We theoretically investigate the electromagnetic response of mixed-size sub-wavelength square hole array (M-SHA) combined with thick metal layer (TML). Near-perfect absorption with bandwidth about 17nm is firstly observed. Field distribution and dispersion relationship indicate that mixed surface plasmons (M-SPs) coupling is supported by M-SHA and TML. The absorption band is proved to be dominated by M-SPs coupling.
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Recently, the development of perfect meta-material absorber [1–4] has introduced a new application field of meta-material. In perfect meta-material absorber, simultaneous electric and magnetic resonance can be respectively supported in an unit cell by introducing electric resonant structure  and magnetic resonator [6,7]. Although simulation indicates that main energy is restricted in dielectric region which permits potential application to be a bolometer , the simultaneous electric and magnetic responses need rigorous structure dimension and design especially at near-infrared or even higher frequencies [1,3]. In fact, perfect absorption can also be found in other cases, for example surface plasmons (SPs) coupling on metal surface [8–14]. Electromagnetic energy is bounded at the interface of two mediums in the form of collective oscillations of the surface electrons when momentum matching condition is satisfied. In other words, no energy is reflected and transmitted. In previous work , sub-wavelength square hole array (SHA) has been shown to have narrow near-perfect absorption (Near-PA) peak at visible frequencies when combined with thick metal layer (TML). The parametric explorations have proved that this behavior attributes to SPs coupling supported by SHA and TML. In this paper, mixed-size sub-wavelength square hole array (M-SHA) is introduced to replace SHA. Mixed surface plasmons (M-SPs) coupling supported by M-SHA and TML is developed to expand the bandwidth of Near-PA. Compared with previous works which show Near-PA at single frequency point [1–4], M-SHA combined with TML maintains Near-PA with absorption rate larger than 95% and simultaneous bandwidth about 17nm.
2. Structure design and simulations
M-SHA consists of periodic alternate arrayed strip-1 and strip-2, which has respective Cell-1 and Cell-2 shown as Fig. 1 . This structure is analogous with that proposed by L. Kuipers et al [16,17]. The square hole in Cell-1 has dimension of a = 100nm and b = 110nm in x and y direction, respectively. Cell-2 is constructed by 90 anticlockwise rotation upon Cell-1, without change of the proportion of metal and period (P = 240nm) in the two strips as suggested in references 16 and 17. M-SHA and TML are separated by a middle dielectric layer as shown in Fig. 1(b). M-SHA, center dielectric layer and TML has respective thickness of ts = 20nm, td = 70nm, tm = 60nm. The computer simulation is performed using finite difference time domain (FDTD) method. In simulation, the polarization direction of electric and magnetic field is along with x and y direction, respectively. Corresponding periodic boundary conditions are considered. The in-plane mesh size is set to be 2nm so as to distinguish the difference of Cell-1 and Cell-2. Drude model is used to describe the realistic characteristic of gold at visible frequencies . The simulated wavelength range is from 500nm to 700nm. The observation planes are designed to be 750nm (larger than the maximum simulated wavelength) away from the adjacent structure surfaces.
3. Simulation results
The simulation results are shown in Fig. 2 . First, suppressed reflection (R) is observed in band between λ- = 591.72nm and λ+ = 608.84nm, which indicates impedance matching at the interface of M-SHA and free space. Second, transmission (T) in overall range is suppressed which attributes to T suppression of TML . Suppressed T and R are simultaneously attained in the band, resulting a Near-PA band with bandwidth about Δλ = 17nm (the gap between two maximum absorption peaks) as shown in Fig. 2. Comparing with single frequency absorption peak in previous work on perfect meta-material absorber [1–4], it is the first time that the broadened Near-PA band is obtained in M-SHA combined with TML.
The distribution of the electric field densities is presented to explain the physical origin of the broadened Near-PA band with the simulation results shown in Fig. 3 . From the electric field density shown in Fig. 3(a), it can be seen that most of energy is concentrated into Strip-2, which indicates that coupling at λ- only exists in Strip-2. While, as shown in Fig. 3(b), strong coupling at λ+ not exists in Strip-2 but in Strip-1. The different distributions of electric field density represent two different SPs coupling modes at λ- and λ+. This behavior is analogous with the discussion about SPs bandgap on metal surface bearing periodic texturing  where different distribution of oscillation of electrons shows different SPs coupling mode at bandgap edge. In this case, the different size of hole in Strip-1 and Strip-2 along the direction of electric polarization is the origin of different SPs coupling mode. As shown in Fig. 1(a), dimension of hole in Strip-1 is a = 100nm in x direction, while it is b = 108nm in Strip-2. It can be concluded that SPs coupling is supported by respective strip in M-SHA combined with TML. In overall Near-PA band, M-SPs are excited in both strips and bound in the two gold/air interfaces of M-SHA, such as that at 600nm shown in Fig. 3(c). The dispersion relationship at the interface of M-SHA and free space is also shown in Fig. 3(d). Apparent bandgap from f- = c/λ- to f+ = c/λ+ is observed. Wave vector is near zero in the bandgap, which results that R is suppressed as shown in Fig. 2.
The composite structure proposed in this paper is a specific case, as shown in Fig. 1. In fact, the structural parameters have significant influence on the electromagnetic behavior of M-SHA combined with TML. Reference 15 has proved that Near-PA has red shift with increasing period of SHA and degenerates into electric resonance of SHA with increasing dielectric thickness. While distinguishing with SHA, the size (especially the dimension of b) of the metal hole in M-SHA combined TML dominates the behavior of M-SPs coupling. As shown in Fig. 4 , the space between the two SPs coupling is broadened when the dimension of b increases. Although the larger space means wider bandwidth, the absorption rate in the band decreases rapidly. For example, absorption is only 60% when b = 116nm, which is much smaller than that (>95%) when b = 108nm. In other words, there exist optimal values of the hole size to obtain a bandwidth with high absorption, such as the presented case shown in Fig. 1. Although the bandwidth of Near-PA in this case is only about 17nm, M-SPs coupling in this case has exhibited indeed its potential ability for breaking the single frequency limitation of perfect meta-material absorber and broadening the bandwidth of Near-PA. Simultaneously, it can be expected that not restricted to two but more mixed-size holes can be introduced to obtain wider bandwidth of Near-PA.
Further, only normal incident light is investigated in the case presented in Fig. 1. In fact, as provided in reference 4, perfect absorption based on meta-material only exists in normal direction. Absorption rate will decrease when incident light is oblique. This conclusion can also been applied in the case shown in Fig. 1. As shown in Fig. 3(a) and (b), perfect absorption needs specific surface plasmons coupling between M-SHA and TML. When oblique incident light is applied, a slight shift of the absorption band should be introduced according to the momentum matching condition : k x ± 2nπ/P = k sp, where k x = (2π/λ)sinα is the wave vector of incident light, 2nπ/P is the grating momentum wave vector, k sp is the wave vector of the SP wave in the two gold/air interfaces of M-SHA and α is the angle of the incident wave as shown in Fig. 1. It is evident that an additional momentum is introduced by oblique incident wave. This will produce a slight change of the SPs coupling wavelength in M-SHA, which has been mentioned in reference 20.
In summary, Near-PA band with bandwidth about 17nm is shown when M-SHA is combined with TML. Theory of M-SPs coupling is developed to explain the absorption bandgap. In practical application, M-SHA combined with TML expands the application of perfect absorber in detection and imaging at visible frequencies. From the view of fabrication, M-SHA combined with TML has simpler configuration when compared with previous work [1–4] on perfect absorption. The single-layer structured surface simplifies the planar fabrication process.
This work was supported by 973 Program of China (No.2006CB302900) and National Natural Science Foundation of China (No.60507014, No.60528003 and No.60778018).
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