Demonstration of Tunable Fano Resonances in a Meta-material Absorber Composed of Asymmetric Double Bars with Bent Arms

In this paper, a metal–insulator-metal (MIM) plasmonic absorber consisting of asymmetric double bars with bent arms located on top of a silica layer coated on a metal film is proposed, and its resonant features are analyzed. The suggested structure supports both Fano and dipole perfect absorption resonances at the near-infrared region (NIR). The asymmetry introduced into the structure can be induced by changing the bending angle or rotation angle of one of the antennas, while the other one remains fixed. Simulation results demonstrate that by applying both asymmetry factors to the structure, one can have two individual Fano peaks at the same time. It is shown that the magnitude, central wavelength, and line width of the Fano peaks are adjustable by controlling the geometrical parameters of the structure. It is also indicated that the quality factor (Q-factor) of the Fano resonance is inversely related to the degree of asymmetry introduced into the structure. According to the simulations, an ultra-narrow resonance peak with a bandwidth of 1.87 nm at the wavelength of 710 nm (corresponding to a Q-factor of 387) can be obtained by controlling the geometrical parameters. It is also discussed that the absorptivity of Fano and the dipole peaks can be adjusted inversely, by manipulating the grapheme chemical potential. The ratio of the absorptivity to the chemical potential of graphene about 275%/eV and 226%/eV is calculated for the Fano peak and dipole peak, respectively. Accordingly, the presented structure is an adjustable NIR absorber with a fully tunable absorption spectrum which can be utilized in various applications from tunable reflectors and photo-detectors to ultra-narrowband and broadband optical modulators.


Introduction
During the recent decades, the efficient tunability of the optical spectrum of meta-material absorbers has intensely attracted the attention of many researchers, since they play a key role in a wide range of applications including tunable optical filters [1][2][3], nano-sensors [4,5], photo-detectors [6][7][8], and optical switches. This efficient tunability stems from the efficiently adjustable electromagnetic (EM) field strengths associated with resonant excitation of plasmons inside the metallic nano-structures [9].
Several efforts have so far been devoted to improve the performance of meta-material absorbers in terms of absorption efficiency. This is realizable through enhancement of the intensity of their electromagnetic plasmon fields at the desired wavelengths. Two typical methods have been proposed to improve the strength of these plasmon fields: (1) optimization of the structural parameters and materials [10][11][12], (2) assembly of the plasmonic nanoparticles in order to create strong coupling interactions between the plasmon fields of neighboring nanoparticles through hybridization [13][14][15][16][17][18].
In addition to the absorption efficiency, there is another important functional characteristic of meta-material absorbers, called the quality factor (Q-factor) of the resonances. Realization of high Q-factor resonance peaks is a crucial task for realistic applications, like sensing because upon which the resolution is dependent. Besides, in some applications like filtering and optical communications, ultrahigh Q-factor resonance peaks are highly desirable.
However, most meta-material absorbers provide absorption peaks with low Q-factors due to not only Joule loss but also radiative loss [17,18]. A simple and effective method to reduce radiative loss of meta-material absorber is to introduce asymmetry into the structure [17][18][19]. For symmetric nano-structures, only plasmons with finite dipole moments can be excited by the incident optical wave. There are also some invisible modes in the spectrum of the device, known as dark magnetic modes which can become visible via breaking the symmetry of the structure [20,21]. In fact, this symmetry breaking enables some interactions that render dark magnetic modes dipole active and therefore visible at optical wavelengths [17][18][19]. The most appealing consequence of this symmetry breaking is the appearance of anti-symmetric resonances, known as Fano resonances, which is associated with a significant increase in the Q-factor of the resonance modes, and extraordinary large plasmon resonance tunability. This higher quality factor stems from the enabled interactions of very narrow dark modes with broad bright modes, via symmetry breaking; and the large tunability is attributed to the high sensitivity of Fano resonances to the changes in the characteristics of the surrounding media such as refractive index and conductivity [14,22].
To date, several studies have been performed on the engineering of Fano-based meta-material tunable absorbers which mostly consist of non-symmetric periodic structures. An ultranarrowband perfect absorber in the near-infrared region based on Fano resonances in a MIM meta-material composed of asymmetry double elliptic cylinders has been investigated by Yu et al. [17]. Giessen et al. showed that coupling strength of plasmon Fano resonances in a metallic photonic crystal can be controlled by varying the thickness of a spacer layer between the gold grating and the waveguide layer [15]. A wide bandwidth plasmonic meta-material absorber containing a broken cross as an elementary cell along with four rectangular loads has been proposed to improve the absorbance and achieve a tunable Fano response [16]. In [18], a crossed ring-shaped meta-surface with highly tunable dual-Fano resonance peaks is proposed and numerically investigated. A Fano-based metamaterial absorber consisting of various parasitic elements including cross and L shapes are studied and the functional characteristics of the device are derived for various configurations of the metallic nano-structure [23]. Li et al. demonstrated that all dielectric symmetry broken meta-surfaces can provide tunable sharp Fano resonances in their absorption spectrum [19]. There are also other types of tunable Fanobased ultra-compact configurations, consist of MIM waveguides side-coupled with a circular or elliptical ring, mainly used in sensing applications [24,25]. The abovementioned studies show that Fano-based meta-material absorbers can offer an effective platform for high-performance modulation, sensing, and filtering applications.
In this study, an ultra-narrow bandwidth tunable plasmonic absorber composed of a periodic array of bar antennas with bent arms, deposited on top of a thin dielectric layer, is numerically investigated. We show that non-symmetric plasmonic antennas can provide much larger EM field enhancements than the symmetric structure, due to the appearance of Fano resonances in the absorption spectrum. The dependence of the central wavelength, magnitude and line width of the absorption peaks upon the structural parameters of the metallic nano-antennas is also investigated. Finally, the influence of adding a layer of graphene on top of the proposed structure, and the dynamic tunability of the optical spectrum under the changes of the chemical potential of the graphene layer, is demonstrated.
The rest of the paper has been arranged as follows. In the next part, the designed structure and its functional principle have been described and the role of each segment has been expressed. Consequently, the simulation methodology and the materials will be described. Afterward, the results on the effect of variable geometrical parameters of the proposed nano-antennas on the absorption spectra of the device will be given and discussed. Then, the dynamic tunability of the device including a monolayer graphene will be studied. The simulations at this study were performed by CST microwave studio software (version 2019). The summary and conclusion remarks will be given in the last section.

Suggested Structure and Its Functional Principle
As shown in Fig. 1, the suggested structure is a triple-layer metal-insulator-metal (MIM) stack composed of a periodic array of double bar antennas with bent arms, located on top of a silica film. The bottom silver layer acts as a reflector and enhances the absorptivity of the resonance peaks, through blocking the incident field from being transmitted. When illuminating the proposed structure, incident light wave interacts strongly with the meta-surface. This may cause the absorp-be calculated by A = 1-R-T formula, where R R and T are the reflectance and transmittance corresponding to S11 and S21 parameters, respectively. S11 and S21 are called scattering parameters and their definition is as follows [26]: When the bottom reflector film exists, S 21 and consequently T are zero, and the absorption is calculated as A = 1-R. In the simulations, the relative permittivity of silica is set as 2.25, and the Drude model is used to model the relative permittivity of silver [27,28]: where p , , and ∞ are the plasma frequency, the collision frequency, and high frequency relative permittivity of silver which are chosen to be 1.38 × 10 16 Hz, 2.37 × 10 13 Hz, and 3.7, respectively [27].
A 2D surface conductivity method has been utilized to model the optical response of graphene. In this method, the monolayer graphene is considered an ultra-thin film which can be expressed by a complex surface conductivity, g , according to the Kubo formula [29]: where intra g and inter g stem from the intra-band and interband transitions, respectively. c , Γ , T , k B , ℏ , and e are chemical potential of grapheme, scattering rate, temperature, Boltzmann constant, reduced Planck constant, and electron charge, respectively. As a matter of fact, the chemical potential of graphene is dependent upon the density of charge carriers, which can be manually controlled by using a variable voltage power supply. Equation (2) describes the inter-band electro-photon scattering, while Eq. (3) represents the intraband transition contribution. The intra-band contribution is usually approximated for ℏ >> k B T and c >> k B T [29]. We have chosen c = 0eV , T = 300 • K , and = 0.3 ps in our simulations, where = 1∕(2Γ) is the electron relaxation time in the monolayer graphene. Besides, the graphene layer  ion spectrum of the device to show a few absorption peaks at resonance wavelengths. The central wavelengths, line widths and peak magnitudes of these resonances are determined by several parameters including size of the bar antennas and their bent arms, the gap size and the dielectric layer thickness. Figure 1 demonstrates three-dimensional and top view schematics of the proposed micro-device. Since the surface of proposed structure is periodic, and the substrate is uniform, the operating principle of a unit cell can be investigated and then generalized to the whole structure. Table 1 illustrates the geometrical specifications of a unit cell of the designed absorber. These parameters were taken in a way that the absorption spectrum of the device in the NIR region presents both dipole and Fano resonances.

Simulation Method and Materials
The suggested structure is numerically analyzed using a frequency domain solver. In the simulations, unit cell boundary conditions are applied for x-and y-coordinates, and open boundary conditions are chosen along the z-axis. A plane wave with electric field (E-field) parallel to the y-axis is radiated on the surface of the unit cell. The absorption spectrum can thickness is chosen to be 0.3 nm, and the size of the air space is about 2500 nm throughout the performed simulations.

Fano Resonance in the Asymmetric Structure
Given the geometrical parameters listed in Table 1, and assuming the structure to be symmetric and there is no reflector film at the bottom of the structure, a single broadband peak is observed at around d = 870 nm (black curve in Fig. 2a), in the reflection spectrum of the proposed absorber. As is expected, by changing the bending angle of one of the antennas ( 1 ), the structure becomes asymmetric, and an extra resonance peak (at f = 755 nm ) is appeared in the spectrum due to the Fano resonance phenomenon. This asymmetric Fano peak rises from the interference between quadruple (dark) and dipole (bright) modes of the metallic structure. As mentioned before, the Fano resonance phenomenon is a result that attributes to the hybridization of surface plasmon resonance effect arising from the asymmetric structure.
This structure has low absorptivity at Fano resonance because a significant amount of the incident light passes through the structure and does not absorb. By adding a silver layer as a total reflector in the bottom of the structure, the Fano resonance becomes much stronger. This is because the reflector layer enhances the interaction between the dark and bright modes. Since the destructive interference between quadruple and dipole modes suppresses the radiative loss of the metallic structure, the appeared Fano resonance has stronger absorption, narrower bandwidth, and consequently higher Q-factor compared to the dipole bright mode (see Fig. 1b).
To figure out the behavior of R and A spectra depicted in Fig. 2, the z component of the E-field at the interface of the dielectric layer and the bar antennas has been investigated and shown in Fig. 3. As comes from the figure, for the dipole resonance, the charge distributions around the antennas are the same, though an opposite trend is seen at the quadruple resonance. This implies that the induced currents are in-phase at the dipole resonance, while they are anti-phase at the quadruple resonance. The interference between the quadruple and dipole modes with anti-phase oscillations results in a very trivial radiative loss at the pertinent wavelength and an ultra-narrow resonance peak (named Fano resonance) emerges. Fig. 2 The reflection response of the device illustrated in Fig. 1, at the NIR. a The absorption spectra of the suggested structure without the bottom reflector layer. b The reflection spectra of the suggested structure in the presence of the bottom reflector layer. Black curve, symmetric structure; red curve, asymmetric structure

The Influence of Geometrical Parameters
As discussed before, the structural asymmetry is the main reason behind the appearance of the Fano resonance in the absorption spectra of the presented structure. This asymmetry can be easily induced and adjusted by changing the bending angle of one of the antennas while that of the other one is fixed. The influence of the changes in α 1 on the Fano resonance, while α 2 = 45 • is shown in Fig. 4. The other structural parameters are considered to be constant as listed in Table 1.
One can understand from the figure that when 1 is not equal to 2 = 45 • , a narrowband Fano resonance peak is appeared in the spectrum at around 755 nm. Moreover, for 1 > 45 • , when 1 becomes larger, the Fano peak is blue shifted and its magnitude becomes larger until it gets near 100%. By contrast, for 1 < 45 • , as 1 becomes smaller, the Fano peak experiences a red shift and its magnitude becomes larger. Regarding the magnitude of the peaks, the magnitude of the Fano resonance increases with the increase of asymmetry, because enlarging the value of α strengthens the excitation of localized plasmons of the dark quadruple mode. The mentioned contradictory behavior of the central wavelength of Fano peaks can be described according to the hybridization theory [30].
An important parameter usually considered in the design of resonant devices is the Q-factor of the resonance peaks that is defined as [31]: where FWHM is the full width at half maximum of the Fano resonance peak, and λ f is its central wavelength. From Fig. 4, one can say that as the difference between α 1 and α 2 gets larger (i.e., the degree of asymmetry increases), the line width of the Fano peak is increased, and its Q-factor is therefore decreased. This can be explained according to a general fact: the Fano resonance Q-factor and the degree of asymmetry of the structure are inversely related. This general fact can be described by the phenomenon of bound states in the continuum, originating from quantum mechanics as an important physical concept of destructive interference [19]. Another way to introduce asymmetry into the proposed structure and inducing Fano resonance is to rotate one of the antennas while the other is fixed (see Fig. 5). In this case, we expect to see an extra Fano peak in the absorption spectrum of the proposed micro-device. Figure 6 illustrates the optical response of the proposed device to the changes of the rotation angle, 1 .
According to Fig. 6, when θ 1 > 0 • , another Fano peak is appeared at around 1550 nm in addition to the Fano peak related to the difference between α 1 and α 2 , which was appeared at around 755 nm . Here, the Fano peak appeared at 755 nm is called the 1st Fano peak, and the peak at 1550 nm is called the 2nd Fano peak. As can be seen in the inset of Fig. 6, increasing the angle of rotation increases the absorptivity of the 2nd Fano peak, and shifts it toward longer wavelengths. We can also learn from the figure that the changes of rotation angle have negligible effect on the absorptivity and central wavelength of the 1st Fano peak.
Owing to the fact that the intensity of the EM radiation is confined and enhanced in the gap between adjacent antennas at quadruple resonance, induced by the anti-phase oscillations of quadruple mode, the size of the gap strongly affects  Fig. 7. It is expected that by making the gap smaller, the intensity of interaction between asymmetric bars is to be increased, resulting in an increase in the value of Q-factor of the Fano resonance peak. This can be seen in the inset of Fig. 7. From this figure, one can also see that the smaller gap results in a significant blue shift of the dipole resonance, but negligible red shift of the Fano resonance peak. As discussed before, Q-factor of the Fano peak is one of the most important parameters of the proposed structure, and the simplest way to increase it is to decrease the degree of asymmetry [19]. This can be done by decreasing the length of bent arms of the antennas. Figure 8 illustrates the behavior of the absorption spectrum for different amounts of bent arm length of the antennas, L b1 and L b2 . As illustrated in Fig. 8, the reduction of L b1 and L b2 leads to a blue shift of the Fano resonance peak and a significant increase of its Q-factor. The inset shows that for L b = L b1 = L b2 = 40 nm , the Fano resonance peak with a Q-factor of 387 (corresponding to a FWHM of 1.83 nm) is appeared at 710 nm. The figure also depicts that further decrease of L b2 and L b1 results in the increase of dipole resonance magnitude but reduction of Fano peak absorptivity which is undesirable.
There are also other geometrical parameters, like antennas' width (Wa) and height (Ha), which strongly affect the absorption spectrum of the designed device. The influences of Ha and Wa on the spectrum of the device are illustrated in Figs. 9 and 10, respectively. Investigation    8 The effect of bent arms' length L b on the absorption spectra of the proposed absorber. The inset shows the relationship between L b and Fano peak central wavelength as well as its absorptivity Fig. 9 The influence of the antennas' height on the optical spectrum of the device. The inset shows the central wavelength of the Fano resonance versus H a

Dynamic Tunability Using a Single-Layer Graphene
There are a lot of methods used to realize dynamically tunable optical absorbers and modulators among which electrical excitation using graphene is the most popular one thanks to its unique electrical and optical features. The most prominent optical characteristic of graphene is the flat absorption spectrum that can be tuned by applying an external E-field. This property can enable the tunability of surface conductivity through alteration of its Fermi energy. Meanwhile, the premium high carrier mobility of graphene (~ 23,000 cm2/V.s for top-gated graphene) makes it an appropriate choice for ultrafast optoelectronic applications. Nevertheless, graphene possesses a very low optical absorption (2.3% for a single layer of suspended graphene). However, using graphene in combination with plasmonic devices can make up for this disadvantage. It means that since graphene shows strong coupling with enhanced EM field in the plasmonic structures, it is possible to realize highly tunable devices with this material. In this section, the consequences of adding a layer of graphene to the structure of the proposed absorber are investigated. Figure 11 shows the 3D schematic of the proposed absorber with a graphene layer added to the structure on top of the silica sheet. As a general fact, the EM field enhancement around the metallic antennas interacts strongly with the graphene layer, resulting in an efficient improvement of the graphene influence on the optical behavior of the device.
To describe the influence of graphene on the absorption spectrum of the designed meta-surface, the absorption Fig. 10 The influence of the antennas' width on the optical spectrum of the device. The inset shows the central wavelength of the Fano resonance as a function of W a Fig. 11 3D schematic of the proposed structure with a monolayer graphene between the metallic antenna and the silica layer spectra with and without graphene layer have been shown comparatively in Fig. 12. As shown in this figure, without graphene, the absorption related to the Fano and dipole resonance peaks is around 99% and 40%, respectively. However, with graphene layer (EF = 0 eV), the absorption related to the Fano peak falls down to 65%, while that of the dipole peak rises to 95%. Indeed, the increase observed in the absorptivity of the dipole resonance comes from the constant absorption of graphene in the NIR that is now strengthen owing to the intense increase of the EM field on the surface stemming from the excitation of the localized surface plasmons (LSPs). However, the decreased value of Fano resonance peak in the presence of graphene and the different reactions of Fano and dipole modes to the existence of the graphene layer can be explained by investigating the E-field and charge distributions around the antennas at the quadrupole and dipole resonances. According to Fig. 3a, for the Fano resonance, a large amount of opposite charges is accumulated in the gap between the antennas. Once the gap is occupied with graphene, the opposite charges are recombined and neutralized via the highly conductive graphene layer, resulting in a strong suppression of the E-field enhancement [32]. Hence, the magnitude and Q-factor of the Fano resonance peak decreases significantly. This is while, as illustrated in Fig. 3b, for the dipole mode, a vertically symmetric distribution of charges is observed in the gap. Since the graphene layer does not affect the accumulation of the same type of charges, no EM field suppression is expected in the presence of graphene at the dipole mode. So, the absorptivity in this wavelength is only influenced by the enhancement of the absorption of graphene due to the excitation of LSP resonances.
As discussed before, the hybridization of graphene with meta-material structures enables the active tunability of the optical spectrum by manipulating the Fermi level of graphene via applying a variable voltage source. Figure 13a exhibits the absorption spectrum of the device under the variations of the graphene chemical potential. It is seen that as the chemical potential increases from 0.7 to 0.9 eV, the absorptivity of the dipole resonance drops by about 55%, corresponding to − 275%/eV modulation of absorptivity per graphene Fermi energy (Fig. 13b). Moreover, the decrease in absorptivity initiated at EF = 0.7 eV and ended at EF = 0.9 eV. The decrease in absorptivity at the indicated range can be assigned to the decrease in the grapheme. Detailed description of this phenomenon is discussed in other similar contributions [9].
On the other hand, as depicted in Fig. 13a, the absorptivity of the Fano peak increases with the increase of the chemical potential. From Fig. 13b, the absorptivity of the Fano peak changes from 0.65 to 0.99 as EF increases from 0.8 to 0.95 eV. Hence, a tunability of 226%/eV can be achieved for the Fano peak. It is worth mentioning that the absorption spectrum of the device for E f = 0.95 eV is the same as that of the device without the graphene layer. This is because, at E f = 0.95 eV , the conductivity of the graphene layer is nearly zero, and thus, there is no effect on the Fano peak. On the other hand, for E f = 0.95 eV , the absorption of the monolayer graphene tends to zero and therefore the graphene layer has no impact on the absorptivity of the dipole mode. Moreover, as shown in the inset of Fig. 13a, a negligible red shift of the Fano peak under the variations of the chemical potential of graphene is observed which can be attributed to the changes of effective refractive index of the surrounding media due to the changes in refractive index of the graphene layer.
Unlike the dipole resonance, the changes in the absorptivity of the Fano peak due to the variations of the Fermi energy stem from the changes in the conductivity of the graphene layer, not its absorption. As mentioned before, the surface conductivity of the graphene layer leads to the neutralization of opposite charges in the gap between the metallic antennas, resulting in a reduction in the absorptivity of the Fano peak. Therefore, it is easy to say that the more the surface conductivity of graphene is, the less the absorptivity of the Fano peak gets, and vice versa. To investigate the behavior of the surface conductivity under the variations of the chemical potential, the real part of surface conductivity for various values of E f is calculated as depicted in Fig. 14. It is clear for this figure that for a Fig. 12 The absorption spectra of the device with and without the monolayer grapheme certain wavelength (e.g., the Fano resonance at 730 nm), the surface conductivity of graphene is decreased by the increase of chemical potential. Therefore, the recombination and neutralization of the accumulated charges in the gap are limited, resulting in lesser suppression of the E-field enhancement.
According to the above discussion, the proposed structure can be utilized as a highly tunable optical modulator with an ultra-narrowband (7.8-nm line width) channel and a broadband (100-nm line width) channel, which behave oppositely. Fig. 13 The effect of variations of graphene chemical potential on the optical response of the device. a Absorption spectra of the device under the variations of the Fermi energy, while the other parameters are fixed as listed in Table 1; b absorptivity of the Fano and dipole peaks as a function of the Fermi energy of the grapheme

Conclusion
In summary, the absorption response of a MIM plasmonic structure, including a dielectric layer sandwiched between asymmetric double metallic antennas and a metallic film, has been numerically investigated. Results revealed that, in addition to the dipole peak, two individual Fano peaks emerged in the spectrum as two structural asymmetry factors were applied simultaneously. Furthermore, an ultranarrowband resonance peak with a bandwidth of 1.87 nm at the wavelength of 710 nm (corresponding to a Q-factor of 387) was obtained by controlling the geometrical parameters. The variation of the absorption spectrum in the presence of an extra layer of graphene has also been surveyed. Since the surface conductivity of graphene is controllable via changing the chemical potential, the observed Fano and dipole peaks were dynamically tunable by applying a variable gate voltage. Modulation of absorption per graphene Fermi energy of − 275%/eV and 226%/eV has been obtained, respectively, for the Fano and dipole peaks. According to the mentioned characteristics, the suggested device can be utilized in a broad range of applications such as tunable reflectors and photo-detectors and optical modulators.
Author Contribution All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Aliakbar Mashkour, Amangaldi Koochaki, Ali Abdolahzadeh Ziabari, and Azadeh Sadat Naeimi. The first draft of the manuscript was written by Aliakbar Mashkour and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Availability of Data and Material
Data will be made available on reasonable request.
Code Availability Simulation results will be made available on reasonable request.

Declarations
Ethics Approval There are no any human participants, their data, or biological material in this study. Not applicable.