Nanoplasmonic Pyramidal Metamaterial Absorber at Optical Frequencies

A pyramidal shaped metamaterial absorber (PMA) supports broadband and polarization independent resonant absorption at optical frequencies. The PMA is designed by stack of alternative plasmonic/dielectric multilayers. These nanoplasmonic pyramids offers resonant absorption characteristics at wide range of optical frequencies. The optimized PMA structure allows 76% spectral absorption and nearly perfect absorption (over 90%) at several bands between range of 400 nm – 1500 nm wavelength. These light absorption characteristics of PMA are useful for photodetection, thermal imaging, thermal emitters, and solar cells etc.


Introduction
Electromagnetic (EM) wave absorbers is the synthesized materials that can prevent the scattering of electromagnetic elds. Electromagnetic (EM) eld absorbers can be divided into two categories based on their mode of operation i.e., resonant and broadband absorbers [1]. Resonant absorbers depend on the material interrelating with the incident waves in a resonant fashion around certain frequency [2,3,4]. There are two scientists who independently created similar devices, who developed EM absorbers are W.
W. Salisbury and J. Jaumann [5,6]. One of these devices, known as the Salisbury screen was rst demonstration of resonant absorber. The resonant electromagnetic eld absorber are based on crossed grating structure that make uses a re ective metal sheet having an engraved shallow periodic framework [7,8]. On the other hand, the wideband absorbers depend on special materials whose characteristics are largely independent of electromagnetic frequency. Ideally such materials are well suited for this purpose that can contribute to inhibition of scattering of electromagnetic radiation over a wideband of frequencies [2]. Absorbers based on geometric transition are commonly used in anechoic chambers. Such absorbers can be categorized as broadband electromagnetic wave absorber. Another type of a broadband absorber, known as the sparse density absorber that relies on a very hollow materials so that its ll-factors can mostly be approximated nearly those of free space [1].
Recently, there is emphasis in scienti c community to design e cient metamaterial-based absorbers.
Metamaterials are the specialized structures with characteristic properties which are not found in nature [9]. These are synthesized with existing materials providing invisible properties in the nature, such as negative refraction [10,11], perfect absorption, and resonant induced transmission [12,13]. Metamaterials can be applied to various eld domains such as perfect lenses [14,15], chiral surfaces [16,17], transformational surface [18], optical cloaking [19], spatial light switching [20,21] and IR camou age and microwave antennas because of the certain useful characteristics [2]. In addition to other applications, the perfect metamaterial absorber (PMA) that can e ciently absorb electromagnetic wave with meta-materials provide tremendous near eld enhancements to improve the performance of solar cells [22], plasmonic sensor [23], thermal emitter and thermal image, photo-detectors [24].
Electromagnetic metamaterials (MMs) can be described as an effective medium and characterized by properties such as complex electric permittivity (ε) and magnetic permeability (µ) [25]. Much of the work in MMs has been focused on the real part of ε and µ, as it contributes to negative refraction etc. It is important to reduce losses and represented by the imaginary part of ε and µ [26,27] for practical applications related with wave propagation. On the other hand, absorbers rely on material losses to induce absorption. Lately, a thin metamaterial absorber (MA) have been projected by Landy et al., wherein electromagnetic resonance enables the MA to achieve matched impedance to free space [27]. The impedance is matching between effective medium forming metasurface with dielectric and background medium frequently free space, rejecting the re ection and e ciently absorbing the incident EM wave [27,28].
Several MAs have been attracted signi cant attention from microwave to optical frequencies [29,30]. However, the absorption bandwidth is frequently narrow due to the resonant nature of MAs. To overcome this problem, the MA units resonate at numerous adjacent frequencies to extend the absorption bandwidth [31,32]. Generally, the metamaterial absorbers are composed of a patterned metal lm overhead a continuous thin metallic lm with a dielectric substrate sandwiched in between them [33,34,4,8]. There are several reports on the extension of absorption bandwidth, however the bandwidth of the absorption still narrow [31], and in several studies the absorption spectrum is distributed to discrete absorption ranges [32].
Plasmonic metamaterial absorbers can also be used to harvest sunlight energy [22]. As the sunlight consists of spectrum ranging from ultraviolet, visible, infrared frequencies and it is often important to tap all the spectrum to fully bene t from the solar energy. Typically, the sun radiation consists of electromagnetic energy between a range of frequencies known as the Solar Spectrum [35]. Within this range the irradiance at different frequency varies i.e., sunlight energy irradiance is approximately 2% UV, 47% visible and 51% infra-red [36]. On the other hand, the shorter wavelength offers corresponding higher electromagnetic energy [37]. A plasmonic metamaterials absorber must be equipped to e ciently utilize all this energy source [39].
In this work, a pyramid metamaterial absorber (PMA) are proposed to provide wideband absorption at optical frequencies. The total absorption is dependent on resonances induced in the nanoplasmonic metasurface and the resonant interference between neighboring re ectors. The interference effects due to the multilayer metasurface are optimized to achieve wideband absorption of light at optical frequencies.
The proposed multilayer absorber offers potential for several applications including solar cell energy harvesting, sensing, photodetectors etc.

Pma Structure
The design illustration of the PMA is shown in Fig. 1, consisting of periodic array of quadrangular frustum pyramids on top of a continuous planar metal lm as the ground layer to prevent the elds in the forward direction. A unit cell of a periodic array is consists of multilayer nanoplasmonic metallic-dielectric quadrangular frustum pyramids. The sample of PMA is composed of ve metal/dielectric layers with a thickness of 10 nm each. The width of each layer increases linearly from the top to the bottom. Each two adjacent metal layers are separated by a dielectric spacer layer with the relative permittivity of 4.4. The metallic nanolayer is composed of gold. The optical properties of gold material are interpolated from experimental data reported by Johnson Christy [38]. The patch size with parameters Wt and W l of PMA mainly dominates the resonance frequency, and the thickness of the dielectric spacer t d controls resonance interference. The ground of PMA is considered as a homogeneous metallic lm of enough large thickness to prevent the transmission of EM waves. The dimensions of the pyramid shown in Fig. 1 are t d = 10 nm, t m = 10 nm, P =100 nm, W l = 90 nm, W t = 50 nm, and the total thickness T = 100 nm (unless stated otherwise). A plane wave is normally incident on the PMA structure polarized along the xaxis having direction of propagation along -z direction. The four-fold symmetry of the structure allows the response of PMA polarization independent.

Simulation Modeling
The simulation of the PM A structure is performed by a Full wave electromagnetic simulation software. In the simulation setup, periodic boundary conditions are used in the x and y directions, and the incident and re ected elds are calculated at port de ned along vertical direction along z-axis.
Electromagnetic (EM) wave impinging on a PMA can be described as transmitted T(λ), re ected R(λ), or absorbed A(λ), which are associated with the energy conservation law: which T(λ), R(λ), and A(λ) are transmissivity, re ectivity, and absorptivity as functions of wavelength λ, respectively.
From the equation (1) we can calculate the absorption as A(λ) = 1 -T(λ) -R(λ). Since the ground is a thick layer of gold, therefore T(λ) = |S 21 (λ)| 2 = 0 is nearly zero. Here, scattering parameter S 21 is the transmission at port 2 given incidence at port 1. Then the absorption calculated as A(λ) = 1 -R(λ), where R(λ) = |S 11 (λ)| 2 is normalized re ected power. Here, scattering parameter S 11 is the re ection at port 1 given incidence at port 1. In order to achieve a high absorption A(λ) low re ectance R(λ) is mandatory. Similarly, as the absorption in PMA varies with frequency, therefore in order to investigate the absorption performance of absorptivity we describe a Relative Absorption Bandwidth (RAB) parameter as follows: W RAB (λ) = 2(λ large -λ short ) /(λ large + λ short ) × 100 2 where λ large and λ short are the large and short wavelength range having absorption A(λ) over 90%, respectively.

Result And Discussions
At the outset, we simulate the absorber for dimension such as thickness t d = 10 nm, t m = 10 nm, period P =100 nm, width W l = 90 nm, W t = 50 nm, and for 5 metallic layers (each metal layer is separated by dielectric spacer as shown in Fig. 1). The simulated re ection spectra are demonstrated in Fig. 2. The designed PMA illustrates the weakest re ection (10%) around resonant wavelength λ 0 = 1000 nm. Since the ground is made of homogenous metal, the transmission is nearly zero in the entire considered frequency range. In addition, Fig. 3 In this section we analyze the absorption characteristics due to variation in geometric parameters and resonance interference due to multilayer structure. The geometric parameters of PMA contribute to the absorption properties. To analyze the evolution of multilayer PMA we rst evaluate the response of single layer absorber. We examine the impact of changing the number of composite layers at xed height of the pyramid.
Starting from single metallic-dielectric layer to ve multilayers using xed parameters i.e., t m = t d =10 nm, and W t = 50 nm / W l =90 nm. Figure 3(a) clearly shows that multilayers contribute signi cantly to overall absorption properties. Absorption due to single layer design remains less than 10% throughout spectrum therefore, W RAB = 0. For 2-layers design results in strong absorption (over 50%) around resonant wavelength λ 0 = 1000 nm and W RAB = 6.58%. Similarly, for 3-layer pyramid design results in strong absorption (over 50%) along with large bandwidth, however resonant wavelength shifted to λ 0 = 900 nm and W RAB = 10.67%. For 4-layers pyramid design results in overall weaker absorption and W RAB = 8.67%. Finally, 5-layers pyramid design results in multiple bands of strong and weak absorption (over 50%) around λ 0 = 1000 nm and λ 1 = 650 nm wavelength respectively. It is clear from Fig. 4(a) that 5-layer PMA structure has the best absorption bandwidth. In addition, several resonances exist that contributes to overall wideband absorption characteristics. The variation in the absorption spectra shows that the broadband absorption is attributed to the combination of many adjacent resonant absorption peaks. Further layers can be added on top of fth layer, however we restrict to ve multilayers in the current PMA design.
Resonance interference can also be controlled by relative width of adjacent patch layers. To demonstrate the effect on absorption due to width of adjacent layers we de ne ratio between W t / W l . For this purpose, the width of the 5-layer PMA structure is varied in the following. Figure 4(b) shows the corresponding simulated absorption spectra effects for parameter W t / W l = 1, 0.75, 0.56, 0.5 and 0.25 respectively.

52.45%
It can be observed that as the ratio W t / W l is reduced, the bandwidth of absorption increases due to resonance interference coupling becoming strong. The optimized absorption of the incident wave takes place at the ratio 0.25. Furthermore, overall spectral absorption ({I}_{abs}) reaches 54.06% for W t / W L = 0.5. The reason behind the strong resonance interference leading to broadband absorption is resonant detuning effect due to relative change in width (W t / W l ) of adjacent layers. Such spectral detuning of resonances contributed from adjacent layers allows an overall wideband absorption support for PMA structure.
The absorption spectrum using ve multilayers of metal/dielectric material at (W t / W l = 0.25) can be further optimized. Keeping all other parameters xed, the thickness of dielectric patches (i.e., t d =10 nm, 20 nm, 30 nm) is varied, while thickness of metallic patches t m keeps constant at 10 nm shown in Fig. 4(c). Similarly, thickness of metal layers (i.e., t m =10 nm, 20 nm, 30 nm) is varied, while thickness of dielectric layer t d is xed at 10 nm shown at Fig. 4(d). A comparison between relative absorption bandwidths of absorption for the various ratios (Wt / W l ) is provided in Table 2.  It can be noted that the optimized absorption is at t d = 10 nm, t m = 30 nm, where W RAB (above 50%) absorption reaches approximately 88 and W RAB (above 90%) absorption reaches around 35 making the absorber appropriate for practical applications. Furthermore, spectral absorption reaches 76.7% between 400 nm -1500 nm range of wavelength.
The absorption spectrum can be further optimized by scaling the period (P) of the unit cell. We choose best result achieved using dielectric width t d = 10 nm and metallic width t m = 30nm. The period (P) along with all the geometrical parameters are either scaled down by 50% or scaled up by 150%.
In order strong absorption (over 90%) we make the scale down and scale up the whole PMA unit cell structure to half (50% P) and one and half (150% P) respectively. Figure 5 shows that the absorption for the original structure (i.e., 100% P) exhibits two absorption peaks above 90% absorption. Furthermore, by scaling up the period and the corresponding geometrical parameters of PMA structure (at 150% P) achieves optimized absorption performance. The comparison for scaling the geometrical parameter (P) is provided in Table 3.  Figure 1 Three-dimensional illustration of the pyramid metamaterial absorber array including the schematic of unit cell. The dimensions of unit cell are W t = 50 nm, W l = 90 nm, P = 100 nm, T = 100 nm, T m = 10 nm, and t d = 10 nm, where subscripts "m" represents thickness of metal, and "d" for dielectric layers. The simulated re ection spectra of the designed PMA shown in Fig. 1

Figure 3
The electric eld distribution of the designed PMA shown in Fig. 1    Absorption spectra of the multilayered metallic-dielectric quadrangular frustum pyramids due to variation in PMA structure from P = 100% to P = 50% and P = 150% at xed number of composite layers, W t / W l = 0.25 and t m = 30 nm.