An Ultra-Thin and Compact Band-Pass Filter Based on Spoof Surface Plasmon Polaritons

In this work, we report an ultra-thin and compact SSPPs-based waveguide band-pass filter with metals etched on the top surface of substrate, and the side and bottom surfaces of substrate also are covered with metals. The size of this filter is <inline-formula> <tex-math notation="LaTeX">$1.07\lambda _{0}\times 0.32\lambda _{0}\times 0.02\lambda _{0}$ </tex-math></inline-formula> (where <inline-formula> <tex-math notation="LaTeX">$\lambda _{0}$ </tex-math></inline-formula> is the wavelength at center frequency). This proposed filter can inherit the merits of rectangular waveguide and SSPPs structure, and its lower cut-off frequency can be tuned by the width of rectangular waveguide, while the upper cut-off frequency can be tuned by the length of complementary comb-like structure. Gradient groove depths are also used to form a smooth transition from rectangular waveguide to SSPPs structure, realizing a good momentum match. The dispersion curves and electric field distributions have been thoroughly investigated to reveal the SSPP-based waveguide filter mechanism. A prototype is fabricated and measured. Both simulations and measurements validate that the band-pass filter proposed in this work has high-efficiency and low-loss transmission properties.


I. INTRODUCTION
At optical frequencies, metals behave as plasmons and have negative permitivities, while dielectric media have positive permittivities, so surface plasmon polaritons (SPPs) can be propagated in the interface between metal and dielectric media and decay exponentially in the direction vertical to the interface [1]- [4]. Because the interaction between Electromagnetic (EM) waves and plasmas is strong, the SPPs act as surface waves that are tightly confined near the interface and propagate parallel to the interface [4]- [8]. When frequencies are reduced down to terahertz (THz) and microwave frequencies, the metals behave as perfectly electric conductors (PECs), and smooth interfaces without period surface variations cannot support the propagation of SPPs anymore [5]- [10]. In the past several years, Spoof SPPs have been proposed to expand the researches of SPPs to lower frequencies. By decorating arrays of slits, holes, and blocks on the metallic surfaces to form artificial structured surfaces The associate editor coordinating the review of this manuscript and approving it for publication was Wei E.I. Sha . [5], [7], [9]- [12], some exotic SPPs-like characteristics can be realized at microwave frequencies, such as near field confinement and highly subwavelength localization. More importantly, the dispersion properties of SSPPs can be tailored by adjusting its geometrical parameters [3]- [6], making it attractive in the practical applications.
In 2013, T. J. Cui and his students proved that an ultrathin corrugated metallic strip can guide the conformal SPP, indicating that the spoof SPP wave is able to propagate along arbitrarily curved surfaces across long distances with very low absorption and radiation loss [13]. Since then, researchers have proposed a series of periodic structures based on corrugated metallic wires to support the propagation of SSPPs [4], [6], [8], [10]- [12]. Especially in recent years, many kinds of functional devices based on corrugated SSPPs structures have been proposed. For example, various plasmonic transmission lines (TLs) have been developed [2], [15], [16], and their characteristics also have been thoroughly analyzed by others, these TLs based on SSPPs structures can be used to enhance the EM field confinement, reduce the crosstalk and improve the transmission efficiency.
Some microwave filters based on the merits of SSPPs structures have been proposed, but among them the majorities are the low-pass filters [4], [8]- [12], [23]- [26]. Just a few works related to the SSPPs band-pass filters have been proposed. For example, [25] presents a suspended strip-line filter based on SSPPs and realizes miniaturized design, but it is a three-dimensional structure. [31] presents a band-pass filter by placing SSPPs sections beside a main SSPPs TL and introducing resonances, leading to transmission zeros to the main SSPPs TL, but this filter also is three-dimensional and its loss is a little high in the operation band. Moreover, most of the reported filters related with SSPPs TLs are based on single conductor transmission lines [4], [8], [10]- [12], [23]- [26], which etches metal on just one single surface of substrate, making it complicated to design or inconvenient to connect with the traditional two-conductor transmission lines.
In this work, we report a kind of simple ultra-thin and compact SSPPs-based waveguide filter with metals etched on the top surface of substrate, and the side and bottom surfaces of substrate also are covered with metals, which not only has high-efficiency and low-loss features but also realizes a controllable band-pass performance. Specifically, the cross section of this proposed band-pass filter shows a rectangular waveguide with a dielectric substrate inside and the sealed waveguide can confine most EM energies within the cavity. Under the fundamental TE 10 mode, the waveguide behaves as a high-pass filter and the lower cut-off frequency of this proposed band-pass filter depends on the parameters of the cross section. By comparison, controlling the upper cut-off frequency of SSPPs-based band-pass filter is relatively easy, so we can change the asymptotic frequency of SSPPs structure to control the upper cut-off frequency. In order to make a better understanding of the physical mechanisms of the proposed filter, the dispersion relations and electric field distributions are carefully analyzed, and the characteristics of our proposed SSPPs-based band-pass filter are verified through both numerical simulations and experimental measurements. The proposed filter has the following several merits: (1) Compact and miniaturized size (1.07λ 0 × 0.32λ 0 × 0.02λ 0 , where λ 0 is the wavelength at center frequency); (2) Working band is controllable by varying the geometrical parameters; (3) Covering the bottom surface of substrate with metals to make it convenient in the traditionally integrated circuits design; (4) High-efficiency and low-loss properties.

II. DESIGN AND ANALYSIS OF UNIT CELL
The unit cell proposed in this work is illustrated in Fig. 1 (a). This proposed unit cell has three layers: the top layer is a complementary symmetric comb-like metallic structures, in which the periodicity, slot width, and gap width between two comb-like structures are marked as p, a, and w l , and the length of comb-like structure is denoted as h, the middle layer is a substrate, and the bottom layer is a metallic surface. The dielectric substrate is chosen as a commercial printed circuit board (PCB) with relative permittivity ε r = 4.3 and the loss tangent tanδ = 0.001, and its thickness t is 1mm, while the metal is chosen as copper with a thickness of 0.035mm. The dispersion relations of this proposed plasmonic structure can be tuned by adjusting the geometrical parameter h. To explore the propagation characteristics of SSPPs structure, we study the dispersion relations using the Eigen-mode solver of the commercial software, CST Microwave Studio. As displayed in Fig. 1(b), the boundary conditions of external area are set to periodic boundaries in the propagation direction of EM wave (z-direction), and in x-and y-directions the boundaries are set as perfectly electric conductors (PECs). To begin with, as illustrated in Fig. 1(b), the proposed structure acts as a rectangular waveguide because the boundaries in x-direction are set as PECs, and w and t represent the width and height of rectangular waveguide, respectively. For TE 10 mode, the cut-off frequency can be calculated as: In the discussion of dispersion relations, we set w as 15.5mm, and then the f c is 4.667GHz. For this work, because of the interaction between both sides of complementary symmetric comb-like metallic structure, there are even-and odd-mode SSPPs propagating along this symmetric SSPPs structure, and their electric field patterns in the cross-section surfaces are displayed in Fig. 1(c). We can conclude from Fig. 1(c) that electric field distributions of odd mode are anti-symmetric, while that of the even mode are symmetric. In order to guarantee that the EM waves propagated inside the rectangular cavity is TE 10 mode, even-mode SSPPs have to be excited. The even-mode dispersion curves of this proposed SSPPs structure with respect to the parameter h are shown in Fig. 1(d). We notice that covering the bottom surface of substrate with metals does not deteriorate so much in maintaining the SSPPs properties, so we can still regard this structure as a plasmonic one, while the plasmonic structures reported in other works just etch metallic structures on a single surface of substrate. We can observe that the dispersion curves deviate obviously from the light and finally approaches the asymptotic frequencies, and the SSPPs waves can be tightly confined by the structured surface and propagate with very low loss. It can be concluded that the larger h is, the lower asymptotic frequency is.
The dispersion curves also have lower cut-off frequencies, and all the lower cut-off frequencies are the same under the same value of parameter w. The reason of the appearance of lower cut-off frequencies is that the proposed plasmonic structure acts as a rectangular waveguide, and the simulated lower cut-off frequency is 4.666GHz under the w of 15.5mm, which agrees well with the calculated one of 4.667GHz. When the value of h is set as 6mm, we draw the dispersion relations with respect to the parameter w, as illustrated in Fig. 1(e). We can conclude that the lower cut-off frequency can be tuned by the value of w, and the larger w is, the lower the cut-off frequency is, while the asymptotic frequencies of the proposed complementary comb-like structure remain stable with different values of w. According to the analysis mentioned previously, we can conclude that the complementary comb-like structure is of band-pass characteristic, and the lower cut-off frequency can be adjusted by the parameter of w, while the upper cut-off frequency can be tuned by the parameter of h.

III. DESIGN OF BAND-PASS FILTER
The configuration of the proposed SSPP-based waveguide band-pass filter is sketched in Fig. 2(a). Particularly, in order to satisfy the PEC boundary set in the x-direction in Fig. 1(b), the majority parts of the side surfaces of this band-pass filter are covered with metals. The microstrip width w s is chosen as 2.1mm to meet the 50 impedance of Subminiature Version A (SMA) connector. This structure has three parts. The first part is a transition section from microstrip line to rectangular waveguide, and the second part is the transition section from rectangular waveguide to SSPPs structure. The third part is used to propagate SSPPs waves. It can be observed from Fig. 1(d) that the deviation from the lightline becomes stronger with increase of parameter h, and the asymptotic frequency becomes lower. If we gradually increase the h from 0mm to h, the EM waves will be gradually confined near to the SSPPs structure, thus there will be a good momentum match between the rectangular waveguide and SSPPs structure.
In order to verify the relationship between the lower cutoff frequency of waveguide filter and w, when the h is fixed as 6mm, the simulated transmission coefficients of S21 with different w values are demonstrated. In Fig. 2(c), it is clearly observed that the cut-off frequency shifts toward lower value with the increase of w, while the upper cut-off frequencies remain stable under different w values, thus the lower cut-off frequency can be adjusted by the modification of width of rectangular waveguide, which is accordance with the theoretical analysis mentioned above. However, we note that the simulated 3-dB lower cut-off frequency under w of 15.5mm is around 5.1GHz, while the calculated one using Eq. (1) is 4.67GHz. To find out the reason which causes this deterioration, we also simulated the transmission properties of rectangular waveguide which removes the comb-like structure form the proposed waveguide filter, and its results are  Fig. 3(b). We can observe that 3-dB cut-off frequency of rectangular waveguide under w of 15.5mm is around 4.76GHz, which is more closely to the theoretical one of 4.67GHz. From the above discussion, we can conclude that adding complementary comb-like structure to the waveguide can lead shift to the lower cut-off frequency. But anyway, we can design a certain lower cut-off frequency of waveguide filter by optimizing the parameter w, as shown in Fig. 2(c).

displayed in
In order to verify the relationship between the upper cut-off frequency of waveguide filter and h, when the w is fixed as 15.5mm, the simulated transmission coefficients of S21 with different h values are displayed. Fig. 2(d) shows that the upper cut-off frequency can be tuned by different values of the length of comb-like structure, and the results are in accordance with the asymptotic frequencies displayed in Fig. 1(d). For example, the asymptotic frequency of SSPPs structure under h of 6mm is 7.47GHz, while the upper 3-dB cut-off frequency of proposed filter is 7.48GHz, and they agree well with each other.
In our design, the value of w and h are chosen as 15.5mm and 6mm, respectively. Based on the analysis above, the lower and upper 3-dB cut-off frequencies should be 5.1GHz and 7.48GHz, respectively. In order to realize a good performance of reflection coefficients (S11) of the proposed filter, all the parameters are optimized and the detailed dimensions are shown in Fig. 2(a) as well. This proposed filter is compact and miniaturized (1.07λ 0 ×0.32λ 0 ×0.02λ 0 , where λ 0 is the wavelength at center frequency). To verify the functionality of the proposed configuration, the sample of the proposed filter is fabricated, as displayed in Fig. 3(d). The simulated and measured transmission and reflection coefficients are displayed in Fig. 3(c) for comparison. We find that the simulated and measured results are in good agreement with each other. The 3-dB transmission coefficient (S21) bandwidth of simulation is from 5.1GHz to 7.48GHz, while that of measurement is from 5.03GHz to 7.22GHz, and the highest S21 of simulation is up to -0.25dB, while that of measurement is up to -0.68dB. The reflection coefficients (S11) of both simulation and measurement are all less than -10dB. Additionally, it should be noted that compared with the simulated results, the measured ones show a little higher in-band insertion loss and poorer selectivity at the upper band and higher S11 at the whole operation band, which is caused by the parasitic properties of the SMA connector and substrate, the soldering imperfection, and the measurement imperfection. As expected, both simulated and measured results prove that the proposed filtering method for SSPPs TL is feasible.
In order to further show the excellent field confinement and good propagation characteristic of the proposed SSPP-based waveguide filter, the simulated magnitudes of energy flows on cross section of y-z plane when x = 0 and the simulated E z -field patterns at 4.5, 5.5, 6, 6.5, 7 and 8GHz are also  simulated and displayed in Fig. 2(b) and Fig. 4. We can observe from Fig. 2(b) that most of the EM energy is highly localized within the rectangular waveguide cavity and a small region above the proposed SSPPs-based waveguide filter. From Fig. 4, we can conclude that the even-mode SSPPs waves can be propagated through the SSPPs structure efficiently at 5.5, 6, 6.5, and 7GHz, which are located in the passband of the proposed filter. The SSPPs waves cannot be propagated through the rectangular waveguide part at 4.5GHz, while the SSPPs waves cannot be propagated through the SSPPs part, which also can verify that the lower and upper cut-off frequencies are adjusted by the parameters of w and h, respectively. From those discussions, we can conclude that the proposed structure can support the propagation of SSPPs waves on its surface, exhibiting potential applications in SSPPs devices.

IV. CONCLUSION
In conclusion, an ultra-thin and compact SSPPs waveguide filter is proposed in this work, which has a different working principle with its former counterparts. The rectangular waveguide acts as a high-pass filter, while the SSPPs TL acts as a low-pass filter. We combined the merits of these two structures into an integration to design a pass-band filter. The lower cut-off frequency can be tuned by the width of rectangular waveguide, while the upper cut-off frequency can be tuned by the length of comb-like structure. Gradient groove depths are used to form a smooth transition from rectangular waveguide to SSPPs structure, thus realizing a good momentum match. The dispersion curves and electric field distributions have been thoroughly investigated to reveal the SSPP-based waveguide filter mechanism. Finally, based on the analysis, a prototype is fabricated and measured. Both simulated and measured results validate the proposed design concept. This work has a very promising future in the development of SSPPs functional devices and circuits in the THz and microwave frequencies.
HUANHUAN YANG (Member, IEEE) received the B.S., M.S., and Ph.D. degrees from Air Force Engineering University (AFEU), Xi'an, China, in 2010, 2012, and 2016, respectively. He was a Joint-Supervision Ph.D. Student with AFEU and Tsinghua University. He is currently a Lecturer with AFEU. His research interests include reconfigurable antenna, reflectarray, metasurface, and RCS reduction technique.
SIJIA LI received the B.Eng. degree in electronics and information engineering from Guangxi University, Nanning, China, in 2009, and the M. Eng. degree in information and telecommunication engineering from Air Force Engineering University, Xi'an, China, in 2011, where he is currently pursuing the Ph.D. degree in electromagnetic field and microwave technology with the Information and Navigation Institute. He has authored or coauthored more than 40 scientific papers in major journals and international conferences. His research interest includes the broadband perfect metamaterial absorber and its application for RCS reduction of antennas.
TONG LI received the B.S. and Ph.D. degrees in electronic and information engineering from Xidian University, Xi'an, China, in 2010 and 2015, respectively. She is currently a Lecturer with Air Force Engineering University. Her current research interests include ultra-wideband communication devices, reconfigurable antennas, and metasurface.