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Abstract
In this paper, we demonstrated a Fano resonant superlattice metasurface structure composed of bilayer trimeric metallic stripes in each unit cell. It can simultaneously support two types of Fano resonances, which individually possesses electric and magnetic properties at microwave frequencies, respectively. The electric Fano resonance is generated by the anti-phase electric mode interfering with in-phase electric mode, while the magnetic Fano resonance stems from the interference between the magnetic modes in the gap area and the anti-phase electric mode in each layer of the bilayer metasurface. In addition, the double Fano resonances are readily tunable by adjusting a variety of distance degrees of freedom in the composite structure. Our proposed model not only provides a possibility to stimulate and control electric and magnetic Fano resonances simultaneously for microwaves, but also holds great potential for biosensing and switching applications for even higher frequency range such as terahertz or optical region.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fano resonances [1,2] arising from the interference between two or more interacting resonances in plasmonics and metamaterial platform attracted much attention in recent years, due to their asymmetric ultra-sharp linewidth possessing wide usage in photonic switching [3–5], nano-lasing [6,7] and sensing [8–11] applications. On the other hand, metasurface, an 2D counterpart of metamaterial that can manipulate the electromagnetic wave at will within an ultra-thin layer, flourishes due to its compact footprint for optical components [12–18]. Exploiting Fano resonances in metasurfaces can be usually realized by designing asymmetric unit-cell structures, such as the detuned plasmonic resonator-pairs [19–21], dipole-quadrupole coupled structures [22–24], on which the anti-phase electric mode can be excited; and other magnetic structures such as asymmetric split-ring resonators [25–29], plasmonic nanoclusters [30,31] and nanoshells [32–34], on which the magnetic dipole mode can be readily be excited. Multiple Fano resonances in a single system can also be achieved by exploiting the interference between multiple resonance decaying pathways [4,9,35–38], such as the interference between multiple electric resonances of different higher modes, and the interference between multiple magnetic resonance between different higher modes. The Fano resonant metasurfaces can be achieved for a wide range of electromagnetic wave spectrum including optical range [39], Terahertz [40] to microwave frequencies [27,41]. However, previous reported systems supporting multiple Fano resonances usually require complex and asymmetric unit cell structures, and only harness single type of resonance modes. The controlling and tuning capabilities of multiple Fano resonances are thus largely limited for various applications.
In this paper, we present a superlattice bilayer metasurface with symmetric unit-cell structure, which has the capability to simultaneously support the anti-phase electric trimer mode in the metasurface plane, and the magnetic dipole mode in the plane perpendicular to the metasurface. Both of the two modes will independently lead to a Fano resonance with typical electric resonance and magnetic resonance characteristics, respectively. Different from previous reported multiple Fano resonances that rely on symmetry-breaking to excite the sub-radiative dark mode, the electric Fano resonance (EFR) and magnetic Fano resonance (MFR) existed in our proposed superlattice bilayer metasurface originate from the lattice induced phase resonances [42] in a simple symmetric configuration. Controlling of those Fano resonances can be performed in a convenient and flexible way by adjusting a variety of distance parameters between individual meta-atoms. In addition, the controlling mechanism does not rely on the variation of the size or shape of meta-atoms, which not only facilitates the fabrication process of the metasurface sample but also improves the controlling precision. Our findings may find many implications in various fields, including biosensings, microwave filters and switches with improved performances.
2. Origin of the EFR and MFR in the superlattice bilayer metasurface
Figure 1(a) shows the schematic of the superlattice bilayer metasurface. The stripes on each layer have the same parameters with length l = 6 mm, thickness t = 0.038 mm and width w = 0.4 mm. They are placed on a dielectric substrate made of Flam-Retardant-4 (FR4) glass epoxy with thickness St and permittivity ε = 4.2. The period in x-direction and y-direction are Px and Py respectively. The x-o-z section schematic map in Fig. 1(a) shows that the metal stripes on the bottom layer are aligned with that on the top layer. In our full-wave simulation, these stripes are considered as perfect electric conductor, which is a good approximate of metal in the microwave range. The incident plane wave with electric field oriented parallel to the y axis propagates along + z direction (wave vector k) as indicated in Fig. 1(a). As we mentioned in the previous reference [43], metallic stripe can support a dipolar resonance mode around wavelength λ~2lneff, where neff is the effective refractive index of surrounding medium, and it can be estimated as a value between the indexes of top layer and the substrate. Therefore, the wavelength of the dipolar resonance is confined in the range between 2n0l and 2nsubl, where n0 and nsub are the refractive indexes of the air and substrate, respectively.
Fig. 1 (a) Schematic of the superlattice bilayer metasurface, the unit cell is arranged along axis x and y periodically. The wave vector k is incident along the z direction. (b) Transmission spectrum from λ = 15 mm to λ = 30 mm exhibiting dual-Fano resonances of the superlattice bilayer metasurface with parameters Px = 10 mm, Py = 10 mm, g = 0.2 mm, and St = 0.8 mm.
The results are obtained by the rigorous Finite Difference Time Domain (FDTD) method with frequency range. The periodic boundaries are applied along both x and y directions of the unit cell to construct the periodic metasurface. Two perfect matched layers (PML) are assigned in z directions to absorb the wave radiated to the free space. A pulsed plane wave source with frequency band from 10 GHz to 20 GHz (duration time 108 fs) is set to normally illuminate the metasurface. Transmission spectra with multiple Fano resonances are extracted by an output port on the other side of the metasurface. In the simulation, extremely dense meshes (dx = 0.02mm, dy = 0.6mm, and dz = 0.019mm) around the stripes are added to keep the stabilization of the simulation.
Figure 1(b) illustrates the transmission spectrum of the metasurface. The curve has two significant sharp peaks at wavelengths λ = 20 mm (marked as A) and 25 mm (marked as C), separately, which correspond to dual Fano resonances with sharp and asymmetric line shapes. Those two Fano resonances are induced mainly by an anti-phase electric mode, and a vertical magnetic mode, respectively. In the following, those two kinds of Fano resonances are referred to as the electric Fano resonance (EFR) and magnetic Fano resonance (MFR) modes [44,45], respectively. Furthermore, comparison of the two modes for electric field distributions of ‘y’ component (Ey) and the magnetic field distributions of ‘x’ component (Hx) illustrate the differences among three cross section profiles in Figs. 2 and 3, respectively.
Fig. 2 Field profiles of the EFR mode with (a) Ey on the top layer of the metasurface plane, (b) Ex on the section z-x of the stripe’s end, (c) Hx on the section y-z of the left stripe at A; (d) Ey on the top layer of the metasurface plane, (e) Ex on the section z-o-x of the stripe’s end, and (f) Hx on the section y-o-z of the left stripe at B.
Fig. 3 Field profiles of the MFR mode with (a) Ey on the bottom layer of the metasurface plane, (b) Ey on the section z-x of the stripe’s end, (c) Hx on the section y-z of the left stripe at C; (d) Ey on the bottom layer of the metasurface plane, (e) Ey on the section z-x of the stripe’s end, and (f) Hx on the section y-z of the left stripe at D.
The Fano resonance with asymmetric spectral line shape is typically produced by interference from a bright mode with wide band spectra and a dark mode with narrow spectra. Figure 2 illustrates the field patterns of the EFR mode at different cross sections of the metasurface. When a plane wave with polarization parallel to the stripe direction normally illuminates on the metasurface, it will excite the subradiative dark mode at about λ = 20.0 mm with ( + - + ) profile in Figs. 2(a)-2(c) and the radiative bright mode at about λ = 21.0 mm with ( - - - ) profile in Figs. 2(d)-2(f), respectively. The electric field Ey mainly constrained on the top layer plane shows a tri-dipolar pattern in Figs. 2(a) and 2(b), respectively. The magnetic field Hx is constrained around the stripes on the top layer as shown in Fig. 2(c). Figure 2(d) illustrates electric field pattern of the bright mode, which exhibits an in-phase profile between the three stripes. The fields on the upper and bottom layers also exhibit an in-phase pattern as shown in Fig. 2(e). In addition, the magnetic field is restricted on the stripe surface, which confirms that EFR mode is indeed originated from the interference between the radiative in-phase electric dipole mode and the subradiative anti-phase electric dipole mode [43].
Beyond the EFR, another kind of MFR is also found at around λ = 25 mm, as shown in Fig. 3. For the peak point C in Fig. 1(b), strong electric field motivated on the bottom layer in Figs. 3(a) and 3(b) is similar as the field profile of the EFR mode presenting on the top layer in Figs. 2(a) and 2(b), on which a tri-electric dipolar pattern with anti-phase profile is stimulated. The magnetic field Hx is constrained on the bottom layer instead of top layer in Fig. 3(c) as well. However, at the dip point D in Fig. 1(b), the electric fields on the end section of the stripes for the top and bottom layers are coupled with each other, with in-phase profile in the horizontal direction while with anti-phase profile in the vertical direction, as shown in Figs. 3(d) and 3(e), respectively. The anti-phase profile in the vertical direction indicates a coil-like vortex electric field pattern around the gap area. At the same time, the magnetic field Hx is concentrated in the gap area between the two layers with large field enhancement, which is the signature of a magnetic dipole mode. Therefore, all the field patterns in the peak and the dip positions of the MFR indicate that, the Fano resonance indeed arises from the interference between the anti-phase electric mode and the magnetic mode in the gap area.
3. Evolution of the EFR and MFR for different coupling parameters
Firstly, the evolution of the transmission spectra is illustrated as a function of period along x direction in Fig. 4(a). From this figure, two significant sharp transmission peaks represent the electric mode and magnetic mode, respectively. The positions of the two extremely sharp line stand very stable around λ = 20 mm and λ = 25 mm for the EFR and MFR modes, respectively. For the EFR, the broad transmission dip (point B in Fig. 1(b)) shifts towards longer wavelength linearly while the sharp transmission peak sustains almost unchanged at λ = 20 mm with Px>8 mm, which is consistent with our previous work [43]. However, the electromagnetic wave can be near-totally reflected except the Fano resonance peak point at λ = 20 mm when Px<8 mm. For the MFR, the broad transmission dip (point D in Fig. 1(b)) shifts toward longer wavelength when Px>10 mm and the peak is unchanged for all scale. Figure 4(b) shows four typical transmission spectra at Px = 4.9 mm, 8.8 mm, 9.7 mm and 13.1 mm, respectively. The red and blue dashed lines clearly illustrate that both the EFR and MFR are robust with respect to the period along x direction.
Fig. 4 Transmission spectra (a) for varying Px from 3 mm to 15 mm when St = 1 mm, Py = 8 mm, g = 0.6 mm, and (b) the fitted Fano line shape at ‘Px = 4.9 mm, 8.8 mm, 9.7 mm and 13.1 mm’ (from up to down).
The period length along y direction is varied while other parameters are fixed to study the evolution of the dual Fano resonances caused by the lateral coupling. Figure 5(a) illustrates the calculated transmittance spectra for varying Py from 6.8 mm to 15.2 mm. At this condition, the sharp transmission peaks, which are indicated by a red color seam between λ = 20~20.5 mm and a white line in a blue gap from λ = 26~27.5 mm, are the EFR and MFR mode respectively. From the spectra map, we can see that the ultra-sharp peak (point A in Fig. 1(b)) have a slight red-shift with increasing Py for both EFR and MFR. However, the broad bright mode (point B in Fig. 1(b)) of EFR shows broad blue-shift among 6.8 mm< Py <10 mm firstly and then becomes narrow linearly red-shifts with increasing Py. In Fig. 5(b), the red and blue dashed lines clarify that the two peaks red-shift when Py is increasing. However, the dip point B shows significant nonlinear shifts.
Fig. 5 Transmission spectra (a) for varying Py, with fixed parameters Px = 10 mm, g = 0.6 mm, St = 1 mm and (b) horizontal cut of (a) at ‘Py = 7.4 mm, 9.8 mm, 13 mm and 15 mm’ (from up to down), respectively.
The evolution of Fano resonances tuned by the local spacing ‘g’ between adjacent metallic stripes is also studied as shown in Fig. 6(a). We can see that, the wavelength of the Fano resonances can be tuned by the local spacing in a larger scale than the previous parameter Py. The sharp transmission peaks increase from 20 mm to 22.5 mm and from 26.3 mm to 28mm when g is increasing, respectively. However, the bright mode B of EFR shows relative stable property among g = 0.6 mm~1.2 mm. Therefore, the dark mode A of EFR can be independently tuned by the interval distance g = 0.6 mm~1.2 mm without changing the bright mode B. In Fig. 6(b), the red and blue dashed line represent the tuned peak modes A and C, the black and yellow dashed lines stand for the stable bright mode B for EFR and tunable bright mode D for MFR. The red and blue dot lines show that the peaks of two Fano resonances shift linearly towards longer wavelength with the interval distance g increasing. However, the broad transmission dip mode B indicated by the black dashed line illustrates an unchanged dip wavelength located at λ = 22.2 mm, which demonstrates an independent dark mode controlling properties by increasing g from 0.6 mm to 1.2 mm in the minor range. Furthermore, the peaks and dips both for EFR and MFR show red-shift simultaneously when g is larger than 1.2 mm.
Fig. 6 Transmittance spectra of dual Fano resonances (a) for varying interval distances (g = 0.6 mm~2.6 mm) between adjacent stripes and (b) horizontal cut of (a) at discrete interval distances: g = 0.6 mm, 0.8 mm, 1 mm, 1.2 mm (from up to down)
Finally, the interval between the double layers of the metasurface is varied to study the vertical coupling properties of the dual Fano resonances. Figure 7(a) shows two vertical lines around λ = 20.3 mm and λ = 26.5 mm, respectively. The two Fano resonances illustrate that the EFR peak and the MFR Peak have great robust properties even the variation of ‘St’ is changed from 0.3 mm to 2 mm gradually. The dip B of EFR at higher wavelength moves to the larger wavelength when St<1.5 mm, while it stands at relative fixed wavelength when St>1.5 mm. Therefore, it is easy to conclude that the robust dual Fano resonances are not sensitive to the interval between the double layers of the metasurface. Figure 7(b) gives the transmission for different distances, which shows a steady confirmation to the robust Fano resonances.
Fig. 7 Transmission of dual Fano resonance as (a) a function of incident wavelength and the distance between the double layers and (b) calculated spectra for different distances St: 0.56 mm, 1 mm, 1.5 mm, 1.8 mm (from up to down), respectively. The red and black dot lines show robust peak modes properties.
The flexible tuning properties of the multiple ultra-sharp Fano resonances supported at the superlattice bilayer metasurface are very useful for many applications. For example, tuning of the position of the ultra-sharp Fano resonances can be used for sensing of the permittivity of a dielectric material. It could also be applied for switching and filter devices that highly riles on the spectra characteristic of the metasurface.
4. Conclusion
In conclusion, dual Fano resonances with both anti-phase electric resonance and magnetic resonance was found in a superlattice bilayer metasurface. Mechanisms of producing electric and magnetic Fano resonances were demonstrated minutely by electric and magnetic field profiles. In addition, the evolution of the dual Fano resonances for different coupling parameters are also systematically studied, which indicates that the dual Fano resonance states around the electric and magnetic resonances stay firmly unchanged, even when the period along x direction and the distance between the double layers are varied. In the contrary, EFR and MFR can be adjusted simultaneously by varying the periodicity along y direction and the local spacing between stripes within each unit cell. Both the peak positions of EFR and MFR show linear red-shifts by increasing Py and g. Our proposed superlattice bilayer metasurface may provide a useful platform in various fields that requires Fano resonances, such as switches and biosensors.
Funding
National Natural Science Foundation of China (NSFC) (61501302, 11604217, 11574218, 11734012, 61764001, 61805053); National Key R&D Program of China (YS2018YFB110012); the Guangdong Provincial Innovation and Entrepreneurship Project (2016ZT06D081); and the Science and Technology Innovation Commission of Shenzhen (JCYJ20170818102640668).
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