In recent years, artificially prepared metamaterial devices have demonstrated unique electromagnetic properties that originate from the coupled interaction between electromagnetic waves and designed periodic arrays of sub-wavelength air holes.^[1–5] Of these designed metamaterial structures, self-symmetric metal/dielectric/metal composite multilayer nanostructures have been studied most widely, both numerically and experimentally.^[6–10] This is because this configuration offers enormous modulation flexibility over the effective medium parameters (including the effective permeability, effective permittivity and effective impedance). In particular, composite multilayer fishnet nanostructures are experimentally demonstrated at optical and infrared wavelengths through patterning nano-scale air holes in composite multilayer stacks, which are subsequently deposited on different types of substrates by reactive ion etching (RIE), focused ion beam (FIB) etching, or metal lift-off techniques.^[11–13] Many experiments have been carried out based on substrate-mounted hollow fishnet composite multilayer nanostructures with non-ideal tapered sidewalls. Measured results proved the existence of the asymmetric reflections, which must be measured from the opposing interfaces of the designed device because of the occurrence of nonzero magneto-electric coupling.^[14] Unfortunately, the supporting substrate and the sidewall angle induced in the fabrication process^[15–19] may result in the undesirable broken symmetry in the metamaterial device. This broken symmetry damages the effective medium model because the electric and magnetic polarizations of the model are characterized based on the electric and magnetic field components. It is therefore necessary to develop a metamaterial device that does not require substrate supporting. Moreover, the unique optical properties of the designed metamaterial device are dependent on the specific structural design, which is aligned using the periodic lattice.^[20] The optical properties of the designed structure are related to the effective permeability and permittivity, which in turn are strongly dependent on the resonant frequency. This optically dispersive behavior always results in the distortion of the electromagnetic signal and narrow operable bandwidth,^[21–24] which naturally restricts the widespread applications of the designed metamaterial device in practice. Therefore, a new nanostructure with non-substrate supporting should be developed to tailor the dispersive behavior of the structure and obtain both low loss and broad bandwidth characteristics, which still satisfy the strict constraints of the nanofabrication approach.

In this paper, we present the numerical and experimental verification of an optically functional metamaterial filter in a three-layer metal–dielectric free-standing configuration that is optimized to produce dual-band properties in a 1 THz–30 THz wave spectral window, and highly reflective behavior outside these bands. This non-hollow fishnet structure shapes the resonant dispersion behaviors of the effective permeability and effective permittivity to satisfy the dual- and flat-band transmission demands. These effective parameters are extracted from the measured transmission and reveal magnetic–electric coupling in these plasmonic resonant bands. The measured transmission of the proposed free-standing structure agrees well with the simulated result, which confirms that this non-hollow fishnet structure can be produced for dual-band metamaterial filter applications. In addition, these resonant bands can be modulated individually. This useful structural design overcomes the limitations of narrow bandwidths, which can thus distinctly increase the available possibilities for practical optical device manufacture.

The proposed structure is composed of a metal/dielectric stack with a compound square air hole array that perforates all silver layers as shown in Fig. 1. The thickness values of the silver, SU-8, and polyimide layers are h₁ = 0.04 μm, h₂ = 0.18 μm, and h₃ = 0.18 μm, respectively, which leads to a total metamaterial thickness of 0.44 μm. The periodicity of the proposed structure is P = 12 μm, and the widths of the main air hole and the sub-holes are w₁ = 4.5 μm and w₂ = 1 μm, respectively. The optical properties of the proposed structure are calculated by using a full-wave electro–magnetic solver (Ansoft 13.0). In the simulations, Floquet ports are used at the bottom and top boundaries of the unit cell to simulate a normally-incident electromagnetic wave, and the periodic boundary conditions are used for the four sidewalls.

Fig. 1.

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	Fig. 1. (a) Top view on the xoy plane. (b) Side view on the xoz plane. The yellow part is the silver layer, the gray part is the polyimide layer, the blue part is the SU-8 layer. (c) The measured and simulated transmission spectra, and the inset shows a photograph of the samples.

To validate the proposed design, the dual-band metamaterial filter is fabricated by the following procedure: a 0.04-μm-thick bottom silver layer is evaporated on a thermally oxidized Si handle substrate at a rate of 1.8 Å·s⁻¹ by electron beam evaporation (ZZL-U400H). A 0.18-μm-thick polyimide layer is deposited on the bottom silver layer by spin-coating a polyimide precursor at a speed of 1950 rpm for 28 s (HD Microsystem PI2556). The polyimide layer is imidized by heating at 135 °C for 38 min and then at 220 °C for 70 min by using a nitrogen-purged convection oven. A 0.18-μm-thick SU-8 layer is then spun on the polyimide layer (MSC-400Bz-6N). The SU-8 layer is baked at 100 °C for 75 s (C-MAG HP10). Another 0.04-μm-thick top silver layer is evaporated on the intermediate dielectric layer. The fabricated metal/dielectric structure is subsequently removed from the substrate by using a buffered oxide etchant to etch the underlying thermal oxide away. The designed main and nano-notch air hole array is patterned on the top and bottom silver layers using a focused ion beam system^[25] (Helios nanolab 600). The measured transmission of the designed structure is achieved (Bruker Optics Equinox 55 Fourier transform infrared spectrometer), and the optical microscopy image of the free-standing dual-band metamaterial filter is obtained (Leica DM4M) as shown in Fig. 1(c). The measured results indicate that two resonant transmission bands are obtained, which are simply named the “first” and “second” bands, as shown in Fig. 1(c).

The optical properties of the proposed structure can be understood through examining the effective medium parameters as shown in Fig. 2. These parameters can offer an insight into how the magnetic and electric responses of the proposed structure vary with frequency, which are nonlocal in nature.^[26] The proposed structure dispersion behavior can be tailored through adjusting the permeability profile in the Drude mode^[27] with a plasma frequency f_e. The effective permeability μ_eff (f) and permittivity ε_eff (f) could be expressed in the following form:

Fig. 2.

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	Fig. 2. Simulated (a) real and (b) imaginary parts of effective medium parameters (permittivity, permeability, and impedance) versus frequency.

To investigate the electromagnetic responses of these transmission bands, the current distributions on the top and bottom layers of the designed structure are calculated, and the results are shown in Fig. 3. The resonant electromagnetic response, which results in the dual-band filtering properties, can be understood through an analysis of the calculated volumetric current distributions. For the fundamental magnetic resonance mode of the first band, parallel current flows can be observed on the top and bottom silver layer as shown in Figs. 3(a) and 3(b).

Fig. 3.

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	Fig. 3. Volumetric current density distributions of the proposed structure at the two magnetic resonance modes. (a) The top silver layer at 9 THz. (b) The bottom silver layer at 9 THz. (c) The top silver layer at 18 THz. (d) The bottom silver layer at 18 THz.

Clearly, the proposed structure shows nearly equal calculated current distributions on the bottom and top silver layers in the first band, and this indicates that neither magnetic nor electric dipole moments are excited by the electric/magnetic fields. The calculated current distributions for the first magnetic resonant mode generate charge accumulation, directional flow, and depletion in an elongated region (dotted line areas) along the edges of the main air hole area of the unit cell as shown in Figs. 3(a) and 3(b). For the second band, anti-parallel current flows can be observed as shown in Figs. 3(c) and 3(d). These anti-parallel current flows are mainly distributed in the square-like regions (dotted line areas) along the x direction between the sub-holes, with a phase difference of 180°. This produces square-like charge accumulation, directional flow, and depletion regions between the sub-holes with different current phases, which indicate that the magnetic resonant mode of the second band can mainly be attributed to these anti-parallel currents.^[31]

To assess the effects of the structural parameters on the transmission bands, three set of experiments are carried out: the first set is for varying air hole width (w₁) with sub-hole width (w₂) fixed, the second set is for varying w₂ with w₁ fixed, and the third set is for varying w₁ and w₂ simultaneously.

In the proposed structure, the structural parameters w₁ and w₂ can naturally affect the optical properties. To obtain an optimized dual-band structural design, the effects of these factors are experimentally investigated. In the first set of experiments as shown in Fig. 4, w₁ is increased from 4.5 μm to 6.5 μm while w₂ remains constant. The first transmission band displays a shift towards higher frequency. It is obvious that an increase in w₁ results in the bandwidth initially 4.0 THz (w₁ = 4.5 μm) increasing, reaching a maximum bandwidth 6.3 THz (w₁ = 6.0 μm), and then decreasing to 3.9 THz (w₁ = 6.5 μm) as shown in Fig. 4. Additionally, the corresponding simulation results are shown in Fig. 5, which also confirms the effect of the w₁ on the first transmission band. However, the bandwidth and the resonant frequency of the second band remain almost unchanged with w₁ increasing. Based on previous discussion, this shows that an effective impedance matching condition is achieved in the first band. When w₁ is increased from w₁ = 4.5 μm to w₁ = 5.5 μm, the impedance matching condition between the designed structure and the free air is improved. When w₁ = 6.0 μm, the perfect impedance matching condition is obtained^[32] in the first transmission band, which leads to the maximum bandwidth as indicated in Figs. 4 and 5. Therefore, the perfect impedance matching condition will be damaged for w₁ > 6.0 μm, which results in the reduction of the bandwidth of the first band shown in Figs. 4 and 5. These measured and simulated results in Figs. 4 and 5 indicate that there is an optimum w₁ = 6.0 μm to obtain the maximum bandwidth of the first transmission band. These measured results indicate that the effective impedance matching condition is possibly determined by the side width w₁ of the main air hole in the first band. Therefore, an increase in w₁ would result in a higher impedance matching between the air interface and the top silver layer, which then leads to the reflection reducing and the bandwidth expanding^[32] as shown in Fig. 4.

Fig. 4.

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	Fig. 4. Measured transmission spectra of the designed structure for different values of w1 (w2 = 1 μm).

Fig. 5.

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	Fig. 5. Simulated transmission spectra of the designed structure for different values of w1 (w2 = 1 μm).

The second set of experiments is carried out in a similar manner as shown in Fig. 6. The side width w₂ of the sub-hole is increased from w₂ = 1.0 μm to w₂ = 3.0 μm while w₁ remains constant. The second band displays an obvious shift towards lower frequency. It is obvious that the bandwidth of the second band is increased from 3.0 THz (w₂ = 1.0 μm) to 4.8 THz (w₂ = 2.0 μm), then reduced to 2.7 THz (w₂ = 3.0 μm). It is because the impedance matching condition is improved in the second transmission band with w₂ increasing. When w₂ is increased from w₂ = 1.0 μm to w₂ = 2.0 μm, the perfect impedance matching condition is obtained^[32] in the second transmission band, which results in the maximum bandwidth in Figs. 6 and 7. This is similar to the results in Figs. 4 and 5. This occurs because the effective impedance matching condition in the second band is mainly determined by the side width w₂. These resonant bands could therefore be modulated individually by optimizing the individual structural parameters (w₁, w₂).

Fig. 6.

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	Fig. 6. Measured transmission spectra of the designed structure with w1 = 4.5 μm for different values of w2.

The third set of experiments is carried out by simultaneously increasing both structural parameters (w₁, w₂) to demonstrate the effects of these parameters on the resonant bands of the designed filter.

Fig. 7.

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	Fig. 7. Simulated transmission spectra of the designed structure with w1 = 4.5 μm for different values of w2.

Figure 8 shows the transmission spectra measured when w₁ and w₂ are optimized simultaneously. The bandwidths of both bands are increased, and these resonant bands move closer to each other. When w₁ = 5.5 μm and w₂ = 2 μm, the first and the second bands merge into a single resonant band with a bandwidth of 7.7 THz as shown in Fig. 8. The simulated results in Fig. 9 are similar to those in Fig. 8. It is because the effective perfect impedance matching conditions in the first and the second bands are achieved simultaneously when w₁ = 5.5 μm and w₂ = 2 μm. These measured and simulated results indicate that the impedance matching condition of the proposed structure is mainly determined by these structural parameters.

Fig. 8.

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	Fig. 8. Measured transmission spectra of the designed structure with different values of w1 and w2.

Fig. 9.

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	Fig. 9. Simulated transmission spectra of the designed structure with different values of w1 and w2.

In this work, we experimentally study a dual-band metamaterial filter. The first resonant band is expanded and shifts to higher frequency by increasing w₁ alone. The second resonant band is expanded and shifts to lower frequency by increasing w₂ alone. Further experimental studies indicate that the first and second band can be modulated to move closer to each other together and merge into a single transmission band by simultaneously optimizing the two structural parameters. This experimental demonstration verifies that the proposed free-standing non-hollow fishnet structure can be used to produce a new metamaterial filter with dual-band properties.