A direct laser-synthesized magnetic metamaterial for low-frequency wideband passive microwave absorption

Microwave absorption in radar stealth technology is faced with challenges in terms of its effectiveness in low-frequency regions. Herein, we report a new laser-based method for producing an ultrawideband metamaterial-based microwave absorber with a highly uniform sheet resistance and negative magnetic permeability at resonant frequencies, which results in a wide bandwidth in the L- to S-band. Control of the electrical sheet resistance uniformity has been achieved with less than 5% deviation at 400 Ω sq−1 and 6% deviation at 120 Ω sq−1, resulting in a microwave absorption coefficient between 97.2% and 97.7% within a 1.56–18.3 GHz bandwidth for incident angles of 0°–40°, and there is no need for providing energy or an electrical power source during the operation. Porous N- and S-doped turbostratic graphene 2D patterns with embedded magnetic nanoparticles were produced simultaneously on a polyethylene terephthalate substrate via laser direct writing. The proposed low-frequency, wideband, wide-incident-angle, and high-electromagnetic-absorption microwave absorber can potentially be used in aviation, electromagnetic interference (EMI) suppression, and 5G applications.

Microwave absorption in radar stealth technology is faced with challenges in terms of its effectiveness in low-frequency regions. Herein, we report a new laser-based method for producing an ultrawideband metamaterial-based microwave absorber with a highly uniform sheet resistance and negative magnetic permeability at resonant frequencies, which results in a wide bandwidth in the L-to S-band. Control of the electrical sheet resistance uniformity has been achieved with less than 5% deviation at 400 Ω sq −1 and 6% deviation at 120 Ω sq −1 , resulting in a microwave absorption coefficient between 97.2% and 97.7% within a 1. 56-18.3 GHz bandwidth for incident angles of 0 • -40 • , and there is no need for providing energy or an electrical power source during the operation. Porous N-and S-doped turbostratic graphene 2D patterns with embedded magnetic nanoparticles were produced simultaneously on a polyethylene terephthalate substrate via laser direct writing. The proposed low-frequency, 10 Those authors have equal contributions to this work. * Authors to whom any correspondence should be addressed.
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Introduction
Microwave absorbers are typically required for aircraft radar cross-section reduction. It is desirable to have a wide absorption bandwidth and a low-profile structure. These two requirements are often in conflict, particularly for frequencies lower than the X-band. Since the first experimental demonstration of metamaterial absorbers (MMAs) by Landy et al in 2008 [1], metamaterial-based absorbers have received increasing attention over the past decade owing to their low-profile advantage. In the early 2000s, the majority of traditional MMA designs relied on chemical etching [2] or computer numerical control machining [3] to meet the requirements for conformal production; however, the absorber performance was unsatisfactory. In the late 2000s, new MMA fabrication methods were introduced, such as ink-jet printing [4] and additive manufacturing [2]. Among the MMA printing techniques, conductive carbonbased printing has provided the best overall performance for MMAs [5]. Therefore, the majority of previous investigations over the past decade have been focused on inkjet printing technology for depositing carbon-based conductive inks owing to its high resolution at the microscale level and the high uniformity of the deposited layer thickness [6]. The sheet resistance tolerance of ink-jet printed carbon-based thin films (graphene <5% [7]; reduced graphene oxide (rGO) and carbon black <3% [8]; carbon nanotube <5% [9]) can be controlled well. However, to obtain the desired sheet resistance (especially a sheet resistance of less than 1000 ohm sq −1 ), an inkjet printer must print hundreds of layers [10], which hinders its practical application. Spray printing and screenprinting technologies have been investigated as alternative methods owing to their excellent manufacturing efficiencies [11]. However, these macroscale printing methods have the disadvantages of complicated procedures, poor uniformity, and poor resolution. Ink preparation for the control of sheet resistance, magnetic permeability, and adhesion is a necessary further manufacturing step following material synthesis [12,13]. The film thickness varied significantly between the pattern centre and edge, resulting in large variations in the sheet resistance. The sheet resistance variation of spray-printed and screen-printed graphene laminates is typically an order higher than that of inkjet printing (screen printing: 16%-33% [14] and 45% [12]; spray printing: 36% [15] and 40% [16]). To satisfy the more precise sheet-resistance variation requirements for modern MMAs, it is desirable to find a new fabrication method that combines more accurate sheet-resistance control with high productivity. Nevertheless, owing to the nature of electromagnetic waves and the electric boundary conditions [17], effective absorption of lower-frequency electromagnetic waves requires a thicker absorber. The trade-off between the absorber thickness and low operating frequency is a challenging issue to address when designing broadband absorbers. It is necessary to combine the three aspects of the absorbing material, absorber structure design, and fabrication method [18] for producing a practical metamaterial microwave absorber.
Laser fabrication of MMAs including laser surface treatment [19,20], laser etching [21,22], laser 'thick film' printing [22], and laser graphitisation [23] was recently attempted. Laser surface treatments and etching technologies have been used to successfully fabricate conformal MMA structures. However, the microwave performance was not ideal owing to the limitations of the MMA material. The 'thick film' mould method involves the use of a laser to create a reversed pattern on a metal film, and conductive inks are then added for printing. These laser-based MMA fabrication methods focus on achieving a higher resolution of the MMA pattern rather than on improving the sheet resistance uniformity, which is key for broad-band MMA.
In our previous study, the laser direct synthesis and writing of functionalised graphene were investigated. Controlling the graphitisation of an organic precursor with an ultraviolet (UV) laser opens up a new possibility for controlling the electrical properties, which could significantly impact the MMA performance [24]. Compared with the aforementioned techniques for MMA fabrication, laser direct writing (LDW) has the potential to print nanocomposite materials with higher sheet resistance uniformity [25][26][27][28]. The capability of in situ nanomaterial generation during LDW is also advantageous [29,30].
In this study, a specifically designed conductive pattern with well-controlled electrical characteristics was manufactured on a flexible polyethylene terephthalate (PET) substrate using UV laser processing. A laser-induced doped graphene (LIDG) pattern with induced magnetic nano-particles forms a metasurface structure (with negative magnetic permeability). The sheet resistance of LIDG could be precisely controlled by varying the degree of crystallisation. Magnetic ferric oxide nanoparticles were simultaneously generated and embedded in graphene to increase the absorption bandwidth of the MMAs. This structure has demonstrated an ultra-wideband with very-low-frequency microwave absorption. This technique achieved patterning, control of sheet resistance and its uniformity, and synthesis of magnetic nanoparticles in a single step, thus demonstrating a significant advantage in terms of manufacturing efficiency.

Formulation of an organic donor ink
The precursor organic ink was composed of polybenzimidazole (PBI) and dimethyl sulfoxide (DMSO) at a 10 wt% PBI concentration. It was prepared by refluxing for 1 h at 140 • C. To generate embedded ferro ferric oxide into the LIDG, iron (II) acetate was introduced into the organic ink at 1 wt% concentration and uniformly dissolved in the ink with an additional half hour of reflux at 140 • C, which is lower than the thermal decomposition temperature of iron (II) acetate of 150 • C [31].

Coating preparation
The ink was coated on PET using a doctor blade (supplied by TOB Co. Ltd) at a running speed of 10 mm s −1 and a 100 µm space (wet coating thickness). This laser technique could be applied to a wide range of substrates. Polymer was selected because PET does not influence the measurement results of the microwave absorption because its permittivity is equal to that of air. The solution was then dried for 30 min in a vacuum oven at 80 • C. The coating thickness was 12-14 µm after drying.

Laser synthesis and direct writing procedure
The LDW process was performed under ambient conditions, using an Edgewave picosecond laser with a pulse width of 10 ps and a laser fluence of 5.74-10.12 mJ cm −2 , operating at 355 nm laser wavelength, at a pulse repetition rate of 4047.4 kHz, and a scanning speed of 100 mm s −1 using a galvo x-y scanner. The diameter of the focused beam spot on the target surface was 40 µm, while the hatch distance for the laser scanning was 20 µm.

Material characterisation
Raman spectroscopy was conducted on the laser-processed samples using a single excitation wavelength of 514 nm. Fieldemission gun scanning electron microscopy (Zeiss Merlin scanning electron microscope with Gemin II) and scanning transmission electron microscopy (Talos F200X) were performed at 200 keV. X-ray photon-spectrometry (XPS) and xray diffraction were used to investigate the atomic structure and surface morphology of the resulting materials. XPS analysis was performed using Kratos Axis Ultra facility equipped with a monochromatic Al-K x-ray source. High-resolution core-level spectra were acquired using a hemispherical energy analyser positioned along the surface norm, with a pass energy of 20 eV. The spectra were calibrated by assigning a binding energy of 689 eV to the CF 2 component at the 1 s core level. XPS core-level profiles were fitted with CasaXPS software using a Gaussian-Lorentzian line shape.
A contact probe station (Jandel, RM3000) and semiconductor characterisation system (Keithley, 4200C) were used to measure the sheet resistance. The carrier mobility was measured using a precision DC Van der Pauw Hall measurement. A static magnetic field was generated using a GMW Magnet 3473, and the electric signal was collected using a Keithley precision source meter 2400 series. The system was controlled using a custom LabVIEW program. During measurement, the DC magnet was set to 0.4 T and the measurement current was 10 µA.

Meta-structure design and microwave absorption measurement procedure
The proposed ultra-wideband microwave absorber was designed and simulated using CST Microwave Studio. The absorbers were mechanically assembled in the following order: silica gel, circular metamaterial layer, silica gel, square metamaterial layer, and copper ground. Two horn antennas (Aaronia AG, PowerLOG 70180) from 700 MHz to 18 GHz were connected to a calibrated VNA (FieldFox Microwave Analyser N9918A, Keysight) as the transmitter and receiver to measure the microwave absorption characteristics. The entire measurement process was carried out in an anechoic chamber.

Meta-surface simulation and design
Square-and circular-shaped metamaterial elements were selected owing to their straightforward geometry and sufficient impedance matching to facilitate the design of the absorber. The metamaterial elements with a solid layout (square and circular) were capacitive. Changes in the shape result in different equivalent resistances and capacitances. The equivalent inductance or capacitance change is very small for the different shapes; however, this does affect matching conditions with free space. The simulated electromagnetic performance of the design was obtained using CST Microwave Studio [32]. The simulated surface power loss density of the three absorption peaks at 2.9 GHz, 7.5 GHz, and 17.3 GHz are presented in figure 1. For a lower absorption frequency (approximately 2.9 GHz), the surface power loss was mainly localised between the square layers (120 Ω sq −1 ). As the frequency increased to 7.5 GHz, the localised surface power loss moved towards the top circular layer (400 Ω sq −1 ). In the case of the higher frequency bands, absorption occurs owing to the combined effect of the surface currents on both layers.
The structure of the proposed MMA was designed to achieve ultrawideband microwave absorption, as shown in figure 2(a), and consists of a 12 × 12 elementary unit cell array. Its dimensions were 240 mm × 240 mm × 15.5 mm. The squares and circles were subjected to laser irradiation and became impedance surfaces. The unirradiated material and ink do not affect the microwave absorption; thus, they do not need to be removed. The basic unit comprised two impedance surfaces, three dielectric substrate layers, and a ground plane. The top wide-angle impedance matching (WAIM) [33] and middle layers (Sub.1 in figure 2(a)) were both fabricated from silicone (Polymax, SILONA translucent Silicone Sheet GP) with a 4 mm thickness, a 2.9 dielectric constant, and a loss tangent of 0.1. The bottom layer (Sub.2 in figure 2(a)) consisted of 6 mm  polyurethane foam sheets with a 1.05 dielectric constant and a loss tangent of 0.02. Circular and square LIDG patterns of different sheet resistances (400 Ω sq −1 and 120 Ω sq −1 , respectively) were printed on PET. A pure copper sheet of the same size was placed at the back of the absorber as the ground plane. The metamaterial unit cells were set by applying periodic conditions across the unit cells of the structure during the simulation. The multilayer structures were periodically arranged on the substrates. The reflection coefficient depends on the local characteristics of the multilayer structures and the interactions between neighbouring cells. The simulated absorption bandwidth of the proposed absorber was approximately 162%. Figure 3(a) illustrates the LDW procedure used for the PET. The silver-black laser-irradiated tracks were the result of laser-induced graphitisation. The morphology of the laser-graphitised PBI exhibited different levels of pores, as shown in figure 3(b), while the laser-graphitised in the presence of Fe 3 O 4 nanoparticles showed significantly fewer nanopores ( figure 3(c)). The thickness of the graphitised layers was approximately 10 µm, which less than the original thickness of 12-14 µm owing to the self-release of CO x and NO x gases, which prevented the oxidation of the graphitised layers dur- ing the laser process. It is worth noting that a layer of PBI remained beneath the graphitised layer, which was adhered to the PET substrate. Therefore, it is important to ensure that the graphitisation depth is less than the total thickness of the coating.

One-step laser synthesis LIDG embedded with Fe 3 O 4
Compared with the C-S bond energy (2.8 eV) in the DMSO and the C-N bond energy (3.14 eV) in PBI, the high 3.49 eV photon energy from the 355 nm wavelength laser resulted in both photochemical and photothermal reactions when interacting with the coated material. The laser processing decomposed the PBI and DMSO at low laser powers into free radical benzene rings as a carbon-source material; free radical dopant elements such as thiophene, pyrrolic, and pyridine; and protective gases, including NO, NO 2 , CO, CO 2 and SO 2 . From the XPS spectra presented in figure 4, 91.52% sp 2 (284.5 eV) originated from the crystallite LIDG. The N and S doping in the LIDG contributes to p electrons of the π system, which can promote the electrical conductivity of LIDG. The S(2p 3/2 ,2p 1/2 ) covalent bond of thiophene at 163.5 eV and 164.7 eV is observed in the graphene structure owing to the spin-orbit couplings. This originates from the photochemical decomposition of the DMSO during graphene synthesis [24]. The N covalent bonds of pyrrolic and pyridinic at 400 eV and 398 eV, respectively, in the graphene structure were different from those in the absence of iron acetate. The concentration ratio of pyrrolic N and pyridinic N was 47:53, which is slightly lower than the concentrate ratio (39.1:29.7) without iron acetate. A greater amount of pyridinic N resulted in fewer edge defects and more abundant mesopores, the majority of which were occupied by nano-Fe 3 O 4 (figure 3(c)). Therefore, the addition of iron II acetate had a thermal effect on the pyridinic N generation and inhibited oxidisation, in contrast to the case of the LIDG fabricated using an infrared laser, which would be dominated by the thermal effect [24].
Owing to the multiple reactions, iron (II) acetate was decomposed by laser irradiation in air. The element distribution mapping of the nanoparticles, as shown in figures 5(a 1 ),(a 2 ) and (a 3 ) demonstrates the generation of magnetic particles of approximately 10 nm in size. The decomposition temperature of iron acetate in air exceeds 290 • C. With an increase in the temperature, magnetite Fe 3 O 4 was initially generated and was subsequently oxidised into haematite with a longer treatment or higher temperature. In figure 5(b 1 ), the Fe 2p peak of Fe 3 O 4 was deconvoluted into Fe 2+ and Fe 3+ peaks. The peak positions of Fe 2p 3/2 and Fe 2p 1/2 were 710 eV and 723.8 eV, respectively. The binding energy of the O 1s peak for Fe 3 O 4 is commonly at 530 eV, as illustrated in figure 5(b 2 ), and that for Fe 2 O 3 was at approximately 527 eV [34]. Moreover, the high reaction kinetics, due to the longer reaction time and higher temperature, caused an increase in the size of the nanoparticles [35]. The fast laser processing speed with  controlled thermal effects realized by selecting an appropriate laser power and repetition rate can generate nanoparticles of a specific size from a liquid precursor and effectively minimise overtreatment to avoid thermal damage to both the coating and substrate.

Sheet resistance control and Raman spectra
Precise control of laser graphitisation is important for tuning the electrical properties of LIDG. The laser fluence on the PBI pattern was gradually increased from 5.74 mJ cm −2 to 10.12 mJ cm −2 to study the relationship between the laserinduced graphitisation and the electrical properties of the material after the laser processing. As shown in figure 6(b), the increasing ratio of the Raman spectra D peak (1350 cm −1 ) over the G peak from 0.92 to 1.34 during the crystallisation stage provides evidence that the degree of carbon crystallisation gradually increases [36]. The sp 2 crystal length (Lα) can be expressed as [37] I (D) where C ′ is a constant related to the wavelength (λ) of the Raman spectralaser. The decreased ratio of the Raman spectrum D peak (1350 cm −1 ) over the G peak from 1.34 to 1.29 was in the defect reducing stage. At this stage, Lα is expressed as In figure 6(a) the crystal length of LIDG with/without nano-Fe 3 O 4 was respectively enhanced from 12.4 to 15 nm and from 11.6 nm to 14.6 nm, owing to the sp 2 C-C bond restoration induced by the gradually increased thermal heating [38]. The thermal energy from iron oxidation resulted in larger crystals than those of pure LIDG. The increase in the laser fluence from 6.2 to 10.12 mJ cm −2 resulted in an increase in the crystal length, which resulted in the increase of the sheet resistance from 75 to 1310 Ω sq −1 . Enhanced graphene crystallisation from the growth of the crystal length can effectively promote electron mobility, as shown in figure 6(e). The volume of the sp 2 bond structure-controlled electron carrier concentration and electron mobility are inversely correlated with the sheet resistance with a constant sample thickness of approximately 3 µm [39,40]. Thus, the sheet resistances of LIDG with and without nano-Fe 3 O 4 were reciprocally related to the length of the crystal. Under the same laser conditions, the sheet resistance of LIDG with nano-Fe 3 O 4 ranged from 57 to 480 Ω sq −1 . The initial 0.8 nm difference between 11.6 nm and 12.4 nm in figure 6(a), due to thermal heating of 3 wt% iron(II) acetate, can effectively reduce the sheet resistance from 1310 Ω sq −1 to 480 Ω sq −1 with a standard deviation from 20% to less than 5%, as shown in figure 6(d).
With an increase in the laser fluence, the difference in the crystal length and sheet resistance between the LIDG with and without nano-Fe 3 O 4 gradually vanished because complete crystallisation occurred, and the excess energy could only damage the sp 2 structure. The controlled deviation ratio of the sheet resistance was between 4% and 6%, when the laser fluence was between 5.74 and 10.12 mJ cm −2 , as shown in figure 6(c). It is worth noting that the uniformity of the sheet resistance was determined by the thickness and uniformity of the graphitised layers, rather than the uniformity of the original coating.
The increasing ratios of the Raman spectra 2D peak (2700 cm −1 ) over the G peak, in the range of 0.36-0.53, provide evidence for the formation of graphene (with less than five layers) and the reduction of amorphous carbon. The increased intensity and symmetric broadening of the 2D peak, as shown in figure 6(b), was owing to the formation of a turbostratic graphene structure, which was due to the in-situ doping and the flow of the protection gas [41].
The 2D Raman spectrum mapping of LIDG embedded with nano-Fe 3 O 4 , as shown in figures 7(a 1 ) and (a 2 ), demonstrates the uniformity of the resulting graphene and is indicated by the colour intensity as the ratios of I (2D

)/I(G) and I(D)/I(G).
The mean values of the I(2D)/I(G) ratio were approximately 0.4. The areas wherein the laser was applied more than once exhibited a relatively higher value of I(2D)/I(G), indicating that laser annealing improved the quality of graphene.
The overlapping of the laser-scanned tracks had no impact on the uniformity of the crystallisation, as demonstrated by the mean values of I(D)/I(G). The sheet resistance mappings of LIDG embedded with Fe 3 O 4 and irradiated at a laser fluence of 6.65 mJ cm −2 and 9.82 mJ cm −2 are presented in figures 7(b 1 ) and (b 2 ), respectively. Both show a high degree of uniformity with less than a 5% and 6% deviation for the designed LIDG with 400 Ω sq −1 and 120 Ω sq −1 , as shown in figures 7(b 1 ) and (b 2 ), respectively.  Figures 9(a) and (c) present a comparison between the simulated and measured absorptions at normal incidence for the transverse-electric (TE) and transverse-magnetic (TM) polarisations. As shown in figure 9(a), the measured absolute bandwidth of the absorber ranged from 1.85 GHz to 18.2 GHz, and the measured fractional absorption bandwidth was approximately 163% in the TE mode under normal incidence. Similarly, for normal incidence under the TM mode, the MMA exhibits ultra-wide fractional absorption bandwidth of approximately 169% from 1.56 GHz to 18.3 GHz. In addition, for both the TE and TM modes, the proposed MMA had an impressive average absorption coefficient within its operating bandwidths of 97.2% and 97.7%, respectively. Furthermore, the absorption bandwidth and absorption coefficient of the proposed MMA exhibited minimal variations across both the TE and TM modes owing to its symmetrical shape. The experimental observations agree with the numerical results; this can be attributed to the utilisation of LIDG technology, which ensures accurate control of the sheet resistance within a 5% accuracy.  To further analyse the performance of the absorber, the absorption of oblique incidences at 20 • , 40 • and 60 • for the TE and TM polarisations was measured and compared with the corresponding simulation results in figures 9(b) and (d).

Effects of pure LIDG on absorption.
When the incident angle is 20 • , for both the TE and TM modes, the absorber can maintain a nearly identical fractional absorption bandwidth and the same absorption coefficient as that under normal incidence. When the incident angle was increased to 40 • , the absorber still had a wide fractional bandwidth of approximately 110% and 118% for the TE and TM modes, respectively, and provided over 93% absorption under both radiations. In the TE mode, when the incident angle was increased to 60 • , the absorber lost its broadband characteristics, but it could still provide over 85% absorption within the majority of the frequency bands. Similarly, at an incident angle of 60 • in the TM mode, the fractional bandwidth of the absorber decreased to 75.3%, with an average absorption of approximately 95%. The measured results demonstrated a excellent absorption performance at oblique incidence angles.

Effects of embedded Fe 3 O 4 nanoparticles on absorption.
The electromagnetic resonance of a MMA is the key to achieving good absorption. Electromagnetic resonance causes disturbances that result in the attenuation of electromagnetic waves [42]. Therefore, impedance matching between the free space and the metamaterial structure is crucial. A transmission-line equivalent circuit model of the proposed absorber is presented in figure 10(a). The WAIM layer and dielectric substrate are modelled as transmission lines. According to the transmission line theory and the calculation method used in [43,44] the input impedance can be represented as where 't 1 , t 2 , and t 3 ' are the thicknesses of the dielectric substrate and the WAIM layer. ε rs and ε rf are the relative permittivities of the silicone substrates, respectively. The free space impedance is represented by Z in at 377 Ω. To match the free space impedance, the lumped elements are derived and calculated as R 1 = 620 Ω, R 2 = 145 Ω, C 1 = 0.075 pF, C 2 = 0.4 pF, L 1 = 1.15 nH, and L 2 = 0.15 nH. The relative permeability (µ r ) was tuned to enhance the impedance matching between the MMA and free space. A small amount of Fe 3 O 4 was embedded into the LIDG using the LDW technique. As the majority of magnetic materials have a high relative permeability, the amount of Fe 3 O 4 mixed in the conductive layer must be controlled precisely within an acceptable minimum range. To measure the magnetic permeability of Fe 3 O 4 embedded in the LIDG thin film, a ring resonator (RR) with a coplanar waveguide (CPW) feed was fabricated and an Fe 3 O 4 embedded LIDG layer (400 Ω sq −1 ) was affixed at the centre of the resonator [12]. The complete model of the resonator with the LIDG was reproduced in CST. Figure 10(b) presents the simulated and measured Sparameters of the RR, where µ r was continuously adjusted until similar trends were observed. The relative permeability (µ r ) of the LIDG embedded with Fe 3 O 4 was approximately 3 with a tangent delta magnetic field of 0.1. Figure 11 presents the measured absorptivity performance of the LIDG MMA with and without the embedded nanomagnetic Fe 3 O 4 for various incident angles from 0 • to 60 • under TE and TM polarisations. As shown in figure 11(  the increase in the bandwidth of the Fe 3 O 4 embedded MMA is mainly owing to the frequency shift to the lower frequency bands, which means that the overall structure had a broader impedance match to free space. This is a significant improvement, as one of the most challenging issues in broadband absorber designs is covering as many lower-frequency bands as possible without compromising the higher-frequency performance and increasing the absorber profile. This improvement is likely to be due to the extra loss provided by Fe 3 O 4 . In the complex permeability, the imaginary part (µ ′ ′ ) represents the loss capability of the magnetic energy. Without Fe 3 O 4 , the LIDG is not a ferromagnetic material, and hence, µ r = 1. When Fe 3 O 4 was embedded (even a very small amount), the magnetic loss of the MMA becomes stronger owing to resonance and ohmic loss [45]. It should be noted that the overall concentration of the embedded Fe 3 O 4 is crucial because it has an extremely large permeability. An excess percentage of ferro ferric oxide embedding causes a mismatch between the absorber and free space, thus resulting in poor absorption. Figure 12 presents a comparison of the performances of the two absorbers (with and without embedded Fe 3 O 4 ) in the TE and TM modes. Both the absorbers maintained excellent average absorptivity. The embedded Fe 3 O 4 MMA exhibited a higher average absorption under oblique incidences of TM polarisation. As for the fractional absorption bandwidth, the Fe 3 O 4 MMA always has a wider bandwidth.

Comparison of microwave absorption performances.
For the purpose of comparison with the previous work, the two main factors of bandwidth and absorber thickness were considered. Pan et al reported the application of rGO laminates for ultra-wideband microwave absorption and demonstrated that a coating with a thickness of over 30 mm provided efficient absorption in the range of 2-10.8 GHz, which hindered its conformal and miniature applications [46]. Assal et al demonstrated a multiband hybrid layer metamaterial-based array for a microwave absorber, with an absorber thickness of approximately 16.2 mm and a high absorption performance of greater than 95% from 2.6 GHz to 18 GHz [47]. However, its low cutoff frequency of 2.6 GHz did not fully cover the S-band, which is crucial for wireless communication and radar applications. Therefore, for real microwave absorption applications, it is important to reduce the material thickness while maintaining a cutoff frequency that is as low as possible. Our work has presented a significantly improved bandwidth of >20%, especially in the low-frequency region.  The absorber, designed and fabricated using LDW, has the widest bandwidth reported thus far, with the lowest thickness in the low-frequency band. Figure 13 presents a comparison of the fractional bandwidth and relative thickness (relative thickness = thickness/λ L , where λ L is the wavelength corresponding to the minimum operating frequency) of conventional, metamaterial [13,[47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65], and proposed absorbers, thus demonstrating the improvement in the microwave absorption achieved by the metamaterial designed and achieved through LDW.

Conclusion
A one-step metamaterial (with negative relative permittivity) synthesis using LDW was demonstrated to produce magnetic Fe 3 O 4 -nanoparticles-embedded graphene on a flexible PET substrate. The laser-fabricated metamaterial patterns consist of N-and S-doped porous turbostratic graphene with different degrees of crystallisation, which facilitates the precise control of the electrical sheet resistance from 57 to 480 Ω sq −1 within a 5% accuracy. The LIDG-based MMA has demonstrated an average absorption coefficient in the range of 97.2%-97.7% for a wide bandwidth of 1.56 GHz-18.3 GHz for microwave incident angles of 0 • -40 • in both the TE and TM modes. With the addition of magnetic Fe 3 O 4 nanoparticles, the bandwidth of the MMA has demonstrated an increase of approximately 4%-8% owing to the extra magnetic loss. The material achieved the highest relative bandwidth and lowest thickness in the L-to-S band reported till date. This method is simple, allows precise control of the sheet resistance over large areas, and introduces a new avenue for the large-scale manufacturing of metamaterials for microwave absorption applications.