Fano resonance in facile symmetric trimeric Babinet metasurface

, U , , ,

Guangxi Key Laboratory of Precision Navigation Technology and Application, Guilin University of Electronic Technology,Guilin 541004, Guangxi Zhuang Autonomous Region, P.R.China

Abstract： A facile symmetric trimeric Babinet metasurface is proposed for producing a Fano resonance in terahertz region. The Fano resonance is excited by an incident wave that interferes with the out-of-phase dark mode when a linearly polarized wave perpendicular to the Babinet slits illuminates the metasurface. By adjusting the structural parameters of the metasurface, the in-phase bright mode can be tuned independently, while the out-of-phase dark mode can be changed linearly, and the quality factor can also be tuned. Overall, a method for tuning the dark and bright modes for Fano resonance is revealed. The tuning mechanism has promise for applications in various fields such as sensors, filters, optical switches, photodetectors, and energy-harvesting devices with advanced performance.

Key words： terahertz device; Babinet metasurfaces; Fano resonance; tunable characteristic; bright mode; dark mode

Two-dimensional metamaterials, known as metasurfaces, have recently emerged as a novel research frontier, since they are significantly capable of tailoring electromagnetic wave with ultrathin thickness at will[1-6]. These remarkable surfaces are composed of two-dimensional arrays of polarizable particles, which can be arranged in a variety of topological structures to create various functionalities, such as negative refractive index[7-8], anomalous reflection[9-11], gradient-index[12-13], resonance-backed[14-15], and versatile holograms[16-18]. When it comes to resonance, the phenomenon of Fano resonance, which is due to interference between a narrow discrete resonance and a broad spectral line[19], has drawn much attention in various fields such as slow light[20-21], sensing[22- 23]and nano-lasing[24-25]. In order to activate the Fano resonance in a metasurface, one usually employs a symmetry-breaking structure such as asymmetric split-rings[26-27], detuned plasmonic and dielectric resonator-pairs[28-29]or dipole-quadrupole coupled structures[30-31]. Further tailoring the Fano resonance via plasmonic nanoclusters[32], nonlinear materials[33]and phase-change materials[34]not only brings about a host of intriguing physical phenomena[35-38], but also has multiple applications[20, 39]. Recently, researchers have found that Fano resonances exist widely in symmetric structures such as nanoscale plasmonic clusters and nano-shells, but their configurational requirements are complicated.

In this paper, we propose a facile symmetric trimeric metasurface array made up of multiple unit cells, each of them consisting of three rectangular Babinet slits, which act as dipolar resonators under the influence of a perpendicular incident plane wave. Finite element method simulations were carried out to obtain a series of parametric results, which indicate that disciplinary redshift and blueshift occur in the transmission spectrum with the altering of certain structural parameters. These results provide an ideal pathway to fabricate a compact, efficient terahertz device based on Fano resonance.

1 Schematic and physical model

Fig.1(a) shows the schematic diagram of the trimeric Babinet metasurface array model. Each unit cell of metasurface structure settled in vacuum is made up of perfect electric conductor (PEC) with periodpx=py=50 μm. Each of the three rectangular slits of the unit cell has lengthhand widthw. The spacing between adjacent slits isd. The incident electromagnetic wave is transmitted along the wave vectorkwhich is perpendicular to the surface. The incident plane waveExwith electric field parallel to thexaxis propagates along thekdirection as indicated in
Fig.1(a). Fano resonance and field properties illustrated in
Fig.1(b) were obtained via simulation.

Fig.1 Trimeric Babinet metasurface and related transmission spectra图1 三孔缝Babinet超表面与相关透射谱

Fano resonance derives from the interference between a radiative bright mode and a sub-radiative dark mode[32]. For the sake of elucidating the principle of Fano resonance, we first explore the features of a typical Fano resonance through simulation. A transmittance spectrum exhibiting Fano resonance is shown in
Fig.1(b), and was obtained by setting the default parameters as follows:w=6 μm,h=30 μm,d=10 μm,px=py=p=50 μm. The predicted transmission coefficient decreases from 0.996 to 0.015 in the frequency range of 4.44-4.46 THz. However, in the range from 4.46 to 5.20 THz, the transmission coefficient increases slowly from 0.015 to 0.999. The Fano resonance possesses high asymmetry and an extremely sharp line, which is a distinct feature different from other resonances, and this significant characteristic derives from the interference between the out-of-phase dark mode at ‘1’ and the in-phase bright mode at ‘2’ in
Fig.1(b). The upper left inset illustratesExfor the dark mode appearing in the Fano dip signified by ‘1’, which shows that the field has the out-of-phase(+-+) distribution in the slits. The distribution ofExin the bright mode denoted by ‘2’ is shown in the lower right inset; this field has the in-phase(---) distribution. A Fano resonance is produced by wide-band bright mode interfering with an out-of-phase field profile dark mode[31]. The specified structural parameters were tuned to illustrate the properties of the bright and dark modes in detail.

2 Results and discussion

The evolution of the transmission spectra of the trimeric unit cell was investigated by altering the width parameterwwhile fixing the other parameters asd=10 μm,h=30 μm, andp=50 μm. The transmittance as a function ofwis shown in
Fig.2(a). The narrow blue line corresponds to the dark mode at 4.41 THz at the dip point, and the broad red area represents the bright mode. Aswis increased, the broad transmission peak shows a slight blueshift, while the narrow transmission dip remains almost fixed at 4.41 THz. This illustrates that the position of the dark mode relative to the bright mode can be independently adjusted by the slit width.
Fig.2(b) and 2(c) show transmission spectra and quality factors respectively for four different widths (w=5.2, 5.8, 6.4 and 7.0 μm). With increasingw, the frequency of the dark mode (indicated by the black dashed line) stays unchanged, while the bright mode denoted by the pink dashed line shows a slight blueshift. In
Fig.2(c), the quality factor (Q-factor) for the Fano resonance decreases from 20.90 (corresponding tow=5.2 μm ) to 16.92 (corresponding tow=7.0 μm). Therefore, we can enhance theQ-factor for the Fano resonance by loweringw.

Fig.2 Related data about altering w图2 改变w的相关数据

The dependence of the Fano resonance on the inter-slit spacingdwas also investigated, fixing the other parameters asw=6 μm,h=30 μm, andp=50 μm.
Fig.3(a) shows the simulated transmittance as a function ofd. In this case, the sharp transmission dip corresponding to the dark mode, manifested by the blue belt in the range 5.06-5.33 THz (corresponding tod=7.3-13.0 μm), shows a redshift with increasingd. Conversely, the red area in the range 5.59 - 6.00 THz (corresponding tod=7.3-12.7 μm), which corresponds to that the bright mode is blueshifted with increasingd.
Fig.3(b) and 3(c) show transmission spectra and quality factors respectively for four different spacings (d=8, 9, 10 and 11 μm). With increasingd, the dark mode denoted by the pink and black dashed lines shows an almost linear redshift, while the bright mode denoted by the red dashed line shows a blueshift, and theQ-factor increases from 11.24 (corresponding tod=8 μm) to 35.28 (corresponding tod=11 μm). Increasingdresults in enhancement of the quality factor for the Fano resonance.

Fig.3 Related data about altering d图3 改变d的相关数据

Fig.4(a) shows the influence on the Fano resonance due to altering the slit lengthhwhile fixing the other parameters asd=10 μm,w=6 μm andp=50 μm. In this case, the sharp transmission dip (dark mode) indicated by the blue area in the range 5.87-3.25 THz (h=20-42 μm) shows a redshift with increasingh; and the wide transmission peak (bright mode) corresponding to the red area ranging from 5.98 to 4.29 THz (h=23-42 μm) is also redshifted ashis increased.
Fig.4(b) and 4(c) respectively show transmission spectra and quality factors for four different lengths (h=22, 26, 30 and 34 μm). With increasingh, the peak denoted by a pink dashed line shows redshift, and the dark (bright) mode denoted by a black (red) dashed line also shows redshift. TheQ-factor decreases from 22.875 (corresponding toh=22 μm) to 12.200 (corresponding toh=34 μm). Making the slits longer results in a lower quality factor for the Fano resonance.

Fig.4 Related data about altering h图4 改变h的相关数据

3 Conclusions

To sum up, we present a model of a facile symmetric trimeric Babinet metasurface cell made up of three dipolar resonators. The genetic mechanism underlying the Fano resonance is revealed by simulating the transmitted electric field component distributions and transmission spectrum. The radiative bright mode and sub-radiative dark mode for the Fano resonance are affected by adjusting three structural parameters. The bright mode can be tuned independently by varying the slit widthw. Linear tuning of the dark mode with increasingdand redshift for both modes of Fano resonance are obtained by parametric analysis.Q-factors of Fano resonance are also predicted, as they may be relevant to potential future applications. This structure has promise in various devices such as sensors, filters, optical switches, photodetectors, and energy-harvesting devices with advanced performance.

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