Fano resonated, ultrathin, flexible and ultrawideband absorption featured nano-metaatom structure with dispersion gap optimized for optical range applications

ABSTRACT This article reports an Ultra wideband nano scale metamaterial absorber with ultrathin and flexible feature for visible spectrum applications. The absorber investigated for

dispersion and Fano resonance characteristics to achieve metamaterial properties as well as independent of asymmetry of structure. Maximum visible spectrum wave interaction with the cascaded

split nano square meta atom also ensured to achieve the absorption at highest percentage in numerical evaluation. The Finite Difference Time Domain (FDTD) method incorporated with CST

microwave studio computational tool used for the entire analysis. Numerical analysis revealed that, on average 86.66% absorption achieved for 560 THz bandwidth peak absorption for the unit

cell was 99.88% and the array shows 99.79%. Dispersion gap optimized based on mode 4 to incorporate all photons for phase and group velocity inside the nano metamaterial absorber.

Furthermore, the Fano resonance wave to identify the high-quality factor at visible spectrum on nanostructure meta atom and direct-indirect visible wave trapped in the structure. The

dispersion gap optimization and Fano resonance make the proposed cascaded split nano square meta atom a significant candidate for visible spectrum applications like solar energy harvesting,

biochemical sensing, optical range application etc. SIMILAR CONTENT BEING VIEWED BY OTHERS POLARIZATION AND ANGULAR INSENSITIVE BENDABLE METAMATERIAL ABSORBER FOR UV TO NIR RANGE Article

Open access 22 March 2022 DESIGN AND OPTIMIZATION OF BROADBAND METAMATERIAL ABSORBER BASED ON MANGANESE FOR VISIBLE APPLICATIONS Article Open access 24 July 2023 SELECTIVE-WAVELENGTH PERFECT

INFRARED ABSORPTION IN AG@ZNO CONICAL METAMATERIAL STRUCTURE Article Open access 12 September 2024 INTRODUCTION The concept of metamaterial or artificially engineered structure with

absorber concept introduced by Landy et al.1. They have described the characteristics of absorbers based on thickness compared to conventional one and numerous articles reported such

metamaterial for applications like energy harvesting2, invisible cloaks3, optical imaging4, absorbers5, filters6, ultra-sensitive sensors7, photovoltaic cells8, etc. In recent years, there

has been a significant emphasis on the investigation of abundant and environmentally friendly solar energy, namely from the visible spectrum, as a substitute for traditional fossil fuels3.

The effectiveness of solar thermal systems relies heavily on absorbers, which convert solar radiation into thermal energy. An ideal absorber should have unity absorptance in UV, visible, and

near infrared (NIR) to convert most radiation into heat, and zero emittance in mid-IR regions4. To achieve a high solar-to-heat conversion efficiency, solar thermal absorbers must possess

spectral selectivity, angular and polarisation independence, as well as excellent thermal stability. These factors are essential because solar radiation is unpredictable, and efficient

operation at high temperatures is necessary3. Optical metamaterials are man-made structures that possess exceptional optical properties not typically observed in naturally existing

materials5. The study investigates the phenomenon of selective absorption in metamaterials that consist of different micro/nanostructures. These structures operate in a wide range of

frequencies, from GHz to IR spectral regions. Examples of these structures include split-ring resonators, fishnets, cut-wires, and photonic crystals6,7,8,9,10,11. Researchers are currently

investigating film-coupled metamaterials in metal-insulator-metal configurations for their potential in thermal emission or selective absorption across the visible to near-infrared spectral

regions. This is particularly relevant as solar energy reaching Earth consists of 48% visible, 43% infrared, and 7.5% ultraviolet radiation6. The utilisation of visible and infrared

radiations is of great importance in solar cell applications, as it is essential to absorb these frequencies in order to achieve the highest possible current output. Even a slight decrease

in light can have a negative impact on conversion efficiency. This could be caused by the presence of small transmission waves from various meta-absorber layers or by minimising reflection

surfaces. These losses significantly restrict the efficiency of solar cells. Hence, Researchers are currently investigating innovative methods, such as the use of Metamaterial absorbers

(MTMA), to improve the efficiency of solar cells and make them more environmentally friendly. These advancements aim to meet the growing energy needs of the future. Research groups are

currently dedicated to enhancing the adaptiveness of solar cells, also known as photovoltaic (PV) cells, while simultaneously striving to decrease material costs. The utilisation of thin

film-based technology decreases the amount of silicon needed per unit cell, resulting in a reduction in the manufacturing cost of these devices4,7. In their experiment, Landy et al.8

developed a highly effective Metamaterial Tunable Microwave Absorber. They made adjustments to the parametric properties of the material in order to achieve optimal absorption at a specific

resonance frequency. This research showcased the promising capabilities of metamaterials in absorbing electromagnetic wave radiation. The dual-band MTMA developed by Dincer et al.5. is

insensitive to both polarisation and incident angle. It demonstrates two distinct maximum absorptions in the GHz region, making it an ideal choice for solar cell applications Dincer et

al.5,9. In this study, Cao et al.10 showcased the application of Multilayer Thin-film Metamaterial Absorber in the high-frequency region for solar cell applications. They successfully

developed a tunable broadband absorber by effectively exciting multiple Plasmon resonances at the optimal frequency. This research highlights the potential of MTMA in enhancing the

performance of solar cells by maximising light absorption across a wide range of frequencies. This study11,12 introduces a novel absorber design that operates in the visual frequency region.

The absorber exhibits polarization independent characteristics, ensuring its effectiveness across different polarisation states. Additionally, it achieves a high absorption amount of over

95%, making it highly efficient in absorbing electromagnetic waves. The absorber is designed using a multi-layer or prism-shaped approach, which contributes to its broadband efficiency.

Furthermore, it is important to highlight that the scope of this study was confined to the frequency range of 1–10 THz. As a result, this limitation has significant implications for the

analysis of the solar radiation spectrum. The application of metamaterial cloaking in solar cells has been explored as a means to improve electrical power generation13. However, a limitation

arises from the polarisation dependency of the cloaking material, which restricts the absorption of a wide range of photons. The ultrathin nanostructure meta-absorber, as proposed by Lin et

al.15 and Rana et al.16, presents a highly sophisticated design technique and achieves superior absorption ratings. The utilisation of Metamaterial Absorbers (MTMAs) extends far beyond

their current application in solar cells. The authors propose that aside from its known capability to alter the dielectric properties of naturally occurring materials, there are additional

captivating prospects for its utilisation within the realm of the Internet of Things (IoT) environment14,15,16,17,18. Numerous scholars have made noteworthy contributions to the field,

focusing on the potential of combining metamaterial characteristics with solar cells to improve efficiency and decrease the cost per unit cell. However, certain factors still need to be

considered to fully harness these benefits. Factors such as, nanoscale metamaterial are mostly studied for symmetrical or asymmetrical shape resonating structure. These resonance natures

work based on the lumped component’s characteristics or mutual contribution of resonating conducting paths. Besides, solar spectrum or energy harvesting focused metamaterials are mostly

analysed on wave propagation interactions. Therefore, Q-factor, energy conversion ratio or polarization impact are generally assessed in reported articles to understand the potentiality in

visible spectrum application scope. Apart from considering these general factors, asymmetric or symmetric-shaped resonator’s discrete continuum state resonance usually get ignored due to

negative indexed features mostly remaining unavailable. Thus, Lorentzian resonance becomes unexplored, and this manuscript considered these factors meticulously to develop Fano resonance

along the resonating structure. In this study, we present a novel design for optimising the dispersion behaviour of a fractal Fano resonated metamaterial absorber (MA) in the visible

frequency region of the solar spectrum. Our proposed design involves a cascaded split nano square structure, which incorporates the unique characteristics of Single Negative (SNG)

metamaterials. By utilising a tri-thin layer material, we aim to achieve adaptability to the solar spectrum and enhance the performance of the MA. The structure is designed and analysed

using the Finite-Difference Time-Domain (FDTD) approach. This involves discretizing the unit cell in both time and space, following Maxwell’s central difference approximation. A tetrahedral

mesh is utilised to model the unit cell for wave propagation, along with the application of typical boundary conditions. This structure is made of a metallic-optical-thin film layer where

the metallic layer has a cascaded split square in both horizontal and vertical directions with (N-1) row symmetry, where _N_ = 5 for a single nano square. The broadband absorption mechanism

was numerically investigated with dispersion behaviour and Fano resonance characteristic based high factor. Thus, the nanostructure has the potential for visible spectrum applications like

energy harvesting or biochemical sensing. DETAIL OF NUMERICAL ANALYSIS The concept of a metamaterial absorber that works for harvesting energy from the solar spectrum is projected to absorb

or trap the visible light spectrum using the dielectric properties variation. The analysis of Metamaterial Absorbers (MTMA) includes both single-layer and multi-layer structures to achieve

optimal absorption. Recent studies18,19,20,21,22,23,24,25,26 have highlighted their polarization insensitivity, but they also note a lower level of absorption. Therefore, improvements in

their geometric design and fabrication methods are necessary to address these challenges. The proposed metamaterial has a cascaded nano split square where the first row is comprised of five

(5) split squares of 88 nm and consecutive rows have four (4). Therefore, the horizontal and vertical axis have compact square shapes to create a centre capacitive gap which enhances the

chances of incident visible light trapping more robustly. Besides, a 90 nm nano square wall works on multiple modes of dispersion to get metamaterial properties. Gold, which represents a

metamaterial absorber cascaded outlook, is a hard, dense, temperature/corrosion conductive substance with an optical range of 90 nanometres and nearly complete resistance to reactions with

acids, oxygen, and alkalis. All three of these properties—permittivity, permeability, and wave propagation—are influenced by the (N-1) row symmetry nano square split symmetrically. A

capacitive tunnel is used by the unit cell to couple each quarter portion of the cascade. The centre section of the cascade is composed of gallium arsenide (GaAs), and the ground layer is

composed of nickel (Ni). The material GaAs is a cross-linked polystyrene that possesses a high refractive index and excellent optical transmission, whereas the material Ni is resistant to

rusting and corrosion, does not react with air, and possesses excellent conductivity. Figure 1a, b presents a geometrical structure with an inset of nano split square dimension, Fig. 1c

shows the 2 × 2 array structure and simulation configuration depicting the proposed MA’s boundary condition in Fig. 1d. Perfect Electric Conductor (PEC) and Perfect Magnetic Conductor (PMC)

along the X and Y axes, respectively, form an ideal configuration in the absorber’s two waveguide ports that are aligned along the Z-axis. The Computer Simulation Technology Electromagnetic

(CST EM) simulator and the Finite Difference Time Domain (FDTD) approach were employed for numerical analysis. Figure 1a and Table 1 illustrate the designed geometrical parameters of the

suggested absorber, while the structure front view is also available. CASCADED SPLIT NANO SQUARE META-ATOM PARAMETRIC ANALYSIS, RESULTS & DISCUSSION E-FIELD AND H-FIELD DISTRIBUTION

Light is an electromagnetic wave that travels in a transverse manner. It can be observed in three different spectra: infrared, visible, and ultraviolet (UV). The solar light’s spectral

energy distribution exhibits a peak intensity of 1.5 eV inside the visible range, which is comparable to the majority of semiconductor materials. Figure 2 displays the numerical performance

of the propagation of electromagnetic waves in the visible light spectrum, including the boundary conditions, electric field (E-field), and magnetic field (H-field). Despite the presence of

three arbitrary resonance frequencies (440, 600, and 900 THz) in the figure, the field distribution is similar across the entire bandwidth of 430 ~ 1000 THz. Considering the vector wave

equations discussed in27. $$\left. \begin{gathered} {\overrightarrow \nabla ^2}{\overrightarrow E _m} - {\gamma ^2}{\overrightarrow E _m}=0 \hfill \\ {\overrightarrow \nabla

^2}{\overrightarrow H _m} - {\gamma ^2}{\overrightarrow H _m}=0 \hfill \\ \end{gathered} \right\}$$ (1) where, \(\overrightarrow {{E_m}}\) and \(\overrightarrow {{H_m}}\)distributed field

component of E-field and H-field respectively. Permittivity (ε), permeability (µ), operating frequency (ω), and conductivity (σ) of the medium through which the signal is transmitted

determine the behaviour of each field component at each phase variation, according to the one-dimensional vector differential operator \(\overrightarrow \nabla\). The proposed MTMA structure

and the upper layer (gold) display a prominent electric field component at the vertical split, leading to substantial capacitance and wave propagation along the Z-direction. The cascaded

split nano square and compactness section contribute to wave absorption, excitation, and mobility. A symmetrical distribution of the electric field component is found at the resonance

frequency of 440 THz, and this distribution remains consistent across the range of approximately 430–1000 THz while considering the propagation of the medium to be uniform. Consequently,

more than 80% of the visible spectrum is absorbed, which has the potential to improve the efficiency of visible spectral energy harvesters by integrating a metamaterial absorber. The

absorption of light can alter the quantity of excited electrons and enhance electron mobility, hence improving the efficiency of devices that capture visible spectral energy28. Similarly, in

Fig. 2, the H-field components exhibit the same Eq. (1) by displaying a combined magnetic resonance along with vertical and horizontal splitting, as well as on the borders of the cascaded

structure. The proposed metamaterial absorber form shows great promise for numerical analysis in terms of vector electromagnetic wave propagation and its potential for enhancing solar cell

efficiency. For numerical analytical verification, it is necessary to examine the fundamental dielectric characteristics of any material and especially while dispersive characteristics,

resonance behaviour, absorption these vital aspects of standardisation that are quite subject to changes. So, this cascaded nano split square unit cell MA is characterised based on

permittivity (_ε_), and permeability (_µ_) extracted from S-parameters using well well-known NRW method27 and depicted in Fig. 3. The Transmission (S21) and reflection (S11) show significant

response between 440 and 750 THz with a magnitude of -44dB (at 522 THz) and − 20.77dB (612 THz), respectively (Fig. 3a). The examination of dielectric properties (illustrated in Fig. 3b, c,

d) indicates that a negative property (negative ε) exists at the designated resonance frequency, whereas the magnetic permeability maintains a positive value. The adverse characteristic

induces an atypical aberration in electromagnetic (EM) waves. Particularly, where EM wave oscillations occur, the middle and ground layers, a robust evanescent field29 is expected to develop

due to the activation of electron mobility by photons. Within this evanescent field, electromagnetic waves deviate from their typical propagation pattern. Instead, energy is locally

concentrated in the vicinity of the source, manifesting as oscillating charges or electrons. The net inward energy flow, as determined by the average Poynting vector across a frequency range

of 500–900 THz, indicates that the proposed Metamaterial Absorber maintains a positive permeability but a negative permittivity. Furthermore, an unanticipated non-resonance point in the

visible spectrum is unveiled by the S-parameters (Fig. 3(a)). Fortunately, this non-resonance point does not have a substantial effect on the absorption efficiency. The relative dielectric

performances (Fig. 3b, c, d) as a single negative nature play an important contribution to ensure the absorption performance both for unit cell and 2 × 2 array structure. POWER DISTRIBUTION

IN NANO UNIT CELL Simulated power distribution in the cascaded split nano square meta atom passes through the dielectric materials and conductive layers. The total distribution includes

accepted power in the nano cell (_P__A_), power outgoing to all ports (_P__out_) (i.e. Transmission and reflection ports) and simulated power (_P__simu_). Figure 4 shows the corresponding

power distribution and loss behaviour of the proposed nano meta-atom. The distribution characteristics follow the principle as mentioned in30 to ensure the propagation of visible spectrum

waves through the structure. In addition, a simulated loss behaviour as well as surface losses also explained. This loss calculation impacts on Q factor during Fano resonance calculation.

However, the total volume of the unit cell nanostructure is 9.72 × 107nm3 approximately, so the total volume losses for the tangential component of the E-field and H-field distribution

(Expression written for E-field) is \(\:{P}_{DL}=\frac{1}{T}\int\:{\left|\overrightarrow{E}\right|}^{2}dV\), where PDL power loss due to volume. In numerical analysis, we kept the basic

material features as per CST solver default value but increased the meshing (Tetrahedrons) up to 90,000 to get precision in filed Jacobian Distribution (JD) approximation. Therefore, the

losses may vary in other approximations like AKS or binomial perturbation. In Fig. 4, the power distribution of gold and graphene almost absorb a similar amount of power between 630 and 1000

THz range, but a small range of variation also exists between 430 and 620 THz. An approximation can concluded by observing the power absorption variation because surface power is always

half of the general power distribution as per the relation, \(\:{P}_{w}=1/2\sqrt{\frac{\pi\:\epsilon\:\mu\:}{\sigma\:}}\int\:{\left|\overrightarrow{H}\right|}^{2}dS\), where symbols

represent the usual meaning. The outgoing power (both for gold and graphene) accordingly varies to both excitation port 1 and port 2 and the simulated power was the same (0.5 W) for the two

conducting materials. DISPERSION BEHAVIOUR OF UNIT CELL AT VISIBLE FREQUENCY Electromagnetic wave propagation through metamaterial follows the Maxwell’s equations, but nonlinear dispersion

during propagation come out with modification of wave equation as follows:

$$\:\frac{{\partial\:}^{2}E}{{\partial\:z}^{2}}=\frac{\mu\:}{{\mu\:}_{r}}\frac{ϵ}{{\epsilon\:}_{r}}\frac{{\partial\:}^{2}E}{{\partial\:t}^{2}}+\frac{\mu\:}{{\mu\:}_{r}}\frac{{\partial\:}^{2}{\iota\:}_{p}}{{\partial\:t}^{2}}$$

(2) The dispersive metamaterial nature on the proposed design assumed that the magnitude of electric field is in half along the Z-axis and _ι__p_ is the 4th order Fano resonated electric

susceptibility. The next section will discuss more about Fano resonance on the structure. Energy density of nano structure metamaterial is difficult to maintain positivity as the nano split

remain a challenge for fabrication. But in numerical study, as the split gap sustain the energy density become positive. Besides, the dispersive meta-atom also supports to preserve a

relatively constant relative dielectric permittivity (_ε__r_) and permeability (_µ__r_). Frequency dispersion for the proposed design typically follow the Drude model31,32 based on operating

frequency ω. For relative permittivity, \(\:{\epsilon}_{r}=1-\frac{{{\omega\:}_{pe}}^{2}}{\omega\:(\omega\:+j{\gamma\:}_{pe})}\) where, \(\:{\omega\:}_{p}\) is plasma frequency in electric

field and \(\:{\gamma\:}_{pe}\) is the propagation loss for corresponding field and relative permeability,

\(\:{\mu\:}_{r}=1-\frac{{{\omega\:}_{pm}}^{2}}{\omega\:(\omega\:+j{\gamma\:}_{pm})}\) where, \(\:{\omega\:}_{pm}\) is plasma frequency in magnetic field with corresponding loss of magnetic

field \(\:{\gamma\:}_{pm}\). In visible spectrum operation, imaginary part of the loss factor for electric and magnetic field can be ignored due to variable light intensity and uncompensated

dispersion characteristics existence. Hence, the typical Drude model dielectric equations can be reduced to truncated power series for further studies of dispersion. The relevant power

distribution already discussed in earlier section and therefore, focus on dispersion performance. Figure 5a shows the 4th order dispersion diagram on visible frequency spectrum. Dispersion

gap from Mode 1 to Mode 4 significantly observed between 700 and 1000 THz. Normal lossless material environment for electromagnetic wave considers the phase constant _β_ = k as wave number.

But the proposed cascaded nano meta-atom comprised of lossy materials though we have considered the magnetic dispersion as basic model. Since β is function of corresponding operating

frequency and it can be obtained using the S-parameters response, so respective phase velocity (_v__p_) and group velocity (_v__g_) derived by\(\:{v}_{p}=\frac{\omega\:}{\beta\:}\) and

\(\:{v}_{g}=\frac{d\omega\:}{d\beta\:}\). Figure 5b shows the _v__p_ and _v__g_ plotting for the proposed nano metamaterial structure. The delay between 400 and 650 THz for the phase and

group velocity is due to compact cascaded structure and less density of E-field distribution as described earlier. Concentration of both E-field and H-field distribution gradually increased

between 650 and 900 THz, therefore, the gap between those velocity is less on that range. At higher frequencies, again the structure losses the field concentration and delay increases.

Overall, the proposed nano structure metamaterial shows a better response for _v__p_ and _v__g_ with respect to dispersive gap minimization. VISIBLE SPECTRUM FANO-RESONANT METAMATERIAL

STRUCTURE MODELLING Coupling or splitting the resonating structure to develop a basic Fano resonance is described in coupling theory33,34,35 when the structure interacts with visible range

waves. Therefore, the proposed cascaded split nano square Fano resonance modelling starts (Fig. 6) with coupling with the adjacent split gap by assuming natural frequency (ωn) for the

initial visible wave incident on the structure. Indirect visible wave (ωi) which originated from reflected resonating coupling nano split ring is another source of incident wave. A schematic

Fig. 6 shows the single channel visible spectrum wave with transmission and reflection direction while incident on cascaded nano ring. During the nearfield interaction between the meta-atom

of the nano square split ring, the Fano resonance can only occur differently coupled radiative time frame. In another way, we can state that the natural frequency time frame (_T_n) is much

smaller than the Indirect visible wave time frame (_T_i ). For a periodic structure, stated for Fano resonant36, the transmission and reflection model for direct and indirect visible waves

as shown in Figure X can be expressed as-

$$\:{\varvec{r}}_{\varvec{F}}=\frac{{\varvec{V}}^{\varvec{i}\varvec{n}\left(\varvec{d}\right)}}{{\varvec{V}}^{\varvec{i}\varvec{n}\left(\varvec{i}\varvec{n}\varvec{d}\right)}}=\frac{\varvec{C}\varvec{o}\varvec{m}\varvec{p}\varvec{l}\varvec{e}\varvec{x}\:\varvec{c}\varvec{o}\varvec{n}\varvec{j}\varvec{u}\varvec{g}\varvec{a}\varvec{t}\varvec{e}\:\varvec{o}\varvec{f}\:\varvec{C}\varvec{o}\varvec{u}\varvec{p}\varvec{l}\varvec{i}\varvec{n}\varvec{g}\:\varvec{M}\varvec{a}\varvec{g}\varvec{n}\varvec{i}\varvec{t}\varvec{u}\varvec{r}\varvec{e}\:\left|\varvec{\delta\:}\right|}{\varvec{F}\varvec{r}\varvec{e}\varvec{q}\varvec{u}\varvec{e}\varvec{n}\varvec{c}\varvec{y}\:\varvec{v}\varvec{a}\varvec{r}\varvec{i}\varvec{a}\varvec{n}\varvec{c}\varvec{e}\:\varvec{o}\varvec{f}\:\varvec{v}\varvec{i}\varvec{s}\varvec{b}\varvec{l}\varvec{e}\:\varvec{w}\varvec{a}\varvec{v}\varvec{e}\:\varvec{c}\varvec{o}\varvec{n}\varvec{j}\varvec{u}\varvec{g}\varvec{a}\varvec{t}\varvec{e}\:{\varvec{f}}_{\varvec{\delta\:}}},{\varvec{t}}_{\varvec{F}}=\frac{{\varvec{V}}^{\left(\varvec{T}\right)}}{{\varvec{V}}^{\varvec{i}\varvec{n}\left(\varvec{d}\right)}}=1+{\varvec{r}}_{\varvec{F}}$$

A general ohmic loss for the proposed design is 377Ω, which incurs a radiative loss and reduces the total time frame for Feno resonance occurrence. In numerical study, these ohmic losses

are incorporated as a part of fabrication limitation. However, this loss also follows the energy conservation feature as like conventional metamaterials reflection and transmission

coefficient works. Now, any resonator structure resonating behaviour needs to be calculated for decay rate from the total stored energy from the visible spectrum wave propagated through the

unit cell. Let’s _W_rT is the total energy, then

$$\:\frac{\varvec{d}}{\varvec{d}\varvec{t}}\left[{\varvec{W}}_{\mathbf{r}\mathbf{T}}\right]=\frac{\varvec{d}}{\varvec{d}\varvec{t}}\left({\left|{\varvec{\delta\:}}_{\varvec{d}\varvec{i}\varvec{r}\varvec{e}\varvec{c}\varvec{t}}\right|}^{2}+{\left|{\varvec{\delta\:}}_{\varvec{i}\varvec{n}\varvec{d}\varvec{i}\varvec{r}\varvec{e}\varvec{c}\varvec{t}}\right|}^{2}\right)$$

For the indirect visible wave radiative part, the radiative time frame would be negligible, so, we can consider it near zero and the decay rate reduces to

\(\:\frac{d}{dt}{\left|{\delta\:}_{direct}\right|}^{2}\). So, based on this decay rate the Fano resonance behaviour on the proposed structure follows with three materials comprising the

gold, nickel and Gallium Arsenide simultaneously acting to achieve the best quality factor. In Fig. 5a, the Fano resonance stems from the interaction between individual modes of these

elements. Spectral repulsion between the modes necessitates that the frequencies of the hybrid direct and indirect modes are mismatched. More complex meta-molecules containing more elements

and resonances enable independent control of the frequencies of the direct and indirect resonances. To understand this Fano resonance impact, we consider the asymmetry (γ) factor mentioned

in37 and conducting layer (Gold) thickness which arbitrarily varies from (40 nm, 70 nm and 90 nm). A significant variation of quality factor was observed based on the γ = 0.06, 0.11 and 0.33

as shown in Fig. 7. When the asymmetry factor is 0.33, the maximum thickness of the proposed design is achieved by varying the direct and indirect wave Fano resonating point spectrally

match and shows a maximum quality factor of approximately 100 between 700 and 750 THz. The oscillating response of between 580 and 650 THz is due to unmatched Fano resonance waves through

the structure. Hence, it is evident that, maximization of the asymmetry factor does not ensure the achievement of quality factor but needs to be matched for the Fano resonance wave to

identify the high quality factor at the visible spectrum on nanostructure meta-atom. However, a comparative study of the proposed absorber for solar cell absorption efficiency calculation

was performed with other recently published articles. In Table 2 shows that some absorbers is different in shape, size and operating frequency20,21,22,23,24 but the proposed MA have

substantial absorption with wide bandwidth. For example, in38,39 both have above 90% absorption but with narrow bandwidth or tuneable bandwidth and structure size dependency is high. Herein,

the proposed cascaded split nano square shape gives above 80% absorption by maintaining operating regions with a wide band. Hence, this MA is a potential structure absorption rating for an

application like solar energy harvesting system efficiency enhancement. CONCLUSIONS Ultra Wideband cascaded split nano square shaped MTMA for visible spectrum based on ultrathin and flexible

nanostructure is numerically demonstrated. This absorber exhibits an absorptivity of higher than 86.66% in a wide frequency range of approximately 440 THz-1000 THz in the visible spectrum

of sunlight. The proposed structure has (N-1) horizontal and vertical symmetry based on nano split square with wide capacitive split to perform as a dispersion gap optimized Fano resonant

metamaterial absorber. The thin triple layer and cascaded shape unit cell make this structure a more suitable form for manufacturing with the usual micro and nanotechnology. Furthermore,

Fano resonance asymmetry analysis primarily shows high-quality factors that this MTMA has strong potential to get higher wave absorption for solar energy harvesting, photonic or optical

range application. DATA AVAILABILITY The corresponding author oversees the data set, which is available upon request. REFERENCES * Landy, N. I., Sajuyigbe, S., Mock, J. J., Smith, D. R.

& Padilla, W. J. Perfect metamaterial absorber. _Phys. Rev. Lett._ 100 (20), 207402 (2008). Article  ADS  CAS  PubMed  Google Scholar  * Wang, Y. et al. Metamaterial-plasmonic absorber

structure for high efficiency amorphous silicon solar cells. _Nano Lett._ 12 (1), 440–445 (2012). Article  ADS  PubMed  MATH  Google Scholar  * Wang, H. et al. Highly efficient selective

metamaterial absorber for high-temperature solar thermal energy harvesting. 137 235–242 (2015). * Feng, Y. et al. Leaves based triboelectric nanogenerator (TENG) and TENG tree for wind

energy harvesting. 55 260–268 (2019). * Dincer, F., Karaaslan, M., Unal, E., Delihacioglu, K. & Sabah, C. J. P. I. E. R. Design of polarization and incident angle insensitive dual-band

metamaterial absorber based on isotropic resonators, 144 123–132, (2014). * Glybovski, S. B., Tretyakov, S. A., Belov, P. A. & Kivshar, Y. S. and C. R. J. P. R. Simovski, Metasurfaces:

From microwaves to visible. 634 1–72 (2016). * Chae, C. G. et al. Experimental formulation of photonic crystal properties for hierarchically self-assembled POSS–bottlebrush block copolymers.

51 (9), 3458–3466 (2018). * Landy, N. I., Sajuyigbe, S., Mock, J. J. & Smith, D. R. and W. J. J. P. R. l. Padilla, Perfect metamaterial absorber, 100 (20) 207402 (2008). * Dincer, F.,

Akgol, O., Karaaslan, M., Unal, E. & Sabah, C. J. P. I. E. R. Polarization angle independent perfect metamaterial absorbers for solar cell applications in the microwave, infrared, and

visible regime, 144 93–101 (2014). * Cao, T., Wei, C., Simpson, R. E. & Zhang, L. and M. J. J. S. r. Cryan, Broadband polarization-independent perfect absorber using a phase-change

metamaterial at visible frequencies. 4 3955 (2014). * Wang, B. X., Wang, L. L., Wang, G. Z., Huang, W. Q., Li, X. F. & Zhai, X. J. I. P. T. L. theoretical investigation of broadband and

wide-angle terahertz metamaterial absorber. 26 (2) 111–114 (2013). * Shen, Y., Pang, Y. Q., Wang, J. F., Ma, H., Pei, Z. B. & Qu, S.-B. J. I. P. T. L. Ultrabroadband terahertz absorption

by uniaxial anisotropic nanowire metamaterials. 27 (21) 2284–2287 (2015). * Schumann, M. F. et al. Cloaking of metal contacts on solar cells, in _CLEO: Science and Innovations_, p. SW1I. 6:

Optical Society of America. (2015). * Samsuzzaman, M., Islam, M. T., Kibria, S. & Cho, M. BIRDS-1 CubeSat constellation using compact UHF patch antenna. _IEEE Access._ 6, 54282–54294

(2018). Article  Google Scholar  * Hossain, M. J. & Faruque, M. R. I. & Islam, M. T. J. P. O. Perfect metamaterial absorber with high fractional bandwidth for solar energy

harvesting, 13 (11) e0207314 (2018). * Islam, M., Ashraf, F., Alam, T., Misran, N. & Mat, K. J. S. A compact ultrawideband antenna based on hexagonal split-ring resonator for pH sensor

application, 18 (9) 2959 (2018). * Ashraf, F. B., Alam, T., Kibria, S. & Islam, M. T. J. M. E. A compact meander line elliptic split ring resonator based metamaterial for electromagnetic

shielding, 8 (2) 133–140 (2018). * Aydin, K., Ferry, V. E., Briggs, R. M. & Atwater, H. A. Broadband polarization-independent resonant light absorption using ultrathin plasmonic super

absorbers. _Nat. Commun._ 2, 517 (2011). Article  ADS  PubMed  Google Scholar  * Zhang, B. et al. Polarization-independent dual-band infrared perfect absorber based on a

metal-dielectric-metal elliptical nanodisk array. _Opt. Express_. 19 (16), 15221–15228 (2011). Article  ADS  CAS  PubMed  Google Scholar  * Pang, Y. et al. Reconfigurable paper-based

metamaterial antenna: Structural transition from 2D to 3D. 1–6 (2024). * Lu, J. et al. Lightweight, ultra-broadband SiOC-based triply periodic minimal surface meta-structures for

electromagnetic absorption. 488, 151056, (2024). * Lu, J. et al. Vat photopolymerization 3D printing gyroid meta-structural SiOC ceramics achieving full absorption of X-band electromagnetic

wave. 78 103827 (2023). * Liu, J. et al. Ferroelectric tungsten bronze-based ceramics with high-energy storage performance via weakly coupled relaxor design and grain boundary optimization,

15 (1), 8651 (2024). * Tian, H., Zhang, X., Zhang, Z. & Liu, Y. & Wu, H. J. J. O. A. C. Low-permittivity LiLn (PO 3) 4 (Ln = La, Sm, Eu) dielectric ceramics for

microwave/millimeter-wave communication. 13 (5), (2024). * Cai, W. J. et al. Carbon nanofibers embedded with Fe–Co alloy nanoparticles via electrospinning as lightweight high-performance

electromagnetic wave absorbers. 43, (6) 2769–2783 (2024). * Selamat, A., Misran, N., Mansor, M. F., Islam, M. T. & Zaidi, S. H. J. J. K. Scattering microwave signal analysis from

triangular loop element of different transparent conductive thin films at Ku-band, 26 83–88, (2014). * Hoque, A. et al. A polarization independent quasi-TEM metamaterial absorber for X and

Ku band sensing applications, _Sensors_. 18, (12) 4209 (2018). MATH  Google Scholar  * Khan, A. D., Khan, A. D., Khan, S. D. & Noman, M. Light absorption enhancement in tri-layered

composite metasurface absorber for solar cell applications. _Opt. Mater._ 84, 195–198 (2018). Article  ADS  CAS  MATH  Google Scholar  * Fang, M. et al. Nonlinearity in the dark: Broadband

terahertz generation with extremely high efficiency. _Phys. Rev. Lett._ 122 (2), 027401 (2019). Article  ADS  CAS  PubMed  Google Scholar  * Hoque, A., Islam, M. T., Almutairi, A. F. &

Chowdhury, M. E. DNG metamaterial reflector using SOCT shaped resonator for microwave applications. _IEEE Access._ 9, 59148–59159 (2021). Article  Google Scholar  * Sun, K. et al. Flexible

multi-walled carbon nanotubes/polyvinylidene fluoride membranous composites with weakly negative permittivity and low frequency dispersion. _Compos. Part A: Appl. Sci. Manufac._ 156, 106854

(2022). Article  CAS  MATH  Google Scholar  * Diepolder, A., Mueh, M., Brand, S., Waldschmidt, C. & Damm, C. Model-based Optimization of Fishnet Metamaterial Lenses under Oblique

Incidence, in _2022 14th German Microwave Conference (GeMiC)_, 01–04 IEEE. (2022). * Haus, H. Waves and fields in optoelectronics, _PRENTICE-HALL, INC., ENGLEWOOD CLIFFS, NJ 07632, USA,

1984, 402_, (1984). * Ruan, Z. & Fan, S. Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle. _J. Phys. Chem. C_. 114 (16), 7324–7329 (2010). Article

  CAS  MATH  Google Scholar  * Fan, S., Suh, W. & Joannopoulos, J. D. Temporal coupled-mode theory for the Fano resonance in optical resonators. _JOSA A_. 20 (3), 569–572 (2003). Article

  ADS  PubMed  MATH  Google Scholar  * Fano, U. Some theoretical considerations on anomalous diffraction gratings. _Phys. Rev._ 50 (6), 573 (1936). Article  ADS  MATH  Google Scholar  *

Khanikaev, A. B., Wu, C. & Shvets, G. Fano-resonant metamaterials and their applications. _Nanophotonics_. 2 (4), 247–264 (2013). Article  ADS  CAS  MATH  Google Scholar  * Chen, P. Y.,

Salas, R. & Farhat, M. Generation of high-power terahertz radiation by nonlinear photon-assisted tunneling transport in plasmonic metamaterials. 19 (12), 124012 (2017). * Zhou, L. et al.

Self-assembled spectrum selective plasmonic absorbers with tunable bandwidth for solar energy conversion. _Nano Energy_. 32 195–200 (2017). Article  MATH  Google Scholar  * Sakhdari, M.,

Hajizadegan, M., Farhat, M. & Chen, P. Y. J. N. E. Efficient, broadband and wide-angle hot-electron transduction using metal-semiconductor hyperbolic metamaterials, 26 371–381 (2016).

Download references FUNDING This research was funded by Kuwait University, Research Project no. EE02/21. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Institute of Climate Change, Universiti

Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia Ahasanul Hoque * Department of Electrical, Electronic and Systems Engineering, Faculty of Engineering and Built Environment, Universiti

Kebangsaan Malaysia, 43600, Bangi, Selangor, Malaysia Mohammad Tariqul Islam * Electrical Engineering Department, Kuwait University, 13060, Kuwait City, Kuwait Ali F. Almutairi Authors *

Ahasanul Hoque View author publications You can also search for this author inPubMed Google Scholar * Mohammad Tariqul Islam View author publications You can also search for this author

inPubMed Google Scholar * Ali F. Almutairi View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS The authors have the following contribution

regarding the article,“Conceptualization, A.H.; methodology, A.H. M.T.I. and A.F.A.; software, A.H.; validation, A.H., M.T.I. and A.F.A.; formal analysis, A.H. M.T.I. and A.F.A.;

investigation, A.H.; resources, A.H.; data curation, A.H.;writing—original draft preparation, A.H.; writing—review and editing, A.H., M.T.I. andA.F.A.; visualization, M.T.I. and A.F.A.;

supervision, M.T.I. and A.F.A; project administration, M.T.I. and A.F.A.; funding acquisition, M.T.I. and A.F.A. CORRESPONDING AUTHORS Correspondence to Ahasanul Hoque, Mohammad Tariqul

Islam or Ali F. Almutairi. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer Nature remains neutral with

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http://creativecommons.org/licenses/by-nc-nd/4.0/. Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Hoque, A., Islam, M.T. & Almutairi, A.F. Fano resonated, ultrathin,

flexible and ultrawideband absorption featured nano-metaatom structure with dispersion gap optimized for optical range applications. _Sci Rep_ 15, 275 (2025).

https://doi.org/10.1038/s41598-024-82254-5 Download citation * Received: 16 September 2024 * Accepted: 03 December 2024 * Published: 02 January 2025 * DOI:

https://doi.org/10.1038/s41598-024-82254-5 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not

currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative KEYWORDS * Dispersion * Ultrathin * Metamaterial * Nano material *

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