Glide symmetry for mode control and significant suppression of coupling in dual-strip SSPP transmission lines Download: 854次
1 Introduction
Surface plasmon polaritons (SPPs) are highly localized surface waves that exist on the interface of metal and dielectric beyond the far-infrared frequency. However, they do not naturally exist at lower frequencies such as terahertz and microwaves, where the metals no longer behave like plasma with negative dielectric constants.1 In order to allow SPPs to operate in the lower frequency bands, spoof surface plasmon polaritons (SSPPs) have been conceived and realized on periodically structured metallic surfaces.2 Similar to the optical SPPs, SSPPs exhibit highly localized electromagnetic (EM) fields, subwavelength resolution, and extraordinary field confinements.3 Furthermore, ultrathin corrugated metallic strips have been proposed as kind of slow-wave waveguide that supports the propagation of SSPPs.4 Different types of SSPP transmission lines (TLs), including single-conductor and dual-conductor ones, have been created in different circumstances. Because of mode and momentum mismatch, transitions from the conventional TLs such as coplanar waveguide and microstrip (MS) are needed to realize high-efficiency excitation of SSPPs.5
On the other hand, the SSPP structures can be considered as special kinds of metamaterials that are composed of periodically arranged subwavelength unit cells. It has been demonstrated that higher symmetries can effectively affect the dispersion characteristics and band gaps of structures.19 Higher symmetry occurs if the periodic structure can be described by additional geometric operations beyond a simple translation or reflection. For example, glide and twist symmetries are two common cases of higher symmetry.20,21 Most recently, metamaterials with glide symmetry have been developed to achieve flexible control of dispersion behaviors and band gaps, so as to provide new solutions for microwave waveguides, functional devices, and antennas.22
Here, we introduce glide symmetry in dual-conductor SSPP TLs and TL arrays for characteristics control. First, the dispersion curves, modal fields, and transmission properties of the glide symmetric TL are studied, and degeneracy of the fundamental mode is investigated. After that, two SSPP TLs, one with glide symmetry and one without glide symmetry, are arranged in parallel as two channels with deep subwavelength separation (which is
2 Glide Symmetry in Dual-Strip SSPP TLs
The SSPP TLs typically consist of metallic strips with subwavelength corrugations and sometimes with ground. Their configurations (e.g., the geometry of the strips) can be adjusted according to specific requirements in applications. There have been several types of SSPP TLs reported in the literature, which could be generally categorized as single-strip, grounded single-strip, and dual-strip.4,7,8 Among them, the dual-strip SSPP TLs contain two layers of antisymmetrically arranged corrugated metallic strips on both sides of dielectric substrate. Compared to the single-strip SSPP TLs of the same size, the dual-strip ones obtain lower cutoff frequency, stronger subwavelength effect and field confinement, further depressed mutual coupling, and easier embedment of lumped elements and active devices.25 In view of these, we introduce glide symmetry in the dual-strip SSPP TLs to further improve the performance of plasmonic circuits.
A unit cell of the dual-strip SSPP TL, which has two antisymmetrically arranged metallic structures, is given in
Fig. 1. (a) A nonglide unit cell in the dual-strip SSPP TL. The line width, period, width, and depth of the slots are , , , and , respectively. In this work, the thickness of the two metal layers is , and the substrate has a relative permittivity of 3.48 with thickness of and width of . (b) A glide symmetric unit cell. The centers of the slots in the upper and lower layers are misaligned with a glide distance of along the axis. (c) The glide symmetric dual-strip SSPP TL. Section I is the MS line at the input and output, and the widths of the upper and lower strips are and , respectively. Section II is the transition section and Section III is composed of uniform glide symmetric unit cells.
To compare the EM properties of the nonglide and glide symmetric structures, dispersion characteristics are studied in the commercial software of CST Microwave Studio. The dashed lines in
The degeneracy of the fundamental mode is also studied in terms of the distribution of EM fields. We choose two cross sections in the unit cell, as indicated by the orange plane and the blue one in
Fig. 3. (Side view) (a), (b) Distributions of the electric fields of the nonglide symmetric structure at the orange and the blue cross sections indicated in Fig. 1(a) , respectively. (c), (d) Distributions of the electric fields of the glide symmetric structure at the orange and the blue cross sections indicated in Fig. 1(b) , respectively.
The entire model of the glide symmetric SSPP TL is shown in
The distributions of the near electric fields are measured in our home-made near-field scanning system, which is mainly constructed by a two-dimensional (2D) stepper and the VNA. The magnitudes of the electric fields right above the nonglide and glide symmetric TLs are measured and plotted in
Fig. 5. Magnitude distributions of the near electric field for (a) the nonglide symmetric and (b) the glide symmetric SSPP TLs at different frequencies.
3 Hybrid Nonglide and Glide Symmetric TL Array
Channel crosstalk is inevitable in compact systems, due to mutual coupling between TLs and components. When TLs are densely arranged, e.g., with subwavelength separation, the EM fields on one TL will give rise to induced currents on other TLs and therefore cause unwanted coupling. In fact, channel crosstalk suppression and signal integrity are two key problems in modern integrated circuits, and, unfortunately, they are almost contradictory. The SSPP TLs have natural advantages in view of coupling suppression, due to the strong subwavelength effect and field confinement. Here, we propose a hybrid array composed of alternatively arranged nonglide and glide symmetric TLs, which possesses extremely low mutual couplings.
A simplified two-channel model is used to investigate the isolation and coupling characteristics of the hybrid TL array, as is given in
Fig. 6. The four-port model composed of two channels; one is the nonglide symmetric TL channel, and the other is the glide symmetric one.
Fig. 7. Simulated isolation coefficients ( and ) and coupling coefficients ( and ) of the two SSPP TLs.
Here,
Next, we use Eq. (2) to compare the coupling coefficient between two identical nonglide symmetric SSPP TLs and that between a nonglide TL and a glide one.
Fig. 8. The normalized and average mode coupling coefficients in two types of TL arrays at different line separations ( and ).
A prototype of the hybrid array containing nonglide and glide symmetric TLs (as given in
Fig. 9. Comparison of the reflection coefficient ( ), transmission coefficient ( ), coupling coefficient ( ), and isolation coefficient ( ) for the hybrid TL array (composed of a glide symmetric TL and a nonglide symmetric TL) and the uniform TL arrays (composed of two nonglide symmetric TLs and two glide symmetric TLs, respectively).
The coupling suppression in the hybrid TL array is also investigated in terms of the distributions of near-electric fields, and low-coupling and high-isolation are observed at different frequencies (2 and 5 GHz) and with different separations (0.6 and 2 mm) in both simulation and experiment results, as presented in
Fig. 10. Distributions of the near-electric field of the hybrid TL array and the uniform TL array with line separations being 0.6 and 2 mm at 2 and 5 GHz, respectively.
4 Experimental Setup and Methods
4.1 S-Parameter Measurement
A VNA (Agilent N5230C) was used to perform spectrum measurements of the two-port networks with one SSPP TL and the four-port networks with two SSPP TLs, including all the scattering parameters.
4.2 Near-Field Measurement
Near electric field distributions in the SSPP TLs were measured in our home-made 2D near-field scanning system in the microwave anechoic chamber at Southeast University. The 2D near-field scanning system includes a VNA (Agilent N5230C) and three electronic motor steppers in the
5 Conclusion
In this work, we introduce glide symmetry, which is a typical type of higher symmetry, to manipulate the dispersion characteristics of the SSPP structure. Mode degeneracy and merged pass-bands are investigated and designed so as to broaden the bandwidth and control the propagation modes of SSPPs. We further propose a hybrid SSPP TL array composed of alternately arranged nonglide and glide symmetric SSPP TLs. Although the two neighboring TLs possess the same composing units, strip width, and feeding structure, mutual coupling has been significantly suppressed due to the mode mismatch introduced by the glide symmetry in the structure. Both simulations and experiments have been carried out for demonstration. This glide symmetric SSPP TL, as well as the hybrid array, can be adopted in highly compact circuits without bringing in extra space and feeding networks. In view of this, we conclude that glide symmetry offers supplementary control of the SSPP waves, which may bring about new solutions in future integrated plasmonic circuits.
Article Outline
Xiao Tian Yan, Wenxuan Tang, Jun Feng Liu, Meng Wang, Xin Xin Gao, Tie Jun Cui. Glide symmetry for mode control and significant suppression of coupling in dual-strip SSPP transmission lines[J]. Advanced Photonics, 2021, 3(2): 026001.