Proposed absorber design

Material, dimensions, and configuration

Absorption mechanism

The absorber’s design evaluations have been detailed to assess the effectiveness of each proposed configuration in terms of absorption. Figure 3 illustrates six distinct designs to obtain the optimal design of the Ultra-Compact Plasmonic Metamaterial (UCPM) absorber. Design-1, depicted in Fig. 3a, features a single flower-shaped resonator positioned atop the insulating layer. In design-2, shown in Fig. 3b, an additional circular flower-shaped ring is incorporated into design-1. Design-3, represented by Fig. 3c, introduces two flower-shaped rings to the structure of design-1. Subsequently, further structures are developed by adding more rings to the initial design-1. These are presented as design-4, design-5, and design-6 in Fig. 3d–f respectively. The reflection and absorption characteristics corresponding to each design are illustrated in Fig. 4a.,b.

The reflection and absorption characteristics corresponding to each design are presented in Fig. 3a–e is illustrated in Fig. 4a,b respectively. Tables 2 and 3 represent the performance of different designs. Table 2 gives the findings from the reflection coefficient curve of different designs aimed at achieving the final structure. Each design, labeled from Design-1 to Design-6 with varying numbers of rings added to a flower-like structure. The investigation into flower antenna designs demonstrates a noteworthy trend. As the number of rings increases, the operational bandwidth widens, and the minimum S₁₁ value initially improves. However, adding rings beyond Design 4 exhibits a detrimental effect, causing the S₁₁ value to degrade. This highlights the effectiveness of the proposed design (Design 5), which achieves the superior combination of the broadest bandwidth and a significantly improved minimum S₁₁ value at a favorable resonant frequency of 670 THz.

On the other hand, Table 3 represents the performance based on the absorption characteristics corresponding to each design structure. The table outlines observations of absorption characteristics curve for various designs, aiming to identify the final structure’s optimal performance. Each design, ranging from Design-1 to Design-6 with incremental additions of rings to a flower-like structure, exhibits distinct bandwidths for absorption exceeding 95%, along with percentage average absorption and peak absorption frequency points in THz. Notably, the evolution from Design-1 to Design-2, incorporating additional rings, demonstrates an expansion in bandwidth and an enhancement in both percentage average absorption and peak absorption frequency point, culminating in the Proposed Design. This design showcases the broadest absorption bandwidth, the highest percentage average absorption, and a peak absorption frequency point of 670 THz, indicating superior absorption characteristics suitable for the intended application.

E & H-field distribution and current density analysis

This section meticulously analyzes the electric (E), magnetic (H) field, and surface current density distributions within the UCPM absorber (Figs. 5, 6, 7) to gain deeper insight into its light absorption mechanisms. Scrutinizing these distributions helps elucidate how the design effectively captures and dissipates incident electromagnetic waves.

In this configuration, the electric field (E) aligns horizontally, while the magnetic field (H) aligns vertically. At the resonant frequency of 670 THz, the nested flower rings exhibit notable charge redistribution, with charges accumulating on the upper and lower sides as shown in Fig. 5a,b. This phenomenon induces an electrical dipole resonance within the rings, fostering strong coupling with the underlying structure. The proposed design leverages a synergistic interaction of electric and magnetic resonances to achieve efficient light absorption. At the resonant frequency (670 THz), the nested flower rings exhibit a distinct electric dipole resonance due to prominent charge redistribution (Fig. 5a,b). This phenomenon fosters strong coupling with the underlying structure.

Additionally, a concentrated magnetic field distribution resides primarily within the intermediate dielectric layer, induced by the magnetic resonance (Fig. 6). The accumulation of opposite charges on the flower ring structures leads to the formation of reverse currents on the top and bottom metal layers. This current flow generates a magnetic dipole resonance within the absorber. The surface current density at the interface between the metal layers and the dielectric spacer directly influences the magnitude of these reversed currents and the resulting magnetic resonance. A higher surface current density signifies a greater current concentration, leading to a stronger magnetic response and a more pronounced resonance effect as represented in Fig. 7a,b. In essence, the interplay between electric and magnetic resonances, coupled with the influence of surface current density, facilitates the effective absorption of incident electromagnetic wave energy within the intermediate dielectric layer.

Effect of incident and polarization angles variation on the absorber performance

The proposed absorber demonstrates remarkable resilience to variations in incident angles. As shown in Fig. 8a, the reflection coefficient S₁₁ remains below − 10 dB (indicating low reflection loss) for incident angles up to 50°. Beyond 50°, the S₁₁ increases, suggesting a decrease in absorption. Moreover, the absorber exhibits excellent polarization insensitivity as represented in Fig. 8b. Regardless of the TE wave’s polarization angle (the angle between the electric field vector and the X-axis), the reflection coefficient spectrum remains consistent. This confirms the absorber’s robust performance under various polarization conditions.

Effects of different structural parameters

Subsequently, the investigation delved into the influence of various structural parameters on the absorption capabilities of the Ultra-Compact Plasmonic Metamaterial (UCPM) absorber. Specifically, scrutinized the impact of altering the thickness (t₁) of the top metallic layer on the absorber’s reflection coefficient, thereby gauging its effect on absorption efficiency, as illustrated in Fig. 9a and Table 4. To elucidate this relationship, this work systematically increased the thickness of t₁ from 3 nm to 11 nm in increments of 2 nm, while maintaining a constant height for the dielectric layer at t₂ = 12 nm. Upon careful examination of the reflection characteristic curves for these variations, a significant observation was made. Each thickness shows a dip or resonance at different frequencies, where the reflection is minimized (the material is more absorptive). Thicker layers tend to shift the resonant frequencies towards lower values, and the sharpness of the resonance also changes. The curve for t₁ = 5 nm shows the lowest S₁₁ value (most negative), indicating the best impedance match around 670 THz. This phenomenon indicates that minimizing reflection leads to maximal absorption efficiency. This article explored the impact of varying t₂ (thickness of substrate layer) from 6 nm to 18 nm in 3 nm increments, while holding t₁ constant at 5 nm. Our analysis focused on observing the reflection characteristic curves for these different heights, intending to identify minimum value of S₁₁ (dB) and the frequency range wherein the reflection coefficient remained below − 10dB. Notably, our findings, as depicted in Fig. 9b and Table 5, highlight the optimal performance achieved when t₂ was set to 12 nm, characterized by the most favorable combination of dips and bandwidth.

The thickness of a material plays a crucial role in determining its wave impedance, which in turn affects the reflection of electromagnetic waves when they encounter different materials. When a wave travels through a medium and reaches the boundary between two materials, part of the wave may be reflected, while another part may be transmitted. The reflection is affected by the impedance mismatch between the materials and the thickness of the second material layer. Each material has a characteristic wave impedance {\({Z}_{e}\left(\text{f}\right)\)}, which is determined by its electrical properties, such as effective permittivity{\({{\upepsilon}}_{eff}\left(\text{f}\right)\}\), and effective permeability \({\{{\upmu}}_{eff}\left(f\right)\}\)^20,21. This characteristic wave impedance {\({Z}_{e}\left(\text{f}\right)\}\), can be expressed by Eq. (3) as:

The effective refractive index {\({{\upeta}}_{eff}\left(\text{f}\right)\)} can be related with effective permittivity \({\{{\upepsilon}}_{eff}\left(\text{f}\right)\}\), and effective permeability \({\{{\upmu}}_{eff}\left(f\right)\}\) as by Eqs. (4) and (5) respectively as:

Whereas the effective refractive index η_eff can be represented as per Eq. (6) When, f = frequency of operation; \(C\) = velocity of light; L_a is transmission length (height of the metamaterial absorber structure).

The environmental impedance (Z₀ ≈ 377 Ω) should be matched with the absorber’s effective characteristic wave impedance for perfect absorption. The reflection coefficient S₁₁ (dB) and transmission coefficient S₂₁ (dB) can be used to characterize the characteristic wave impedance \(\left\{{Z}_{e}\left(\text{f}\right)\right\}\), of the absorber as Eq. (7).

The material’s thickness influences the wave’s phase after it travels through the material. Depending on the thickness of the material relative to the wavelength of the wave inside the material, constructive or destructive interference can occur between the incident and reflected waves, significantly affecting the overall reflection. The effect of material thickness comes into play because the wave may travel through the material and experience multiple internal reflections. These reflections can interfere either constructively or destructively, depending on the path length (related to thickness) and wavelength. The bottom and top metals generate capacitance with the help of a dielectric layer. The capacitance of the structure depends strongly on the dielectric thickness and is inversely proportional to the dielectric thickness. As the thickness increases, the capacitance decreases; thus the absorption bandwidth moves linearly from left to right. Also, the dielectric layer confined most of the wave within it and made a structure highly procurable for absorption.