively, while change the groove depth h from 5 to 30 mm. The transmission spectrum is calculated for a 170 mm long corrugated strip with different groove depth. In the calculation, we include both the input and output coupling ports that will be used in the real measurement (details can be found in the next section), where standard SMA connectors are utilized for the input and output of microwave signal and a section of co-planar waveguide (CPW) is employed to couple between the SMA connector and the CSP strip. As illustrated in Fig. 2, when the groove depth is about 5 mm, only the fundamental mode is supported, with a cutoff at about 9 GHz. The transmission increases with the operation frequency due to a more confined surface wave established along the CPS structure as a result of the increasing deviation of the dispersion curve from the light line. When the groove depth increases, the first or the second high-order mode manifests itself within a certain frequency band, respectively. As the groove depth increases, each mode band shifts to lower frequency and the transmission efficiency increases.
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31158
Fig. 2. Transmission spectrum of a long CSP structure as a function of the groove depth.
Both the fundamental and the high-order modes have a sharp cutoff frequency which decreases with the increase of the groove depth. An approximate estimation of the cutoff frequency of each band can be inferred from Eq. (1). Although Eq. (1) is obtained from a onedimensional structure of groove array, it can be employed roughly for the CPS structure with thin metallic strip, since the dispersion curves do not change much with the thickness of the metallic strip. However, for the CPS structure in Fig. 2, the effect of the dielectric substrate should be considered. The corrugated metallic film on the PCB substrate can be treated as an array of vertically aligned coplanar strip line, thus the effective permittivity can be estimated by [32]
ε r − 1 K ( k ′ ) K ( k1 ) (2) , 2 K ( k ) K ( k1′ ) where, K denotes the complete elliptic integral of the first kind, and k = a / d , k ′ = 1 − k 2 , k1 = sinh (π a / 4t ) / sinh (π d / 4t ) , k1′ = 1 − k12 , respectively. Therefore the cutoff frequency can be estimated from the following modified dispersion relation by replacing k0 with ε eff k0 in Eq. (1): a (3) β 2 − ε eff k02 = ε eff k0 tan ε eff k0 h . d As indicated by the dashed line in Fig. 2, the estimated cutoff frequency of each band set an upper limit, and the small deviation from the calculated transmission spectrum can be attributed to the finite thickness of the strip not considered in Eq. (1). This rough estimation of the cutoff frequency could be useful in designing the multi-transmission bands in the CSP structure. Similar to the previous analysis of high-order spoof SPP modes in one-dimensional structure of groove array in [30], let us consider the condition for high-order modes supported by the ultrathin CSP structure through the dispersion relation Eq. (3). If there appears a highorder mode spoof SPPs, its band begins at the intersection of its dispersion curve with the light line, at which β = ε eff k0 . From Eq. (2) and (3), we can obtain the frequency corresponds to the intersections by πc (4) , ωc = N ε eff h
ε eff = 1 +
(
)
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31159
where, N is a positive integer denoting the order of the mode and c the light speed in free space. The fundamental mode do not have a cutoff, which corresponds to the order of N = 0. For a high-order mode with N ≥ 1, the band exist between the intersection of dispersion curve with the light line and the asymptotic frequency at the edge of the first Brillouin zone, that is th N π / h ≤ β ≤ π / d . Therefore, the condition for the appearance of the N order mode becomes h > Nd . The simulation illustrated in Fig. 2 roughly agrees with this condition as the first (N = 1) or second (N = 2) high-order mode appears when the groove depth is larger than 8 mm or 16 mm, respectively. For a given groove depth, the supported spoof SPP mode number is estimated by 1 + int(h / d ) . It is also evident in Fig. 2 that the transmission efficiency of the fundamental propagation mode can achieve almost 95%, especially near the cutoff frequency for a case with a larger groove depth. This is due to the good impedance match of the CPW to the CSP strip for larger groove depth at low frequencies. However, for the first or the second high-order mode, the total transmission efficiency drops to 60% or 35% (peak value), respectively. This is due to the increase of the impedance mismatch between the CPW and the CSP strip as the increase of the operation frequency, and a portion of the input energy has been reflected indicated by the calculation of the reflection coefficient of the input port (not shown).
Fig. 3. Dispersion curves (a), and the transmission spectrum (b) calculated from a 170 mm long thin metallic corrugated strip on a PCB substrate with h, d, a, w fixed as 15 mm, 8 mm, 3 mm, and 4.5 mm, respectively. The open circles indicate the calculated time-averaged power density ratio of two cross-sections near the input and output edges.
Figure 3 also compares the calculated dispersion curve with the transmission spectrum for a particular value of the groove depth h = 15 mm. Both the fundamental (mode 0) and the first high-order mode (mode 1) are supported by the CSP structure. Within the frequency band of mode 0 and mode 1 determined by the dispersion curve transmission peaks are obtained which confirms a propagating spoof SPP wave along the CSP structure. The peak transmission efficiency is about 90% or 50% for the fundamental mode or the first high-order mode respectively, due to the impedance mismatch in the coupling structure of input and output ports, especially at higher frequency. It is noted that the transmission does not go to zero at the band-gap between mode 0 and mode 1 or the frequencies beyond the cutoff of the mode 1, which is due to the small radiation energy that coupled to the output port. To verify the net power propagation efficiency along the CSP strip excluding the influences of the coupling sections, we choose two cross-sections about 20 mm away form the input and the output edges of the corrugated thin film strip, and calculated the ratio of time-averaged power density (i.e., the Poynting vector, S = 0.5Re E × H∗ ) across the two planes. The result is
shown in Fig. 3, which demonstrates a propagation efficiency of almost 100% for the
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31160
fundamental mode and 95% for the first high-order mode along a 130 mm CSP strip (about five free-space wavelengths at the center frequency of the first high-order mode). This indicates that the CSP structure could support well confined fundamental mode as well as the high-order modes of spoof SPP wave propagating with high efficiency and low radiation loss.
Fig. 4. The simulated electric field distributions for (a) the fundamental mode, (b) the first high-order mode, and (c) the second high-order mode, at 2.4 GHz, 7.7 GHz and 13.3 GHz, respectively. The left, middle, and right columns indicate the z component of the electric field evaluated at the top of strip in the x-y plane, the electric field amplitude at the y-z plane that cuts the metal strip symmetrically, and in the cross-section perpendicular to the strip, respectively.
Fig. 5. The simulated magnetic field distributions for (a) the fundamental mode, (b) the first high-order mode, and (c) the second high-order mode, at 2.4 GHz, 7.7 GHz and 13.3 GHz, respectively. The upper or lower row indicates the magnetic field distribution in the crosssections perpendicular to the strip in y-z, or z-x plane, respectively.
To illustrate the EM fields of spoof SPP modes in the CSP structure, we calculate the electric and magnetic field distribution in a corrugated copper strip on a PCB substrate with h, d, a, w fixed as 22 mm, 8 mm, 3 mm, and 4.5 mm, respectively. To analyze the first three modes (N = 0, 1, and 2), we demonstrate the field distribution in Fig. 4 and Fig. 5 at operation frequency of 2.4 GHz, 7.7 GHz and 13.3 GHz, which correspond to the fundamental, the first and the second high-order modes, respectively. As demonstrated in Fig. 4 and Fig. 5, both the fundamental and the high-order modes have tightly confined field patterns to the metal strip illustrating typical features of SPP modes with little scattering loss. For the fundamental mode the EM fields distribute mostly inside the metallic slot with a maximum magnitude near the open end and decreased value in the slot, while for the high-order modes the EM fields #197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31161
distribute inside the metallic slot as well, but exhibit N minima and the maximum magnitude moves into the slot. This can be understood by viewing the groove in the structure as a short section of coplanar strip which behaves as a resonator with one end shorted and the other end open to the air. Thus, each band of the spoof SPPs can correspond to a resonant state of the coplanar strip. The spoof SPP wave propagation in the CSP structure is consequently supported by the stimulating and coupling of the resonant state of each groove with EM field distribution similar to that described in Fig. 4 and Fig. 5. 3. Experimental results To verify the multi-mode spoof SPP wave propagation in the CSP structure, several samples of ultrathin metallic corrugated strip have been fabricated by standard PCB technique and experimentally tested at microwave frequency (shown in Fig. 6). To carry out direct measurements of the transmission spectrum of multi-mode propagation, we employ SMA connectors to input and output microwave signal and measure the transmission through an Agilent N5244A vector network analyzer. To couple the SMA connectors to the single conductor CSP structure, a section of CPW (w0 = 1 mm, and s = 0.8 mm) with a characteristic impedance of about 100 Ω is used by directly connecting the center strip of the CPW to the CSP strip, as shown schematically in Fig. 6(a). The parameters of the fabricated samples are optimized to achieve proper impedance matching between the CPW and the CSP strip, especially at low frequency (not possible to get a wideband impedance match with this simple CPW), and the resulted optimal parameters are the same as described in Fig. 2 with varied groove depth.
Fig. 6. (a) The schematics of the proposed CSP structure with input and output CPW sections, and (b) the photograph of the fabricated sample with SMA connectors.
Samples with different groove depth have been tested to verify the supporting of different mode spoof SPP wave propagation. Fig. 7 displays one result for a sample with groove depth of h = 22 mm, which could theoretically support 3 modes, inferred from the calculated dispersion curves. The measured results shown in Fig. 7 clearly verified the propagation of the fundamental mode (mode 0) and the high-order modes (mode 1, and mode 2 for N = 1, and 2). The measured transmission could achieve a peak value of 85% for the fundamental mode due to good impedance match, while 50% or 30% for the first or the second high-order mode, respectively. The transmission bands for different modes agree with the calculated dispersion curves roughly well. Within the bands, the transmission increases with the frequency and achieves a peak value near the cutoff frequency defined by the asymptotic frequency of dispersion curves, due to that more confined surface wave is established with lower radiation loss. We believe the transmission for high-order modes could be enhanced by carefully design of the coupling of the input and output ports to the CSP strip with more complicated wideband CPW transition sections.
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31162
Fig. 7. (a) Calculated dispersion curves, and (b) the calculated and measured transmission spectrum from a 170 mm long thin metallic corrugated strip on a PCB substrate with h, d, a, w fixed as 22 mm, 8 mm, 3 mm, and 4.5 mm, respectively, supporting three modes of spoof SPP wave propagation.
Fig. 8. Simulated (solid lines) and measured (dashed lines) transmission spectrum for the CSP structures with different groove periodicity or width. (h = 22 mm, and w = 4.5 mm)
The band property is mainly determined by the groove depth; however, we also study the influences by other geometrical parameters. Fig. 8 displays the transmission spectrum for CSP structures with different periodicity d or width a of the groove. It is found that neither the periodicity nor the width of the groove has obvious effect on the band property. The highly confined EM wave and the ultrathin nature of the metallic film and dielectric substrate of the CSP structure enable it to be easily bended to propagate the spoof SPP wave along curved surface. To test the CSP modes propagation along curved surface, we investigate the surface wave transmission property of a 90 degree vertical bend structure as shown schematically in Fig. 9(a). It is found from the simulated EM field distribution (Figs. 9(c) and 9(d)) that well confined spoof SPPs of both the fundamental and the high-order modes could be established along the bended CSP structure. The bending of the structure does not influence the EM field patterns of the fundamental and high-order modes. No obvious decrease of the field amplitude is observed in the high-order mode propagation (Fig. 9(d)) which indicates a low bending lose even at higher operation frequency. The bending radius is
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31163
70 mm, which is about half the wavelength at the peak frequency of the fundamental mode, or twice the wavelength at the peak frequency of the first high-order mode.
Fig. 9. The schematics (a) and the photograph of a fabricated sample (b) of a 90 degree bend of the CSP structure. (c) and (d) illustrate the simulated electric field component perpendicular to the surface distributed along the bended metal strip at frequency of 2.5 GHz (the fundamental mode), and 7.8 GHz (the first high-order mode), respectively. (with a = 3 mm, h = 22 mm, d = 8 mm, and w = 4.5 mm)
Direct measurement of the transmission of the spoof SPP modes has been carried out through input and output coupling ports at the two ends of the 90 degree bend as shown in Fig. 9(b). Fig. 10 compares the transmission results between a bended and a straight CSP structure. The measurements agree with the simulation results well. For the fundamental mode, similar transmission spectrum has been obtained for the bend and unbend structures with same peak transmission of about 85%, same transmission bandwidth, and same cutoff frequency, indicating no obvious influence from the bending of the structure. While for the high-order mode, the bending of the structure has a slight influence. It does not change the cutoff frequency, but induces a shrink of the transmission band. This can be explained by the bending that enable the less confined surface wave at lower frequencies to radiate in the highorder mode band. There is also a slight decrease of the peak transmission of about 10% (from 52% to 47%) due to the bending loss. However, the experimental result clearly indicates that both fundamental and high-order modes can be supported to propagate with acceptable low bending loss on curved structure with bending radius comparable with the wavelength.
Fig. 10. Comparison of the simulated and measured transmission through the 90° bend (with a radius of 70 mm) and straight CSP structures with same length. (a = 5 mm，h = 22 mm，d = 8 mm，w = 4.5 mm)
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31164
4. Conclusions
In conclusion, we have analyzed the high-order mode transmission of spoof SPPs along the thin CSP structure composed of corrugated metal strip with periodic array of edge grooves on a thin dielectric substrate in the microwave frequency range. It shows that well confined surface wave of both the fundamental and high-order modes can be supported by the CSP structure, and the mode number is mainly determined by the depth of the grooves. Direct measurement of the transmission spectrum has been carried out on fabricated samples, which verifies the theoretical analysis and the numerical simulations. Furthermore, high-order mode of spoof SPPs propagation with acceptable bending loss is confirmed on curved structure due to the ultra-thin nature of the CSP structure. The multi-band propagation with pre-determined band property can be utilized to design novel functional devices such as filters, resonators, and couplers. We also believe that the multi-band transmission characteristic can be easily scaled to terahertz frequency and may find applications in developing planar surface plasmonic devices and circuitry in both microwave and terahertz domain. Acknowledgments
This work is partially supported by the National Nature Science Foundation of China (61371034, 61101011, 60990322, 60990320), the Key Grant Project of Ministry of Education of China (313029), the Ph.D. Programs Foundation of Ministry of Education of China (20100091110036, 20120091110032), and partially supported by Jiangsu Key Laboratory of Advanced Techniques for Manipulating Electromagnetic Waves.
#197799 - $15.00 USD Received 16 Sep 2013; revised 4 Dec 2013; accepted 4 Dec 2013; published 10 Dec 2013 (C) 2013 OSA 18 November 2013 | Vol. 21, No. 23 | DOI:10.1364/OE.21.031155 | OPTICS EXPRESS 31165
