A planar strongly confined spoof surface plasmonic waveguide with compact cells

A new planar waveguide structure, based on spoof surface plasmon polaritons (SSPPs), is proposed featuring compact size, low loss, and good subwavelength field confinement. Compared with the rectangular- and trapezoidal-type cells in the conventional spoof surface plasmonic waveguides (SSPWs), the proposed cell has 50.7% and 27.8% size reduction at the same cut-off frequency, respectively. Moreover, the simulated electrical field distributions show that there are good improvements in the field enhancement and subwavelength confinement. To further validate the transmission characteristics of the proposed waveguide, coplanar waveguide (CPW) and corresponding transition structures are used to get a high efficient mode conversion. A CPW-SSPW-CPW structure on a dielectric board is designed, fabricated, and measured in the microwave region. Good agreement is achieved between the simulated and measured results. The last results show that the proposed waveguide has low insertion loss and flat group delay in an ultra-wideband from 2.4 to 10.3 GHz.

Keywords: Dispersion; electromagnetic field confinement; periodic structure; spoof surface plasmon polaritons (SSPPs)

Surface plasmon polaritons (SPPs) are the surface electromagnetic modes that propagate parallel to the interface between metal and dielectric, and attenuate exponentially in the vertical direction [[1]]. They have the advantages of strongly localized electromagnetic wave and subwavelength size in the optical regime, which is beneficial to overcome the diffraction limit [[2]]. As an important extension of SPPs in microwave and terahertz frequency bands, the so-called spoof surface plasmon polaritons (SSPPs) was proposed by Pendry [[5]] and experimentally validated by Hibbins [[7]]. Aided by the metallic surface with subwavelength periodic array drilling holes or grooves, the SSPPs inherit most of the properties of SPPs, such as subwavelength localization, field enhancement, and SPP-type dispersion. Therefore, such surface electromagnetic modes can be realized at any desired frequency band based on single metallic transmission structures.

Subsequently, various kinds of high performance SSPP waveguides have been proposed with good transmission and compact size, such as domino structure, rectangular grooves, and trapezoidal grooves, etc. [[8]]. Among them, three-dimensional good conductor and semiconductor structures seriously limit the practical applications in integrated circuits. So, planar ultra-thin SSPP waveguides in the microwave region have received much attention because they can be fabricated by the PCB process easily. They have been widely applied in many microwave component designs including power divider [[17]], filter [[20]], antenna [[25]], and amplifier [[26]], etc. However, at microwave frequencies, the total size of most structures is still large and the confinement of electromagnetic waves is usually weak especially when the operation frequency is far away from the cut-off frequency [[27]]. Thus, the SSPP waveguides still remain to be further investigated.

As we know, the transmission characteristics, total size, dispersion, and subwavelength field confinement are the key factors for spoof surface plasmonic waveguides (SSPWs). In this paper, a new compact planar SSPW consisting of an ultra-thin metallic strip structure with periodic subwavelength groove arrays on a PCB board is proposed in the microwave frequency regime. Compared with the conventional plasmonic waveguide with rectangular and trapezoidal grooves, the proposed structure can realize 50.7% and 27.8% size reduction and improve the field confinement ability to SSPP waves. To validate the proposed waveguide, a CPW-SSPW-CPW structure was designed, fabricated, and measured. The last simulated and measured results demonstrate the proposed waveguide that has good transmission, tight electromagnetic field confinement, and flat group delay in an ultra-wideband from 2.4 to 10.3 GHz. Therefore, the high performance and compact size of the proposed SSPW show a good application prospect in the future microwave or terahertz integrated circuit.

Conventional microstrip photonic or electromagnetic bandgap cells are widely designed and investigated to support the guided waves in the microwave frequency region. Typically, the cell in [[29]] is a compact structure and has been widely used in power amplifier, antenna, filter, etc. In this work, this kind of cell is extended and investigated to support the SSPP wave by removing the metal ground. Figure 1(a) shows the schematic diagram of this cell. In contrast, the other two cells, shown in Figure 1(b,c), are trapezoidal- and rectangular-type groove mentioned in [[17], [27]], respectively. In order to obtain the propagation characteristics of the SSPP structures, the dispersion relation of structural perfect electric conductor (PEC) unit is directly calculated by using the eigen-mode solver of the commercial software, CST Microwave Studio.

PHOTO (COLOR): Figure 1. Schematic diagram of three perfect electric conductor cells. (a) Proposed structure, (b) trapezoidal groove, (c) rectangular groove.

When H = 5 mm, a = 1 mm, d = 5 mm, p = 4 mm, q = 1 mm, b = 1.25 mm, c = 0.25 mm, and the thickness of the metal strip is 0.035 mm, the rectangular occupying areas of the three cells (as drawn in Figure 1) are all the same. Figure 2 shows the corresponding dispersion curves of the fundamental mode. From the figure, it is clear that all the curves deviate far away from the light line, which is similar to the dispersion behaviors of SPPs in optics. That is to say, the fundamental modes are non-radiative. They are the surface electromagnetic wave modes. So, they can be used as a transmission structure. It can also be found that the proposed cell has the minimum asymptotic frequency, 10.6 GHz, which means it has the most compact size. Furthermore, in order to compare the occupying areas more intuitively, the variable, H, of the trapezoidal and rectangular structures are set as 6.92 and 10.14 mm, respectively, to make all the three asymptotic frequencies the same, i.e. 10.6 GHz. It can be calculated that the corresponding occupying areas are 25, 34.6, and 50.7 mm2. It means that the proposed structure in Figure 1(a) realizes 27.8% and 50.7% size reduction, respectively. Therefore, it is a good candidate to build a compact spoof surface plasmonic waveguide.

PHOTO (COLOR): Figure 2. Dispersions for the three cells.

To further investigate the transmission properties, the coplanar waveguide (CPW) and transition structures are used to achieve a smooth momentum matching and a high efficient mode conversion between the CPW and SSPW [[15]]. Figure 3 shows the designed waveguide where the metal strip is on a dielectric substrate F4B with relative dielectric constant of 2.65 and a thickness of 0.5 mm. It consists of three parts: 1) 50 Ω-coplanar waveguides (width: 5 mm, gap: 0.26 mm, l1 = 5 mm, and w = 18 mm), 2) transitions with flaring ground and gradient depth grooves to achieve impedance matching between the two waveguides where l2 is 50 mm, and 3) SSPP structure with 24 periodic cells (l3 = 120 mm).

PHOTO (COLOR): Figure 3. Layout of the proposed waveguide.

Aided by the CST Microwave Studio, the subwavelength field confinement ability is simulated. When the observing frequency is set as 8 GHz far away from the asymptotic frequency, Figure 4(a) gives the normalized electric field amplitudes along Line A (the distance from the side of cells is 1 mm) in the metal plane. In contrast, the other two curves of rectangular and trapezoidal grooves are also given. From Figure 4(a), it can be found that the amplitude and roll-off of the proposed structure are discernibly larger and sharper than the other two. It means that the proposed structure can ensure effective confinement to SPP waves. Figure 4(b) gives the simulated planar electrical field amplitude distributions on the metal surfaces and the yz-planes at x = 67.5, 52.5, and 62.5 mm corresponding to the maximum amplitude values of the three waveguides, respectively, which are illustrated as dash arrow lines in Figure 4(a). It can be found that the electromagnetic fields are well confined along the strips. The red area of the proposed structure is biggest which means it has the best field enhancement. Therefore, the SSPP wave can be tightly confined to waveguide surface and propagate with low loss. Figure 5 gives the simulated scattering parameters to validate the propagation performance of the mentioned three waveguides. It can be seen that the electromagnetic waves can propagate well in an ultra-wideband. From 2.4 to 10.3 GHz, the insertion loss of the proposed waveguide is within −3 dB. For the other two waveguides, the insertion losses are almost in the same level. It means that smooth matching and good mode conversion between CPW to SSPW are realized in all three structures. The difference is the cut-off frequency as mentioned in Figure 2. So, from the simulated scattering parameters, the compactness of the proposed structure is validated again.

PHOTO (COLOR): Figure 4. Normalized electric field distributions of three waveguides. (a) Amplitudes varying on observed Line A, (b) planar field amplitude distributions.

PHOTO (COLOR): Figure 5. Simulated scattering parameter curves of three waveguides.

To demonstrate the performance of the proposed waveguide, it was fabricated and measured by Agilent E8361A PNA microwave network analyzer. For comparison, Figure 6(a) gives the simulated and measured scattering parameters. Good agreement is achieved especially for the return loss, S11. When the frequency approaches the cut-off frequency, the insertion loss S21 drops below −40 dB quickly. It can be observed that the measured amplitude curve is below −3 dB after 7 GHz. This is due to the deformation in the measurement because the substrate is thin and soft. It happens when the SMA connectors are connected to the cables. But generally, the simulated and measured results are in good agreement with each other. Similarly, Figure 6(b,c) shows the photographs and scattering parameter results of the mentioned trapezoidal and rectangular groove structures, respectively. The insertion losses are also below −3 dB after 7 GHz and drop quickly near the cut-off frequencies.

PHOTO (COLOR): Figure 6. Photograph and measured results of the waveguides. (a) Proposed waveguide, (b) trapezoidal groove waveguide, (c) rectangular groove waveguide, (d) group delay of proposed structure.

Furthermore, to evaluate the transmission performance of the proposed spoof surface plasmonic waveguide, the group delay, a key factor for guided wave structure, is simulated and measured as shown in Figure 6(d). Within the passband, the maximum value is 2.8 ns, and the curve is flat below 8 GHz. It can satisfy the most signal requirements in integrated circuits. Therefore, the measured results validate that the proposed SSPW has good propagation performance.

In this paper, a new planar spoof surface plasmonic waveguide featuring compact size, good transmission, tight subwavelength field confinement is proposed and investigated. Compared with the conventional SSPP structures, the total size has been greatly reduced and good electromagnetic field enhancement is achieved in the subwavelength localization. To validate the transmission performance, a CPW-SSPW-CPW structure based on the PCB technology is designed and fabricated. Good agreement is achieved between the simulated and measured results. The proposed waveguide shows low insertion loss and flat group delay in an ultra-wideband from 2.4 to 10.3 GHz. Therefore, it is a very promising candidate to propagate the SSPP waves in the future microwave and terahertz integrated circuits.

No potential conflict of interest was reported by the authors.