A polarization-insensitive dual-band plasmonic metamaterial absorber for a sensor application

A polarization-insensitive dual-band plasmonic metamaterial absorber is proposed, which is constituted by merely the metal nano-cylinder and a continuous metallic ground separated by a middle dielectric layer. Two resonance peaks with over 97% absorbance derived from ‘the fundamental resonance and the surface lattice resonance are realized. The effective medium approach and the transmission line modeling show good agreement with results from numerical simulation. In addition, we demonstrated that proposed dual-absorber retain nearly perfect absorbance for all polarization angles of both TE and TM modes on normal incidence. It is different from previous work that the dual-frequency response is obtained by combining two subunits of different sizes. Importantly, the second absorption peak result from surface lattice resonance with narrow line-width has large sensitivity perform and high quality factor, which has significant potential in the application of biosensors and monitoring.

The first metamaterial absorber composed of metal-dielectric-metal was demonstrated by Landy in 2008 [46]. Since then, metamaterial absorbers have received extensive attention, and many absorbers have been proposed. However, most reported metamaterial absorbers have the shortcomings, including single absorption bandwidth, difficulty in manufacture and polarization sensitivity, which significantly hinder their practical applications [20,23]. It is necessary to design dual-or multiband metamaterial absorbers with polarizationinsensitivity. It is an effective method to obtain the dual-band or multiband response by combining the resonance of the superunit structure at several discrete frequencies [47][48][49][50][51][52][53]. For example, Feng et al demonstrated dual-band and multiband infrared absorber by horizontally arranging several subunits of different sizes into one unit cell [47]. Guo et al presented ultra-broadband absorber by using four subwavelength resonators in the infrared region [48]. Zhang et al reported a dual-band absorber by vertically stacking two distinct dielectrics [49]. However, these reported approaches face two challenging problems: large size unit problems and technical difficulties in manufacturing at higher frequencies such as terahertz, infrared, and visible region.
Herein, we demonstrate a polarization-insensitive dual-band plasmonic metamaterial absorber constituted by merely a metallic nano-cylinder and a continuous metallic ground separated by a middle dielectric layer. It is found that there are two distinct absorption bands whose peak absorption (about 96.5%) in the fundamental mode and peak absorption (99%) with surface lattice resonance. It is different from previous work that the dualfrequency response is obtained by combining two subunits of different sizes. The proposed dual-band absorber makes use of the overlap of the fundamental frequency resonance and the surface lattice resonance of the periodic structure formed by a single metal pattern, and thus making the proposed dual-band absorber quite easy to manufacture than previously reported structures. Importantly, the absorption peak results from surface lattice resonance not only has narrow line-width but also shows significant sensing characteristics for slight changes in the surrounding media. Furthermore, numerical simulations demonstrate the proposed absorber could retain high absorption level at large angles of polarization.

Structure and design
The proposed dual-band metamaterial absorber is shown in figure 1, which is consists of three layers. The top layer is a gold cylinder. The middle layer is the dielectric layer and the bottom layer is gold film. The gold cylinder-dielectric gold structure is abbreviated as GCDG. The structure is fabricated on a glass substrate. The gold cylinder had a radius (R) of 0.366 um, thickness of t=57 nm. The middle dielectric layer had a dielectric constant of 1.96 [23] and a thickness h=35 nm. The thickness of the ground layer gold film is L=0.1 um, and the lattice constant is P=0.765 um. The dielectric constant of gold is from reference [47,48]. The finite difference time domain (FDTD) method is used to get the exact results. In the simulation, the periodic boundary condition is applied along the x and y direction, and perfectly matched layers are set along z-direction. The absorption of the structure is obtained by = -- , where transmission » T 0, when the thickness of metal plate (L=0.1 um) is much larger than the skin depth. The perfect absorption can achieve as reflection close to zero (i.e. the equivalent impedance of metamaterial absorber structure matched to air).

Results and discussion
The reflectivity, transmission and absorption spectra of the GCDG structure are shown in figure 2. It is clear that the reflectivity curve have two significant dips result from two distinct type resonances. The transmission T is zero owing to the presence of the metallic bottom layer, which blocks the transmission of the incident beam. Therefore, two discrete nearly perfect absorption peaks appear, the absorption of which are 96.5% (F 1 = 281.1 THz) and 99% (F 2 =424.5 THz), respectively. The peak F 2 at 424.5 THz has the absorption line-width of 6 THz, which is about one-sixth of the peak F 1 at the 281.1 THz (the absorption line-width 30 THz). Furthermore, the quality factor (Q) is written as = Q F FWHM, / where F and FWHM are the resonance frequency and the full width at half maximum, respectively [22,23]. The Q value of peak F 2 is about 71, which is 8 times of peak F 1 . It is known that the narrow line-width and high Q value are promised for sensing performance. This result is confirmed in below figure 10. It is demonstrated that the peak F 2 has the sensitivity 200 THz/RIU and figure of merit 33, which are superior to better than that of the many sensing devices, see below table 1.
The absorption mechanism of the proposed absorber can be analyzed by the impedance match theory. We retrieve the electromagnetic parameters through the parameter inversion method [34]. Figure 3 shows the retrieved parameters for the proposed absorber including the effective permittivity, permeability and impedance. It is found that at the resonance peaks F 1 =281.1 THz and F 2 =424.5 THz, the impedance Z 1 =0.96-0.32i and Z 2 =0.99+0.26i, respectively, which are ideally match to the free space impedance at the frequency.
To estimate the effective input impedance of the metamaterial absorber, the transmission line modeling [41][42][43][44][45] is introduced in figure 4. Figure 4 where =j 1 . k h and k t are the respective wave vector of the dielectric layer and gold particle layer. At two resonance absorption frequency 281.1 THz and 424.5 THz, effective input impedance calculation by equation (3) are 0.94-0.29i and 1.01+0.22i, respectively, which are approximately identical to the figure 3. It is proved that the condition of impedance match to the free space impedance at the resonance frequencies.
The peak F 2 with narrower absorption line-width and higher Q come from the surface lattice resonance of the basic unit, while the peak F 1 arises from the fundamental resonance. To give an intuitive argument, we show the dependence of absorption spectra on the different lattice constant in figure 5. It can be found that the peak F 2 shift to less frequency with the increase of the lattice constant P, while the shift of peak F 1 is neglected. Therefore, the physical mechanism of peak F 2 is attributed to surface lattice resonance, which is distinct from previously reported sandwich structure with only EM resonance or interference mechanisms [24,25]. The surface lattice resonance can be predicted approximately by the first-order diffraction mode of grating [23]. The resonance frequency can by expressed as

( ) ( )
Where c is the light speed in air, b is a numerical factor, n is the refractive index of the device surrounding, i and j are the grating diffraction orders, and P is the grating constant (or the unit period). The function relationship of the resonance frequency on the lattice period P is shown in figure 6. It can be seen that the resonance frequency  linearly rises with the lattice period P decreasing. The theoretically predicted the resonance frequency indicated by pentagram agrees roughly with the result of simulation when the lattice period P varies from 0.765 um to 0.795 um. The resonance frequency of surface lattice resonance in simulation results have a little deviation for the theoretical value of the one-order diffraction modes. This is because a surface lattice resonance involves the interplay of the dipole resonance and the first order diffraction mode [22,23].
To reveal the physical mechanisms of the two resonance peak, the electromagnetic field and surface current distribution of the GCDG structure are shown in figure 7 and figure 8, respectively. Figure 7(a), (c), (e), (g) are   figure 7(e). The induced dipole resonance caused a strong coupling effect with the bottom metal plate, resulting in the magnetic field distribution mainly gathered in the bottom edges of the metallic cylinder, as shown in figure 7(g). Therefore, the surface current distribution determined by the dipolar response is formed, as shown in figure 8(a). As a result, peak F 1 result from the fundamental electric and magnetic dipole resonance.
Whereas, at the resonance frequency F 2 =424.5 THz, the electromagnetic field distribution features the surface lattice resonance [23]. It is seen in figure 7(b) and 7(d) that the electric field distributions mainly concentrate symmetrically on the top surface edges of the cylinder. Figure 7(f) shows a larger number of positive and negative charge are accumulated symmetrically on the top surface edges of the cylinder, generating a pair of anti-parallel currents that form a complete loop between the top and bottom metal layer, as shown in figure 8(b). The magnetic field is distributed in the top cylinder edge and the middle dielectric layer, as show in figure 7 (h). Thus, the peak F 2 is attributed to lattice resonance [1,23]. Therefore, we proposed a new approach to obtain dual-band absorber by combining two different resonance modes in a single pattern structure.
In lots of situations, it is desirable to design a polarization insensitive absorber [9,26]. Figures 9(a) and (b) show the dependence of the GCDG absorber on the polarization angle for the TE and TM modes, respectively. It is found that the location of absorption peaks and absorbance remained unchanged as the polarization angle change from 0 to 90 degree at normal incidence. It is easily understood because of the high degree of symmetry for the metallic cylinder in figure 1.
Since the first absorption peak has a high Q value, it is promising for sensing application [25,29]. For verification, figure 10(a) shows the dependence of the absorption spectrum when the surrounding refractive index (RI) from n=1.0 (air) to 1.1 with the interval of 0.02. From figure 10(a), we can find that peak F 2 is redshift, while the peak F 1 changes weakly with the increase of the RI. The functional relationship between the resonance peak F 2 and the RI (n) is shown in figure 10(b). It is shown that resonant peak redshift linearly with the increasing the RI of surrounding. Additionally, the absorption bandwidth and absorption are almost unchanged due to the impedance of the proposed absorber matched to the free space.
To evaluate the sensing performance of the proposed absorber, the sensitivity (S) and the figure of merit (FOM ) are defined as follows [22,23]: where DF and Dn are the changes of the resonance frequency and RI, respectively. From equation (2), the sensitivity and FOM of the resonance peak F 2 are 200 THz/RIU and 33, respectively. This is larger than the value than previously reported light devices, see table I [51][52][53][54][55][56][57][58][59][60][61][62].The high Q and sensitivity have potential application in detection and sensing.

Conclusion
A simple design of polarization-insensitive dual-band plasmonic metamaterial absorber composed by only a gold nano-cylinder and a continuous gold ground separated by a middle dielectric layer is reported. Two distinct absorption peaks derived from the fundamental resonance and the surface lattice resonance with over 97% absorbance are presented. The effective medium method and the transmission line modeling are consistent with the simulation results. In addition, proposed dual-band absorber is insensitivity for all polarization angles of both TE and TM modes on normal incidence. Importantly, the absorption peak result from surface lattice resonance has high Q and a large sensitivity, which has significant potential in the application of biosensors.