Ultrahigh Nonlinear Responses from MXene Plasmons in the Short‐Wave Infrared Range

Surface plasmons in 2D materials such as graphene exhibit exceptional field confinement. However, the low electron density of majority of 2D materials, which are semiconductors or semimetals, has limited their plasmons to mid‐wave or long‐wave infrared regime. This study demonstrates that a 2D Ti3C2Tx MXene with high electron density can not only support strong plasmon confinement with an acoustic plasmon mode in the short‐wave infrared region, but also provide ultrahigh nonlinear responses. The acoustic MXene plasmons (AMPs) in the MXene (Ti3C2Tx)–insulator (SiO2)–metal (Au) nanostructure generate in the 1.5–6.0 µm wavelength range, exhibiting a two orders of magnitude reduction in wavelength compared to wavelength in free space. Furthermore, AMP resonators with patterned Au rods exhibit a record‐high nonlinear absorption coefficient of 1.37 × 10−2 m W−1 at wavelength of 1.56 µm, ≈3 orders of magnitude greater than the highest value recorded for other 2D materials. These results indicate that MXenes can overcome fundamental plasmon wavelength limitations of previously studied 2D materials, providing groundbreaking opportunities in nonlinear optical applications, including all‐optical processing and ultrafast optical switching.


Introduction
Atomically thin 2D materials, such as graphene and black phosphorus (BP), are capable of generating confined surface plasmons in the mid-infrared or terahertz regime due to the early transition metal such as Ti, Mo, or Nb, X is carbon and/or nitrogen, and T x denotes surface terminations such as ─OH, ═O, and ─F. [12]Among the MXenes, a titanium carbide (Ti 3 C 2 T x ) MXene has a single-sheet thickness of under 1 nm and a high electrical conductivity of over 20000 S cm −1 . [14,15]A Ti 3 C 2 T x laminate film exhibited a plasma frequency in the range of 280-300 THz, [16] indicating that 2D Ti 3 C 2 T x MXenes are metallic and have great potential to support plasmons in the SWIR region.Additionally, Ti 3 C 2 T x MXene films exhibited high third-order nonlinear susceptibility [17,18] over the visible-to-SWIR range due to the formation of ångström-thin gaps between the 2D layers [10] and a relatively narrow electronic band gap, [17] enabling ultrathin SWIR nonlinear applications such as saturable absorbers [17] and optical information conversion. [18]ere, this study demonstrates that APs of Ti 3 C 2 T x MXene, named acoustic MXene plasmons (AMPs), extend the spectral range of 2D material-based plasmons to the SWIR region and enable record-high SWIR nonlinear responses in ultrathin structures.The theoretical analysis revealed the generation of subwavelength plasmons in the SWIR region on the surface of a few-nanometer-thick Ti 3 C 2 T x MXene film on a fused silica substrate.The wavelength of MXene plasmons is significantly reduced (≈ 0 /112) in a Ti 3 C 2 T x -SiO 2 -Au multilayer structure by activating the AMP modes.We experimentally confirmed the existence of the AMP mode by measuring the shift in the resonant wavelength according to the geometrical dimension of the nanorod-shaped AMP resonator.The AMP resonator with a 5 nm thick Ti 3 C 2 T x shows plasmonic wavelength decreased to ≈ 0 /15 and exhibits a record-high nonlinear response with a nonlinear absorption coefficient of 1.37 × 10 −2 m W −1 at a wavelength of 1560 nm, which is approximately a 1000 times higher than the highest value reported for other 2D materials in the SWIR region.

Acoustic MXene Plasmons
Figure 1a illustrates a structured configuration comprising a Ti 3 C 2 T x MXene layer, accompanied by a dielectric SiO 2 spacer and a thick gold metal.This arrangement has been meticulously optimized for AMP mode excitation.The MXene layer, characterized by its high electron density, serves as a nonlinear plasmonic material.Notably, Ti 3 C 2 T x MXene demonstrates exceptional optical nonlinearity attributed to its multiple atomically thin air spacers (referred to as d-spacing) situated between conducting layers, along with a narrow electronic bandgap (ranging from 0.05 to 0.1 eV), [17] distinguishing it from other 2D materials.Moreover, due to its elevated electron density, the MXene layer generates surface plasmon modes in the SWIR frequency range.This plasmonic effect is further intensified by the AMP mode when combined with the image charges present on the thick gold's surface.
For MXene preparation, the well-delaminated Ti 3 C 2 T x MXene flakes were synthesized by selectively etching the monoatomic aluminum layer from the parent Ti 3 AlC 2 MAX phase via the minimally intensive layer delamination (MILD) method, [14] and a few nanometer-thick Ti 3 C 2 T x MXene films were prepared using spin-coating of delaminated Ti 3 C 2 T x dispersions onto a fused silica substrate [see Figures S1-S3, Supporting Information].Ad-ditionally, the following structures were introduced to activate the AMPs: a 10 nm thick SiO 2 layer was deposited on top of the MXene film and covered with an Au layer, as shown in the transmission electron microscopy (TEM) image in Figure 1b.A 2 nm thick Al layer was introduced between Au and SiO 2 for adhesion.Figure 1c shows the measured real (ʹ) and imaginary (ʺ) permittivities of Ti 3 C 2 T x with thicknesses of 5 and 10 nm in the spectral range from near-infrared (NIR;  = 0.8-1.3μm) to SWIR ( = 1.3-3.0μm).This measurement was conducted using two ellipsometers: M-2000 Ellipsometer (J.A. Woollam) for the wavelength range of 0.9 -1.7 μm; and IR-VASE Mark II (J.A. Woollam) for the wavelength range of 1.6 -6.0 μm.During these measurements on Ti 3 C 2 T x with thicknesses of 5 and 10 nm, uniform optical responses were observed at all angles, implying their isotropic properties at these small thicknesses.The plasma frequencies (ʹ = 0) of the 5 and 10 nm thick Ti 3 C 2 T x films were measured to be 292 THz ( p = 1045 nm) and 287 THz ( p = 1027 nm), respectively, indicative of metallic properties (ʹ < 0 and ʺ > 0) in the SWIR region.Here, the high plasma frequency of Ti 3 C 2 T x is attributed to its high electron density (7.5 × 10 14 cm −2 ), [19] which far surpasses that of highly doped graphene (8 × 10 12 cm −2 ) or BP (2 × 10 13 cm −2 ). [1,5]Interestingly, they have slightly different permittivity properties despite the little difference in their thicknesses (5 and 10 nm).This is because the MXene films contain stacks of conductive Ti 3 C 2 T x monolayers separated by subnanometer gaps in the out-of-plane direction, which contain Li ions and strongly bonded water molecules trapped during the synthesis.The thickness difference of 5 nm may originate from a different number of Ti 3 C 2 T x monolayers and a variation in the width of interlayer gaps. [16]ased on the measured permittivities of Ti 3 C 2 T x , we calculated the field distributions (|E z |) along the out-of-plane (z) direction in the thick SiO 2 -Ti 3 C 2 T x (10 nm)-thick SiO 2 and thick SiO 2 -Ti 3 C 2 T x (10 nm)-S i O 2 (10 nm)-thick Au structures at a wavelength of 1560 nm, as shown in Figure 1d,e, respectively.These figures demonstrate the presence of MP and AMP modes, which strongly confine the electric field in the vicinity of the MXene surface.In addition, the figures highlight the differences in field confinement between the MP and AMP modes [see Figure S4, Supporting Information].In the MP mode, the electric field spreads away from the MXene surface and has a relatively long decay length ( = 50 nm) (Figure 1d), whereas, in the AMP mode, the electric field has a relatively short decay length ( = 20 nm) indicating the energy is tightly confined in the 10 nm thick SiO 2 spacer between Au and MXene (Figure 1e), which is similar to the AP mode in graphene or gap-plasmon mode in noble metals. [17,18]or a quantitative analysis of the MP and AMP structures containing 5 and 10 nm thick Ti 3 C 2 T x layers , we analytically solved the dispersion relations for the MP and AMP modes and derived an effective refractive index [20] of the AMP modes as a function of the SiO 2 spacer thickness at a frequency of 192 THz, as shown in Figure 1f,g.As shown in Figure 1f, the AMP mode exhibits a higher wavevector (or higher effective refractive index) than all the other MP in the SWIR region, owing to stronger field confinement.For example, at a frequency of 192 THz, the 10 nm thick Ti 3 C 2 T x AMP mode has a wavevector that is 2.22 times greater than those of the 10 nm thick Ti 3 C 2 T x MP mode (k AMP /k MP = 2.03), where the effective refractive index of the AMP mode is calculated to be 10.26.The 5 nm thick Ti 3 C 2 T x AMP mode is calculated to have a wavenumber 1.47 times greater than that of the 10 nm thick Ti 3 C 2 T x (k AMP,5nm /k AMP,10nm = 1.47) at a frequency of 192 THz.In addition, as shown in Figure 1g, the wavevector (or the effective refractive index) of the AMP mode increases with the reduction of spacer thickness from 30 to 1 nm.In this calculation, we used a minimum spacer thickness of 1 nm to minimize the nonlocal quantum effects in the plasmonic mode, maintaining the validity of classical computational approaches.It is noteworthy that within a spacer thickness range of 1-5 nm, there is a potential reduction in the effective refractive index attributable to quantum effects, as indicated in references. [21,22]Additionally, we maintained a constant refractive index of 1.45 for the spacer material across all thicknesses.For AMP modes with 5 and 10 nm-thick Ti 3 C 2 T x layers, the effective refractive index increases by 2.98 and 4.03 times, when the spacer thickness is reduced from 10 to 1 nm, respectively.According to the classical model, the effective refractive index of the AMP mode drastically increases as the spacer thickness approaches zero.This is attributed to the strong confinement of electromagnetic field within the spacer, leading to enhanced field localization.During this process, the mode becomes more characteristic of electronplasma, indicating that the electromagnetic energy is increasingly concentrated in the MXene and Au layers. [23]Furthermore, in the case of a monolayer of Ti 3 C 2 T x with a thickness of 1.0 nm, the effective refractive index of the AMP mode reaches a value of 112.In the frequency range between the plasma frequency (f p = 292 THz) and the surface plasmon frequency (f sp = √ 2f p = 206 THz), the wavevector of the AMP mode decreases due to significant absorption loss, where the interband transition in Ti 3 C 2 T x dominates over the intraband transition (Drude response). [13,16]

AMP Resonators
To further confine the AMP mode in the lateral direction (inplane direction) and improve the coupling with external light, we designed an AMP resonator by patterning Au in the AMP structure in the form of a nanorod, as shown in Figure 2a.Here, the optical energy is vertically confined to the SiO 2 spacer (thickness = g), as shown in the inset of Figure 2a, and laterally to the Au nanorod area (L x × L y ).The lateral dimensions (L x , L y ) of the Au nanorods mainly determine the resonances in a given AMP mode.
To investigate the characteristics of the AMP resonator, we designed a periodic square (L x = L y ) Au nanorod structure that is independent of the linear polarization direction due to its 90-degree geometric symmetry [see Figures S5 and S6, Supporting Information].We employed the finite-difference time-domain (FDTD) simulation method to design the resonator and calculate the field distribution and resonant spectrum [see Experimental Section].Figure 2b shows the calculated E z profile of the first-order resonance mode of the AMP resonator with L x and L y of 400 nm and a period (P) of 1 μm.The thicknesses of the Ti 3 C 2 T x (t), SiO 2 spacer (g), and Au nanorods were fixed at 10, 30, and 100 nm, respectively.As shown in Figure 2b, the electric field is tightly confined to the SiO 2 spacer between Au and MXene, with the highest intensity spots located at the edges of the Au nanorod.Here, the AMP resonances satisfy the Fabry-Pérot resonance conditions with strong reflections (or wavevector mismatches) of the AMP mode at the edges of the Au nanorods [see Experimental Section].Based on this design, we fabricated periodic AMP resonators by removing the PMMA resist and Au layer from the prepared AMP structure using e-beam lithography and liftoff techniques, as shown in Figure 2a [see Figure S7, Supporting Information].We prepared AMP resonators of various dimensions to verify the AMP mode by tracking the resonant wavelength based on the resonator size as follows: nm], g = 30 nm, and t = 10 nm, where M ranges from 1.0 to 3.5 in increments of 0.5.Figure 2c shows a scanning electron microscopy (SEM) image of the fabricated AMP resonator with M = 3.0.The resonances were measured from the reflection spectra of the AMP resonators using a Fourier-transform infrared (FTIR) spectrometer (Thermo Scientific, Nicolet iN10Mx) with a 15× objective lens.The reflectance spectrum of a 100 nm thick gold film deposited on a silicon wafer was used as the reference.
Figure 2d,e shows the measured and calculated reflectance spectra of the AMP resonators with various L values, respectively.Each spectrum in these figures is vertically offset by 0.2 to enhance visualization.Here, the spectrum was plotted as a function of the wavenumber (k = 2f/c), where f is the frequency, c is the speed of light, and the reflection dips corresponding to the firstorder and third-order resonance modes are marked by brown squares and purple rhombuses, respectively.These figures verify that the AMP modes are activated in the SWIR range (3333-7142 cm −1 ), and the measured AMP resonances are in good agreement with the computed results.Notably, the resonance linewidth widens as the resonance wavenumber approaches the surface plasmon frequency of 6700 cm −1 .This is because the absorption loss increases rapidly as the frequency approaches the surface plasmon frequency.The sharp increases, shown in Figure 2d, at a wavenumber of 1200 cm −1 for all L values can be attributed to SiO 2 phonon vibrations, which interfere with the formation of the AMP mode.The Ti 3 C 2 T x material also has vibrational modes in the mid-infrared (MIR) range, for example, O-H bonding at a wavenumber of 3300 cm −1 owing to the functional groups at the surface termination sites; [10] however, these were not noticeable in the reflectance spectra because the energy of the AMP mode was more concentrated in the SiO 2 layer.
The measured and calculated spectra are shown in Figure 2f and mapped in the form of a dispersion curve.The wavenumber k p on the x-axis was transformed through the relationship k p,1st = (-arg(r))/L, which is the first-order resonance condition of the Fabry-Pérot resonator, and the relationship k p,3rd = (3arg(r))/L, where r is the reflection coefficient of the AMP mode at the edge of the resonator, [24] and the phase shift of r is set to 0.18 for first-order resonances and 0.4 for third-order resonances [see Experimental Section].We note that the reflection coefficients of plasmon waves can vary with the type of resonance mode and frequency range. [24]In this figure, the color plot displays the set of calculated reflectance spectra, shown in Figure 2d, where the brown squares and purple rhombuses indicate the locations of the measured reflection dips of the first-order and third-order resonance modes shown in Figure 2e, and the black dotted line is the dispersion curve of the AMP mode shown in Figure 1e.Clearly, the measured resonances (purple rhombuses) are in good agreement with the dispersion of the designed AMP mode (black dotted line), and the black dotted line is also in good agreement with calculated reflection dips.Therefore, these experimental results clearly demonstrate that the AMP mode operating in the SWIR region is present in the designed AMP structure and can be further localized through the AMP resonator.

Ultrahigh Nonlinear Response from AMP Resonators
Ti 3 C 2 T x MXenes are highly nonlinear materials with high thirdorder susceptibility  (3) at optical frequencies owing to their relatively narrow electronic band gaps. [17]When these Ti 3 C 2 T x MXenes are effectively coupled with AMP resonators, high nonlinear responses related to  (3) , such as high third-harmonic generation (THG) and high nonlinear absorption, can be expected in   and S9, Supporting Information].For t > 10 nm, the Kerr coefficient shows small variations with t and is measured to be n 2 = [(1.08 ± 0.45) + i (2.10 ± 0.49)] × 10 −8 cm 2 W −1 .In contrast, for t < 10 nm, both the real and imaginary values of n 2 increase rapidly with decreasing t and reach n 2 = (2.6 + 6i) × 10 −8 cm 2 /W at t = 5 nm.This rapid increase in n 2 is attributed to the intersubband transition between the energy states of Ti 3 C 2 T x quantized by its nanometer thickness. [25]long with the high Kerr coefficient of the ultrathin Ti 3 C 2 T x MXene layer, the nonlinear response can be improved by field enhancement through the AMP resonator.To maximize the optical energy entering the MXene layer in the AMP resonator, we additionally designed a resonator with different SiO 2 and MXene thicknesses.Figure 3b shows the maximum intensity enhancement in the volumetric space within the MXene layer of the AMP resonator as a function of t at different SiO 2 spacer thicknesses (g).A plane-wave beam with a wavelength of 1560 nm was incident on the resonator from air.As shown in this figure, the intensity enhancement increases with the decrease in both the SiO 2 and MXene thicknesses; therefore, we set the MXene and SiO 2 thicknesses to 5 and 10 nm, respectively, considering the fabrication limitations.In addition, to tune the resonance to the wavelength of 1560 nm, L x and L y were designed to be 420 and 150 nm, respectively, and the period was fixed at 1 μm.With this configuration, the AMP resonator exhibits a resonant mode exclusively for x polarization.Under these conditions, the maximum intensity enhancement within the MXene layer was calculated to be 120.Figure 3c shows the distribution of the electric field amplitude |E| of the AMP resonator along the xy-plane, where the electric field is tightly localized at the edges of the resonators, and a surface lattice resonance (SLR) between the periodic resonators is observed [26,27]   The grey circles represent graphene. [41]The purple circles represent transition metal dichalcogenides (TMDCs), [28][29][30][31][32][33][34] including MoS 2 , MoTe 2 , Bi 2 Te 3 , Bi 2 Te 2 Se, Bi 2 TeSe 2 , BiSe 3 , WS 2 , MoSe 2 , Wse 2 , Mo 0.5 W 0.5 S 2 , SnSe 2 , ReSe 2 , As 2 Te 3 , TiSe 2 , and SnS.The orange circles indicate perovskites, [42][43][44][45][46][47][48][49][50] including CsPbBr 3 , MAPbBr 3 , MAPbI 3 , CH 3 NH 3 PbBr 3 , BaTiO 3 , SrTiO 3 , and (BA) 2 (FA)Pb 2 Br 7 .Finally, the cyan circles represent MXenes, [35][36][37][38][39][40] such as Ti 3 C 2 T x , V 2 CT x , Ti 2 CT x , Nb 2 CT x , Mo 2 CT x , W 2 CT x , Mo 2 CT x , and MoCT x .
where  is the angular frequency), and Γ was calculated to be 27.2%.Figure 3d shows the distribution of W in the AMP resonator along the xz-plane, where a significant portion of the energy density is observed within the MXene layer.We fabricated the designed AMP resonator, as shown in Figure 3e, and observed that the resonant wavelength was ≈1560 nm in the x-polarized beam from the transmission spectrum (Figure 3f).
The asymmetric shape of the transmission spectrum is due to the coupling between the SLR and AMP resonance modes. [26,27]o characterize the THG emission and nonlinear absorption capabilities of MXene, we illuminated a 1560 nm femtosecond laser (pulse width of 100 fs and repetition rate of 80 MHz) on the fabricated AMP resonator array.Figure 4a shows the intensity of the THG signal ( 3 = 520 nm) measured from the AMP resonator after passing it through a short-pass filter.We also compared the THG signals of the 5 nm thick MXene film on the fused silica substrate, under the same measurement conditions.As shown in Figure 4a, all three signals follow the THG emission characteristics proportional to the cube of the pump laser peak intensity.The intensity of the THG signal emitted from the AMP resonator was 325 times higher than that emitted from the fused silica substrate and 168 times higher than that of the 5 nm thick MXene film on the fused silica substrate.This result demonstrates that the AMP resonator contributes to the significant increase in the  (3) nonlinear signal through strong field enhancement and confinement.
We additionally quantified the nonlinear absorption coefficient, which is another important indicator of the  (3) nonlinear response, for the AMP resonator array, using the OA signal via the z-scan measurement technique [See Figures S10 and  S11, Supporting Information].For comparison, a structure with a 5 nm thick MXene layer on the fused silica substrate was also measured.Figure 4b shows the z-scan transmission curves of the OA signals for the two structures at average femtosecond laser powers of 4.19, 11.0, and 254 MW cm −2 .In the case of the 5 nm thick MXene film on fused silica, the transmittance increased at z-scan = 0 for the low-intensity input beam (4.19 MW cm −2 ), indicating a normal saturable absorption.However, when the intensity of the incident beam was increased to 254 MW cm −2 , there was nonlinear reverse saturable absorption (RSA) due to the nonlinear multiphoton absorption mechanism, in which the transmittance dropped by 8.4% at z-scan = 0. From this z-scan curve, we calculated the Im [n 2 ], Im [ (3) ], and nonlinear absorption coefficient () to be 6 × 10 −8 cm 2 W −1 , 5.01 × 10 −13 m 2 V −2 , and 4.83 × 10 −5 m W −1 , respectively [see Experimental Section].Interestingly, in the case of the AMP resonator, the z-scan transmission curve rapidly dropped by 52% at z-scan = 0 even at a low intensity of 4.19 MW cm −2 .This clearly shows that a strong nonlinear RSA occurred with the thin MXene layer through the AMP resonator.The Im [n 2 ], Im [ (3) ], and  values of the AMP resonator were calculated to be 1.7 × 10 −5 cm 2 W −1 , 1.422 × 10 −10 m 2 V −2 , and 1.37 × 10 −2 m W −1 , respectively, indicating that the occurred nonlinear absorption was 283 times greater than that of 5 nm MXene film on fused silica.

Discussion
[44][45][46][47][48][49][50] As shown, the overall nonlinear absorption coefficient tends to increase with the decrease in the thickness of the 2D material.This can be understood as follows: the energy state is more quantized with the decrease in the thickness of the 2D material, and thus, the interband transition between energy states is further enhanced.The  value measured from 5 nm thick Ti 3 C 2 T x on fused silica was 4.83 × 10 −5 m W −1 , which was ≈8.8 times higher than the highest value of 5.48 × 10 −6 m W −1 . [29].Moreover, the measured  (1.37 × 10 −2 m W −1 ) from the AMP resonator was ≈10 3 times higher than the highest value recorded for 2D materials in the SWIR region.In Figure 5, we compare the dispersion relations of plasmon modes supported by Ti 3 C 2 T x to those of other 2D materials and ultrathin noble metals.Plasmons in 3-nm-thick Au exhibit a low wavevector and a small effective refractive index (k p /k 0 ) of less than 3 in the SWIR range, which is the result of its high plasma frequency value. [51]In contrast, graphene and BP, which are widely studied 2D conductive materials, display high wavevectors and large effective refractive indices greater than 10 2 across the frequency range from THz to LWIR.][54] WTe 2 and Bi 3 Te 2 , which are transition metal dichalcogenide (TMDC) materials, support plasmon modes with high wavevectors in THz range for WTe 2 [55] and in the LWIR range for Bi 3 Te 2. [56] However, their plasmon modes are not permitted in higher frequency ranges due to interband transitions overpowering intraband transitions (Drude-like response).TaSe 2 , another TMDC material, supports plasmons in the SWIR range with high electron density, but its effective refractive index is limited to below 10 within a very narrow interband range. [57]In contrast, Ti 3 C 2 T x studied here displays a broad frequency distribution for plasmon modes with high wavevectors, spanning from MWIR to SWIR range.Specifically, Ti 3 C 2 T xbased AMP mode, generated by a structure consisting of a 1nm-thick SiO 2 layer and a monolayer of Ti 3 C 2 T x (with a thickness of 1.0 nm), can theoretically achieve a maximum effective refractive index of 112 in the SWIR range.Furthermore, the AMP mode in a structure composed of a 5-nm-thick Ti 3 C 2 T x and a 10-nm-thick SiO 2 layer was experimentally measured to have an effective refractive index of 15 in the SWIR range ( = 1.56 μm).This measurement closely agrees with the numerically calculated value of 16.2.We also anticipate that other MXenes, besides Ti 3 C 2 T x , can be implemented to realize the acoustic plasmon mode at different frequencies, allowing for strong light confinement and nonlinear effects in the spectral range beyond the SWIR region.

Conclusion
By incorporating Ti 3 C 2 T x MXene into a carefully designed nanostructure platform, we have demonstrated that it supports strongly confined surface plasmons and a large nonlinear response in the short-wave infrared (SWIR) region.The ultrathin Ti 3 C 2 T x in a MXene-insulator-metal structure generated strong acoustic plasmons in the SWIR region.The AMP resonator with patterned Au metal reduced the plasmon wavelength by two to three orders of magnitude, surpassing existing 2D materials as well as noble metals as an efficient plasmonic material.Additionally, the AMP resonator exhibited a record-high nonlinear absorption coefficient of 1.37 × 10 −2 m W −1 at  = 1560 nm, which was attributed to not only the large field enhancement of external light with the AMP resonator but also the considerable nonlinearity of pristine MXene originating from its unique electronic structure and sub-nanometer interlayer spacings.These extreme field confinement and nonlinear effects with MXene plasmons in the SWIR region have the potential to revolutionize high-optical frequency nonlinear applications, including all-optical processing and ultrafast optical switching. [58,59]These advancements provide superior performance, compact dimensions, and reduced complexity, exceeding the capabilities of traditional optical communication and logic devices.

Experimental Section
Fabrication of AMP Resonator: Nanometer-thick Ti 3 C 2 T x films were prepared using diluted delaminated Ti 3 C 2 T x aqueous dispersions through spin casting.The delaminated Ti 3 C 2 T x MXene flakes were synthesized through selective Al element etching from the Ti 3 AlC 2 MAX phase powders (40 μm size, Carbon Ukraine) through the modified minimally intensive layer delamination (MILD) method [14] [see Supporting Information text for details].Prior to depositing the MXene sheets, the fused silica substrates (iNexus, Inc. 4500 Quartz Wafer, Fused Silica) were sequentially cleaned using UV-ozone treatment and in acetone, ethyl alcohol, and isopropyl alcohol, and fabricated by 0.01 wt% 3-aminoprypyl trimethoxysilane for self-assembled monolayer (SAM) treatment.The thickness of the MXene film was adjusted by the concentration of the MXene dispersion: solutions with concentrations of 5, 10, 15, 20, 30, 40, and 45 mg mL −1 were used to fabricate films with approximate thicknesses of 5, 10, 15, 20, 30, 40, and 45 nm, respectively.Films were spin-cast onto fused silica substrates using a 0.6 mL solution first at 5000 revolutions per minute (RPM) for 60 s and then at 7000 RPM for 10 s.The resulting films were dried on hot plates at 90 °C for 30 s.After MXene coating on fused silica, few tens of nanometer-thick SiO 2 layer was deposited with sputtering.Next, the PMMA resist was spin-coated onto the SiO 2 layer, and the periodic patterns were produced using e-beam lithography.After dipping the sample in the developer MIBK:IPA = 3:1 for 80 s, 2 nm thick Al and 40 nm thick Au layers were sequentially deposited using a thermal evaporator.Finally, a liftoff process was performed by removing the PMMA resist and dipping the sample in acetone under sonication.
Z-Scan Measurement: A femtosecond laser (FemtoFiber pro NIR) beam with a center wavelength of 1560 nm and a power density of 0.254 GW cm −2 was used to illuminate the sample.An objective lens with a focal length of 60 mm was used for incidence on the sample to obtain the CA signal.Scanning the sample from −10 to 10 mm in the optical-axis direction, this work obtained the z-scan curve for the CA signal.In addition, this work collected the OA signal by placing a beam splitter in front of the objective lens to normalize the CA signal.To extract the Re [n 2 ] value of Ti 3 C 2 T x , the measured CA curve was fitted using the equation T CA where k is the wavenumber, n 2 is the Kerr coefficient, and I is the laser peak intensity.L eff = (1-e −t )/ is the effective length of Ti 3 C 2 T x , where  is the absorption coefficient, and z 0 is the Rayleigh distance of the Gaussian beam. [48]To obtain the Im n 2 value of Ti 3 C 2 T x , this work fitted the OA curve using the equation T OA (z) = ∑ ∞ m=0 (−2kIm [n 2 ]IL eff ) m (m + 1) −3∕2 [(z∕z 0 ) 2 + 1] −m , where m is an integer. [60]In addition, this work obtained Im[ (3) ] using the equation Im[ (3) ] = , where n represents the refractive index of MXene,  v is the vacuum permittivity, c is the speed of light,  is the angular frequency of light, and  is the nonlinear absorption coefficient. [60]umerical Calculation: The FDTD simulation method (Lumerical software) was used to predict the reflectance spectra and field distribution around the AMP resonator.For material dispersion, this work adopted the permittivities of SiO 2 and Au obtained from literature [61] and fitted the permittivity of Ti 3 C 2 T x using the Drude model  =  0 −  2 0 ∕( 2 + iΓ).With the fitting process, it was found that  0 = 10.72+3.7i, 0 = 3.9 eV, and Г = 0.25 eV for the 5 nm thick Ti 3 C 2 T x , and  0 = 10.5+4i, 0 = 4.0 eV, and Г = 0.232 eV for the 10 nm thick Ti 3 C 2 T x .For the FDTD simulation domain, this work imposed a periodic boundary condition in the xy-plane to simulate an infinite periodic array of AMP resonators and employed perfectly matched layers (PMLs) in the z-direction.For the PMLs, the maximum number of layers was used to minimize the scattering error at their edges.
Determination of Reflection Phase Shift in AMP Resonator: To obtain the dispersion curve from the measured and calculated spectra shown in Figure 2f, this work adopted the Fabry-Pérot model to estimate the resonant wavelength of the AMP resonator. [24]Under linearly polarized light illumination, the AMP mode in the resonator propagates in 1D and is experienced at the edge of the resonator, resulting in a standing wave inside the resonator.Light is strongly confined inside the AMP resonator while satisfying the following standing-wave condition k p L x + arg(r) = n, where n is zero or a positive integer, and arg(r) is the reflection phase shift of the AMP mode at the edge of the AMP resonator.To determine the value of arg(r), this work employed mapping of the reflectance spectra with different L x , as illustrated in Figure 2f.In Figure 2f, the wavevector of the AMP resonator is given by k p = (-arg(r))/L for first-order resonances and by k p = (3-arg(r))/L for third-order resonances, which is determined from the spatial frequency of the structure [24] and the reflection phase shift.This wavevector of the AMP resonator is theoretically identical to the wavevector of the AMP mode, k AMP , which is obtained from the dispersion relation shown in Figure 1.With the optimization technique, this work found an arg(r) value of 0.18 for first-order resonances and 0.4 for third-order resonances, suggesting that the dispersion curve of k AMP corresponds to the resonant frequency of the reflectance spectra of the AMP resonator.

Figure 1 .
Figure 1.MXene plasmons.a) Concept of acoustic MXene plasmon (AMP) mode and electronic band gap of MXene.b) Transmission electron microscopy (TEM) image of a multilayered structure supporting the AMP mode.c) Permittivity of Ti 3 C 2 T x with thicknesses of 10 nm (red curve) and 5 nm (blue curve).The solid and dotted lines indicate the real and imaginary parts of the permittivity, respectively.d,e) Calculated E z field distribution of d) MP mode in SiO 2 -Ti 3 C 2 T x -SiO 2 configuration and e) AMP mode in SiO 2 -Ti 3 C 2 T x -SiO 2 -Au multilayers at  = 1560 nm.For the calculation, 10 nm thick Ti 3 C 2 T x and SiO 2 layers were used, with the same thickness as shown in (b).f) Dispersion relations of acoustic MXene plasmon (AMP) and MXene plasmon (MP) modes.The red and blue solid lines indicate the dispersion relation of AMP with MXene thicknesses of 10 and 5 nm, respectively, and the green solid line indicates the dispersion relation of MP with the thickness of 10 nm.The black dotted line indicates the volume and surface plasmon frequency of pristine Ti 3 C 2 T x .A 10 nm thick SiO 2 is used for all the calculations in the AMP and gap-plasmon modes of Au. g) Effective refractive index of AMP mode with MXene layers of thicknesses of 10 nm (blue solid line), 5 nm (red solid line), and monolayer (black solid line) -and of MP with a 10 nm thick MXene layer (green solid line) with respect to the spacer thickness.This calculation assumes a constant refractive index of 1.45 for the SiO 2 spacer.

Figure 2 .
Figure 2. Resonances in AMP resonators.a) Schematic of an AMP resonator comprising an Au nano-antenna placed on a SiO 2 -Ti 3 C 2 T x -SiO 2 multilayer.The inset shows the analytically obtained E z field distribution inside the AMP resonator.b) E z field distribution around the AMP resonator at resonance in the xz-plane.c) SEM image of the fabricated AMP resonator with a lattice size of 900 nm, L x = L y of 600 nm, and MXene thickness of 10 nm.d,e) Calculated (d), and measured (e) reflectance spectra of the AMP resonator with L x = L y with different widths.Each spectrum is vertically offset by 0.2 to enhance visualization.The brown square and purple rhombuses indicate the first-order and third-order resonances of the AMP resonator, respectively.f ) Calculated reflectance spectrum with different wavenumbers, obtained using the relationship k p = (-arg(r))/L x for first-order resonances (upper figure) fitted with arg(r) = 0.18; and k p = (3-arg(r))/L x for third-order resonances (bottom figure) fitted with arg(r) = 0.4.The black dotted line indicates the analytical dispersion relationship of AMP, and the brown square and purple rhombuses indicate the experimentally measured resonance locations in the AMP resonator.

Figure 3 .
Figure 3. Engineering nonlinearity and field confinement in AMP resonator.a) Measured n 2 value of Ti 3 C 2 T x layer with different thicknesses, deposited on fused silica, using data obtained from the z-scan curve.The red and blue dots indicate the real and imaginary values of the nonlinear refractive index, respectively.b) Calculated intensity enhancement of the AMP resonator at the top surface of Ti 3 C 2 T x with different Ti 3 C 2 T x thicknesses.For the calculation, SiO 2 thicknesses of 10 nm (black curve), 20 nm (red curve), 30 nm (blue curve), and 40 nm (green curve) are used.c) E-field distribution of the AMP resonator at the interface between the SiO 2 layer and Au pattern.d) Energy density distribution of the AMP resonator in the y = L y /2 plane.E-field and energy density distribution is calculated at the resonant wavelength of 1560 nm.e) SEM image of the fabricated AMP resonator.f) Measured transmission spectrum of the fabricated AMP resonator with x-polarization (red solid line) and y-polarization (blue solid line).The yellow lines indicate the pump wavelength for the nonlinear signal.

Figure 5 .
Figure 5.Comparison of dispersion relations of various 2D materials and ultrathin noble metals over a frequency range from THz to NIR.The red stars denote the experimental and theoretical results for the AMP resonator.The red rhombuses represent the AMP mode that includes a 1 nm thick dielectric spacer, as determined from theoretical calculations.The black, purple, blue, grey, and yellow circle marks represent graphene, including acoustic plasmon mode, Bi 3 Te 2 , WTe 2 , TaSe 2 , and 3-nm thick gold, respectively.The dark and light green rhombuses indicate BP with different crystal orientations.Circle and rhombus marks represent measured and calculated values, respectively.