Subwavelength Metawaveguide Filters and Metaports

This paper proposes an alternative technique for the design of miniaturized waveguide filters based on locally resonant metamaterials (LRMs). We implement ultrasmall metamaterial filters (metafilters) by exploiting a subwavelength (sub-λ) guiding mechanism in evanescent hollow waveguides, which are loaded by small resonators. In particular, we use composite pin-pipe waveguides (CPPWs) built from a hollow metallic pipe loaded by a set of resonant pins, which are spaced by deep-subwavelength distances. We demonstrate that, in such structures, multiple resonant scattering nucleates a sub-λ mode with a customizable bandwidth below the induced hybridization band gap (HBG) of the LRM. The sub-λ guided mode and the HBG, respectively, induce pass and rejection bands in a finite-length CPPW, creating a filter, the main properties of which are largely decoupled from the specific arrangement of the resonant inclusions. To guarantee compatibility with existing technologies, we propose a subwavelength method to match the small CPPW filters to standard waveguide interfaces, which we call a metaport. Finally, we build and test a family of low- and high-order ultracompact aluminum CPPW filters in the X and $K_{u}$ bands (10–18 GHz). Our measurements demonstrate the customizability of the bandwidth and the robustness of the passband against geometrical scaling. The three-dimensional printed prototypes, which are 1 order of magnitude smaller and lighter than traditional filters and are also compatible with standard waveguide interfaces, may find applications in future satellite systems and 5G infrastructures.

Figure 1

Concept of LRMW. (a) Cluster of local resonators in free space induce strong multiple scattering near their resonance frequency, f_r. (b) Single-mode host waveguide with characteristic impedance Z₀, propagation constant k, and cutoff frequency f_c. (c) LRMW created by loading an ensemble of subwavelength resonators inside a host waveguide. (d) Simpler version of LRMW using a one-dimensional (1D) periodic array of resonance inclusions, with a subwavelength periodicity of a. Schematic of the band diagrams of 1D LRMWs in two different regimes, where dashed lines show the host mode (HM) and lower and upper polaritons (LP and UP, respectively) are indicated by solid lines: (e) host waveguide is above cutoff (f_r > f_c) and (f) host waveguide is evanescent (f_r < f_c). In the second case, two different cutoff frequencies are considered, where f_c1 > f_c2, leading to different bandwidths for sub-λ modes (LP) BW₂ < BW₁.

Figure 2

Implementation of a waveguide-based LRMW. (a) Unit cell of a 1D CPPW structure is made by one ultrathin pin, with height h_r, inserted in a rectangular waveguide of length a ≪ λ with a width of W. Pin and bottom wall, made of a perfect electrical conductor (PEC), are in contact, and PBCs are along x. (b) Corresponding band diagram for W = 19 mm (propagative host) and W = 7 mm (evanescent host). (c) Electric field distributions of the lower and upper (LP and HP) modes for the evanescent regime (W = 7 mm). (d) CPPW waveguide filter is formed using six unit cells directly connected to standard WR75 waveguide adapters (19 mm wide), on both sides. (e) Transmission spectra of the filter for two different regimes. Shaded blue region shows the HBG. (f) Group velocity of subwavelength modes below the stop band.

Figure 3

Variation of the guided mode dispersion band for various values of (a) width of the pipe, W; (b) height of the pins, h_r; (c) period, a; and (d) radius of the pins, r. Shaded region shows the HBG. For each panel, values of fixed parameters are indicated in parentheses.

Figure 4

Bandwidth tuneability. Transmission spectra of (a) single-pin CPPW filter for various values of W and a, and (b) sixth-order CPPW filter for various values of W, with sharp selectivity at f_o.

Figure 5

CPPW filters with standard waveguide ports (WR75), considering h_r = 5 mm, a = 2.5 mm. (a) One row of pins, which are randomly positioned around the y axis with maximum deviation Δy = ±2 mm, Δx = ±1 mm from a periodic 1D array; (b) two-dimensional (2D) array of periodic pins, comprising two rows of pins with distances a_x = 2.5 mm; (c) two rows of pins, which are arranged with a maximum random deviation of Δy = ±2 mm, Δx = ±1 mm; (d) squeezed CPPW, for which all geometrical parameters are scaled down by 80% in the guiding direction (y axis), making the device shorter and the pin cross section oval. (e) Scattering transmission spectra (S₂₁) for all these various pin arrangements.

Figure 6

Short-length WR75 waveguide, loaded by a resonant pin with size h_p, where h_p < h_r. Transmission spectrum, S₂₁, for various values of h_p.

Figure 7

Designing metaports. Transmission spectra for structures built by inserting 2 × 2 arrays of pins with height h_p = 3.5 mm (a) inside and near one standard port WR75 (A) and in the proximity of the connection of WR75 to an evanescent waveguide with W = 7 mm (B); (b) adjacent to the connection border of WR75 and a one-pin CPPW filter (C).

Figure 8

Efficiency of the designed metaport in a realistic filter. (a) Sixth-order CPPW filter with h_r = 5.15 mm, connected to metaports at both sides with h_p = 3.5 mm, (b) field distribution of the CPPW filter and metaports and a CPPW filter at 12.5 GHz. Effect of a metaport on (c) S₁₁ and (d) S₂₁ of the CPPW filter.

Figure 9

(a) Top and (b) three-dimensional (3D) views of the compact WR75 filter with two pins; (c) measured and simulation results for S₂₁ and S₁₁.

Figure 10

(a) Top and (b) 3D views of second-order CPPW filter with thicker walls, including metaports (h_p = 3.5 mm). (c) Transmission spectra of second-order filters, for W = 5 and 7 mm, extracted from simulation and experiments. (d) Measured S₂₁, which shows an insertion loss of 0.5 dB.

Figure 11

(a) Fabricated sixth-order CPPW filters with different widths W = 3, 5, and 7.4 mm, comprising metamaterial ports and improved matching. (b) Transmission spectra of CPPW filters (S₂₁) extracted from simulation and experiments, indicating the fractional BW in percent.

Figure 12

(a) Manufactured standard CPPW filter and its scaled-down version (80% along y direction), considering W = 7.4 mm. (b) Scattering spectra (S₂₁ and S₁₁) for the CPPW filter and its scaled-down version.

Figure 13

Fabricated aluminum CPPW filters, with and without silver plating, and their scattering spectra, highlighting the reduction of insertion losses after silver plating.

Figure 14

Distributed model of a CPPW.

Figure 15

(a) Decomposition of a CPPW in the evanescent regime into direct-coupled pins and an evanescent pipe. (b) Lumped-circuit model of coupled resonant pins, where $m_{ij}=j\omega C_{ij}+(1/j\omega L_{ij})$. (c) Distributed element model of an evanescent pipe. (d) General distributed model of a CPPW.

Figure 16

Variation of evanescent coupling versus pin separation distance, a, and width of the pipe, W.

Figure 17

(a) Unit cell of a CPPW, composed of a thin pin (r ≪ W and r ≪ a), W = 8 mm, h_r = 5 mm, and the electric field distribution around the pin. (b) Band diagram of the CPPW for various values of h_g, which shows the HBG for all cases and a converged sub-λ mode for h_g > 3 mm. (c) Coaxial cavity with a = W = 8 mm, h_r = 5 mm, and 2r = W/2. (d) Sensitivity of the guided-mode dispersion to the top gap size in an infinite array of coaxial unit cells. (e) Sixth-order combline filter with h_r = 5 mm and 2r = W/2. (f) Transmission spectra of the combline filter with a total length of 6a = 6W for various values of W. Very different from CPPWs, the frequency band of combline filters shifts significantly when h_g or W is varied, providing evidence of a very different guiding mechanism.

Figure 18

Different host waveguides. Example of sixth-order CPPW filter with coaxial ports, based on (a) rectangular metallic pipe, compatible with planar structures; (b) cylindrical metallic pipe with a diameter of 10 mm; (c) band-gap material walls, where the walls have rods with length h_w = 7 mm. (d) Transmission scattering spectra (S₂₁) of all these different CPPWs.

Figure 19

Different resonators. Alternative LRMWs compatible with WR75 standard waveguide using (a) unit cell of parallel uniaxial 1D periodic helical wires with two turns, a height of 4.2 mm, and diameter of 1.5 mm; (b) typical field distribution in the passband; (c) transmission spectra for two different values of pipe width. (d)–(f) Same as (a)–(c) but for 1D periodic parallel rings (torus), with diameters of 5 mm.