At the outset, we simulate the absorber for dimension such as thickness td = 10 nm, tm = 10 nm, period P =100 nm, width Wl = 90 nm, Wt = 50 nm, and for 5 metallic layers (each metal layer is separated by dielectric spacer as shown in Fig. 1). The simulated reflection spectra are demonstrated in Fig. 2. The designed PMA illustrates the weakest reflection (10%) around resonant wavelength λ0 = 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(a)-(b) provides the electric field distribution on the surface of gold layers at 1000 nm wavelength having strong intensity surrounding the top layers of the pyramid. Similarly, Fig. 3(c)-(d) provides the normalized electric field distribution at 500 nm wavelength having highest intensity around top layer.
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 first evaluate the response of single layer absorber. We examine the impact of changing the number of composite layers at fixed height of the pyramid.
Starting from single metallic-dielectric layer to five multilayers using fixed parameters i.e., tm = td =10 nm, and Wt = 50 nm / Wl =90 nm. Figure 3(a) clearly shows that multilayers contribute significantly to overall absorption properties. Absorption due to single layer design remains less than 10% throughout spectrum therefore, WRAB = 0. For 2-layers design results in strong absorption (over 50%) around resonant wavelength λ0 = 1000 nm and WRAB = 6.58%. Similarly, for 3-layer pyramid design results in strong absorption (over 50%) along with large bandwidth, however resonant wavelength shifted to λ0 = 900 nm and WRAB = 10.67%. For 4-layers pyramid
design results in overall weaker absorption and WRAB = 8.67%. Finally, 5-layers pyramid design results in multiple bands of strong and weak absorption (over 50%) around λ0 = 1000 nm and λ1 = 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 fifth layer, however we restrict to five 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 define ratio between Wt / Wl. 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 Wt / Wl = 1, 0.75, 0.56, 0.5 and 0.25 respectively.
Table 1
Comparison between bandwidth of 50% and 90% absorption wavelength for varying ratio Wt / Wl.
Type (nm) | 50% Absorption Threshold | 90% Absorption Threshold | Spectral Absorption (\({\text{I}}_{abs}\)) |
Range of wavelength (nm) | WRAB | Range of wavelength (nm) | WRAB |
Wt / WL = 1 | 0 | 0 | 0 | 0 | 38.29% |
Wt / WL= 0.75 | 0 | 0 | 0 | 0 | 47.19% |
Wt / WL = 0.56 | 652 – 561 = 91 965.4 – 668.1 = 297.3 | 15 36.4 | 1200 – 1126 = 74 | 6.36 | 52.60% |
Wt / WL= 0.5 | 687.1 – 648.1 = 39 845 – 784 = 61 1012.5 – 932.2 = 80.3 | 5.84 7.49 8.26 | 983.8 – 973 = 10.8 | 1.1 | 54.06% |
Wt / WL= 0.25 | 500 – 400 = 100 893 - 598 = 295 1029 – 1001 = 28 | 22.2 39.6 2.8 | 707 - 690 = 17 865 – 840 = 25 | 2.4 3 | 52.45% |
It can be observed that as the ratio Wt / Wl 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 Wt / WL= 0.5. The reason behind the strong resonance interference leading to broadband absorption is resonant detuning effect due to relative change in width (Wt / Wl) 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 five multilayers of metal/dielectric material at (Wt / Wl = 0.25) can be further optimized. Keeping all other parameters fixed, the thickness of dielectric patches (i.e., td =10 nm, 20 nm, 30 nm) is varied, while thickness of metallic patches tm keeps constant at 10 nm shown in Fig. 4(c). Similarly, thickness of metal layers (i.e., tm =10 nm, 20 nm, 30 nm) is varied, while thickness of dielectric layer td is fixed at 10 nm shown at Fig. 4(d). A comparison between relative absorption bandwidths of absorption for the various ratios (Wt / Wl) is provided in Table 2.
Table 2
Comparison between bandwidths & WRAB of 50% and 90% absorption in case of changing td and tm.
Type (nm) | 50% Absorption Threshold | 90% Absorption Threshold | Spectral Absorption (\({\text{I}}_{abs}\)) |
Range of wavelength (nm) | WRAB | Range of wavelength (nm) | WRAB |
td = tm =10 | 500 – 400 = 100 893 - 598 = 295 1029 – 1001 = 28 | 22.2 39.6 2.8 | 707 - 690 = 17 865 – 840 = 25 | 2.4 3 | 52.45% |
td = 20 tm= 10 | 932 - 400 = 532 1049 – 992 = 57 | 79.9 5.6 | 703 - 652 = 51 786 -773 = 13 885 - 858 = 27 | 7.5 1.7 3.1 | 67.2% |
td = 30 tm= 10 | 1025 - 400 = 625 1137 – 1112 = 25 | 87.7 2.2 | 675 – 644 = 31 972 - 930 = 42 | 4.7 4.4 | 71.1% |
td = 10 tm= 20 | 956 - 400 = 556 1060 - 1010 = 50 | 82 4.8 | 500 – 900 = 100 656 - 625 = 31 746 – 680 = 66 | 14.3 4.8 9.3 | 73.7% |
td = 10 tm= 30 | 1029 – 400 = 629 | 88 | 570 - 400 = 170 640 – 622 = 18 712- 680 = 32 990 – 949 = 41 | 35 2.9 4.6 4.2 | 76.7% |
It can be noted that the optimized absorption is at td = 10 nm, tm = 30 nm, where WRAB (above 50%) absorption reaches approximately 88 and WRAB (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 td = 10 nm and metallic width tm = 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.
Table 3
Comparison between bandwidths & WRAB of 50% and 90% absorption in case of scaling up or scaling down of unit cell of PMA structure.
Type | 90% Absorption Threshold | 50% Absorption Threshold | Spectral Absorption (\({\text{I}}_{abs}\)) |
Range of wavelength (nm) | WRAB | Range of wavelength (nm) | WRAB |
50% P | 795 – 400 = 595 | 85.6 | 718 – 698 = 20 | 2.8 | 52.18% |
100% P | 1029 – 400 = 629 | 88 | 570 - 400 = 170 640 – 622 = 18 712- 680 = 32 990 – 949 = 41 | 35 2.9 4.6 4.2 | 76.8% |
150% P | 705 – 680 = 25 546.8 – 400 = 148.6 | 3.76 5.04 | 1171 – 400 = 771 | 98.15 | 76.7% |
It can be observed that scaling down the structure to 50% P the overall spectral absorption (\({\text{I}}_{abs}\)) reduces to 52.18 %. n comparison, the overall spectral absorption (\({\text{I}}_{abs}\)) of 100% P and 150% P reach ~76 %. Also the best absorption of EM takes place at 700 nm and 1000 nm reaches to approximately 96.64% and 99.93%. The increase in absorption with the relatively wider unicell period is attributed to expanded total cross-sectional area covered by the absorber multilayers.