In recent years, the use of compact metamaterials configured to achieve perfect electromagnetic wave absorption has aroused widespread research interest. However, multidimensional and multishape nanoplasmonic design requires complicated fabrication processes, posing a great challenge to achieve high-performance, large-area optical absorbers in the visible spectral range. As a result, scholars have turned their attention to designing large-area devices with simple production processes, the most prominent structure being the metal-insulator (MI) double-layer configuration [1]. In a metal-insulator-metal (MIM) chamber or metal-insulator-metal-insulator (MIMI) cavity, the ultrathin metal top layer develops an electromagnetic field resonance that matches the surface impedance, which is beneficial for reducing reflection and improving light absorption; the dielectric middle layer forms a Fabry-Pérot cavity, and thus improves absorption (high field intensity); and the thick bottom layer effectively blocks the propagation of electromagnetic waves and reduces light transmission [2-4]. Shu et al. [2] found that the optical absorption of Ag/dielectric/Ag in the visible-to-near-infrared region was greatly affected by not only the thicknesses of the top and middle layers, but also the angle of incidence. Li et al. [4] used a 30-nm-thick top metal layer to design a large-area Ag/dielectric/Ag structure and achieved peak absorption of 97% with a bandwidth of ~17 nm. However, these systems cannot achieve strong absorption over a wide spectral range. Ghobadi et al. [5] proposed to achieve broadband (400–1,150 nm) perfect absorption with a MIM system through changing the thickness of the top metal layer and the metal filling fraction. Based on a low-quality-factor asymmetric highly lossy Fabry-Perot cavity, Li et al. [6] reported a MIM system that achieved almost perfect absorption (as high as 99.5%) across the entire visible spectral range (400–800 nm) with large incident-angle (over ±60°) independence.

To further the perfect-absorption features of layered metamaterial systems, other modified MIM structures have also been designed. Chen et al. [3] reported that a tripled bilayer MgF₂/Ag structure can achieve an absorption of >90% over the range of 900–1,900 nm at vertical incidence. Deng et al. [7] demonstrated the broadband perfect SiO2/Cr/SiO2/Au absorber, with the ideal permittivity of the metal layer for broadband absorption derived using the impedance transformation method. Applications of the absorption of MIM or MIMI structures have also been reported. Min and Veroni [8] theoretically investigated the absorption-switching characteristics of MIM plasmonic waveguides, and Chamoli et al. [9] proposed a one-dimensional MIM plasmonic grating as a visible-light perfect absorber, and its application in glucose detection. However, exploration of the optimized intermediate dielectric layer in the MIM structure, which addresses broadband perfect absorption and the impact of the system’s operating environment on absorption, has rarely been reported.

Typically, photonic and plasmonic systems are classically described based on the local, internal dielectric function (or conductance) of the material, and the geometry and shape of the structure [10-12]. Nevertheless, when the characteristic size of metal nanostructures is in the nanometer range (especially from 10 to 20 nm), the accuracy of description by traditional classical electromagnetism decreases, due to nonlocal and quantum effects [12-17]. To solve the dilemma, mesoscopic forms of quantum nanoplasmas are introduced, and the Feibelman d parameter was developed to build a bridge connecting the classical and quantum regimes [16, 17]. This theoretical method is based on the quantum surface response function, Feibelman d⊥ and d∨ parameters, by taking the electron gas to be uneven in the surface region, yet at the same time describing the properties of the internal structure with classical functions.

In this work, we analyze the light absorption and transmission characteristics of the MIM structure under three different circumstances [air, seawater, and an environment with large refractive index (RI)] by using the nonclassical Fresnel reflection-coefficient calculation under the d-parameter boundary conditions. To realize perfect light absorption over a broad wavelength range, the thickness and dielectric constant of each layer are optimized. In air, when the thickness of the top metal layer is 15 nm and the intermediate dielectric layer has a thickness of 70 nm and dielectric constant in the range of 0.86–3.40, the absorption of the system exceeds 98% across 680–1,033 nm. In seawater, when the thicknesses of the top metal and intermediate dielectric layers are 15 and 50 nm respectively, light absorption of ≥98% can be achieved over the wavelength range of 480–960 nm within the dielectric-constant range of 0.82–3.50. In an environment with large RI, ≥98% light absorption over 400–1,200 nm can be achieved when the dielectric constant of the dielectric layer is over 3.0. In addition, the effects of the angle of incidence on the broadband absorption of the system are also analyzed. When the system is put in a high-refractive-index environment, >90% light absorption over 400–1,200 nm can be achieved for a TM wave with incidence angle up to 40°.

Figure 1 shows the schematic diagram of the MIM system. The top and bottom metals are the same. The top metal layer excites the electric and magnetic resonances, and matches its impedance to the surrounding environment to reduce light reflection. The intermediate dielectric layer forms a F-P resonator, confining the light field and thus helping to improve the light absorption. The bottom metal layer functions to block the propagation of electromagnetic waves. The thicknesses of the top thin metal layer, the intermediate dielectric layer, and the bottom thick metal layer are expressed as D_M1, d, and D_M2 respectively.

Figure 1. Schematic diagram of the MIM structure. In regions 0–4, εI, ε₁, ε₂, ε₃, and ε₄ indicate the respective dielectric coefficients. MIM, metal-insulator-metal.

For TM (or TE)-polarization waves, the y component of the magnetic (electrical) field of regions 0 to 4 (corresponding to the incident layer, the top metal, the dielectric layer, the bottom metal, and the outlet layer respectively) can be expressed as

(1)$$\left\{\begin{array}{l}H{\left(E\right)}_{0y}=\left[e^{i{K}_{Iz}\left(z+\frac{d}{2}+D_{M1}\right)}+r•e^{-i{K}_{Iz}\left(z+\frac{d}{2}+D_{M1}\right)}\right]•e^{i\left(k_{x}x-wt\right)},z<-\left(\frac{d}{2}+D_{M1}\right)\\ H{\left(E\right)}_{1y}=\left[a_1•e^{i{k}_{1z}\left(z+\frac{d}{2}\right)}+b_1•e^{i{k}_{1z}\left(z+\frac{d}{2}\right)}\right]•e^{i\left(k_{x}x-wt\right)},-\left(\frac{d}{2}+D_{M1}\right)<z<-\frac{d}{2}\\ H{\left(E\right)}_{2y}=\left[a_2•e^{i{k}_{2z}z}+b_2•e^{-i{k}_{2z}z}\right]•e^{i\left(k_{x}x-wt\right)},\frac{d}{2}<z<\frac{d}{2}\\ H{\left(E\right)}_{3y}=\left[a_3•e^{i{k}_{3z}\left(z-\frac{d}{2}\right)}+b_3•e^{-i{k}_{3z}\left(z-\frac{d}{2}\right)}\right]•e^{i\left(k_{x}x-wt\right)},\frac{d}{2}<z<\frac{d}{2}+D_{M2}\\ H{\left(E\right)}_{4y}=t•e^{i{k}_{4z}\left(z-\frac{d}{2}-D_{M2}\right)}•e^{i\left(k_{x}x-wt\right)},\frac{d}{2}+D_{M2}<z\end{array}\right.$$

Here k_iz (i = I, 1, 2, 3, and 4) is the z-direction wave vector for each region, and k_x is the wave vector in the x direction.

Regardless of the external charge and current, the normal macroscopic dynamic boundary conditions at the interface of two media are $\widehat{n}\times \left({\stackrel{\rightharpoonup }{E}}_2-{\stackrel{\rightharpoonup }{E}}_1\right)=0$ and $\widehat{n}\times \left(H_2-H_1\right)=0$. However, the introduction of the d parameter renders the macroscopic boundary conditions inapplicable. Therefore, boundary conditions that embody the d parameter may be considered: ${\stackrel{\rightharpoonup }{E}}_{2,\vee }-{\stackrel{\rightharpoonup }{E}}_{1,\vee }=-d_{\perp }{\nabla }_{\vee \left({\stackrel{\rightharpoonup }{E}}_{2,\perp }-{\stackrel{\rightharpoonup }{E}}_{1,\perp }\right)}$, ${\stackrel{\rightharpoonup }{H}}_{2,\vee }-{\stackrel{\rightharpoonup }{H}}_{1,\vee }=i\omega d_{\vee \left({\stackrel{\rightharpoonup }{D}}_{2,\vee }-{\stackrel{\rightharpoonup }{D}}_{1,\vee }\right)\times \widehat{n}}$. After introduction of the d parameter, the components of the electric and magnetic fields parallel to the interface are no longer continuous, and the discontinuous orders are proportional to the d parameter.

For MIM systems, at the interfaces of zones 0–1 and 1–2 the boundary conditions for the parallel and vertical interfaces of electromagnetic fields are utilized:

(2)$${\stackrel{\rightharpoonup }{E}}_{i,\vee }-{\stackrel{\rightharpoonup }{E}}_{i-1,\vee }=-d_{\perp }{\nabla }_{\vee \left({\stackrel{\rightharpoonup }{E}}_{i,\perp }-{\stackrel{\rightharpoonup }{E}}_{i-1,\perp }\right)},$$

(3)$${\stackrel{\rightharpoonup }{H}}_{i,\vee }-{\stackrel{\rightharpoonup }{H}}_{i-1,\vee }=i\omega d_{\vee \left({\stackrel{\rightharpoonup }{D}}_{i,\vee }-{\stackrel{\rightharpoonup }{D}}_{i-1,\vee }\right){\times }^n}$$

Here the value of i is taken in the range of 0–2. For our MIM systems the thickness of the bottom metal layer is 200 nm. Considering that the bottom metal is very thick, all of the incident light can be reflected back into the cavity and the transmittance is 0, so the absorption of the MIM system is

(4)$$A=1-R=1-{\left|r\right|}^2.$$

According to the boundary conditions, the reflection coefficient r_TM can be expressed as

(5)$$r_{TM}=-1+\frac{2{\epsilon }_1{k}_I}{\left(-i\ast r_1+r_2\right)-r_{11}}.$$

Here

r₁₁ = 4_{εI ε1}k_I k₁ (r₃ + i (−r₄ − r₅ + r₆ (r₇ + _ε1 k₃ ω))) / ((−r₁ + i (−r₂))) r₂₂),

r₂₂ = −(−r₁ + i(−r₂)) m₁² (−r₃ − i (r₄ − r₅ − r₆ (r₇ − ε₁ k₃ ω))) + (r₁ + i (ε₁ kI + εI k₁)) (r₃ + i (−r₄ − r₅ + r₆ (r₇ + ε₁ k₃ ω)), where r₁ = d⊥ (εI − ε₁) k², r₂ = ε₁ kI − εI k₁, r₃ = d⊥ (ε₁ − ε₂) k² (−ε₂ (−1 + f ⁴) k₃ ω + (1 + f ⁴) k₂ (k₃ σ + ε₃ ω)), r₄ = ε₂² (−1 + f ⁴) k1 k₃ ω, r₅ = ε1 (−1 + f ⁴) k₂² ε₃ ω, r₆ = ε₂ (1 + f ⁴) k₂, and r₇ = ε₃ k₁ ω.

TE waves are incident upon the MIM system, and the reflection coefficient r_TE is

(6)$$r_{TE}=r_{11}^{\prime }+\frac{r_{12}^{\prime }}{r_{22}^{\prime }}$$

where r′₁₁ = 1 + 2kI μ₁ / (−k₁ μI + r′₁), r′₁₂ = −(4kI k₁ μI μ₁²(2k₂ (k₃ μ₂ + μ₃ k₂) + (((−1 + f ⁴)k₃ μ₂ − μ³ ((1 + f ⁴)k₂ )) (k₂ μ1 − μ₂ (k₁ + ir′₂))) / μ₁, r′₂₂ = (−k₁ μI + r′₁) (m₁² (k₁ μI − r′₁) (−r′₃ − r′₄ (ik₁ + r′₂) + r′₅ (k₃ μ₁ + μ₃ (−k₁ + r′₆))) − (k₁ μI + r′₁) (r′₃ + r′₄ (−ik₁ + r′₂) − r′₅ (k₃ μ₁ + μ₃ (k₁ + r′₆)))). Here r′₁ = μ₁ (kI + id⊥ (εI − ε₁)μI ω²), r′₂ = d⊥ (ε₁ − ε₂) μ₁ω², r′₃ = (−1 + f ⁴) k₂² μ₁ μ₃, r′₄ = i (−1 + f ⁴) μ₂² k₃, r′₅ = (1 + f ⁴) k₂ μ₂, and r′₆ = iμ₁d⊥ (ε₁ − ε₂) ω².

In the above equations f = e^i∙k₂z∙d/₂, m₁ = e^i∙k₁z^∙DM₁, μI, μ₁, μ₂, μ₃, and μ₄ are permeabilities, and ω is the angular frequency. In this work, d_∨ = 0 and d_⊥ = (1.41 + 0.33i) × 10⁻¹⁰. For the wavelength region of 400–1,200 nm, we use Eq. (4) to analyze the optimal dielectric constant of the intermediate dielectric layer, corresponding to the maximum absorption for TM and TE waves that are incident upon the system in different environments, and to analyze the effect of the angle of incidence on absorption.

In this work, adopting titanium as the metal, we discuss the polarized-wave absorption of the MIM system in three different environments: Air, seawater, and an environment with RI of 1.74. First, we analyze the absorption characteristics (maximum absorption A_max ≥ 98%) of the system, as a function of the thickness of the top metal layer and the dielectric constant of the intermediate dielectric layer, when the system is put in air. Second, the absorption features of the system are calculated when it is embedded in seawater. Next, the absorption characteristics of the system are discussed when it is placed in an environment with a larger RI of 1.74. Finally, we discuss the effect of incidence angle on the absorption of different polarized waves in different environments.

3.1. System Placed in Air

When the system is placed in air and the thickness of the intermediate dielectric layer is kept constant, the TM-wave absorption characteristics of the system as a function of the metal-layer thickness and the dielectric-layer dielectric constant are shown in Figs. 2(a)–2(c). A_max of the TM-polarization wave does not have an obvious dependence on the thickness of the top metal layer. However, increasing the thickness (from 10 to 15 to 20 nm) of the top metal layer greatly shifts the high-absorption region to longer wavelengths, and also widens the high-absorption bandwidth. At this time, the short-band absorption of the system decreases relatively, consistent with results from the literature [5]. In addition, the dielectric-constant range supporting A_max is also expanded and shifts to lower values. This is because that absorption of the system is determined by the total optical path in both the top metal and intermediate dielectric layers. To achieve high absorption, constant total optical path length can only be maintained through decreasing the optical path in the dielectric layer when the metal thickness is increased; since the thickness of the dielectric is unchanged, its dielectric constant must decrease.

Figure 2. Light-absorption map of the metal-insulator-metal (MIM) system placed in air for a TM (or TE) wave, with respect to incident wavelength λ and the dielectric constant ε₂ of the dielectric layer. (a)–(c) The dielectric layer’s thickness remains a constant value of 60 nm while the top metal layer’s thickness is 10, 15, and 20 nm respectively. (d)–(f) The top metal layer’s thickness remains unchanged at 15 nm while the dielectric layer’s thickness is taken to be 30, 50, and 70 nm, respectively.

When the thickness of the top metal remains unchanged and the thickness of the dielectric layer is varied, the absorption characteristics of the system are shown in Figs. 2(d)–2(f), and are very different from the case of changing the thickness of the top metal layer. When the thickness of the dielectric layer increases from 30 to 50 to 70 nm, the high-absorption parameter space expands significantly: Not only does the high-absorption region shift to longer wavelengths, but also the dielectric constant corresponding to A_max moves to higher values, and the dielectric-constant range expands. This is because when the thickness of the top metal layer is kept constant, light absorption (conductance matching) mainly depends on the phase accumulated in the intermediate dielectric layer, which is in turn determined by the optical path [2]. Therefore, when both the thickness of the dielectric layer and its dielectric constant increase, A_max will shift to longer wavelengths, which is consistent with the previous literature [6].

We also analyze the wide-spectrum absorption response of the system to a TE-polarized wave, and find that the absorption characteristics are almost identical to that for the TM wave. When the thickness of the intermediate dielectric layer remains unchanged and the thickness of the top metal is taken as 10, 15, and 20 nm, the results for the TE-polarized wave are very similar to those in Figs. 2(a)–2(c). When the thickness of the top metal layer is unchanged and the thickness of the dielectric layer increases from 30 to 70 nm, the results for the TE-polarized wave are similar to those in Figs. 2(d)–2(f).

From the above analysis, we find that when light is incident perpendicular to the MIM system, broadband light absorption can be realized and the absorption is polarization-independent. This indicates that such MIM systems can function as ideal perfect absorbers. In actual operation, for high absorption of TM waves a moderate real part and large imaginary part should be guaranteed, while for high absorption of TE waves a moderate imaginary part and large real part should be fulfilled. Here we have achieved high absorption of both TM and TE waves, and determined the dielectric-constant region of the intermediate dielectric layer for achieving ≥94% light absorption over a wide spectral range.

3.2. System Placed in Seawater

Placing the system in seawater, we also analyze the light-absorption response of the system, and find that the surrounding environment has a significant impact on absorption. As shown in Figs. 3(a)–3(c), when the intermediate dielectric-layer thickness is kept unchanged and the top metal thickness is 10, 15, and 20 nm respectively, the dielectric-constant range for achieving A_max with TM waves becomes wider, the dielectric constant for A_max become smaller, and the high-absorption region shifts to longer wavelengths. These absorption-changing (under different top-metal-layer thickness) trends are the same as those when the system is put in air. However, for high-intensity absorption the wavelength scope and dielectric-constant range of the system in seawater are wider than those in air [comparing Figs. 2(a)–2(c) and Figs. 3(a)–3(c)]. For example, the system placed in seawater can achieve ≥94% light absorption across 400–1,200 nm and over the dielectric-constant range of 0.11–5.0 [see Fig. 3(b)], while the system placed in air can achieve ≥94% light absorption only in the wavelength range of 480–1,083nm and over the dielectric-constant range of 0.01–4.41 [see Fig. 2(b)]. In addition, when only the thickness of the top metal layer is changed [comparing Figs. 2(a)–2(c) and Figs. 3(a)–3(c)], the dielectric-constant range supporting A_max is larger in seawater than in air.

Figure 3. Light-absorption map of the metal-insulator-metal (MIM) system placed in seawater for a TM (or TE) wave, with respect to incident wavelength λ and the dielectric constant ε₂ of the dielectric layer. (a)–(c) The dielectric layer’s thickness remains a constant value of 60 nm while the top metal-layer’s thickness is 10, 15, and 20 nm respectively. (d)–(f) The top metal layer’s thickness remains unchanged at 15 nm while the dielectriclayer’s thickness is taken to be 30, 50, and 70 nm respectively.

As shown in Figs. 3(d)–3(f), when the thickness of the top metal layer is kept at 15 nm and the thickness of the dielectric layer increases from 30 to 70 nm, not only does the dielectric constant for broadband A_max increase and the high-absorption spectral range shift to longer wavelengths, but also the dielectric-constant range and wavelength scope corresponding to the broadband A_max change. For example, as the thickness of the dielectric layer is increased from 30 to 50 nm, the dielectric-constant range for A_max is expanded from 0.21–3.61 to 1.01–4.61, and the wavelength range is expanded from 400–685 nm to 478–960 nm. Generally, the absorption-changing trends are the same as those when the system is put in air. The high-absorption wavelength range and high-absorption dielectric-constant range of the system are wider when the system is put in seawater than in air. In addition, the dielectric constant corresponding to A_max is larger in seawater than in air.

After analyzing the wide-spectrum absorption response of the system for a TM wave in seawater, we calculate the TE-wave absorption of the system, and find that the absorption behaviors are very similar. When the dielectric thickness is unchanged, as the top metal layer increases, the wide-spectrum absorption maximum shifts towards lower dielectric constant and longer wavelength [see Figs. 3(a)–3(c)]. This is the same as the spectral response for TE-polarization waves incident from the air to the system, except that the dielectric-constant range and wavelength range corresponding to A_max are increased. When the thickness of the metal layer remains unchanged and the thickness of the dielectric layer increases, the dielectric constant corresponding to the broadband A_max increases, and the corresponding wavelength redshift is shown in Figs. 3(d)–3(f). In addition, as for TM waves, the dielectric constant corresponding to A_max is greater in seawater than in air when the system parameters are the same [see Figs. 2(d)–2(f) and Figs. 3(d)–3(f)].

3.3. System Placed in an Environment with Large RI

We further analyze the light-absorption response of the system when it is placed in an environment with large RI. It is also found that the RI of the surrounding environment plays an important role in the system’s absorption. As shown in Figs. 4(a)–4(c), when the intermediate dielectric-layer thickness is kept at 60 nm and the top metal thickness is 15 nm, the wavelength range for achieving A_max for TM waves is the widest for an environment with large RI. Comparing Figs. 4(a)–4(c) to Figs. 2(a)–2(c) and Figs. 3(a)–3(c), it is clear that the dielectric-constant value for A_max becomes larger, to achieve broadband absorption. When keeping the thickness of the top metal at 15 nm and changing the thickness of the dielectric layer, the absorption characteristics are shown in Figs. 4(d)–4(f). Comparing Figs. 4(d)–4(f) to Figs. 2(d)–2(f) and Figs. 3(d)–3(f), the dielectric-constant value for A_max also becomes larger for wide-wavelength absorption. After analyzing the wide-spectrum absorption response of the system for TM wave in environment with large RI, we also calculate the TE-wave absorption of the system in identical cases, and find that the absorption behaviors are very similar.

Figure 4. Light-absorption map of the metal-insulator-metal (MIM) system placed in an environment with large refractive index (RI) for a TM (or TE) wave, with respect to incident wavelength λ and the dielectric constant ε₂ of the dielectric layer. (a)–(c) The dielectric layer’s thickness remains a constant value of 60 nm and the top metal layer’s thickness is 10, 15, and 20 nm respectively. (d)–(f) The top metal layer’s thickness remains unchanged at 15 nm and the dielectric layer’s thickness is taken to be 30, 50, and 70 nm respectively.

With finite-difference time-domain (FDTD) solutions, we obtain the light-absorption distribution at a fixed wavelength (λ = 600 or 960 nm) inside the system when it is embedded in air, seawater, and a large-RI environment, and the results are shown in Fig. 5. In all cases strong light absorption occurs in the top metal layer, and shows rapid attenuation towards the bottom metal layer. The whole system functions as a hybrid Fabry-Perot cavity with a low quality factor [6]. For either incident-light wavelength (600 or 960 nm), the absorption in the top metal layer grows with increase of the environment’s RI.

Figure 5. Light-absorption distribution inside the metal-insulator-metal (MIM) system at a single wavelength of λ = 600 nm [indicated in (a), (c), and (e)], and at λ =960 nm [indicated in (b), (d), and (f)], when the system is put in air [(a) and (b)], seawater [(c) and (d)], and an environment with refractive index (RI) of 1.74 [(e) and (f)].

3.4. The Effect of Angle of Incidence on Light Absorption

We further calculate the light absorption of the MIM system under different angles of incidence for a TM wave, when the system is put in air and seawater, and the results are shown in Fig. 6. As can be seen, under small incident angles (<15° in air and <30° in seawater) the system experiences strong absorption over a wide spectral range; With increasing incident angle, light absorption decreases significantly, which is similar to what is reported in the literature [6].

Figure 6. Light-absorption map of the metal-insulator-metal (MIM) system under different angles of incidence θ and incident wavelengths, for TM waves incident from air (a)–(c), seawater (d)–(f), and an environment with refractive index (RI) of 1.74 (g)–(i). The MIM system has parameter values d = 50 nm and D_M1 = 10, 15, and 20 nm respectively.

For incidence from air at a small angle (0° to 33°), absorption decreases over a wide spectral range as the thickness of the top metal increases [see Figs. 6(a)–6(c)]. In seawater, when the thickness of the top metal increases to 20 nm, at small angles the wave absorption is significantly reduced in the range of 400–580 nm [see Fig. 6(f)]. Comparing Figs. 6(a) and 6(d), for small incident angles the system has strong absorption over a wide spectral scope for both environments. Absorption decreases as the angle of incidence increases, and strong absorption has a larger incident-angle range at shorter wavelengths than at longer. Putting the system in a higher-index environment (seawater) helps to attain high absorption over a larger incident-angle range (30°) than that in a lower-index environment (air), and the high-absorption wavelength range is also much broader in the former case.

Unlike TM waves, when TE waves are considered, light absorption by the MIM system does not show an obvious dependence on its environment, and each polarization shows similar light-absorption dependence on incident angle (see Fig. 7). What’s interesting is that in the short-wavelength region (from 416–590 nm), TE waves can be strongly absorbed (≥90%) by the system over a large incident-angle range (up to 65°), as indicated in Fig. 6(a). In addition, for TE waves at small incident angles, the absorption decreases gradually with increasing wavelength, but when the angle of incidence exceeds 50° the absorption shows negligible dependence on wavelength, and uniform low absorption is maintained over a wide spectral region.

Figure 7. Light-absorption map of the metal-insulator-metal (MIM) system under different angles of incidence θ and incident wavelengths, for a TE wave incident from air (a)–(c), seawater (d)–(f), and an environment with large refractive index (RI) of 1.74 (g)–(i). The system has parameter values d = 50 nm and D_M1=10, 15, and 20 nm respectively.

From the above analysis, it is found that polarized waves can be highly absorbed by the MIM system when the incidence angle is small, whether the system is put in air or seawater, and the absorption decreases with increasing incident angle. The absorption behavior of the system put in air is consistent with results in the literature [5]. While the TM-wave absorption of the system exhibits strong environmental dependence, the TE-wave absorption shows negligible dependence. Comparing Eqs. (5) and (6), where environmental influence is included in the factors of εI and kI, it can be found that the reflectivity (and also the absorption) of TM and TE waves have different environmental dependence. Based on calculations using Eqs. (5) and (6), we find that the absorption variation for a TM wave is much greater than that for a TE wave under the same environmental change (RI from 1 to 1.74). This can be explained by the fact that TM and TE waves have different electric field distributions in the dielectric, which leads to different polarization and consequently different absorption. In addition, for the same environment, as the incident angle increases the absorption of TM waves declines faster than that of TE waves. As shown in Figs. 6(a) and 7(a), when the angle of incidence of the 830-nm wave increases from 0 to 30°, the absorption of a TM wave drops from 90.1% to 67.0%, while the absorption of a TE wave only decreases from 80.4% to 76.0%. We also reach similar conclusions for other layer thicknesses of the MIM system, as described in Figs. 2 and 3.

Based on electromagnetic wave calculations under the d-parameter boundary conditions, we have designed a MIM system for achieving broadband absorption of polarized waves (both TM and TE) when the system is placed in three different environments (air, seawater, and an environment with RI of 1.74). We have found that this metamaterial layered system can act as a perfect absorber over a wide spectral range, especially in high-RI environments.

Whether in air or seawater, when the thickness of the top metal layer increases, the high-absorption A_max wavelength of polarized waves (both TM and TE) redshifts, and the dielectric constant of the intermediate dielectric layer supporting high absorption also decreases. When the thickness of the top metal layer is unchanged and the thickness of the dielectric layer increases, the dielectric constant corresponding to broadband A_max increases, and the corresponding wavelength region redshifts. Comparatively, the MIM system placed in seawater can achieve a wider wavelength range and dielectric-constant range for high light absorption than the system in air. In an environment with RI of 1.74, the change trend of absorption with thickness and dielectric constant is similar to those in air and seawater. When the dielectric constant is higher than 3.0, ≥98% absorption can be achieved over the range of 400–1,200 nm.

Finally, we have also analyzed the effects of angle of incidence on absorption in different environments. The environment has a greater effect on the correlation of absorption and incident angle for a TM wave than for a TE wave. Increasing incident angle results in reduced absorption, significant attenuation of which occurs at a smaller angle in air than in seawater. In addition, strong absorption of shorter-wavelength bands can be achieved over a wider range of incident angles than for longer-wavelength bands.

Such MIM systems are lithography-free and have simple fabrication processes, and have excellent optical absorption properties for either type of polarized wave. Thus they will not only provide a new type of light-harvesting systems, but also will give some clues for designing new layered metamaterial devices that can enhance the control of light propagation and absorption.

The authors declare no conflict of interest.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

Natural Science Foundation of Shanghai (China, No. 19ZR1427100); the National Natural Science Foundation of China (61306072, 61675129); the Technique Foundation of Shanghai Technical Institute of Electronics & Information (HX-22-TX034).