Introduction

Recently, there has been a growing demand for optical and photonic devices in the Terahertz (THz) band owing to their several applications in security, stealth, communication and upcoming 6G technology1,2,3,4. Moreover, advanced communication systems demand ultrathin, low-profile, and flat optical devices to be integrated easily with them. Now a days, artificial materials called metamaterials have been getting a huge significance owing to their unique and exotic features which differentiate them with natural materials5,6,7. These materials have the capability to control the incoming waves by reflecting, transmitting, absorbing and then use them to develop various devices like flat lenses8, polarization converters9, optical filters10, sensors11,12, antennas13, and absorbers14,15,16,17. Metamaterial absorbers are the key and essential components in communication systems because they can be integrated with the systems to mitigate and absorb unwanted interference or radiation. These absorbers can be employed in many applications such as radar-cross-section reduction18, stealth communication19, isolation-enhancement in antennas13,20, EM interference in microwave circuits21 and solar-photovoltaics22,23,24,25 etc. They are designed in various operating frequencies from microwave, THz to infrared4,26,27,28,29,30.

Initially, Landy et al.31 provided an experimental evidence of nearly perfect absorbing structure back in 2008. Although the absorber was originally designed for the narrowband microwave frequency range, then the people investigated various metasurface-based absorbers for different operating spectrums, spanning from microwaves to ultraviolet wavelengths32,33,34,35,36. This fundamental advancement has garnered significant attention towards the field of meta-absorbers owing to their extremely thin profile, low-profile, and easy integration with advanced integrated systems. The literature extensively explores the studies on various types of absorbing structures, including single, dual and multi frequency band, wideband, and polarization-insensitive tailored for the series of applications31,37,38. Notably, the narrow-band absorbers could be effective in applications such as color-filtering and absorption-driven sensing10,12. Achieving multi-band absorption typically involves using either multiple-resonance structures within a single absorber unit cell or employing multiple layers of structures39. Consequently, broadband absorbers offer a wide range of applications, encompassing solar energy harvesting, EM interference, bolometers, stealth communication, and a myriad of other fields19,21,40.

In terahertz (THz) band, achieving broadband absorption characteristics is a challenging and difficult task. Usually, multi-layered, and multi-sized resonators methods are used to enhance the broad spectral response of a THz absorber and they are avoided in advanced communication and sub-THz band of 6G communication owing to their drawbacks including large size, difficult fabrication process and high cost etc.39,41. Apart from these methods, fractal techniques are also used to enhance the absorption bandwidth of an absorbing structure. Although, a considerable bandwidth is enhanced with this method but again the fractal-based designs are not very simple to fabricate, it faces challenges due to their complicated and complex geometric shapes because fractals are self-similar repeated patterns and arranged in a specific pattern within a proposed resonator3,42. Several THz absorbers have been reported in the past by adopting the above-mentioned bandwidth enhancement approaches. For example, a multi-layered THz absorber is developed43 which showed wideband absorption features and they employed multi-stacked layers of graphene to attain the large bandwidth. Similarly, a fractal-based absorber is designed for THz frequency absorption3. However, the complex and multifaceted topology of fractals presents significant fabrication challenges, leading to increased fabrication costs. In the THz band, multi-layered and fractal-based methodologies are commonly used to enhance the absorption bandwidth of these absorbers44,45,46,47. Additionally, graphene-based THz absorbers have also been extensively exploited but the control on graphene and fabrication is challenging and time consuming. Therefore, there is a need to implement simple, cost-effective, and broadband absorbing structures in THz band with ultrathin and single-layer geometry.

This communication introduces a compact, cost-effective solution aimed at achieving a wide absorption response within the THz band from a miniaturized, single-layer metamaterial structure. The proposed absorbing setup comprises a singular circular ring constructed from a RuO2-based resistive material with significantly higher sheet resistance than conventional metallic resonators. This unique design is imprinted onto a lossy dielectric polyimide substrate, backed by a metallic gold pattern. Our developed absorbing structure demonstrates the capability to achieve a substantial absorption bandwidth spanning from 3.78 to 4.25 THz, maintaining a consistent absorption rate of over 90%. Furthermore, we conducted an analysis to evaluate its absorption performance under various sheet resistance values within the top layer. Additionally, we characterized its angular stability and polarization insensitivity through oblique incident and polarization angle analysis, foreseeing its potential in diverse applications such as communication, imaging, and integrated circuits within the THz domain.

Design and simulation of RSA

The proposed resistive surface-based absorber (RSA) features a standard three layers device topology with top as a RuO248 based circular ring with a sheet resistance of 80 Ω/sq, a middle dielectric material of polyimide (εr = 3.5, \(\tan {\updelta } = 0.0027\)) and a bottom ground mirror to diminish the transmitted waves, as outlined in Fig. 1. The circular ring is chosen as the top FSS due to its simple design and ease of fabrication. Other geometric shapes, such as loops and crosses, can also be optimized and they also demonstrate similar results because they possess LC resonances. To perform the simulation of this absorber, an ohmic sheet of sheet resistance of 80 Ω/sq is employed and it is considered as a RuO2. It is worth noting that any resistive material can be considered as an ohmic sheet in CST simulation software because we just need to add its sheet resistance. The proposed THz absorber can be fabricated using inkjet printing technology48. The process begins with cleaning the polyimide substrate, followed by depositing the bottom gold layer using sputtering or evaporation. Next, a resistive material of RuO2 is selected and loaded into the printer. The pattern of the proposed FSS is then printed onto the polyimide substrate, making a periodic array of metamaterials.

Figure 1
figure 1

The design topology of the designed RSA showing its geometric parameters (a) top view of the unit cell and (b) side view of the unit cell and (c) 3D periodic arrays of unit cell.

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The RSA’s specific design parameters comprise P = 100 μm, R2 = 45 μm, R1 = 30 μm, and dielectric thickness (hs) = 50 μm. The bottom gold mirror has a thickness of 2 μm. This design was chosen over previously studied THz absorbers because it contains simple and plain geometry which gives us the freedom and feasibility in fabrication. In contrast, most of the previously studied THz absorbers either contain a multi-layer design or composed of an expensive metal of gold. All the mentioned attributes make this absorbing structure a cost-effective and promising choice for THz applications.

To characterize the absorption capabilities of the proposed RSA, it is simulated and designed using the full-wave simulation tool CST Studio. The model incorporates unit-cell boundary conditions along the x–y axis and an open add space in the z-direction. To observe its spectral features, an incident THz wave is illuminated onto the front surface RSA. The proposed absorber blocks the transmission due to the presence of a bottom gold mirror, and the reflection characteristics are controlled by the impedance of the RSA. The absorption rate of the proposed RSA is calculated as A = 1–R–T, where A denotes absorption, R represents reflection, and T indicates transmission efficiencies. Additionally, in terms of s-parameters, it is simplified further as A = 1–|S11|2.

Equivalent RLC model of RSA

An RLC equivalent circuit of the designed RSA is demonstrated to estimate its analytical absorption, and it is then compared with the simulated one.

To construct this RLC model, we employ the s-parameter retrieval technique49,50, which helps us to estimate and observe the complex impedance of the proposed RSA.

The equivalent circuit model of the proposed RSA is depicted in Fig. 2b. The top FSS equivalent circuit model comprises a series of LC components. This model employs a lossy dielectric substrate to represent the transmission line length, with the bottom ground plane serving as a short circuit. Additionally, as the FSS is constructed using resistive material of RuO2, the model integrates a series resistor R. Therefore, the cumulative circuit of the proposed absorber can be modeled as series RLC.

Figure 2
figure 2

(a) Complex impedance characteristics of the proposed RSA and (b) equivalent analytical RLC circuit model of the proposed RSA.

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Figure 2a indicates the real and imaginary part of the impedance of proposed RSA. The black solid line depicts the real component, and the dashed red line represents the imaginary part of the impedance of the proposed RSA. The real part gives us the overall losses of the absorbing structure while imaginary component shows the resonance behavior of the proposed RSA. As we know, the top FSS is comprised with a circular-ring therefore, it gives the series LC response. Finally, we use the complex S11 parameter which is taken from the CST simulations and try to construct an RLC circuit for the proposed RSA. Understanding the impedance behavior is crucial and a key parameter in constructing an RLC circuit for any geometric shape or unit cell. As our proposed design comprises a circular ring, it exhibits the behavior of an LC series circuit with a combination of resistor R because it features a resistive material incorporate them.

The impedance values of the top FSS and the dielectric spacer can be determined by employing the following equations49:

$$ Z_{FSS} = R - j\left( {\frac{{1 - \omega^{2} LC}}{\omega C}} \right) $$
(1)
$$ Z_{S} = jZ_{0}^{TE} \tan \left( {\beta h_{s} } \right) $$
(2)

where \(Z_{0}^{TE} = \frac{{\omega \mu_{0} }}{\beta }\), \(\beta = \sqrt {\varepsilon_{0} k_{0}^{2} - k_{t}^{2} }\), \(k_{0} = \omega \sqrt {\mu_{0} \varepsilon_{0} }\), \(k_{t} = k_{0} \sin \theta\), \(h_{s}\) is the dielectric thickness.

Furthermore, the Zin and Γin can be evaluated from the following expressions.

$$ Z_{in} = Z_{FSS} \parallel Z_{S} $$
(3)
$$ \Gamma_{in} = \frac{{Z_{in} - Z_{0} }}{{Z_{in} + Z_{0} }} $$
(4)

Figure 2b depicts the equivalent RLC circuit of the proposed RSA and the full-wave simulation absorption and analytical absorption which is estimated through circuit modeling approach are shown in Fig. 3. It is obvious that the simulated absorption results and the analytical absorption, calculated through circuital approach are close to each other, showing the advantage of the circuit modeling technique. Moreover, the circuital approach provides a precise and convenient method for assessing the spectral characteristics of metamaterial structures. However, full-wave simulations require substantial computing power and considerable time to process extensive structures based on metamaterials.

Figure 3
figure 3

Comparison of the absorption coefficient of the full-wave simulation method and RLC circuit model.

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Results and discussion

In this section, we assess the performance of the proposed RSA under various parametric conditions. Initially, a normal incident THz wave is applied to the top surface of the designed RSA, and its spectral performance is depicted in Fig. 4. Figure 4b illustrates the transmitted, reflected, and absorptive behaviors of the proposed RSA, which effectively absorbs the entire range of THz waves from 3.78 to 4.25 THz, when incident waves are exposed to the RSA.

Figure 4
figure 4

Spectral features of the proposed RSA. (a) S11 component and normalized impedance and (b) absorption features along with its reflection and transmission.

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Impedance analysis serves as a fundamental theory to characterize the performance of the proposed RSA which helps in determining the absorption. It provides knowledge about the behavior of the reflected wave, allowing us to calculate absorption through matching the absorber impedance with the free-space impedance.

In this section, we present the impedance analysis of the designed RSA to demonstrate its impedance matching behavior with free space. The absorption characteristics of this absorber rely on the reflection coefficient of the design, which in turn depends on how closely the impedance matches with that of free space. Figure 4a illustrates the normalized impedance of the RSA across the desired operating frequency spectrum. It’s evident that the impedance closely approaches unity within the frequency band spanning from 3.78 to 4.25 THz. This close impedance matching contributes to the RSA exhibiting a broad absorption response, surpassing 90% efficiency within this frequency range, which can be observed in Fig. 4b.

In examining the impact of sheet resistance from the resistive ohmic sheet employed on the top surface, we investigate the absorption characteristics of the proposed RSA across varying sheet resistance values, as depicted in Fig. 5. The sheet resistance (Rs) was varied within a range of 40–90 Ω/sq in increments of 10 Ω/sq. The analysis revealed that the RSA exhibited optimal performance at Rs = 80 Ω/sq, while still demonstrating considerable absorption bandwidth for other Rs values. Notably, achieving such an extensive absorption bandwidth is not possible with a conventional metallic resonator when employing a single-layer design configuration.

Figure 5
figure 5

Trend of the absorption characteristics by tuning different sheet resistances of the top circular ring.

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It's important to highlight that this resistive ohmic structure enables the creation of a broad absorptive surface with a straightforward and easily manufacturable design geometry. Moreover, this approach doesn’t compromise cost efficiency or add complexities to the fabrication process. Furthermore, this simple and cost-effective design shows significant advantages including single-layer, ease of fabrication when compared to the existing THz absorbers.

Moreover, an analysis of the electric field patterns associated with the proposed RSA is presented which helps to gain a deeper understanding of the physical interpretation of the absorption phenomena. To visualize the electric field, we specifically selected two operating frequency points: 3.9 THz and 4.2 THz. The corresponding intensity distributions are depicted in Fig. 6. In Fig. 6a, the electric field pattern at the lower frequency of 3.9 THz is displayed, with the highest intensity being concentrated at the upper and lower portion of the circular-shaped micro-ring. Similarly, at the higher operating frequency of 4.2 THz, it is apparent that the electric field intensity is also predominantly localized along the top and bottom part of the micro-ring resonator, as shown in Fig. 6b. It is important to note that at the lower operating frequency of 3.9 THz, the intensity of the e-field is higher compared to the higher operating point of 4.2 THz, due to the maximum absorption value at this frequency point compared to 4.2 THz. This observation validates that absorption at this frequency region primarily takes place at the upper and lower edges of the circular-shaped resonator. Consequently, the resistive circular-shaped ring plays crucial roles in significantly enhancing the overall absorption efficiency. The absorption enhancement in the metamaterial cavity is due to the localized fields at specific resonant frequencies. When the incident waves match these resonant frequencies, particularly those of localized surface plasmons, the interaction between the free space and the metamaterial is significantly increased. This strong localization of plasmon resonances leads to enhanced absorption. Additionally, the circular-shaped resonator generates dipole-like resonances51,52 at both the upper and lower ends, leading to the induction of localized surface plasmon resonances. These resonances contribute significantly to enhancing the absorption efficiency.

Figure 6
figure 6

The representation of the electric field intensity of the proposed RSA (a) f = 3.9 THz and (b) 4.2 THz.

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Furthermore, conducting angular stability analysis holds significant importance as it is essential for predicting the performance of the suggested RSA when subjected to diverse incident angles of incoming THz waves. This analysis aids in understanding the interaction between the input waves and the proposed design across varying angles, ultimately allowing for the comprehensive examination of absorption trends. To investigate the fluctuations in the absorption capabilities of the designed RSA, the incoming THz waves are applied to the proposed design at varying angles ranging from 10° to 50°, with a step size of 10°, as illustrated in Fig. 7. At an angle of θ = 10°, the suggested RSA demonstrates nearly the same absorption range as observed at θ = 0°. Upon increasing the incident angle from 10° to 20°, the absorption window slightly narrows, yet it consistently encompasses the frequency bandwidth between 3.9 and 4.2 THz. However, at higher incident angles ranging from θ = 30° to 50°, the designed RSA experiences a reduction in its bandwidth due to significant anisotropy at oblique angles. It is important to note that the proposed RSA exhibits identical absorption characteristics for both TE- and TM-mode excitations.

Figure 7
figure 7

Absorption features of the proposed RSA by changing oblique incident angles. (a) TE wave polarization and (b) TM wave polarization.

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Additionally, absorptivity has been examined by altering the rotational angles (polarization angles) of the EM THz waves. In this context, the rotational angle (φ) ranges from 0° to 90° with an increment of 30°, as depicted in Fig. 8. This analysis proves highly effective in forecasting the polarization insensitivity of the proposed structure, given the unknown polarization behavior of incoming waves. For an absorber to be efficient and resilient, it should effectively absorb all polarization states of incident waves. Therefore, when designing an absorber, the geometry of the structure ought to possess a four-fold symmetric nature. Such symmetry ensures a polarization-insensitive response. Figure 8 distinctly illustrates that the suggested RSA exhibits nearly identical absorption behaviors across all specified polarization angles due to its composition of circular-ring shaped unit cells, fulfilling the essential criterion of four-fold symmetry.

Figure 8
figure 8

Absorption features of the proposed RSA by changing polarization angles.

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Multi-reflection interference theory

This section presents the interference theory based on multiple reflection which helps to understand the transmitted and reflected waves between the top surface and the ground-plane, as illustrated in Fig. 9. The top periodic FSS arrays serve the purpose of impedance-tuning surfaces, while the lower groundsheet is considered a metallic plate with negligible thickness, functioning as a reflector. As EM waves approach the upper periodic arrays, they enter the spacer through the phenomenon of impedance matching. Subsequently, the dielectric spacer undergoes multiple reflection phenomena, as illustrated in Fig. 9. The mathematical quantities associated with them can be expressed as: \(r_{12}^{\prime } = r_{12} e^{{i{{\varphi }}_{{{\text{r}}12}} }}\) and \(t_{12}^{\prime } = t_{12} e^{{i{{\varphi }}_{{{\text{t}}12}} }}\). The transmitted component encounters the lower ground reflector, reflecting to the dielectric spacer with a reflection amplitude of − 1 and a complex propagation phase \(\beta = nk_{o} h_{s}\), Here \(h_{s}\) represents the substrate thickness and \(k_{o}\) stands for the free-space wavenumber. Once more, there is a partial transmission-reflection with corresponding energy levels of \(r_{21}^{\prime } = t_{21} e^{{i{{\varphi }}_{{{\text{t}}21}} }}\) and \(r_{21}^{\prime } = r_{21} e^{{i{{\varphi }}_{{{\text{r}}21}} }}\), respectively. Due to these multiple reflection steps, a destructive interference occurs. Ultimately, the total reflection can be determined using the following expression, as outlined in53,54.

Figure 9
figure 9

System model of the multi-reflection interference theory.

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Figure 10 outlines the spectral characteristics of the interference theory including the amplitude and phase of the reflected-transmitted waves. To show the consistency between the simulation and interference theory, the calculated absorption has been compared with the full-wave simulation. Figure 10c illustrates a comparison between the calculated and simulated absorption, showing a close alignment between them.

Figure 10
figure 10

Analytical results of the interference theory (a) amplitude, (b) phase and (c) absorption characteristics.

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Conclusion

In summary, this study presented an innovative and cost-effective solution aiming to achieve extensive absorption in the THz band utilizing a miniaturized, single-layer metamaterial structure. The proposed structure is composed of a single circular ring constructed from a RuO2-based high impedance material with significantly higher sheet resistance compared to conventional metallic resonators. The proposed RSA showcased a large absorption bandwidth spanning from 3.78 to 4.25 THz, maintaining a consistent absorption rate exceeding 90%. Furthermore, we conducted a comprehensive analysis to evaluate its absorption performance across various sheet resistance values within the top circular ring. Additionally, angular stability and polarization insensitivity analysis were performed through oblique incident and polarization angles. Moreover, the simulated absorption of the proposed RSA is validated using the RLC circuit model and the interference theory method. This proposed absorber exhibited promising potential across a diverse application, including communication, imaging, and an integrated circuits operating within the THz band.