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We propose a wide-angle, polarization-independent and dual-band infrared perfect metamaterial absorber made of double L-shaped gold patches on a dielectric spacer and opaque gold ground layer. Numerical and experimental results demonstrate that the absorber has two near-unity absorption peaks, which are result from magnetic polariton modes generated at two different resonant wavelengths. In addition, the proposed structure also shows good absorption stability in a wide range of incident anglesfor both TE and TM incidences at azimuthal angle φ = 0°. Moreover, we demonstrate that such structure has good absorption stability for a wide range of azimuthal angles due to the excitation of perpendicular magnetic polariton modes within the asymmetric double L-shaped structure. Such structure will assist in designing magnetic polaritons absorbing element for infrared spectroscopy and imaging.
© 2015 Optical Society of America
1. Introduction
Metamaterials are artificially-created media with uniquely engineered electric permittivities and magnetic permeabilities [1] and have attracted considerable interests in applications such as negative refraction [2–6], superlenses [7,8] and optical cloaking [9,10]. Recently, a “perfect” absorber with near-unity absorption can also be realized by metamaterial which is first proposed by Landy et al. [11]. By utilizing intrinsic loss, with the aid of appropriate structural design of the metamaterial, kinds of perfect metamaterial absorbers are designed at specific wavelength ranging from microwave region [11–13] to the optical wavelength [14,15], as well as in the infrared [16–19] due to the significantly improved sensitivity in chemical and biological sensing applications [20]. Strategies of absorbers in the mid-infrared also include composite grating superabsorber [21], photonic crystal superabsorber [22], broadband nanoresonator absorber [23]. Liu et al. [24] have designed a single band mid-infrared absorber using a cross-pattern metamaterial. Ye et al. [25] have further investigated the omnidirectional and polarization-insensitive properties of the cross structure. Since the single band infrared absorber has the limitation in applications such as spectroscopy and imaging [26], a dual band or multi-band infrared absorber and emitter is more desirable. Liu et al. [17] have further studied a dual-band absorber by laterally assembling a subunit to the original cross-pattern unit cell. Chen et al. [27] have studied a dual band perfect absorber by breaking the symmetry of the cross structure, but the asymmetric structure is always polarization-sensitive for incident waves. Further dual band perfect absorbers are also designed in the near infrared using elliptical nanodisks [28] and in the far infrared using electric-field-coupled resonator [29]. According to the above mentioned studies, a symmetric structure [24,25]is usually needed to realize a polarization-independent absorption; on this basis, a compound unit cell [17,28,30–33] or multilayered structure [13,19,34,35] is further required to exhibit a dual band or multi-band perfect absorptions, which makes the manufacturing process more complex. Therefore, it is desirable to design a dual band or multi-band perfect absorber with polarization-insensitive characteristic in a relatively simple structure, which has not been demonstrated in previous researches. In this paper, we propose a dual-band, wide-angle and polarization-independent infrared metamaterial absorber using double asymmetric L-shaped structure. It is shown that the absorber has two distinct nearly 100% absorption peaks. By analyzing the electric field distribution at the resonant wavelengths, we reveal that the dual band absorptions are generated by magnetic polariton modes excited at two different resonant wavelengths. Moreover, the absorption peaks can be tuned by the geometry parameters of the double L-shaped metamaterial. The wide-angle stability in both TE and TM incidences of the perfect absorber is also investigated.
2. Single L-shaped metamaterial absorber
The schematic of the unit cell for the proposed single L-shaped metamaterial absorber is illustrated in Fig. 1(a) and 1(b). Gold is set as the L-shaped patch and bottom metal layer with Drude model for the dielectric function, . Here the plasma frequencyrad/s and the collision frequency rad/s [36], where a gold nanostructure at the same wavelength regime was studied. SiC layer is chosen as the dielectric spacer with dielectric constant 10.8 and loss tangent 0.003. The thicknesses of the SiC layer and gold layer are td = 0.27 μm and tm = 0.1 μm, respectively. The structure has a lattice period of = 2.6μm in both x-direction and y-direction. The width and length of the single L-shaped patch are w and l, respectively. The transmission coefficient and reflection coefficient of the proposed structure are calculated from a commercial finite element method solver by CST Micro Wave Studio [37]. Here, we consider transverse electric (TE) wave impinging on the structure in x-z incident plane (where the azimuthal angle φ = 0°, which is the angle between the projection of incident light on x-y plane and x-direction) with an incident angle of to z–direction as demonstrated in Fig. 1(c), while the transverse magnetic (TM) incident wave would have an electric field on the x-z plane and a magnetic field along y-direction. Periodic boundary conditions are used for both x-and y-directions.
Fig. 1 (a) Top view and (b) side view of a unit cell of the single L-shaped metamaterial absorber, (c) TE incident wave impinging on the structure in x-z incident plane (where the azimuthal angle φ = 0°) with an incident angle of θ to z–direction.
Since the thickness of the metallic film used here is much larger than the typical skin depth in the infrared, the reflection is the only factor limiting the absorption. The absorption is given by A = 1-|S11|2 where |S11| represent the reflection coefficient. The simulated absorption spectra of the single L-shaped structure with different incident angles in the whole working range (5 μm-10 μm) for both TE and TM configuration are shown in Fig. 2(a) and 2(b).
Fig. 2 Absorption spectra of single L-shaped metamaterial with different incident angles for (a) TE configuration and (b) TM configuration, where the azimuthal angle φ = 0° and the length l and width w are respectively set as 0.8 μm and 0.4 μm.
It can be seen that the single L-shaped metamaterial at φ = 0° incident plane has dual band absorptions and a wide incident angle stability of absorption in TM configuration, but not in TE case. This is due to the fact that the intensity of the magnetic field on x-y plane decreases with the incident angle θ increase, thus the magnetic polaritons which contribute to the strong absorption (that would be convinced in next sections) cannot be effectively excited. Moreover, the oscillating direction of magnetic polaritons in the single L-shaped structure is related to azimuthal angle φ which should have an impact on the absorption stability. In order to build an L-shaped structure with good absorption stability and polarization insensitive, one need to modify the single L-shaped metamaterial to strengthen the absorption for TE incident wave for a wide range of incident angles and to exhibit good absorption stability for a wide range of azimuthal angle.
3. Structure design of the double L-shaped metamaterial absorber
By introducing an additional asymmetric L-shaped gold patch, we propose an asymmetric double L-shaped metamaterial absorber as illustrated in Fig. 3(a) and 3(b). The geometry parameters and material parameters are the same as that of the original single L-shaped structure, and the vertical distance between two L-shaped patches is d1 = 0.4 μm. The gold-based double L-shaped metamaterial is fabricated by standard electron-beam lithography and a lift-off procedure, and the SEM image of the sample is shown in Fig. 3(d). The TM wave at φ = 0° incident plane impinging on the double L-shaped structure is demonstrated in Fig. 1(c). Periodic boundary conditions are used for both x-and y-directions.
Fig. 3 (a) Top view and (b) side view of a unit cell of the L-shaped metamaterial absorber, (c) TM incident wave impinging on the structure in x-z incident plane (where the azimuthal angle φ = 0°) with an incident angle of θ to z–direction, (d) SEM image of the fabricated L-shaped metamaterial absorber.
4. Theoretical analysis and discussions
The absorption spectra of the double L-shaped structure at θ = 45°and φ = 0° for both TE and TM incident wave are shown in Fig. 4(a). Two perfect absorption peaks reaching 99.98% at λ1 = 5.86 μm and 99.96% at λ2 = 7.54 μm are observed in TE configuration, while 98.34% at λ3 = 6.03 μm and 98.90% at λ4 = 7.59 μm for TM incidence is observed. As an effective medium, metamaterials can be characterized by a complex electric permittivity ε(ω) = ε1(ω) + iε2(ω) and magnetic permeability μ(ω) = μ1(ω) + iμ2(ω). To exhibit resonant metamaterial absorber, our aim is to make the impedance (, which can be derived by S-parameter retrieval methods [2]) of absorber matching that of free space to achieve minimized reflection. The effective impedance for TE configuration is derived from the reflection and transmission coefficient of the L-shaped metamaterial, as illustrated in Fig. 4(b). It is clear to see that the real part of impedance is nearly 1 at λ1 and λ2, which matches that of free space.
Fig. 4 (a) The absorption spectrum of perfect absorber under the incident angle of θ = 45° and φ = 0°for both TE (red solid line) and TM (blue dotted line) configurations; (b) the imaginary part (solid line) and real part (dotted line) of the effective impedance in TE configuration.
To give a clear understanding of the dual band absorptions, the distributions of z component of the electric field profile in TE configuration at resonant wavelengths λ2 = 7.54 μm and λ1 = 5.86 μm on the double L-shaped patches and the bottom metal layer are shown in Fig. 5 and Fig. 6, respectively. It is shown in Fig. 5(a) that the electric field mainly distribute at the tail region of horizontal arm (x-direction) and vertical arm (y-direction) of the asymmetric double L-shaped patches at λ2 = 7.54 μm, while the electric field at the corner of the L shaped-patches are weak. In addition, the electric field distribution on the bottom metal layer at the same resonant wavelength is shown in Fig. 5(b), we can see that the electric field profile are just opposite in sign compared with that on the double L-shaped patches, which indicates that two induced current loops around the SiC dielectric spacer are formed. This characteristic of the electric field distribution reveals that magnetic polaritons are excited in each of the L-shaped patches, resulting in magnetic resonances. Furthermore, we should note that the oscillating direction of the two magnetic polaritons formed within the asymmetric double L-shaped structure is perpendicular to each other, which makes the absorber polarization-insensitive for a wide range of φ.
Fig. 5 The z component of electric field distribution at resonant wavelength λ2 = 7.54 μm on (a) double L-shaped patches and (b) bottom metal layer in TE incidence under the incident angle of θ = 45° and φ = 0°.
Fig. 6 The z component of electric field distribution at resonant wavelength λ1 = 5.86 μm on (a) double L-shaped patches and (b) bottom metal layer in TE incidence under the incident angle of θ = 45° and φ = 0°.
Similarly, we investigative the z component of electric field profile at resonant wavelength λ1 = 5.86 μm. Results in Fig. 6(a) show that the electric field are concentrated at the corner of the L shaped-patches, while the tail region of horizontal arm (x-direction) and vertical arm (y-direction) of the asymmetric double L-shaped patches are weak. In Fig. 6(b), we can see that the electric field distribution at the same resonant wavelength on the bottom metal layer are opposite in sign compared with that on the double L-shaped patches, which means that two induced current loops around the SiC dielectric spacer at the corner regions are formed. This indicates that different magnetic polariton modes are excited at the two resonant wavelengths, which generate the dual band absorption.
We have further investigate the stability of dual band absorptions with incident angle θ varying from 0° to 80° in Fig. 7(a) for the TE configuration and in Fig. 7(b) for the TM configuration at φ = 0°. In TE configuration, a dual band absorption up to 96% is realized when θ varies from 0° to 60°, where the highest absorption is obtained at θ = 45°. With the incident angle larger than 60°, the intensity of the two absorption peaks drops quickly. This is due to the fact that a component of magnetic incident field in the magnetic polaritons oscillating direction should be existed. In other word, it requires a component of magnetic field in x-y plane to excite the magnetic polaritons at φ = 0°. For TE incidence, the magnetic field in x-y plane is Hx-y = Hcosθ, where H is the intensity of incident magnetic field. Since the intensity drops quickly at θ >60°, thus resulting in a weaker magnetic resonance. In TM configuration with θ varying from 0° to 80°, the intensity of the two absorption peaks are still above 99%, and this is result from the stable component of magnetic incident field in the magnetic polaritons oscillating direction. Meanwhile, a slight blue shift of the two absorption peaks occurs with θ tending to larger value, which is mainly caused by the off- phase oscillating effect in each unit cell [25].
Fig. 7 Absorption spectra as a function of incident angle θ at φ = 0° (a) for TE polarization and (b) for TM polarization, and the intensity of absorption is given by the colormap.
Note that all the results abstained above are in the condition of the azimuthal angle at φ = 0°. Next, we investigate the stability of dual band absorptions at θ = 45° with different azimuthal angles φ for the TE configuration in Fig. 8(a) and for the TM configuration in Fig. 8(b). We can see that the intensity of the two absorption peaks is stable varying with different azimuthal angles from 0° to 80° because that the incident plane wave can be decomposed into two components with the magnetic field in the x–z or y–z plane, which can effectively excite the corresponding magnetic polaritons at the two resonant frequencies and then will be greatly absorbed. Notably, the present simulation results demonstrate that this structure have quite a wide azimuthal angle absorption for both TE and TM configurations. When φ is arbitrary value, taking TE configuration as an example, the magnetic field is Hx = Hcosθsinφ in x-direction and Hy = Hcosθcosφ in y-direction, thus the azimuthal angle φ is related to the oscillating direction of the magnetic field in x-y plane. However, the magnetic polaritons generated within the asymmetric L-shaped structure is perpendicular to each other at the resonant wavelength, which makes the absorption of double L-shaped structure insensitive with φ.
Fig. 8 Absorption spectra as a function of azimuthal angle φ at θ = 45° (a) for TE polarization and (b) for TM polarization, and the intensity of absorption is given by the colormap.
The influences of length l and width w of L-shaped patches on the absorption spectrum are also numerically demonstrated in Fig. 9. We find that both absorption peaks possess red shift with l increasing from 700 nm to 1000 nm in Fig. 9(a), where w is fixed at 0.4 μm unchanged. When w varies from 550 nm to 250 nm and l is fixed at 0.8 μm, the absorption peaks at short wavelength has a red shrift, while the other absorption peak possesses a blue shift as shown in Fig. 9(b). This indicates that the resonant frequencies of the absorption peaks are impressible by the geometry of the structure, and selective frequencies of the absorption peaks can be achieved.
Fig. 9 The absorption spectrum in TE incidence under the incident angle of θ = 45° and φ = 0°.varies with (a) lengths l of the L-shaped patches while w is fixed at 0.4 μm and (b) widths w of the L-shaped patches while l is fixed at 0.8 μm, and the intensity of absorption is given by the colormap
Since the absorption is generated by the magnetic polaritons, the above characteristics of the absorption spectrum can be explained by LC circuit model. The schematic of the equivalent LC circuit for the L-shaped resonator is demonstrated in Fig. 10, where Lm is the inductance of two parallel plates, Le is the inductance attributed to the drifting electrons of the nanoscale metal patches, Cm is the capacitance between two parallel plates sandwiched by the dielectric spacer and the capacitance Cg accounts for the contribution of the air gap between gold patches.
According to the circuit model illustrated in Fig. 10, the total impedance can be expressed as [38],
The magnetic resonance occurs when Ztot = 0, and the magnetic resonance condition can be derived as,Since Lm and Le are inversely proportional to the effective length leff of the magnetic polaritons at the resonant wavelength, Cm and Ce are proportional to leff, the magnetic resonant frequency is related to leff. From the electric field distribution at the two resonant wavelengths as demonstrated in Fig. 5 and Fig. 6, we can obtain that the effective length of the magnetic polaritons at λ2 = 7.54 μm is proportional to l-0.5w, and the effective length of the magnetic polaritons at λ1 = 5.86 μm is proportional to l + 0.5w, and this is the reason why the absorption spectrum behaves differently at the two resonant wavelengths with the variations of length l and width w. It can be concluded that w has a strong impact on the wavelength interval between the two absorption peaks, while the absorption peak at 7.54 μm is more sensitive to l.5. Experimental demonstration
The absorption of the sample is calculated by A = 1-T-R, where the transmission T is zero of the sample restricted by the gold ground layer. FTIR experimental technique is used to measure the sample reflection, and the experimental setup is shown in Fig. 11. Since the dimension of the sample is small (side length of sample is about 500 µm), a small hole is covered on the sample which has a strong impact on the detected reflection signal intensity. Therefore, the spectrum of sample reflection is measured under near normal incidence (here is about 22 degree) and unpolarized light to ensure large light flux.
The experimental absorption spectrum of the sample is shown in Fig. 12, along with the theoretical results for TE incidence at θ = 22° and φ = 0°. The dispersive model [39] of dielectric constant of SiC is adopted in theoretical calculation, and the geometry parameters of the L-shaped patches are chosen as w = 0.5 μm, l = 0.8 μm. From the experimental results (black-solid line), we can locate two strong absorption peaks. The intensity of the absorption peak at 6.2 μm is 88.5%, while the other peak at 6.9 μm is 82.7%. By comparing with the theoretical results, we can see that the measured absorption peak at 6.2 μm agrees well with the theoretical data, while the absorption peak at 6.9 μm has a slight blue shift due to the fabrication imperfections and roughness of the L-shaped structure. In general, the dual band absorption of the L-shaped metamaterial is verified both numerically and experimentally.
Fig. 12 Experimental(black-solid) and theoretical (red dash line is in TE incidence) results of the absorption spectrum of L-shaped metamaterial absorber at θ = 22° and φ = 0°.
6. Conclusions
We have numerically and experimentally demonstrated the absorption characteristics of a dual-band perfect absorber in the infrared regime. This absorber comprises a SiC dielectric layer sandwiched by an asymmetric double L-shaped gold patches and a gold ground. Two perfect absorption peaks are obtained with an incident angle of θ = 45°. The absorption spectrum varying with the geometric parameters of the L-shaped patches is also investigated. According to the distributions of the z component of electric field profile within the absorber, we obtain that the dual band perfect absorptions are result from magnetic polariton modes formed at two different resonant wavelengths. Furthermore, the perfect absorber also shows good stability over a wide range of azimuthal angle and incident angles for both TE and TM incidence. The polarization-independent property of the absorber is atributted to the mutually-perpendicular characteristics of magnetic polaritons excited within the asymmetric double L-shaped structure. This wide-angle, polarization insensitive, dual-band absorber infarared absorber offers potentials for thermal detectors and infrared imaging.
Acknowledgments
The authors are thankful for financial support from the National Natural Science Foundation of China under Grant Nos. 51176041 and 51121004.
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