Recently, a conformal surface plasmon (CSP) structure has been successfully proposed, which is very promising for application of planar plasmonic devices in the frequency ranging from microwave to mid-infrared [Proc. Natl. Acad. Sci. U.S.A. 110, 40-45 (2013)]. Here we investigated the dispersions and electromagnetic (EM) field patterns of a symmetric CSP structure in which the two sides of the planar metal strip are symmetrically corrugated by groove arrays. The symmetric CSP structure can support both the symmetric mode (even mode) and the anti-symmetric mode (odd mode) of surface wave propagation. Based on the even mode, we analyzed the EM wave coupling between two adjacent symmetry CSP strips, and then designed and analyzed two planar CSP waveguide devices in the terahertz frequency: a frequency splitter and a 3 dB directional coupler. To verify the functionality and performance of these waveguide devices, we scaled down the working frequency to microwave and designed similar devices with scaled geometry. We implemented microwave experiments on the fabricated prototypes, and the tested device performances have clearly validated the functionality of our designs. The symmetric CSP structure is believed to be very applicable in future design of novel planar plasmonic device and circuitry.
© 2014 Optical Society of America
Surface plasmon polaritons (SPPs), which are surface electromagnetic (EM) waves propagating along the metal/dielectric interface at optical frequencies , have attracted increasing attentions due to their remarkable capability of guiding and localizing EM wave into sub-wavelength scales during the last decade [2–4]. The unique properties associated with SPPs have potential applications for designing highly integrated circuits and devices in the areas of optoelectronics, materials science, and biosensing.
In the terahertz and microwave frequency bands, although SPPs cannot be supported on smooth metal surfaces, recently introduced concept of plasmonic metamaterials could still support the highly confined surface EM waves at lower frequencies, which are also called as spoof SPPs or designer SPPs [5–19]. The plasmonic metamaterials usually consist of textured metal surface with sub-wavelength scale corrugations or dimples, and all of them 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 planar plasmonic metamaterial has been proposed to support spoof SPPs [20–23], which are named as conformal surface plasmon (CSP) due to its ultra-thin and flexible nature, paving the way of developing versatile surface wave integrated devices or circuits at lower frequencies bands, especially at terahertz region.
The proposed planar CSP structure is a thin metallic strip with corrugated periodic grooves on one side that could support well confined surface wave along the strip. It has been mentioned that symmetric CSP structure with same corrugated grooves on both sides of the strip could also support surface wave with both even mode and odd mode, and the even mode is less sensitive to bending losses compared to that of the single-sided CSP structure . However, most of the studies are conducted on the single-sided CSP structure due to its simple structure [20–23]. In this paper, we focus on the detailed study of the symmetric CSP structure, and analyze the dispersions as well as the field patterns of the even and odd modes supported by the symmetric CSP structure. We also design a frequency splitter and a 3 dB directional coupler at terahertz region by using even mode supported by the symmetric CSP structure. To verify the functionality and performance of these waveguide devices, we scale down the working frequency to microwave and design similar devices with scaled geometry. We implement microwave experiment on the fabricated prototypes, and the tested performances of the devices have clearly validated the functionality of our designs.
2. Analysis of the symmetric CSP structure
The basic symmetric CSP structure is composed of a thin metal strip of width w on top of a dielectric slab with thickness t, of which the two sides are symmetrically corrugated by one dimensional arrays of grooves with depth h, width a, and lattices constant d, as illustrated in the inset of Fig. 1. It has been previously confirmed that well confined spoof SPPs can be supported on either side of the corrugated metal strip . Owing to the thin central strip of the symmetric CSP structure, the SPP waves supported by the two sides will interact with each other, and split into two supermodes: even mode (symmetry mode) and odd mode (anti-symmetry mode). We employ the commercial software based on the finite element method to numerically calculate the dispersion relation of the symmetric CSP structure. As an example to implement in the terahertz frequency band, structured thin metallic film with thickness of about 100 nm is deposited on polyimide substrate with thickness of about 20 μm. The parameters d, a, w are chosen as 50 μm, 40 μm, and 79 μm, respectively, while the dielectric substrate has a relative dielectric constant of 2.9, loss tangent of 0.003. Different groove depth h has been considered to study its effect on the dispersion property. The calculated dispersion curves with two branches corresponding to even and odd modes are displayed in Fig. 1, where only the fundamental mode of CSP has been analyzed. The dispersion curve for the higher-frequency branch (the odd mode) does not start at the origin, which is due to the fact that only non-radiative modes are taken into consideration. When decreasing the groove depth, the dispersion curves shift to higher frequency. For comparison, the dispersion curve for the single-sided CSP strip (half structure) has also been shown in Fig. 1, which lies in between those of the odd and even modes, closer to that of the even mode.
To explore the modal property, Fig. 2 illustrates the simulated electric ðeld (Ez component) distributions at the top of strip for both even and odd mode at 0.7 THz and 1 THz, respectively. As demonstrated in Fig. 2, both the even and the odd modes have tightly confined field patterns to the metal strip illustrating typical features of spoof SPPs modes with little scattering loss. For the even mode, the EM field oscillates in phase (symmetry) at the two sides of the metal strip, while for the odd modes the EM field oscillates out-of phase (anti-symmetry) at the two sides. Compared with the odd mode, the even mode has a much broader working frequency band ranging from very low to its asymptotic frequency, and also has a larger propagation constant at fixed frequency, implying strong confinement of the SPP waves. Besides, the even mode is less sensitive to bending losses and more convenient to excite due to its symmetric EM field distribution. In the following sections, we will focus on utilizing the even mode in the symmetric CSP to design spoof SPP waveguide devices.
To study the metal loss effect on the spoof SPP wave propagation, we calculated the propagation lengths for different symmetric CPS structures composed of gold or perfect electric conducting (PEC) film and compared in Fig. 3. As indicated, the propagation length is sensitive to the metal loss especially at shorter wave length due to the increasing ohmic losses with increasing operating frequency. However, by simply reducing the groove depth h, the propagation length can be increased. Therefore, we could optimize the CPS structure to partially reduce the metallic loss effect on the spoof SPP propagation.
3. Design of the CSP waveguide devices
Considering two adjacent parallel CSP waveguides as shown in the inset of Fig. 4(a), the coupling between them can be well understood through the coupled mode theory [24–26]. The EM fields can completely switch between the two adjacent parallel waveguides through certain coupling length if only the two adjacent parallel waveguides have the similar propagation constant. The power transmitted through the propagating waveguide (direct arm) P1 and its adjacent waveguide (coupled arm) P2 can be written as Eq. (2), n or n0 is the refractive index distribution of the surrounding dielectric medium or the CSP waveguide respectively, which can be determined from the dispersion relations in Fig. 1. Ejt and Ejx (j = 1, 2) are the normalized transverse and longitudinal electric field distribution of CSP waveguide j, respectively. The coupling length corresponding to full power transfer from the direct arm to the coupled arm of the waveguide is defined as 
For the coupled CSP waveguides showed in the inset of Fig. 4(a), owing to the subwavelength periodicity, the CSP structure can be considered as a homogeneous effective medium. Therefore, the coupling coefficient of the coupled structure can be roughly estimated by Eq. (2). The calculated coupling coefficient from the simulated EM field distribution is shown in Fig. 4(a) for different separation gap g. Thus the coupling length can also be regulated by g, which is quite useful in the further design of CSP devices. For a given separation gap of g = 3 μm, the coupling coefficient is about κ = 907 m−1 at 0.2 THz, therefore the coupling length can be calculated by Eq. (3) with Lπ/2 = 1731 μm. To verify the theoretical calculation, we simulated the S parameters (transmission spectrum) of the coupled CSP waveguides (with one input and three output terminals) with a coupling length L0 of 1731 μm and displayed in Fig. 4(b). The first three minima of S21 and S31 on the transmission spectrum correspond to 0.19 THz, 0.41 THz, and 0.61 THz, while the calculations from the coupled mode theory (through Eq. (2) and (3)) are 0.2 THz, 0.43 THz, and 0.64 THz, respectively, roughly agreed with the simulations. This indicates that the coupled mode theory can be roughly utilized in the design of the CSP coupling devices.
It is noticed from Eq. (1) and (3) that for a given length L0, if (n = 1, 2, 3…), the input EM wave will switch from the direct arm to the coupled arm, and the full power can be output from port 3. Conversely, if the coupling length (n = 1, 2, 3…), the full power will be outputted from port 2 without any coupling to the coupled arm. This is also evident in the calculated transmission spectrum in Fig. 4(b), since the coupling length Lπ/2 is dependent on the working frequency. According to this feature, we can control the power coupling and design CSP waveguide coupling devices by choosing suitable coupling length.
As an example, we first designed a simple CSP frequency splitter in the terahertz frequency as schematically shown in Fig. 5(a). It consists of two identical straight CSP waveguides (A and B) that approach each other by means of cosine bend, and have a straight interaction region with length L, and separation gap of g. In the design the initial values for L and g are determined by the coupled mode theory through Eq. (1) to (3), and then optimized through EM simulation, since the interaction length L estimated by Eq. (3) should be modified due to the existence of the cosine bend region .
To verify the performance of the designed frequency splitter, we calculate the transmission spectrum of the splitter by integrating the longitudinal component of the Poynting vector in four perpendicular planes located near the input and output terminals of the waveguides. At terahertz frequency although the metallic loss could slightly affect the propagation length, we could still assume the metal film as a PEC for simplicity to exclude metallic dissipation for device size of about several wavelengths. The geometrical parameters are optimized as d = 50 μm, a = 40 μm, h = 37 μm, w = 79 μm, L = 360 μm, and g = 3 μm. The polyimide is used as the dielectric substrate with a thickness of 20 μm, relative dielectric constant of 2.9 and loss tangent of 0.0035. The calculated transmission spectrum is displayed in Fig. 5(b). The EM energy can be almost fully output from output terminal 3 at around 0.25 THz and switched to output terminal 2 at around 0.55 THz, while the output terminal 4 does not have any exited EM power within the frequency band from 0.2 THz to 0.65 THz. The central frequencies of the two pass bands can be easily varied by careful design of the coupling length and the gap between the CSP strips. To illustrate more clearly the performance of the frequency splitter, we also calculate the electric field distribution (Ez component) at the surface of the structure, as shown in Fig. 5(c) and 5(d), where the operation frequency is fixed at 0.25 THz and 0.55 THz, respectively. The electric field distribution has clearly suggested the functionality that the splitter is able to switch the output EM power to terminal 2 and 3 at different frequency band.
According to the coupled mode theory, when the two coupled waveguides have different propagation constants the EM energy cannot be full switched from one waveguide to another, and we can choose appropriate propagation constants to achieve a EM energy coupling ratio of 50% . As a second example, we can simply design a CSP 3dB directional coupler based on the above feature. We employ two CSP waveguides with different groove depth hA and hB so that the two coupled waveguides could have different propagation constants. The schematic of the proposed directional coupler is very similar to that of the CSP splitter discussed previously (as shown in Fig. 5(a)). Though optimization the parameters hA, hB d, a, w, L, and g are set as 32 μm, 37 μm, 50 μm, 40 μm, 79 μm, 10 μm, and 30 μm, respectively, and the dielectric substrate is the same as that used in the frequency splitter. We still omit the metallic loss in the grooved strip and calculate the transmission spectrum of the CSP directional coupler, as displayed in Fig. 6(a). The EM energy is almost equally divided and exited through output terminal 2 and 3 in the frequency band from 0.4 THz to 0.47 THz, while the output terminal 4 does not have any exited EM power. Furthermore, we also simulate the electric field distribution (Ez component) at the surface of the CSP directional coupler at 0.45 THz and display in Fig. 6(b). It is clear that the EM field is partially coupled from the direct arm to the coupled arm and simultaneously exited from the output terminal 2 and 3 with equal amplitude, indicating the functionality of a 3 dB directional coupler.
4. Experimental verification of the CSP waveguide devices at microwave frequency
One of the advantages of the spoof SPP devices is their easy scalability in the frequency ranging from mid-infrared down to microwave. The CSP structure can be easily scaled down to the microwave frequency . To verify the functionality and performance of the previously proposed CSP waveguide devices, we scale down the working frequency to microwave and design similar devices with scaled geometry. We scale up 100 times the geometry of the frequency splitter and directional coupler proposed previously, and their transmission characteristic can switch to microwave range without much change of their functionalities. We therefore implement microwave experiments to test the performance of the two waveguide devices.
The prototype samples of the two devices have been fabricated in a printed circuit board (PCB) with dielectric constant of 2.55, loss tangent of 0.0035, and thickness of 0.5 mm. The symmetry grooved strip is made of copper film with thickness of 0.035 mm on one side of the PCB. To carry out direct measurement of the transmission spectrum, we employ SMA connectors to input and output microwave signal, and a section of tapered co-planar waveguide (CPW) is inserted between the SMA connector and the CSP strip to match the impedance. The transmission spectrum between the input and the output terminals is measured through an Agilent N5244A vector network analyzer. The sample of the frequency splitter is shown in Fig. 7(a). The simulation and measurement results are displayed in Fig. 7(b), which agree with each other well. The 3 dB bandwidths corresponding to two passband of the frequency splitter are about 2.2 GHz and 2.1 GHz, with center frequency around 3.39 GHz and 7.42 GHz, respectively. The slight change of the center frequencies of the two pass bands (not exactly the 1/100 scaled down) is due to the decrease of the effective dielectric constant. The insertion loss at the lower or higher pass band is about −1.8 dB or −1.3 dB, respectively, which is mainly caused by the metallic and dielectric loss, as well as the impedance mismatch between the CPW and the CSP strip.
For the 3 dB directional coupler, owing to the change of dielectric substrate, the coupling constant κ is also changed. Therefore, we need to re-calculate the κ by the regulation of the separation distance between the two wave guides. The optimized separation g is set as 1.75 mm. The fabricated prototype sample of directional coupler is shown in Fig. 8(a). To achieve better impedance matching between the CPW and the CSP strip, we employ gradual changed grooves depth at the four terminals of the two coupled CSP waveguides. The calculation and the measurement results of the transmission spectrum are illustrated in Fig. 8(b). Within the frequency band from 6.0 - 9.0 GHz, The transmission from the input terminal 1 to output terminal 2 or 3 (the S21 or S31) is always around −5 dB. Although a slight insertion loss is induced due to metallic and dielectric loss, as well as the impedance mismatch, the EM energy can be divided equally to the two output terminal 2 and 3. The functionality of the 3 dB directional coupler is roughly verified.
In conclusion, we have analyzed the spoof SPPs along the planar symmetric CSP structure on a thin dielectric substrate in the terahertz frequency range. It shows that well confined spoof surface wave of both the odd and even modes can be supported by such symmetric CSP structure. Based on the CSP structure, two planar waveguide devices, the frequency splitter and the 3 dB directional coupler, have been designed at terahertz frequency range by careful analysis of the EM wave coupling between two adjacent symmetry CSP strips. To verify the performance of the proposed waveguide devices, we scaled down to microwave frequency by simply scaling up the geometry of the devices and made direct measurement of the transmission spectra on the fabricated prototype samples at microwave frequency band, which validate the theoretical analysis and the functionality of the frequency splitter and the directional coupler. We believe that the symmetric CSP structure is a very promising surface waveguide component and could find applications in further development of other novel planar surface plasmonic devices and circuitry in both microwave and terahertz domain.
This work is partially supported by the National Nature Science Foundation of China (61371034, 61101011, 60990322), the Key Grant Project of Ministry of Education of China (313029), the Ph.D. Programs Foundation of Ministry of Education of China (20120091110032), and partially supported by Jiangsu Key Laboratory of Advanced Techniques for Manipulating Electromagnetic Waves.
References and links
1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
6. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]
9. E. Hendry, A. P. Hibbins, and J. R. Sambles, “Importance of diffraction in determining the dispersion of designer surface plasmons,” Phys. Rev. B 78(23), 235426 (2008). [CrossRef]
11. 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(3), 175–179 (2008). [CrossRef]
12. A. Fernández-Domínguez, E. Moreno, L. Martin-Moreno, and J. F. Garcia-Vidal, “Guiding terahertz waves along subwavelength channels,” Phys. Rev. B 79(23), 233104 (2009). [CrossRef]
13. 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(2), 754–764 (2010). [CrossRef] [PubMed]
15. N. Talebi and M. Shahabadi, “Spoof surface plasmons propagating along a periodically corrugated coaxial waveguide,” J. Phys. D Appl. Phys. 43(13), 135302 (2010). [CrossRef]
16. Y. J. Zhou, Q. Jiang, and T. J. Cui, “Bidirectional bending splitter of designer surface plasmons,” Appl. Phys. Lett. 99(11), 111904 (2011). [CrossRef]
17. 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(22), 21189–21198 (2011). [CrossRef] [PubMed]
18. Y. J. Zhou, Q. Jiang, and T. J. Cui, “Multidirectional surface-wave splitters,” Appl. Phys. Lett. 98(22), 221901 (2011). [CrossRef]
19. E. M. G. Brock, E. Hendry, and A. P. Hibbins, “Subwavelength lateral confinement of microwave surface waves,” Appl. Phys. Lett. 99(5), 051108 (2011). [CrossRef]
20. 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(1), 40–45 (2013). [CrossRef] [PubMed]
21. 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(15), 151912 (2013). [CrossRef]
22. X. Shen and T. J. Cui, “Planar plasmonic metamaterial on a thin film with nearly zero thickness,” Appl. Phys. Lett. 102(21), 211909 (2013). [CrossRef]
23. X. Liu, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “High-order modes of spoof surface plasmonic wave transmission on thin metal film structure,” Opt. Express 21(25), 31155–31165 (2013). [CrossRef] [PubMed]
24. H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991). [CrossRef]
25. A. Ma, Y. Li, and X. Zhang, “Coupled mode theory for surface plasmon polariton waveguides,” Plasmonics 8(2), 769–777 (2013). [CrossRef]
26. B. Alexandra and S. I. Bozhevolnyi, “Directional couplers using long-range surface plasmon polariton waveguides,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1233–1241 (2006). [CrossRef]
27. H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, 1984).