2.1.

Ti3C2 MXene Synthesis

${\mathrm{Ti}}_3{\mathrm{C}}_2$ MXene was first synthesized using the mixed acid method previously described in the literature.¹⁴ Briefly, 2 mL HF (50%, Acros Chemical), 12 mL HCl (36% to 38%, Fisher Chemical), and 6 mL water were added to a polypropylene bottle and magnetically stirred. Next, 1 g of ${\mathrm{Ti}}_3{\mathrm{AlC}}_2$ powder (Millipore Sigma, 910775) was slowly added to the mixture, stirring at 300 RPM and 35°C. The mixture was stirred for 24 h. The solution was then placed in a centrifuge at 3500 RPM for 5 min. The supernatant was subsequently decanted into a suitable waste container. Water was then added to the remaining sediment, and the contents were shaken well by hand. The centrifugation and washing steps were repeated until the supernatant exhibited a neutral pH. The remaining sediment, a mixture of multilayered and monolayered MXene, was resuspended in water and placed in a centrifuge for 1 h at 3500 RPM. The resulting dark supernatant, consisting of mono and few-layered MXene, was collected and placed in a separate collection bottle. Water was added to the sediment remaining in the centrifuge tube, the contents were shaken well by hand, and the mixture was again placed in a centrifuge for 15 min at 3500 RPM. The washing and centrifugation steps of the sediment were repeated until the supernatant became clear. The sediment left behind in the centrifuge tube consisted of multilayered MXene and was discarded. Finally, the monolayered and few-layered MXene was stored in the collection bottle and was further concentrated via centrifugation at 10,000 RPM for 10 min. In this final step, the clear supernatant was removed, and the MXene sediment was resuspended in a suitable volume of water to achieve the desired concentration. The final MXene suspension was then mixed with a proprietary binder to form a sprayable MXene formulation (Ballydel Technologies, product #MX001).

2.2.

Electromagnetic Characterization

The coding-metasurface technique necessitates a comprehensive understanding of the material properties of the MXene ink to develop an accurate model for wideband optimization. Although measuring the properties of freestanding MXene layers can be challenging, their characterization becomes feasible when the properties of the substrate to which the MXene adheres are known. To this end, we employed a free-space focused beam method to characterize the complex permittivity of the MXene coatings applied to a polycarbonate substrate. The 3D printed substrate was 1.27 mm thick and had a measured permittivity of 2.65. It is observed that the measured dielectric permittivity of the substrate deviates from conventional values,^15,16 ranging from 2.75 to 2.85, due to the presence of air pockets caused by the 3D printing process, resulting in an effective permittivity. The uniform layer of MXene ink was deposited on the polycarbonate substrate with a measured average thickness of $3.1\mu \mathrm{m}$. The sample was placed in the center of a free-space focused beam system, as depicted in Fig. 2, and the transmission and reflection coefficients were measured from 18 to 40 GHz. A standard transfer matrix method¹⁷ was used to determine the permittivity through the two-layered dielectric sample by using the known thicknesses, the permittivity of the substrate, and the transmission through the slab. The unknown frequency-dependent complex permittivity of the MXene layer was then determined by varying its complex permittivity computationally until the simulated transmission and reflection coefficients matched the measured values.

Fig. 2

Two-layered dielectric slab with known $d1$ and $d2$ thicknesses, transmission and reflection coefficients, and substrate permittivity used to calculate MXene complex permittivity.

The sheet resistance ($R_s$) of the layer composed of MXene and polyurethane can be adjusted to achieve optimal performance of the metamaterial absorber. $R_s$ is defined by the expression

We conducted a sweep of full-wave simulations where the sheet resistance of the absorbing layer was varied over a wide range. It was found that a sheet-resistance in the range of $100\mathrm{\Omega }/\mathrm{sq.}$ resulted in metasurface designs with a high level of absorption over the frequency band of interest. Additionally, it was found experimentally using our selected deposition method that a print thickness of $\sim 3\mu \mathrm{m}$ resulted in consistent and uniform deposition of ink on the substrate. Based on these results, the complex permittivity of the MXene/polyurethane composite was tuned to achieve the desired sheet-resistance by varying the mass percent of polyurethane in the ink formulation for our desired print thickness of (Fig. 3).

Fig. 3

Measured complex permittivity of MXene ink fit to a Debye dispersion model from 18 to 40 GHz.

The complex permittivity properties of MXene ink were measured and are depicted in Fig. 3. The data was fit to a standard Debye dispersion model,¹⁸ represented as follows:

The following values were obtained from the Eq. (4) and later incorporated into the design of the metasurface: ${\epsilon }_s=7,503.6$, ${\epsilon }_{\infty }=924.9$, and $\tau =12.71$ pico-seconds.

3.1.

Optimization Algorithm

An iterative optimization algorithm was developed to synthesize the unit cell pattern of the MXene metasurface absorber. This design approach relies on the previously measured complex permittivity properties of the MXene ink in addition to the thickness and substrate properties. While a wide variety of metasurface patterns could be used, we employed the 1-bit coding-metasurface technique. In this method, each unit cell is divided into a 2D array of smaller square “pixels” that either contain MXene or do not. This approach is commonly referred to as a one-bit coding metasurface due to each pixel either having (i.e., “1”) or not having (i.e., “0”) conductive material. This binary coding system provides a convenient structure for iterative optimization approaches, such as genetic algorithms or particle swarm optimization (PSO). A similar design approach has been used in other studies, such as Ramachandran et al.¹⁹ to create multiple narrowband absorption peaks, Mourad et al.²⁰ to reduce the radar cross section of a perfect electric conductor plate, or Zheng et al.⁹ to design a reconfigurable millimeter wave (MMW) antenna.

It should be noted that a direct search algorithm for the optimal unit cell pattern would require an impractical number of computational resources. For example, the unit cell used in this study, composed of a simple $10\times 10$ array of “pixels,” contains $2^{100}$ possible patterns. Thus, a more intelligent approach that leverages the various symmetries is necessary. To this end, we further sectioned the unit cell into eight quadrants, as shown in Fig. 1. We imposed mirror symmetries along the horizontal, vertical, and diagonal axes denoted in the figure. This reduced the number of unknowns by approximately a factor of eight and reduced the number of possible patterns by a very substantial amount ($\sim 2^{(N/8)}$). We then employed the iterative optimization algorithm shown in Fig. 4. Here, the user first defines the incident field conditions (i.e., frequency band, incident angles, and polarization states), substrate and MXene properties (i.e., layer thicknesses and permittivities), and unit cell dimensions (i.e., period and the number of pixels in both the x and y directions). For most absorber designs, the substrate thickness is chosen to be one-quarter of the material wavelength at the center of the frequency band of interest. The unit cell period is generally preferred to be small enough such that only the zeroth diffractive order propagates at the highest frequency (i.e., shortest wavelength) but not too small such that the smallest features (i.e., pixels) become too difficult to fabricate.

Fig. 4

Flowchart for the metasurface optimization process. After user constraints and objective function is defined, the PSO iterative process begins until the global minimum is found.

The iterative algorithm begins with a random set of metasurface patterns, analyzed over the desired incident field conditions using a full-wave EM solver. While several solvers could be used for this purpose, we found that the rigorous coupled wave method (RCW) produced accurate results with the lowest computational expense. The RCW method is well-known in the photonics community for providing efficient full-wave solutions of periodic layered surfaces. Our specific custom implementation of RCW followed the approach described in a study by Lalanne and Morris²¹ and returned reflectance results, $R(f,\theta )$, from each test pattern over the range of frequencies and incident angles of interest. A single metric, or objective function, was then calculated as a means of quantifying what is considered an improved result. For our wideband absorber application, we used the objective function given in Eq. (5), which attempts to minimize the average reflectance over the range of illumination conditions

The PSO method is then used to intelligently vary the coding metasurface pattern until either the algorithm has converged or the user stops the algorithm after an acceptable result is found.

3.2.

Design Examples

To assess the effectiveness of MXene as an absorbing metasurface material, a series of optimization simulations was performed within the K and Ka frequency bands (18 GHz to 40 GHz), utilizing the previously described algorithm. Three distinct design simulations were conducted, each imposing unique period and frequency band constraints while maintaining key parameters, such as MXene sheet thickness ($3.1\mu \mathrm{m}$), MXene permittivity (as detailed earlier), substrate thickness (1.27 mm), and substrate dielectric constant (2.65). These simulations were devised to identify MXene-based geometric patterns capable of minimizing the average reflectance at normal incidence. Demonstrating MXene’s potential to absorb EM energy across multiple frequency bands effectively, Fig. 5 presents an overview of the designs, and average reflectance results catering to wide and narrowband applications.

Fig. 5

Optimized design examples using MXene as absorbing metasurface material.

The first simulation targeted narrowband performance at 2 GHz bandwidth, utilizing a 4.5 mm period to minimize the reflectance from 21 to 23 GHz. The optimization process yielded an average reflectance of 0.7% in the specified frequency window and is plotted in Fig. 6 from 18 to 40 GHz, highlighting its designed bandwidth as a solid line and illustrating narrowband absorptance. In contrast, the second simulation focused on wideband performance within the K-band (18 to 26 GHz) utilizing a period of 5 mm, resulting in an average reflectance of 2.3% across this band. Finally, the third simulation again aimed to optimize wideband performance, targeting the Ka frequency band (26 to 40 GHz) instead. This design used a period of 6 mm and yielded an average reflectance of 2.4% across the entire frequency band. The third metasurface example, showcasing wideband performance in the Ka-band, was selected for fabrication to validate the model’s accuracy due to its superior performance, larger bandwidth, and utilization of the higher frequency, MMW band.

Fig. 6

Reflectance of optimized metasurface design examples using different constraints, including varying periods and frequency bands. The metasurfaces were optimized for frequency bands indicated in the legend.

4.1.

Hybrid Processing

The design method and simulation results for the optimized metamaterial absorber are realized through fabrication using hybrid, additive, and subtractive techniques to provide greater options in the design concerning substrate availability and reduction of material processing cost and time. The substrate was created using a multi-tool platform that allowed the 3D printing of the polycarbonate feedstock using fused filament fabrication and a micro-milling tool to smooth the top surface to the desired thickness. The substrate was then provided to Ballydel, Inc., who deposited the MXene ink using a standard model airbrush kit to coat the surface in the same way as was done in the characterization steps, attempting to control the thickness of the ink as much as possible. The absorber was placed in a laser etching/engraving system with a 420 mm lens attachment, and the unit cell design was imported into the software to create the periodic array, applying the previously tested and determined etching parameters (power, frequency, and speed). The laser etching process took approximately 15 min for the 4″ × 4″ ($101.6\mathrm{mm}\times 101.6\mathrm{mm}$) surface to fully etch the periodic array, resulting in an entire fabrication time of around 4 h. A copper ground plane was then attached to the underside of the absorber with commercial adhesive spray.

4.2.

Metrology

Measurements of the dimensions with respect to each fabrication process were performed to identify the accuracy of the actual feature sizes compared to the design, informing the performance results gained from the EM measurements in the next section. With respect to the substrate thickness, eight measurements across the surface were taken [Fig. 7(a)] using a coating thickness gauge accurate to $1.0\mu \mathrm{m}$. It was found that the substrate thickness varied from 1.21 to 1.31 mm with a mean value of 1.24 mm. This represents only a 2% average deviation from the desired substrate thickness of 1.27 mm.

Fig. 7

(a) Final fabricated absorber consisting of periodic MXene elements. (b) 20× zoom image of the interface between etched MXene ink and substrate. (c) Color map images were taken using a laser confocal microscope, showing the etched interface indicating deformation and peaks.

The thickness of the MXene ink is a critical parameter that determines the optimal absorbing performance of the features, and Fig. 7(b) shows a 20× zoom image of a portion of the unit cell, shows some visual flaws associated with pitting and edge issues with MXene deposition (black portion). Laser measurements were taken using the Keyence VK-X series microscope to characterize the laser-etched MXene geometries. Figure 7(c) shows color map images of two different post-etched elements of the boundaries between the substrate and MXene ink, where greater thickness is indicated by the brighter colors (yellow/red). The average variation of the thickness of ink was measured over five different elements across the surface, and while the thicknesses ranged from 1.9 to $6.7\mu \mathrm{m}$, the average thickness was calculated to be $3.6\mu \mathrm{m}$. As demonstrated later in this manuscript this variation in ink thickness likely had a measurable impact on the overall device performance.

The dimensions of the metamaterial unit cell geometry could potentially affect the frequency-dependent absorption results if they differ from the design dimensions. Figure 8 shows the results of side-by-side measurements that were again taken using the Keyence confocal microscope. Each of the 11 measurements was taken 3 separate times on different unit cells over the surface of the etched metasurface to characterize the variation of the etching method. Figure 8 lists the averages of each of those measurements and the calculated average percent error based on the actual dimensions of the design. The table shows that the most significant percent error of any of the measurements is less than 8%, and the lowest is 0.14%. The laser etching method of patterning proved to be fairly consistent over the test samples with little variation between measurements; however, some of the more significant discrepancies could affect the magnitude of absorption.

Fig. 8

Confocal imaging of metasurface features showing measured dimensions next to designed values. Error values are presented in percent as either larger than (+) or smaller than (-), the design dimensions.

5.1.

Testing Methods

The EM performance for the fabricated MXene-based metamaterial absorber was performed using two distinct methodologies: (1) a focused beam measurement system and (2) an NRL arch. The focus beam measurement system, illustrated in Fig. 9(a), employed a Gaussian beam to evaluate the absorber’s response under normal incidence from 18 to 40 GHz. In contrast, the custom-designed NRL Arch [Fig. 9(b)] facilitated bistatic measurements, enabling an assessment of the absorber’s effectiveness across varying incident angles from 26 to 40 GHz. The arch was constructed with a semi-circular curvature and brackets positioned at 10-deg intervals from the center. The EM characteristics were analyzed through the evaluation of transmission, reflection, and absorption components, with their cumulative sum equating to unity. Furthermore, the incorporation of a copper-backed absorber rendered the transmission component negligible. The reflectance of the absorber, expressed as a percentage, was determined by quantifying the reflection coefficient and subsequently calculated.

Fig. 9

Testing methods used in the study: (a) a monostatic, focus beam measurement system converging a Gaussian beam on a sample at normal incidence and reflecting energy back to the horn antenna. (b) NRL arch measurement platform with testing available at 10-deg increments from the center.

5.2.

Measurement Results and Discussion

The reflectance measurements were conducted with the focus beam system at normal incidence across the frequency range of 18 to 40 GHz and juxtaposed against the simulated design spanning 18 to 44 GHz, as depicted in Fig. 10. Within the targeted Ka-band (26 to 40 GHz), where the metasurface optimization was focused, an absorptance exceeding 93% was observed. Across this band, the calculated average reflectance remained at a low value of 2%. This performance was consistent with the simulation-derived value of 2.4% average reflectance in the Ka-band. Notably, the fabricated absorber exhibited a broad-spectrum absorptance in the frequency ranges of 25 to 40 GHz, encompassing over 90% absorptance over a 15 GHz bandwidth. Evident in this analysis is the strong agreement between the simulated accuracy of the coding-metasurface model and the realized performance of the fabricated absorber. This coherence was particularly pronounced within the band of 27 to 40 GHz, where the reflectance alignment lay within a $\pm 3.5\%$ range. The experimental results thus validate the model’s predictive capabilities while affirming the absorber’s proficiency in attaining desired absorptance and reflectance characteristics in the design band. However, the discrepancies outside the design band ($<26\mathrm{GHz}$) prompted further evaluation that will be addressed later in the text.

Fig. 10

Reflectance given in percent of the simulated design metasurface and the measured results demonstrating a greater than 93% absorptance at normal incidence in the Ka-band.

The absorber’s evaluation encompassed varying incident angles, utilizing both the simulated RCWA method and the fabricated metasurface via the NRL Arch. The presented measurements at a 10-deg angle shown in Fig. 11, similar to the normal incidence graph, revealed good performance even at slight angles, demonstrating absorptance exceeding 91%. The computed results returned a 3.4% average reflectance over the entire band, slightly deviating from the simulated average reflectance of 2.4%. Within the frequency range of 29 to 40 GHz, the reflectance difference between measured and simulated results remained below 2.6%. However, at lower frequencies, a notable elevation in reflectance difference, ranging from 2.6% to 8.2%, emerged between model and measured values from 26.5 to 29 GHz. These results highlight the absorber’s consistent performance under varied angles and offer insights into the frequency-dependent discrepancies for future analysis and refinement.

Fig. 11

Measured and simulated design reflectance results over the Ka-band at a 10-deg incident angle.

Using the NRL Arch, measurements were conducted employing horn antennas situated at 20-degree angles from the center, with both measured and simulated results depicted in Fig. 12. As anticipated, the absorber’s performance declined at this elevated angle; nevertheless, it produced an absorptance exceeding 90% from 27.1 to 40 GHz and an average reflectance of 3.9% within the 26.5 to 40 GHz range. This is similarly compared to a simulated average reflectance of 2.6%. Notably, the most substantial deviations were observed at lower frequencies, with reflectance differences between simulated and measured values ranging approximately from 3% to 10% spanning 29 to 26.5 GHz while remaining below 3% reflectance difference from 29 to 40 GHz. This analysis emphasizes the absorber’s wideband performance despite the pronounced increase in reflectance at the lower frequency range.

Fig. 12

Measured and simulated design reflectance results over the Ka-band at a 20-deg incident angle.

The design process successfully identified a metasurface geometry that effectively lowered reflectance within the Ka-band and was subsequently validated through fabrication. Nevertheless, discrepancies between the simulated and measured outcomes prompted further investigation. To better understand the underlying cause of this discrepancy, we conducted additional simulations based on the metrology data extracted from the fabricated device.

The reduced $x$ and $y$-dimension feature sizes identified in the metrology results were applied in the initial simulation. The outcomes demonstrated an increase in reflectance by up to 7% compared to the simulated curve, thereby aligning more closely with the measured results, as observed in Fig. 13. Subsequently, the second simulation incorporated metrology thickness measurements that revealed a minimum MXene thickness value of $1.9\mu \mathrm{m}$. Again, the outcome demonstrated an increase in reflectance focused in the lower frequencies of up to a 24% increase compared to the original simulated curve. The final simulation encompassed both width feature size adjustments and thickness modifications depicted in Fig. 13, incorporating the simulated metrology results. This approach yielded a reflectance difference of less than 4% between the resulting simulation and the measured fabricated results across the majority of the frequency band. These findings underscore two significant observations: first, while all three dimensions of the MXene ink metasurface features notably influence reflectance errors in the fabricated absorber, the thickness dominates the resulting simulation and measurement disagreements; secondly, the coding-metasurface and RWCA modeling is successful in harnessing MXene’s distinct properties for the creation of effective metasurfaces.

Fig. 13

Alternate simulations based on metrology results of fabricated metasurface showing the adjusted dimensions more closely matching measured results.