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Abstract
This paper shows a strategy to realize ultra-broadband absorption of multi-spectral coverage. A vertical cascaded plasmonic absorber constructed by multilayer helical metallic nanostructure wrapped in a pyramid-shaped dielectric jacket is presented and investigated by numerical simulations. By premeditated planning of the scale proportions of the spirals and the dimension size of the pyramid-shaped dielectric, more than 90% of absorption is realized in 189-3896 nm, an ultra-wide spectral range that basically covers the bands of near-ultraviolet, visible light, and near-infrared. The excitation mechanism of electromagnetic resonance and the formation process of light trapping are both included in the investigation through the analysis of electromagnetic field distribution. The localized surface plasmon mode in the metallic nano-spiral and the Fabry-Perot cavity mode with the gap plasmon resonance in the dielectric gap cooperatively make a significant contribution to reduce the reflection and form the ultra-broadband absorption. The simulation results show that the proposed absorber is basically insensitive to the incident angle and polarization angle, which basically keeps more than 90% absorption within the incident angle of ± 80 °. Such a specific implementation idea can also be applied to the terahertz region by modifying the geometrical size of the structure. This presented design implies new viability to develop the broadband photodetectors, solar cells, and thermal emitters.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, a kind of artificial composite material has long been pursued thanks to its excellent abilities to tailor the electromagnetic wave (EMW), which is called metamaterial. Such a subwavelength periodic structure processes eminent adaptability from microwave to terahertz and optical frequencies. Through the premeditated customization of the patterns of metamaterial, the amplitude and phase of EMW can be adjusted arbitrarily to modulate the propagation of electromagnetic waves effectively. This extraordinary property opens a new field of vision for both civil and military electromagnetic devices [1–3].
As one of the most significant applications of metamaterials, energy-absorbing has gained plenty of attention in invisibility cloaks [4,5], thermal emitters [6,7], solar cells [8,9], reduction in radar cross-section [10,11], and so forth. Although up to now, numerous variants of metamaterial-based absorbers have been proposed and thoroughly investigated. In 2015, Liao et al. [12] designed a bilayer grating absorber in the infrared regime with excellent wide-angle stability, whose absorption is larger than 0.99 in the range of 0–20 °. In 2018, Zhang et al. [13] proposed a dual-band metamaterial absorber for normal incidence based on a five-layer metal-dielectric-metal stacked structure. As demonstrated in their simulations and experiments, such a design exhibited two absorption peaks above 95% in the visible region. In the same year, the research group of Tan et al. [14] presented an ultrasensitive metamaterial absorber sensor with a three-dimensional split resonator, which breaks the conventional two-dimensional metamaterial design method. The sensing performance of their design possessed a maximum refractive index sensitivity of 34.40% RIU−1.
A common drawback of narrow absorption band still haunts them, which is originated from the limitation of resonance bandwidth. How to achieve total absorption in a broad spectral range together with high efficiency and fabrication simplicity has been put on the table as a huge challenge, and waited for all kinds of feasible solutions. A classical strategy for near-perfect absorption is to use the localized surface plasmon (LSP) formed by the high intrinsic damping of metal to achieve the so-called light trapping [15–17]. Then, through the special topological arrangement in horizontal [18–20] or multi-sized resonators stacking in vertical [21–23], the broadband absorption can be obtained by the convergence and fusion of multiple narrow-band resonant frequencies. But the bulky volume and complex fabrication are still the stumbling blocks for their research progresses. Furthermore, some productive methods such as the excitation of the magnetic/electric plasmon resonance (or both of them) in the metal-dielectric-metal nanostructures, and the utilization of the slow-light waveguide constructed from conical hyperbolic metamaterial, are successively investigated for effectively absorbing and trapping the electromagnetic waves over an ultra-wideband frequency spectrum. For instance, Hao et al. [24] proposed an optical absorber composed of the Au/Al2O3 spacer/Au structure to realize a 88% absorption at the wavelength of 1.58 µm. Ding and his colleague [25] proposed and experimentally demonstrated an ultra-broadband absorber based on a conical hyperbolic metamaterial array.
Nowadays, how to improve the efficiency of solar energy absorption by photo-thermal and photo-voltaic devices, how to realize the electromagnetic cloaking for escaping the capture of infrared radar detection, how to use ultraviolet spectrum absorption for bio-molecular detection, and how to prevent the crosstalk effect of optical interconnection in integrated circuits. These research hotspots and posers are urgently waiting for adaptive solutions, in which the design of an ultra-wideband optical absorber covered multiple spectra is a key to break the limitation to provide more potential application.
In this paper, a multi-spectral covered plasmonic absorber is numerically investigated, whose near-unity absorption can be realized in the near-ultraviolet, visible light, and near-infrared bands. The absorption is mainly originated from three factors: the field localization effect brought by the LSP mode, the Fabry-Perot (FP) cavity mode, and the gap plasmon resonance formed in the spacer gap. The combination of horizontal and vertical coupling makes the absorption greatly enhanced. The essential physical mechanism and design demonstration process are discussed and analyzed in detail. By reasonably optimizing the dimensions of different dielectric layers and the scale factors of embedded spirals, the absorption bandwidth can be improved by the required manipulation. As a result, the displayed ultra-broadband plasmonic absorber with high-quality features will be a better candidate for promoting the comprehensive potential development of infrared, visible, ultraviolet, and another multi-spectrum. It is worth paying attention to how to use experiments to verify the given design, which is not included in the content of this work.
2. Structure design
The structural configuration of the unit cell for the presented absorber is schematically illustrated in Fig. 1. The main structure is constituted of nine vertical cascade Archimedes spirals (AS) and a pyramid-shaped dielectric supported by a flat metallic mirror
Fig. 1. Schematic views of the unit cell for the presented plasmonic absorber: (a) the side view, (b) the vertical view, (c) the stereoscopic perspective, and (d) the enlarged detail view of the first ASs.
Each AS can be considered as a plasmonic resonator, and to trigger the effective excitation of the LSPs, silver is adopted for all the metallic parts, whose dispersive dielectric constant meets the Drude model [26]:
From the bottom to the top in Fig. 1(a), nine AS are assigned to three groups in a group of three. In the bottom AS group (Group 1), the turning directions of the bottom and top AS are the same but own a 180 ° reversal with the intermediate one, which can effectively eliminate the polarization conversion phenomenon caused by the asymmetry of the spiral structure itself and further contribute to the absorption enhancement. Such an arrangement also appears in the other two groups.
As shown in Fig. 1(d), the turns number N and radius ratio α (the ratio of the final radius to the initial radius r1=8.5 nm before and after spiral rotation) of the bottom AS are 12 and 20.3, respectively. Taking the size of the bottom AS in Group 1 as the basic denominator, the scaling proportions along the x-y dimension of the second and third ASs in Group 1 to the first one have been customized, whose proportional values are k11 = 0.81, k22 = 0.5. Similarly, the same proportion distribution also appears in Group 2 and Group 3. It is noteworthy that the spirals in Group 2 and Group 3 have an additional scale reduction compared to Group 1, respectively, which is k33 = 0.6897, k44 = 0.3655, respectively. Therefore, from a global perspective, the scaling proportions of nine ASs shrink k1=1, k2=1×k11 = 0.81, k3=1×k22 = 0.5, k4=1×k33 = 0.6897, k5=1×k11×k33 = 0.5587, k6=1×k22×k33 = 0.3449, k7=1×k44 = 0.3655, k8=1×k11×k44 = 0.2961 and k9=1×k22×k44 = 0.1828 times in turn, as shown in Fig. 1(c). In addition, all the ASs thicknesses are constant to w=90 nm in the process of scaling.
Diverting the attention to the design of dielectric, a truncated pyramids configuration is employed as an anti-reflection device to provide gradual variations of reflection and refraction in the concave dielectric cavity, which provides the foundation for the enhancement of absorption. The pyramid dielectric is made up of the Al2O3 (the relative permittivity is 2.28 and the loss tangent is 0.04) [27], and it is composed of three square slabs with the thicknesses of h1+h2+h3+2w=304 nm, h1+h2+h3+3w=394 nm, and h1+h2+h3+3w=394 nm, separately. The lateral period of the bottom square dielectric slab is p1=536.5 nm, and a lateral side reduction has appeared which lets the side lengths of the upper two dielectric slabs be determined as p2=k33×p1=370 nm and p3=k44×p1=196.1 nm. We can see distinctly from Figs.1(a) and (c) that there are one AS attached to the top of pyramid-shaped dielectric and eight AS embedded in it, of which the first and second AS counted from the bottom are wrapped in the large dielectric slabs, the third to fifth in the medium-sized dielectric slabs and the sixth to eighth in the small dielectric slabs.
All detailed formulations of the parameters are recorded in Table 1. The settings of the Master-Slave boundary along the x- and y-axes are used to simulate such a periodic structure. When the incident light along -z-axis is impacted to the proposed absorber, the illustrations for transverse electric (TE) and transverse magnetic (TM) waves are shown in Fig. 1(c) and the following results are simulated by the commercial software HFSS.
Table 1. The detailed parameters of the presented plasmonic absorber
3. Results and discussion
Absorption A(ω) is one of the most important indexes to measure the performance of an absorber, which is described by two frequency-dependent parameters including reflectivity R(ω) and transmissivity T(ω). Further, R(ω) and T(ω) can be expounded by the scattering parameters as shown below
It can be informed from Eqs. (2) to (4) that to maximize the absorption, we need to keep the R(ω) and T(ω) as low as possible. On the one hand, the thickness of the bottom silver plate (w1=150 nm) is greater than the penetration depth, which acts as an optical opaque mirror to block the transmission of light. As a result, the T(ω) should almost completely approach 0 in the working wavelength. On the other hand, through the special planning and designing of the dimension sizes of the spirals and dielectric, a gradient change of refractive index between air and dielectric is produced to make the impedance of the overall structure better match the free space. Hence, the R(ω) will be effectively suppressed in a wide operating wavelength.
In Fig. 2, the reflectance, transmittance, and absorption spectra of the proposed absorber for normal incidence are simulated and presented under TE and TM modes. It is obvious that whether in TE or TM mode, the near-perfect absorption is exhibited in 189–3896 nm with the relative bandwidth of 181.49%, which basically covers the near- (300–400 nm) and mid-ultraviolet band (200–300 nm), the visible band (400–780 nm) and the near-infrared band (700–2500 nm), and partially dabbled in the far-ultraviolet band (100–200 nm) and mid-infrared band (2500–25000 nm). This feature greatly enriches its application fields, such as infrared thermography, invisibility cloak, ultraviolet biological measurement, and so on.
By means of S-parameter inversion, the normalized equivalent impedance Zr of the proposed absorber is calculated by Eq. (5) to judge the matching degree with the free space impedance for achieving perfect absorption [28,29]. Such a case will be realized when the real part and the imaginary part of Zr close to 1 and 0, respectively. Figure 3 shows the Zr of the proposed absorber for TE and TM modes, where the red and blue curves correspond to the real part and the imaginary part. It is clear from Fig. 3 that the real part of Zr is floated around 1, while the imaginary part is around 0. This means that an effective impedance matching appears between the absorber and the free space so that more electromagnetic waves can enter into the structure and be lost without being reflected.
Fig. 2. The reflectance, transmittance and absorption spectra of the proposed absorber: (a)TE mode, and (b) TM mode.
Fig. 3. The real part and the imaginary part of Zr of the proposed absorber: (a) TE mode, and (b) TM mode.
In the practical application of a natural electromagnetic environment, a stable ultra-broadband absorber, which can leisurely handle the arbitrary-directional incoming beam with various polarization forms, is extremely requisite. Figure 4 and Fig. 5 show the absorbance spectra varied with different polarization angles (maintaining normal incidence) and incident angles (for TE and TM modes), respectively. From Fig. 4, the 360 ° omnidirectional absorption spectrum concretely exhibits a kind of roughly polarization insensitivity in the mid- and high- operating band above 1500 nm, only slightly fluctuates before 1500 nm, but its absorption value is always kept above the threshold of 0.9. Furthermore, Fig. 5 shows the wide-angle stability of absorption from the perspective of two modes. As for the TE mode in Fig. 5(a), we can intuitively see that the absorption maintains above 0.9 steadily to a great extent in the ultra-wide incident angle range of ± 70 °. Even when the incident angle keeps growing to ± 80 °, it is just slightly insufficient that the absorption weakens to about 0.7 in the range of 1555–2880 nm, but it is still within the acceptable scope. On the other side in Fig. 5(b), the absorption for the TM mode maintains stabilization within the incident angle of ± 40 °. The continuous enlargement of the incident angle will lead to splitting at 1042 nm, and as the partitioned wavelength, the absorption in 187–1000 nm and 1213–3000 nm are kept above 0.8 within the incident angle of ± 80 °. Therefore, in the overall situation, the proposed absorber can get rid of the sensibility of polarization form to a certain extent for normal incidence, and keep independent of the incidence angle in an ultra-broad operating band whether in TE mode or TM mode. The comparisons with some similar existing reports are presented in Table 2 [30–33]. The research groups of Wu et al. [30] and Cao et al. [31] have made good progress in the aspect of operating bandwidth and angular stability, but they still have some limitations to hold a satisfactory section thickness. The case of Wang et al. [32] is just the opposite of theirs. The performances of Zhong et al.’s design [33] have a certain degree of improvement in many aspects but are extremely sensitive to polarization. In addition, many reports about the high-performance absorbers by nonmetal structures in the visible and infrared bands are also beginning to emerge in recent years. Zhao et al. [34] used the cascaded all-dielectric multilayer structure to open an absorption window with high rectangularity in 6.3–7.5 µm and almost maintained it with the oblique incidence angle at 45 °. Liao et al. [35] utilize the dielectric nanowire grids to produce perfect absorption based on the guided-mode resonance theory, but the drawback is the narrow bandwidth. So we can see that it is an arduous challenge to coordinate the compatibility of ultra-broad bandwidth and wide-angle stability while attempting to maintain a relatively thin section thickness. Our proposed design has conspicuous superiorities compared with most of the present reports and well fulfills the requirements of bandwidth, angle stability, and section thickness in the overall situation.
Table 2. The comparison with other wide angle broadband absorbers
To get a further comprehension of the physical origin and mechanism of ultra-broadband absorption, the electromagnetic field distributions at 2000nm, 348 nm, and 239 nm in TE and TM modes are presented in Fig. 6, where the effective non-zero field components are corresponded to be |Ey|, |Hx|, |Hz| for TE mode, and |Hy|, |Ex|, |Ez| for TM mode, respectively. When the incident light is impacted on this absorber, the electric field components |Ey| are localized at the cores of the AS, which are located in the middle and lower dielectric layers. Therefore, the LSP mode will be excited at the metal-dielectric interface. The reflection of the overall structure is largely decreased due to the huge localized field concentration, and these behaviors are illustrated in Figs. 6(a)-6(c) at 2000nm. With the reduction of operating wavelength, at 348 nm in Figs. 6(d)-6(f), the local distributions of electric field component |Ey| begin to influx to the compact ASs in the upper dielectric layer, and strong field confinements are observed at the AS-air interface, which demonstrates the clear characteristics of surface plasmons polariton. In the meantime, the field distribution patterns in the inverted tower dielectric spacer present a relatively weak FP cavity resonance and the excitation portent of gap plasmon resonance, and similar discussions have been studied in some previous grating structures [36,37]. Such phenomena are illustrated at 239 nm in Figs. 6(g)-6(i) more distinctly. The magnetic field |Hz| shows that the energy localization has been mainly transferred to the top dielectric and the four-order gap plasmon resonance is characterized in the dielectric spacer at this wavelength. The situations for TM mode in Figs. 6(j)-(r) take no need to go into details due to the similar principle explanation as mentioned above.
Fig. 6. The electromagnetic field distributions of the presented plasmonic absorber: (a)-(c) |Ey|, |Hx| and |Hz| at 2000nm for TE mode, (d)-(f) |Ey|, |Hx| and |Hz| at 348 nm for TE mode, and (g)-(i) |Ey|, |Hx| and |Hz| at 239 nm for TE mode, (j)-(l) |Ex|, |Hy| and |Ez| at 2000nm for TM mode, (m)-(o) |Ex|, |Hy| and |Ez| at 348 nm for TM mode, and (p)-(r) |Ex|, |Hy| and |Ez| at 239 nm for TM mode.
In conclusion, the ultra-broadband absorption property can be explicated by two main parts. One is the vertical coupling caused by LSP, whose excitation concentration region gradually approaches the top layer with the decrease of wavelength. The other is the transverse coupling brought by the FP cavity mode and the gap plasmon resonances, and the latter of which is particularly significant in low-wavelength regions. The electromagnetic field distributions |Ey|, |Hx|, |Hz| of the presented plasmonic absorber without the silver plasmonic resonators are presented in Fig. 7. Compared with Fig. 6, we can further verify that the LSP effect is triggered by the silver resonators and affects the absorption performance in the high wavelength region. With the decreasing of wavelength, FP cavity and gap plasmon resonances gradually begin to produce a marked effect, which makes a great contribution to the low wavelength absorption. By adjusting the structure configuration and dimensional parameters of the AS plasmonic resonators, the manipulation of the strength and position of surface plasmons can be realized. In addition, the trimming of the size of different dielectrics is aimed to enhance the FP cavity and the gap plasmon resonances for minimizing the reflection. Various types of resonances interact with each other at different wavelengths, resulting in a large broadening of the absorption band.
Fig. 7. The electromagnetic field distributions of the presented plasmonic absorber without the silver plasmonic resonators: (a)-(c) |Ey|, |Hx| and |Hz| at 2000nm, (d)-(f) |Ey|, |Hx| and |Hz| at 348 nm, and (g)-(i) |Ey|, |Hx| and |Hz| at 239 nm.
In addition, some intrinsic analyses of the absorption mechanism have made a thorough inquiry. First, the comparison of the absorption spectra with or without the silver plasmonic resonators is presented in Fig. 8(a) for a more comprehensive understanding. We can see that if all the silver plasmonic resonators are removed and only the pyramid-like dielectric layer is retained, the absorptivity is dropped greatly after 602 nm, showing the appearance of multi-frequencies absorption between 310–602 nm, and continuous broad operating band with the absorption higher than 0.9 before 310 nm. This phenomenon further confirms the fact that the LSP dominates the absorption in a high-wavelength band, while the FP cavity and the gap plasmon resonances lead the absorption in a low-wavelength band. Then, Fig. 8(b) exhibits a gradual evolution demonstration of the proposed plasmonic absorber. When our design is only composed of the underlying dielectric layer embodied in the AS Group 1, it is mainly characterized by multi-band absorption, whose noteworthy band with the absorption higher than 0.9 is located at 343–594 nm (the relative bandwidth is 53.58%). On this basis, by stacking a smaller dimensions dielectric layer and inserting the AS Group 2, the absorption of both high-frequency and high-wavelength regions have been significantly optimized and improved, but the effect in 548–637 nm slightly lacks the follow-up impetus. With the supplement of the top layer dielectric and the AS Group 3, the absorption spectrum tends to be complete, and the final performance is 189–3896 nm with a relative bandwidth of 181.49%.
Fig. 8. The comparison of various absorption spectra: (a) the case with or without the silver plasmonic resonators, and (b) the evolution demonstration process.
Moreover, some discussions on structural parameters are also included in the scope of the in-depth study. Figure 9 shows the effect of the compactness of the spiral coiling (the spiral turns number N) on the absorption spectrum. We can find that with the increase of the spiral coiling compactness, the absorption in the low-wavelength regions under TE and TM modes are improved to a certain extent. Figure 10 and Fig. 11 are absorption contrasts of different scaling proportions (k11 and k22), respectively. When k11 increases from 0.61 to 0.91, the high cut-off wavelength of absorption higher than 0.9 under TE and TM modes are both significantly shifted to the higher wavelength region, but the absorptivity of TE mode (around 1279 nm) and TM mode (around 554 nm and 1497 nm) deteriorate to diverse degrees. For k22 varies from 0.3 to 0.6, if this scaling proportion is too small, the absorption of TE mode will drop below 0.9 at 1185 nm. The phenomenon of TM mode shows an appearance of two main absorption weakening regions for the inappropriate selection value of scaling proportion. After comprehensive observation, it is not hard to know that the influences of two scale factors are mainly reflected in the low wavelength, which make the absorption curves more uneven and turbulent. On the other side, the responses on the absorption at a high wavelength are mainly manifested in the frequency shifting and convergence of the absorption peak. The analysis of structural parameters plays a guiding role in the process of improving and optimizing the proposed design. By considering the wide bandwidth and high absorption, N=12, k11 = 0.81, and k22 = 0.5 are chosen as the optimal values.
4. Conclusions
In summary, an obvious strategy to promote absorption enhancement and bandwidth extension is proposed by designing a vertical cascaded plasmonic absorber in this paper. Through the specially designing of the truncated pyramid dielectric layer and the silver plasmonic resonators with different scale factors, the near-perfect absorption is simulated in 189–3896 nm with a relative bandwidth of 181.49%. The changes in polarization angle and incident angle can only slightly affect the performance of the proposed absorber. The effects of plasmon resonances and FP cavity resonance are thoroughly discussed in the electromagnetic field distribution and the absorption comparisons (with or without the silver AS resonators). Meanwhile, the evolution demonstration diagram of the design process intuitively shows us the origin and formation mechanism of absorption enhancement, which lies in the interaction of horizontal and vertical coupling. These advantages, including ultra-wide bandwidth, near-perfect absorption, and angle stability, enable the proposed absorber scheme to make great achievements in solar energy collection, electromagnetic stealth, biological monitoring, electromagnetic compatibility, and so forth.
Funding
Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYCX21_0720).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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