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Abstract: We propose a new type of three-dimensional frequency selective structure (3D-FSS) in form of subwavelength staggered metallic frames, and demonstrate a new design concept of confining and guiding surface wave propagation through the transmission tunnels for spacial filters. Both qualitative analysis by current loops and full-wave simulations show that the strong coupling along metallic frames can enhance the performance of frequency response, such as a sharper roll-off, clean out-of-band rejection, as well as angle and polarization insensitivity. Moreover, different unit cell shapes are introduced to confirm the universality of the design concept. Finally, a 3D-FSS with staggered rectangular frames was realized by experiment.
© 2016 Optical Society of America
1. Introduction
Frequency selective surfaces (FSSs) have been investigated for filtering electromagnetic waves, particularly in the microwave and radio frequency bands [1–4] for decades, and have been recognized as the foundation of the modern field of metamaterials [5, 6]. It has wide applications in radar cross section (RCS), electromagnetic compatibility, terahertz sensing, telecommunications [7–10]. It is usually required that a FSS has the merits of wide bandpass, sharp roll-off (steep edge), and insensitive to polarizations and incident angles of an incoming electromagnetic wave in such applications. The conventional FSSs are consisting of single-layer or multi-layer of two-dimensional (2D) periodical planar structures, unfortunately, which are difficult to realize the mentioned characteristics at the same time. In recent years, a special type of FSS has been recognized as three-dimensional frequency selective structures (3D-FSS) [11–13], distinguished from conventional FSS, attracting growing attentions.
The filtering mechanisms of most 2D-FSS can be interpreted using equivalent LC circuit resonance, waveguide cutoff or multi-layer coupling. These mechanisms apply on existing 3D-FSS as well. However, instead of simple multi-layer structure, in 3D-FSS design, extra structures between planar 2D layers are introduced. Such 3D arrangement provides extra freedom for design procedure, therefore exhibits superior performance features, such as wide bandwidth, stable in-band filtering response, sharp cut-off and wide out-of-band rejection. The existing 3D-FSS designs are based on several methods, such as utilizing waveguide principles [14], equivalent circuit models [15] or effective medium concept [16, 17]. Respectively, the inter structures between layers work as confinement for waveguide walls, transmission lines for resonant path or left-hand material for desired dielectric constant. The inter structures can be periodic arrays of micro-strip line board, metallic plate pieces, via holes or resonance metallic lines.
In this work, we provide a new perspective on designing FSS and propose a new type of band-pass 3D-FSS with staggered subwavelength units. As a matter of fact, the essential function of a band-pass space filter is to guide wave propagating through, therefore the structure for such purpose does not have to be limited to waveguide or transmission lines as have been realized. We notice that there is coplanar waveguide band-pass filter, which has been constructed using planar surface structured waveguide [18, 19]. The surface waveguide filter can be realized by simple metallic frames. The parallel polarized wave is confined along the surface and transmitted properly according to designed passband, as shown in Fig. 1. Inspired by such planar surface waveguide filter [20], we build periodical rectangular frames as a planar surface filter, obtaining a 3D structure. Such new design concept overthrows the layered pattern in almost all existing FSS design.
We present in the following, a 3D-FSS fully constructed using metallic frames, which exhibits a rectangular shaped transmission coefficient curve with sharper roll-off and wider out-of-band rejection. The designed FSS is insensitive to incidence angle within 40 degrees for both TE and TM wave.
2. Design and analysis
To guide the surface wave propagation through, we periodically arranged staggered rectangular metallic frames as a 3D structure, as shown in Fig. 2(a). It is composed of staggered vertical and horizontal metallic frames. The unit cell is shaped like a brick wall frame, 90 degrees rotationally symmetric around the z axis, and self-repeated along x, y or z directions. The 3D structure is based on a planar staggered frame, which supports parallel polarized surface wave only within a certain band, with excellent band-pass frequency response, as has been confirmed by simulation, shown in Fig. 2(b).
Fig. 2 (a) The structure of proposed 3D-FSS with 3 × 3 unit cells (b) Frequency response when unit cell dimensions are a = 4.50 mm (0.43λ), b = 1.30 mm (0.13λ), w = 0.26 mm (0.03λ), t = 1.56 mm (0.15λ), Tx = 3.12mm (0.3λ), Ty = 3.12mm (0.3λ), Tz = 5.02mm (0.5λ). Here, the structure is filled with low loss dielectric media FR-4 (εr = 4.3) for impedance match.
In order to reveal the physical mechanism of the band-pass behavior, we observed the difference between wave transmission in the passband and stopband. The simulation is carried out by the commercial software CST microwave studio. The boundary conditions are periodical along x and y directions, while open in z direction. The simulation is based on FEM algorithm.
In the calculated case, there are 5 transmission poles fp1-fp5 within passband, matching maximum power transfer condition, which props up a wide passband from 12.1 to 15.4 GHz approximately. Closely looking at the induced current pattern formed at fp1 = 12.2 GHz and fp5 = 15.3GHz in Fig. 3, we can see current flow in the looped paths showing noticeable differences. Nevertheless, both formed loop paths bridge the power flow toward the z direction by strong coupling between staggered loops in sequence, which leads the power through the whole structure with high efficiency. Through a careful check of the loop path formed at the pole frequency fp1 and fp5, we found that the length of path p1 is 2(a + w/2) + 2b (11.86mm), which perfectly matches the wave length at λp1 in FR-4 (11.86mm), and the length of path p5 equals to 1.5(a + w/2) + 2b (9.55mm), which also accurately matches the wave length at λp5 in FR-4 (9.46mm), giving strong evidences of the coupling mechanism of the 3D-FSS in passband. On the other hand, none of such regular current loop can be excited for stopband outside of passband range. The wave is simply reflected around the boundary of the structure.
Fig. 3 Schematic of coupling process through the structure at transmission poles (a) 12.2GHz and (b) 15.3GHz
The designed 3D-FSS as seen in Fig. 2 is actually composed of two identical surface waveguides perpendicular to each other; it is naturally insensitive to the polarization of incidence. The transmission characters with incidence angles up to 60 degrees are shown in Fig. 4. There will be two effects on transmission coefficient with the increasing incident angles. One is that TE-incidence shifts to higher frequencies; another is that TM-incidence emerges bigger ripple within pass band. We can see that the passband is stable within 40 degrees. Besides these excellent features, the frequency response also shows steep edges, which are superior to most of reported frequency selective surfaces. Such rapid roll-off side band can only be found in the frequency filters in microwave circuit or in waveguides. It is hard to achieve such steep roll-off in typical band-pass FSS designs, in which the roll-off is usually improved by impedance matching through wave reflecting between separated layers of patched FSS, or by thick waveguide whose cut-off frequency is comparable with wavelength for aperture FSS. In this design, since the coupling established among staggered metallic frames is much stronger than that in existing multi-layer FSS designs, steep edges can be achieved with only 4 staggered periods as shown in Fig. 5. At the same time, the power is confined and transmitted along the surface of metallic frames, rather than trapped in waveguide cavity, breaking the limitation of waveguide cut-off frequencies and minimizing dimensions of unit cells.
Moreover, we realize that the coupling loops exhibited above are not necessarily limited to a rectangular shape; it can be established as long as metallic frames are staggered and guiding surface wave propagation. We tried two other different designs with rhombus and hexagon frames. Essentially they are the same structures which can confine and guide wave propagations around the surface of metallic frames. Their characteristics exhibit only slight differences as shown in Fig. 6, proving great flexibility in such designs.
3. Experiments
A prototype of the designed 3D-FSS is fabricated and measured to verify our design. Since it is not straight forward if fabricate through traditional manufacturing processes, 3D printing technology is employed to build the unusual structure by photo polymerization using UV light cured resin. We firstly printed a resin frame in designed shape, and then coated it with conductive silver paint. The fabricated structure is shown in Fig. 7 (a). The total size of the structure in Fig. 7 (a) is 141 × 141 × 48 mm3, and the dimensions of unit cell are a = 10 mm, b = 6 mm, w = 1 mm, which is different with simulated dimensions because the limitation of minimum size of manufacturing. The 3D-FSS was measured by the free space method using a pair of horn antennas in the anechoic chamber [21]. The frequency response of this model is not optimized because of our fabrication constraints. There are no dielectric media fulfilled in the frames for better free space impedance match. And the surface roughness is rather large, up to 0.1mm due to the limitation of 3D printing technique. Nevertheless, the measurement results in Fig. 7 (b) show that a passband with rapid roll-off is achieved for both TE and TM wave, as expected. The curves in Fig. 7 are normalized for better comparison, however the measured data is about 10dB less than it should be, resulting from the roughness of the surface and imperfections in the experiments. In any case, the experiment’s results are strong validation of this new type of 3D-FSS design.
Fig. 7 (a) The prototype of the fabricated 3D-FSS (b) Measured results of fabricated FSS varying with incident angles.
4. Conclusion
In this paper, we proposed a new type of band-pass frequency selective structure in 3D forms, as well as a new design concept. The designed 3D-FSSs are distinguished by steep edge, insensitivity to angles, polarizations and clean out-of-band rejection. The essential design idea is to confine and guide wave propagation through metallic frames, acting as surface waveguide filter. The physical principle of the presented 3D-FSS is clearly interpreted with the description of current loop path, with which we can accurately identify the passband. In this design, surface waveguides transmit waves by restraining power along metallic surface rather than by trapping energy in cavity, which breaks the limitation of cut-off frequency and minimizes dimensions of unit cells. Finally, the strong couple mechanism produces faster roll-off than any multi-layer FSS designs. Such 3D-FSSs also have the merits of flexible shape, lightweight, free-standing and facilitating integrated design of the reticular structure into all kinds of radomes. In this work, we converted the dimension in circuit transmission lines filter into 3D spatial filter i.e. FSS in form of folded surface waveguides, and verified the concept with various differently shaped metallic frames, opening a new perspective in FSS design.
Acknowledgments
This work is supported by the National Basic Research Program of China (973 Program) under Grant Nos. 2012CB315601.
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