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Abstract
A metamaterial perfect absorber (MPA) using elliptical silver nanoparticles is proposed and investigated to provide 100% absorption for both transverse electric and transverse magnetic polarizations with a wide range of incident angles and polarization independence. Metamaterial absorbers with narrow absorption performance over a wide frequency range are significantly desired in sensing applications. Incident angle insensitivity and polarization angle independence are key features of MPAs. The output characteristics are examined using the three-dimensional finite difference time domain method. The effective medium theory and transmission line theory are applied to investigate the simulation results. Here, the 100% absorption occurs at resonance wavelength of λres = 2290 nm, and maximum sensitivity and figure of merit become 200 nm/RIU and 720 RIU-1, respectively. The results show that an absorption spectrum is insensitive to the incident angle of 0°–60°. The proposed device can be used as a high-performance biosensor and photodetector.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Plasmonic metamaterials are artificially designed materials that function by manipulating the complex effective electric permittivity and magnetic permeability [1,2]. Plasmonic metamaterials are attracting increasing interest and play an important role in several new research fields such as electromagnetic cloak [3], negative refraction [4], photovoltaics [5], thermal emission control [6], stealth application [7], epsilon-near-zero structure [8], and so on [9,10]. Owing to their unusual characteristics, they have broad uses in optoelectronics, such as infrared spectroscopy [11], switch [12], modulator [13], filter [14], and sensors [15–18]. Reducing the size of the structures from micro to nano or decreasing the working wavelength increases the light-matter interaction and leads to amazing features. Nanostructures have tunable properties such as electrical conductivity, absorption and scattering with enhanced performance over their bulk counterparts.
The localized surface plasmon resonance (LSPR) is caused by the interaction of collective oscillation of electrons with metallic nanostructures. LSPR metamaterials have the excellent ability to confine light at the nanoscale and transform it into thermal energy, which is a fundamental property in designing absorbers.
By engineering the effective impedance of the plasmonic platforms, metamaterial perfect absorbers (MPAs) can obtain strong light absorption ability unattainable with natural materials. In 2008, the first MPA was introduced and designed by Landy et al. [9] based on the metal-insulator-metal structure at microwave frequency. Since then, much research has been done through experiments or simulations to achieve perfect absorption such as using metamaterials and plasmonic configurations [19,20], all-dielectric and chiral structures, and other types or multifunctional absorbers [21–23]. Also, different materials and configurations can be used [24–27]. Plasmonic ideal absorbers have been widely promoted in recent years and used as sensing devices [28,29]. As a result of the impressive development of biosensors, several applications such as sensing cholesterol [30], gas [31], blood types [32], and other kinds [33–35] have been examined extensively.
Scientists are interested in the possibility of manipulating the absorption ratio with metal nanostructures. For example, the plasmonic absorber with grooved metal film proposed by Zare et al. [36] exhibits a high absorption level above 90% in the near-infrared region. MPAs are significantly affected by incident angle insensitivity as well. For instance, the wide-angle MPA using the hybrid of spoof plasmonic structure is proposed by Zhou et al., which the absorption amount is 90% for incident angle up to θ = 50° [37].
In this paper, an MPA based on the elliptical silver nanoparticles in a layered structure has been proposed. It contains a metallic substrate, thin dielectric film as a spacer, and a metamaterial layer. The three-dimensional (3D) finite difference time domain (FDTD) method is used to investigate the output characteristics and sensing spectra. Also, the variation of the geometrical parameters, changing the dielectric and plasmonic materials on the outcomes, are examined. The outputs approve that this device is remarkable for sensing with a high sensitivity value. The designed structure displays a good incident angle insensitivity for transverse electric (TE) and transverse magnetic (TM) polarization waves, as well.
2. Structure design and modeling
Figure 1 shows schematically the proposed metamaterial absorber (MA) as well as its unit cell, where the elliptical silver nanoparticles are on the top of the structure. The two-dimensional array is considered to be the basic model of an absorber in which its size determines the full width at half-maximum (FWHM) [38–40]. In this paper, a metal/insulator/metal (MIM) structure and LSPR are combined in a same platform. Merging MIM and LSPR in a same configuration has provided interesting systems for sensing and detecting. The substrate is silver with the Lorentz-Drude permittivity model [10], according to the following equation:
Fig. 1. (a) 3D view of the designed metamaterial array. (b) Magnified 3D view of the different unit cells and the top-view (x-y) and the side view (x-z) of the unit cell.
Also, the front view (X-Y) and cross-section (X-Z) of the unit cell are illustrated in Fig. 1(b). The bottom layer is a silver (Ag) with a thickness of d, which is used to zero the transmission. The middle dielectric film with a thickness of g is Al2O3 with a refractive index of 1.75. The values, symbols, and units of all parameters are listed in Table 1.
Table 1. The symbol and quantity of the model parameters
The fabrication of this configuration can be done with high accuracy and high repeatability [42]. The absorber was fabricated using standard electron beam lithography. A 80 nm silver film was first deposited onto a silicon wafer, followed by deposition of an Al2O3 film with electron beam evaporation. Then, for creating an array of 90 nm thick elliptical silver nanoparticles, a thick photoresist film is spin-coated onto the substrate, and the square patterns are transferred from photomask to photoresist via UV exposure. An ion beam energy of 600 eV with a beam current density of 500 mA/cm2 was used to create elliptical nanoparticles from cylindrical forms for three minutes. Figure 2 shows a schematic of the fabrication procedure for obtaining elliptical silver nanoparticles.
3. Analysis and results
We study the output characteristics of the proposed design using an FDTD method. By this method, complex structures can be designed in the computational region. During the present simulation, the input electromagnetic wave propagates toward the negative z-direction. The periodic boundary conditions are taken into account along both the x and y axes. A mesh override region with a step of 1nm in every direction was used to ensure the accuracy of the results. The output spectrum of the designed MAs with different polarizations is depicted in Fig. 3. As can be seen, when the polarization changes from TM to TE, the resonance wavelength, absorption power, and the full-width at half maximum (FWHM) of the structure remain essentially unchanged. As seen, this model holds a 100% absorbance by the FWHM of 200 nm for TE and TM polarization. Therefore, we do not need to worry about the polarization of incident light. The bottom Ag layer has a thickness of d = 80 nm, which is greater than the penetration depth (δ) of silver. Thus, the transmission ratio is negligible due to the electromagnetic wave that cannot penetrate the bottom layer in these absorbers.
Fig. 3. Absorption diagrams of the designed MA under normal incidence with different source polarization (s and p).
The electric and magnetic fields distributions in the x-y and x-z planes at resonance wavelength for TM polarization are shown in Fig. 4. As seen in Figs. 4(a) and 4(b), the electric field tends to be confined near the nanoparticle edges. Also, at that resonance wavelength, it is coupled to the metal-dielectric interface, which demonstrates the excitation of the surface plasmon polaritons [43]. Commonly, the physical mechanism of MA is based on the localized surface plasmon (LSP) and propagating surface plasmon [44] and the combination of these resonances [43]. Figures 4(c) and 4(d) show the magnetic field distributions at resonance conditions. Observations show that confined magnetic fields within dielectric films produce LSP resonances [45].
Fig. 4. Electric fields distributions on (a) x-y and (b) x-z planes. Magnetic fields distributions on (c) x-y and (d) x-z planes at resonance wavelength of 2290 nm.
3.1 Equivalent circuit model
In the design of a MA, we try to decrease the reflection through impedance matching with the medium in a design that has a metal ground film. The metallic ground plane is placed to eliminate the transmittance. Therefore, all incident energy can be absorbed within the MA. Using the effective medium theory [46,47], we can characterize our designed metamaterial structure as a homogeneous object with the effective permittivity (ɛeff(ω)=ɛ1(ω)+iɛ2(ω)) and permeability (µeff(ω)=µ1(ω)+iµ2(ω)). It is possible to tune ɛeff(ω) and µeff(ω) of the metamaterials by varying the geometrical parameters of the design, which can be obtained by the sensitivity (S) parameters [47].
An effective material has the following impedance:
where Z0 = 377 Ω is an impedance of free space.According to transmission line theory, Fig. 5 shows an equivalent circuit model of a proposed unit cell. This equivalent system contains three parts. The first is a metal patch surface with a height of h = 90 nm, which contacts a free space transmission line (Z0) from the top side. The structure of the model is an R-L-C series circuit with an impedance of ZB. Resistance and inductance are induced by the metal patches. The values of the resistor for ohmic losses R in the THz range vanish. Then, the circuit consists of L-C parameters is shunted with transmission line Zg. The second part of the circuit shows the Al2O3 dielectric layer transmission line, Zg, with a thickness of g = 12 nm. The last part explains the metal Ag plane at the bottom structure with thickness d = 80 nm. In the transmission line model, this layer turns into a short circuit. Then, the impedance of ZL for the Ag plane goes to zero.
Figure 5 depicts that Z1 becomes an equivalent impedance of the transmission line Z1 = Zg+ZL. Hence, the input impedance Z1 = Zg for the matched transmission line at the bottom layer expresses as
Fig. 6. The impedance of the proposed MA model. The vertical dashed line denotes the absorption peak wavelength at 2290 nm. The horizontal lines denote the real and imaginary parts of the impedance at λ = 2290 nm, respectively.
3.2 Results and discussions
The figure of merit (FOM) and sensitivity (S) are two key measurable variables in plasmonic sensors that describe the success of the detecting mechanism [48,49]. Sensitivity is an essential factor in defining the detecting validity of the device. Generally, the definition of sensitivity is Δλ/Δn, where Δλ and Δn represent resonance wavelength and refractive index changes, respectively [50]. In our designs, the detecting tool is based on analyzing the changes in the resonant wavelengths as a function of material under sensing (MT) refractive index in a sensing area. An MT refractive index changes within 1~1.4 in steps of 0.1. To increase sensitivity, we need a larger wavelength shift.
The absorption power for different MT refractive indices is depicted on Fig. 7, while we hold a redshift by increasing the refractive index. The maximum sensitivity value is 200 nm/RIU. Table 2 provides the complete information on Fig. 7.
Fig. 7. (a) The change of absorption value by the n, (b) absorption value as a function of n, and (c) The FOM value.
Table 2. The Complete Information of Sensitivity Analysis
Additionally, FOM is an essential parameter that is usually applied to estimate the sensor performance, which is defined as FOM=ΔA/A.Δn, where ΔA is a change of absorption induced by the change of the refractive index [51,52]. The refractive index changes from 1 to 1.1, and other parameters remain constant. In Fig. 7(c), we show the FOM value with a change of 0.4 in the refractive index. An FOM of 720 RIU-1 is demonstrated here, significantly comparable to other published plasmonic-based sensors [53,54].
Here, different geometrical parameters of the design are investigated for their effect on the absorption characteristic of the structure. The height of nanoparticles (h), the radius of nanoparticles (r), periodicity (width of each unit cell, P), and the angle of the incidence (θ) are examined.
Figure 8 explains the change of the absorption spectrum by changing h value in the proposed configuration. The h parameter is changed from 10 nm to 100 nm, while the other geometrical parameters remain constant. Increasing h presents a blue-shift. As shown, a perfect absorption happens in the case of higher nanoparticles (for h = 70 nm to h = 100 nm).
Figure 9 shows the change of the absorption spectrum by changing r in the proposed structure. Moreover, r is changed from 260 nm to 500 nm, while the other parameters remain unchanged. According to Fig. 9, increasing r results in a redshift without changing the absorption ratio in resonance wavelength, and the output power does not change significantly by increasing r. An increase in the resonance wavelength results from a decrease in the effective electrical length.
Fig. 9. The change of absorption value by the (a) r and (b) absorption value as a function of nanoparticle radius.
Besides the parameters examined above, the structure periodicity (P) has an important impact on resonance wavelength, which enables the structure to be reduced in size and shift the resonance wavelength upward. By changing the periodicity from 510 nm to 350 nm, the resonance wavelength shifts from 2290 nm to 2405 nm; see Figs. 10(a) and 10(b).
Fig. 10. The change of absorption value by the (a) P and (b) absorption value as a function of period.
Also, the incidence angle of incoming light waves plays a significant role in the absorber’s performance. Thus, analyzing the incident angle effect must be done significantly. Figure 11 depicts the calculated output spectra as a function of incident angle (θ). Within a range of 0°<θ<60°, one can see that the absorption is extremely stable for both TM and TE polarizations. This phenomenon can be explained by the fact that the upper layer of our absorber (Elliptical nanoparticles) is a symmetrical structure and that the magnetic field orientation is maintained.
Fig. 11. The change of absorption value with varying incidence angle (θ) for (a) TE and (b) TM polarization.
Furthermore, as listed in Table 3, compared with some previously published papers, the sensing behavior of our proposed MA is considerably better.
Table 3. Summary of the some representative structure for MAs.
4. Conclusion
In summary, we proposed and studied a design of MPA based on the metal/dielectric/metal configuration. The structure consisted of elliptical silver nanoparticles, an Al2O3 dielectric layer, and a substrate silver layer. Simulation results with the 3D FDTD method clarified that a designed absorber has a 100% absorption for both TE and TM polarizations. Also, the MPA presents polarization independence and keeps a high absorption ratio up to a wide range of incident angles (0°<θ<60°), demonstrating excellent tolerance in incidence angle. Furthermore, as a refractive index sensor, maximum sensitivity and FOM of S = 200 nm/RIU and 720 RIU-1 were obtained, respectively. This work will guide the design of high-performance devices with both perfect absorptions and polarization-insensitive, which might be useful in several future applications.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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