Simple designs for polarization independent, metamaterial absorbers at mid-infrared wavelengths and over wide angle of incidence are evaluated computationally. One design consists of an array of circular metallic disks separated from a continuous metallic film by a dielectric film, and shows over 99.9% peak absorbance and a resonant bandwidth of about 0.2 μm wavelengths. The effects of various geometric parameters are analyzed for this metamaterial. Another design consisting of an array of stacked metal-dielectric-metal disks is shown to have an absorbance of over 90% in a comparatively large band of over 1 μm bandwidth, although with a lower peak absorbance of 97%.
© 2012 Optical Society of America
During the past decade, there has been a phenomenal growth in the understanding and applications of metamaterials . Metamaterials are composite structured materials, structured at sub-wavelength scales, and depend on the structure to give rise to electromagnetic resonances. As the structures are sub-wavelength in size, metamaterials can usually be described by properly chosen effective medium properties. Due to the resonant behavior, metamaterials can exhibit extreme values of the effective medium parameters such as large and/or negative dielectric permittivity  and permeability .
The very resonant nature of metamaterials usually renders them dissipative, a property that has inhibited the use of metamaterials in many applications. Large absorption can, however, be desirable in many applications and can be difficult to achieve due to poor impedance matching to free space. The absorptive properties of metamaterials can be optimized to form highly absorbing metamaterial structures . In fact, structured surfaces with absorption coefficient approaching unity over specific spectral bands have been demonstrated. The design of such absorptive metamaterials can be scaled from microwave  and terahertz  through the infrared  almost into optical frequencies . Optimized metamaterials with high absorption have been proposed for applications such as thermal spatial light modulators , plasmonic sensors , thermal bolometers , solar thermo-photo-voltaics , heat coupler devices for photo-thermal reshaping  and anti-reflection coatings on opaque surfaces .
The design of most of these metamaterial structures is based on simultaneous resonant excitation of an electric dipole and magnetic dipole, and typically consists of a trilayer system. The top layer on which radiation is incident is a structured metallic layer, separated from the bottom continuous metallic layer by an intermediate dielectric layer of a suitable material. Note that the very large absorption results in these structures inspite of using non-dissipative dielectric materials and low ohmic losses in gold, particularly at THz and infrared frequencies. Several designs have been given in the literature for the top structured layer such as cross shaped resonators , electric split ring resonators  and rectangular/square patches . Many of these structures are not truly in the homogenizable limit as their unit cell sizes range from λ/2 to λ/6 . As the absorption is derived from only a single metamaterial layer, however, this has not been a contentious issue.
The structured units on the top act as electric dipole resonators driven by the electric field of the incident radiation. A second resonance with an anti-parallel currents in the two metallic layers can be excited by the magnetic field component of the incident radiation. These two anti-parallel currents along with the displacement field in the intervening dielectric act to form circulating current loops with a confined magnetic field in between. This situation is very much like the case of negative magnetic permeability in the fishnet structures  and wire pair structures . The induced circulating currents result in a magnetic dipole moment which can strongly interact with the magnetic field of the incident radiation . If the electric and magnetic dipole resonances occur at same frequency, then a strong localization of electromagnetic energy results in the metamaterial structure. Tuning the electric and magnetic resonance frequencies and their relative strengths can give rise to an optimal impedance matching for the incident radiation, thereby giving rise to strong absorption of the radiation.
In this paper, we present designs for polarization independent, wide angle, highly absorbing ultra-thin metamaterial absorbers for infrared frequencies. Our simple designs consist of disk shaped structures that are optimal from the perspective of rapid micro-machining processes such as laser micro-machining and lithography. The optimization of absorbance with respect to the ground plane thickness has been specifically studied by computer simulations. In comparison to the existing literature on the perfectly absorbing metamaterials, we find that the ground plane can be made extremely thin and the minimum thickness primarily depends on the skin depth of the metallic film. There is a smaller dependence on the disk and dielectric layer thicknesses. This effect is physically understood by the nature of the images charges formed in the ground plane. We also find that it is not necessary to have a continuous ground plane, and an array of three stacked disk of metal-dielectric-metal can also perform optimally as a metamaterial absorber with a broader bandwidth.
Our metamaterial structure consists of metal-insulator-metal trilayer patterned into a two dimensional periodic array: a disk resonator at the top with a continuous ground plane at the bottom separated by a continuous dielectric film [see Fig. 1(a)]. The circular nature of the disks is expected to give rise polarization independent excitation of the resonance. We chose a square lattice for the array. Gold is chosen to be the metallic element due to its chemical stability and low ohmic loss while the dielectric layer is ZnSe, an excellent infrared material with good thermal and mechanical properties. The properties of metamaterial absorber structures were calculated using the COMSOL Multiphysics package based on the finite element method. The dielectric permittivity of gold was modeled using the Drude expression17]. The dielectric permittivity of ZnSe in the wavelength of interest is taken from well known experimental results . The radiation was assumed to be incident along the X-axis on the metamaterial layers parallel to the Y–Z plane. The three dimensional unit cell was simulated using periodic boundary conditions along the Y–Z directions so that structure can be regarded as an infinite two dimensional array. The incident radiation is a transverse electromagnetic wave applied using wave-port boundary conditions . The frequency dependent reflectance[R(ω)] and transmittance[T(ω)] were obtained from the S-parameters in the simulation package and the absorbance was calculated as A(ω)= 1–R(ω)–T(ω).
In Fig. 1, we show the electromagnetic fields in the unit cell of an absorbing metamaterial structure with 1 μm diameter gold disk of thickness 100 nm and dielectric film thickness 60 nm. The incident wave is at the resonant wavelength 5.48 μm with an intensity of 0.25 W/cm2. The electric field distribution in Fig. 1(b) clearly shows the excitation of a dipole as well as a concentration of the electric field within the capacitive film in the gap between disk and the ground plane shown. The magnetic field distribution shown in Fig. 1(d) clearly indicates the localization of magnetic field in the insulating layer which is caused by oppositely oriented current sheets on the disk and the ground plane[Fig. 1(c)]. The currents in the two layers are slightly unequal or slightly out of phase, a feature that has been recently pointed out . Thus, there is a simultaneous excitation of an electric as well as a magnetic resonance. In Fig. 1(e) the Poynting vector associated with the radiation is depicted and the electromagnetic energy clearly flows into the resonator formed by the trilayer system. The resistive heating depicted by a color map in Fig. 1(f) shows that there is tremendous localized absorption within the metallic regions. The absorption in the continuous gold film is also in the regions near the disk only.
A change in the disk diameter will result in a shift of the electric resonance frequency, and hence, result in a change of the effective dielectric permittivity [ε (ω)] of the system. In comparison, a change in the dielectric layer thickness primarily affects the magnetic resonance and will control the effective magnetic permeability [μ (ω)] of the system. The capacitive coupling to the ground plane will also control the ε (ω), but to a lesser extent. Thus, the combination of the diameter of disk and layer thickness can optimized to effectiv match the impedance of the structure, , to vacuum, thereby strongly coupling the incident radiation to the resonant structure.
We show in Fig. 2(a) that the peak absorption can be shifted to larger values by reducing the dielectric layer thickness. The absorption in an optimized structure with 1 μm disks and various dielectric layer thicknesses, where the peak absorbance exceeds 99.9% is shown. These structures have continuous dielectric and gold films. A reduction in the dielectric layer thickness results in a red shift of the resonance as well as an optimization of the absorption. This can be understood by noting that the capacitance of the resonator increases with the reducing thickness and the resonance frequency, where L is inductance and C is capacitance of the structure, reduces. Note that when the dielectric layer thickness decreases although the inductance might also appear to reduce, the frequencies are large enough that magnetic resonance frequency no longer scales up with the reducing geometric inductance .
Our simple design shows a wide band absorbance of more that 90% for both TE and TM waves with an oblique incident angle ranging from −45° to 45,° as shown in Fig 2(e). It is observed from the figure that absorbance remains greater than 99% for both TM and TE waves for incident angle ranging from −25° to 25°. The absorbance varies more weakly with incident angle for TE polarized radiation as the entire electric field is parallel to the disk at all angles, while for TM polarization the electric field component normal to disk decreases at larger angles.
In Fig. 2(b) the behavior of the absorption band with the ground plane thickness is shown. In literature, this aspect has not been widely studied and it has been only noted that the dependence is weak . We begin by analyzing the role of ground plane. Principally at these frequencies, gold behaves somewhat as a perfect conductor, whereby mirror images of the charge distributions on the disk are formed on the continuous gold film. This is consistent with the oppositely flowing currents in the two metallic layers. We show in Fig. 2(b), the absorption in structures with varying ground plane thicknesses while keeping the dielectric layer thickness and disk diameter constant. It is seen that as long as ground plane thickness is a few times the skin depth of the gold film (25 nm at 5.5 μm wavelength, see for example ), the peak absorbance remains high(>99%). In complete agreement to our expectations, once the ground plane thickness is smaller than the skin depth the absorbance reduces and the reflectivity becomes large. For the ground plane thicknesses lesser than the skin depth, image charges are not effectively formed and proper magnetic resonance can not be established. This results in a dielectric dipole resonance without proper impedance matching resulting in a substantial reflection. Note that the transmittance through these resonant structures remains small (1% transmittance for 10 nm ground plane) even when the ground plane thickness is very small. In Fig 2(b) the spectral absorbance for metamaterial, with disk thickness 100 nm and ground plane thicknesses 50 nm, 100 nm, 150 nm, 200 nm are shown. The dielectric layer thickness is the same (60 nm) for all. It is seen that the peak absorption wavelength shifts to smaller values by moderate amounts with increasing ground plane thickness. This is caused by the reduced capacitance due to presence of more negative dielectric permittivity material for increased ground plane thickness. We further show that as the ground plane thickness approaches the skin depth, the peak absorbance keeps reducing, while red shifting by significant amounts. Note that this effect can not be understood if one considers the metal to be a perfect conductor. It is found that near unit absorption can still be achieved by reducing the ground plane thickness as long as the ground plane thickness is few times more than the skin depth. When the ground plane thickness approaches or becomes smaller than the skin depth of gold, the peak absorbance starts reducing from unity. Fig. 2(c) shows this reduction for ground plane thicknesses of 10 nm, 20 nm and 50 nm and a large red shift for the case of 10 nm ground plane.
The effect of the finite skin depth can be used to define the relative thickness of the disk and ground plane. In Fig 2(d), the effect of the gold disk thickness on absorbance is shown. It is found that the absorption decreases from unity as the gold disk thickness decreases. This effect arises because the charge distributions on the gold disk’s surface can not be reflected properly in the ground plane due to the finite skin depth. This is particularly true for the charges on the top surface of the gold disk.
We have also investigated the absorbance for a metamaterial structure consisting of two metal disks of 100 nm with a dielectric disk of 60 nm thickness sandwiched in between [see the inset in Fig. 2(f)]. The diameters of all disks are 1 μm. We found a large peak absorbance of more than 97% at 5.26 μm with an enhanced bandwidth as compared to the metamaterial structure with a continuous dielectric and gold films. The broadband absorption in these structures is due to a confined surface current in the bottom gold disk in comparison to the continuous ground plane. We note from our simulations that the surface currents in the ground plane disperse out away from area of the disk at off-resonance frequencies. In comparison, in the case of stacked disks, the surface currents are confined to the area of the disk at all frequencies. Hence a broadband absorption of over 1 μm bandwidth, although the extent of absorbance is reduced (90%) over this band due to imperfect impedance matching. The transmittance in the area of the stacked disks is noted to be almost zero.
In conclusion, we have provided a simple design consist of resonant disk-like metallic particle coupled to continuous dielectric and metallic films for highly absorbing metamaterial for mid-infrared wavelengths. These metamaterial structures exhibit high absorption of over 99.9% over large angular ranges of incident wave. Further, the absorption is reasonably polarization independent. We have investigated in detail the role of the ground plane thickness and shown that the minimum ground plane thickness is limited by the skin depth only. Another metamaterial absorber design consisting of stacked metal-disk-metal circular disk is shown to provide for broadband absorption (bandwidth1 μm), but with a smaller peak absorbance of 97%.
The authors acknowledge funding from the Instruments Research and Development Establishment (DRDO), Dehradun under grant no. 47542/S. GD acknowledges the Council for Scientific and Industrial Research, India, for a fellowship.
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