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To begin with, let us study the excitation of SPPs in the scenario schematically shown in Fig. 1a. In this case, we can consider a thin layer of MXene (Ti3C2Tx) with thickness "a" sandwiched in between two semi-infinite dielectrics with refractive index n1 and n2 (bottom and top media, respectively). With such configuration, the excited SPPs can exist traveling along the z axis with the electric and magnetic fields being along the (z, y) and (x) axis, respectively (i.e., a TM wave described by E = [0, Ey, Ez] and H = [Hx, 0, 0]). Based on this, the scenario depicted in Fig. 1a can be mathematically described via an effective propagation constant βSPP which can be extracted by analysing the propagation of SPPs in an insulator-metal-insulator (IMI) configuration (insulator-MXene-insulator in our case). As a result, βSPP can be analytically calculated by solving the following transcendental equation23-25:
Fig. 1 Insulator-MXene-Insulator configuration for SPP propagation.
a Sketch of the I-MXene-I structure consisting of a Ti3C2Tx thin film of thickness a placed in between of two semi-inifnite media with refractive index n1 (SiO2, bottom material) and n2 (Air, top material). b, c analytical results of the real and imaginary components of the effective refractive index for the SPPs (nSPP), respectively, considering MXenes thin films with a = 75 nm (red), a = 27 nm (black) and a = 14 nm (blue). d–f Electric and magnetic (Hx) field distributions on the yz planes showing the propagation of SPPs along the z axis at the telecom wavelength of λ0 = 1.55 µm considering MXenes with a = 75 nm, a = 27 nm, and a = 14 nm, respectively. g Hx field distribution along the propagation z axis at y = x = 0 (Air-MXene interface) for the MXenes with a = 75 nm (red), a = 27 nm (black) and a = 14 nm (blue)$$ \tanh \left( {ak_{MXene}} \right) = - \frac{{\varepsilon _1\varepsilon _{MXene}k_2k_{MXene} + \varepsilon _2\varepsilon _{MXene}k_1k_{MXene}}}{{\varepsilon _1\varepsilon _2k_{MXene}^2 + \varepsilon _{MXene}^2k_1k_2}} $$ (1) with $k_{1,2,MXene} = \sqrt {\beta _{SPP}^2 - \varepsilon _{1,2,MXene}k_0^2}$ with subscripts 1, 2, and MXene representing the bottom, top, and centre media from the I-MXene-I configuration of Fig. 1a, respectively, ε is the complex relative permittivity of each medium and k0 is the wavenumber in free-space. Finally, we can define an effective refractive index for the SPPs propagating in such configuration as the ratio between the effective propagation constant and k0, as follows23:
$$ n_{SPP} = \frac{{\beta _{SPP}}}{{k_0}} $$ (2) Let us now evaluate the performance of the I-MXene-I structure shown in Fig. 1a for SPP excitation. Without loss of generality, we can consider that the top and bottom materials are air and silicon dioxide (SiO2), respectively. Let us also consider that both semi-infinite media are non-dispersive with electromagnetic parameters of ε2 = 1 (n2 = 1) and ε1 ~2.073 (n1 = 1.44), respectively. As described in the introduction, MXenes have the potential to revolutionise 2D-based technologies as they offer a range of optical, mechanical, and electronic properties, which are important in applications such as energy storage and even cancer research4, 26. In our present work, we aim to evaluate the possibilities of using MXenes for SPP generation and show its potential use in future SPP-based technologies. As it will be discussed below, we will demonstrate how MXenes could be used, for instance, in sensing applications using optical fibers. To achieve this, here we make use of Ti3C2Tx thin films. The complex relative permittivity of the MXenes is modelled using an analytical fitting of the experimental data provided in ref. 15. We consider three thicknesses: a = 14 nm, a = 27 nm, and a = 75 nm (both the experimental and fitted values used in this manuscript are provided in the Supplementary Materials section 1).
With this configuration, the analytical calculations of the real and imaginary components of the effective refractive index of the SPPs (nSPP) calculated from Eqs. (1, 2) are shown in Fig. 1b, c, respectively, for the three values of a under study. Here, we evaluate the response of the I-MXene-I structure within the spectral range from 1.45–1.65 µm to show the potential of MXenes for SPP propagation at telecom wavelengths. It is important to note that these scenarios could also be implemented at longer wavelengths (potentially within the near and mid infrared) using different MXenes as long as the design wavelength is larger than the plasma wavelength, a condition needed for the existence of SPPs23. For the MXenes considered here, design wavelengths should be above ~1.27 µm, ~1.18 µm, and ~1.14 µm as these correspond to the plasma wavelengths for this MXene with a thickness of a = 14 nm, a = 27 nm and a = 75 nm, respectively (see Supplementary Materials Section 1 for the complex relative permittivity of the MXenes). From the results shown in Fig. 1b, c, one can observe how both the real part and imaginary components of nSPP increase when reducing the thickness of the films. For instance, at the telecom wavelength of λ0 = 1.55 µm, Re{nSPP} is ~1.47, ~1.60, and ~2.71 for a = 75 nm, a = 27 nm and a = 14 nm, respectively while Im{nSPP} is ~0.09, ~0.91, and ~4.14 for the same values of a, respectively. In this context, it will be expected that SPPs will exist for the a = 75 nm MXene while they will not be strongly bounded to the interfaces for a = 27 nm and a = 14 nm within the frequency range under study due to the large losses represented by Im{nSPP}.
To further evaluate the response of the I-MXene-I configurations for SPPs, we carried out numerical simulations using the commercial software COMSOL Multiphysics®. Here, a 3D model was considered with SPPs in the I-MXene-I from Fig. 1a being excited via a narrow slit placed at the left-hand-side of the structure and propagating along the z-axis25, 27, 28. With this setup, a snapshot of the electric field and out plane (Hx) magnetic field for the three thicknesses of the MXenes (a = 75 nm, a = 27 nm, and a = 14 nm) at the telecom wavelength of λ0 = 1.55 µm are shown in Fig. 1d, e, respectively. As observed, the SPPs are not completely clear for a = 27 nm and a = 14 nm. This is in agreement with the discussion above and with Fig. 1c where Im{nSPP} is very large at the telecom wavelength of 1.55 µm. However, note how the SPPs propagate in the I-MXene-I when using a = 75 nm (Fig. 1d). For the sake of completeness, the Hx field distribution on the top surface (y = 0) of the MXenes (Air-MXene interface) was extracted from Fig. 1d–f and the numerical results are shown in Fig. 1g, demonstrating how SPPs propagate along the z axis with less losses when a = 75 nm, in good agreement with the analytical calculations from Fig. 1b, c.
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To fully analyse the I-MXene-I structure shown in Fig. 1a for SPP propagation, here we study the case when the top semi-infinite material is different than air. This configuration is of importance to achieve a full manipulation of SPPs given that the nSPP can be tuned depending on the materials present in the system (as shown in Eqs. (1, 2)). This performance is known in the scientific community and has been exploited in the past in applications such as SPP-based waveguiding, sensing, focusing, and steering of SPPs23, 27, 29-32. In this context, let us focus on the MXene with a = 75 nm (results for values of a = 27 nm and a = 14 nm are provided in the Supplementary materials document). The bottom semi-infinite region is again SiO2 as in Fig. 1 while two different values are considered for the top medium (n2 = 1.25 and n2 = 1.55).
With this setup, the analytical calculations of the real and imaginary components of the effective nSPP are shown in Fig. 2a, b, respectively, considering n2 = 1.25 (black curve) and n2 = 1.55 (red curve). From these results it is clear how the effective nSPP can be tuned by simply modifying the material on top of the MXenes. Moreover, note how the values of Im{nSPP} are increased when increasing n2, as expected. However, Im{nSPP} remain small compared to the cases shown in Fig. 1c for thinner MXenes (see also Supplementary materials for the effective nSPP values considering MXenes with a = 27 nm and a = 14 nm with varying n2). For the sake of completeness, the numerical results of the Hx along the z axis at x = y = 0 are for both values of n2 are shown in Fig. 2c along with the electric field and Hx field distributions on the yz planes in Fig. 2d, e, respectively, considering n2 = 1.25 (top panels) and n2 = 1.55 (bottom panels). From these results, it can be seen how SPPs are excited in the I-MXene-I configuration, demonstrating its potential for SPP-based applications at telecom wavelengths.
Fig. 2 Effect of changing the top dielectric in an I-MXene-I configuration.
a, b analytical results of the real and imaginary components of nSPP, respectively, considering a MXene thin film with a = 75 nm sandwiched in between of a semi-infinite SiO2 medium (bottom medium) and a dielectric medium with varying n2 (top medium), see inset on the left for the schematic representation. c Hx field distribution along the propagation z axis at y = x = 0 (I-MXene interface) considering an MXene with thickness a = 75 nm and different materials for the top semi-infinite medium: n2 = 1.25 (black) and n2 = 1.55 (red). d, e numerical results of the electric field and Hx field distributions on the yz planes, respectively, considering different materials for the top dielectric: n2 = 1.25 (top) and n2 = 1.55 (bottom) -
In the previous sections we have discussed how MXenes hold potential to support SPP propagation at telecommunication wavelengths. As SPPs can be implemented in a wide range of applications, we envision that SPP-based technologies can be revolutionized by translating well-known applications in the optical range and potentially implement them at longer wavelengths, particularly at telecom wavelengths such as those studied in this work. In this section, we demonstrate the case of a SPP-based sensor using MXenes placed on top of an optical fiber as an example of the potential of such 2D materials for SPP-based technologies. Note that, as described in the previous sections, to excite SPPs in I-MXene-I configurations, the design wavelength should be larger than the plasma wavelength of the MXenes, hence, it would be possible to design SPP-based devices at longer wavelengths. However, as our aim is to exploit MXenes together with standard telecommunications optical fibers, the spectral range is then selected to be the same as the one used in Figs. 1 and 2 (1.4–1.65 µm) as it corresponds to the low attenuation C-band spectral range (a fundamental band for telecommunication technologies).
To begin with, the schematic representation of the structure under study is shown in Fig. 3a. Here we consider a single mode optical fiber consisting of a core with diameter dcore = 8 µm (made of SiO2 slightly doped with Germanium, Ge) having a refractive index of ncore = 1.445. The cladding is made of SiO2, ncladd = 1.44. To ease the calculations, and without loss of generality, we consider the MXene to be the only dispersive media in the system. As in the previous section, here we focus our work on thin MXene films with height a = 75 nm having a length along the x axis of LMX = 60 µm. (see Fig. 3a). Finally, the cladding on top of the core of the fiber is cut at a distance d from the core and the MXene is placed on top (see top inset of Fig. 3a for a schematic representation). For completeness, we provide a side view of the optical fiber sensor using MXenes on the right inset from Fig. 3a. To analytically calculate the effective refractive index of the SPP mode excited in the system shown in Fig. 3a, we can consider that such mode will be mainly bounded in the region n2-MXene-cladding. Based on this, the structure from Fig. 3a can be approximated to be equivalent to the I-MXene-I configuration discussed in Fig. 1a (and Eqs. (1 and 2)), reproduced in Fig. 3b.
Fig. 3 SPP-based telecom sensor: optical fiber loaded with a MXene thin film.
a schematic representation of a single mode optical fiber loaded with a thin MXene film with height a = 75 nm (front and side views). The SiO2-Ge core has a diameter of dcore = 8 µm. b Sketch of the equivalent structure considered for the analytical calculations. c–e numerical results of the real part of the effective SPP mode, nSPP (red circles) and y polarized core mode, neff (green line) along with the analytical results of the Re{nSPP} of an I-MXene-I structure (blue line). f–h Numerical and analytical results of the values for the imaginary component of the effective refractive index for the same modes as in (c–e). i Numerical results of the reflection coefficient for a 3D optical fiber sensor using loaded MXene as in (a) considering a top dielectric with n2 = 1.17 (blue line), n2 = 1.23 (green line) and n2 = 1.28 (black line). The spectral location of the minimum reflection are presented as black dotted lines. j Theoretical and numerical results of the spectral location of the resonances (minimum reflection coefficient) considering values of n2 ranging from 1.12 to 1.29With this configuration, the structure from Fig. 3a was numerically evaluated using the modal analysis from COMSOL Multiphysics® considering that the MXene is placed at a distance d = 2 µm from the core. Finally, the structure was numerically simulated and the real and imaginary components of the effective nSPP were recorded for a total of 100 modes in the spectral range from 1.45 to 1.65 µm. The numerical results of the Re{nSPP}and Im{nSPP} for the SPP mode along with the effective refractive index for the y-polarized core mode (neff) are shown in Fig. 3c, f, respectively, considering that the dielectric material on top of the MXene is air (n2 = 1). As observed, Re{nSPP} is different from the values of neff for the y-polarized core mode within the spectral range under study, meaning that there is no coupling between these two modes. Moreover, note that the analytical results calculated using the structure shown in Fig. 3b and defined by Eqs. (1 and 2) are also plotted as blue lines in Fig. 3c, f, demonstrating an excellent matching between them.
Now, what would happen if the top material is modified as in the I-MXene-I configuration studied in the previous section? This is an important question if one wants to exploit the structure from Fig. 3a as a sensor. To evaluate this case, the same process as in Fig. 3c, f was repeated using numerical simulations but now for values of n2 = 1.15 and n2 = 1.25. The numerical calculations for the Re{nSPP} along with the values of neff for the core mode are shown in Fig. 3d, e for both values of n2, respectively. The results for the imaginary components are also presented in Fig. 3g, h for completeness. As in Fig. 3c, f, the analytical values for the Re{nSPP} and Im{nSPP} were also calculated using Eqs. (1 and 2) and the results are also shown in Fig. 3d, e and Fig. 3g, h, respectively. Note that an excellent agreement is again obtained demonstrating how the analytical formulation can be accurately used to design the structure shown in Fig. 3a. By comparing the results from Fig. 3c–e, it can be seen how the Re{nSPP} is shifted towards longer wavelengths when increasing n2. Additionally, note that for n2 = 1.25, Re{nSPP} approaches to the effective refractive index of the y-polarized core mode (neff) i.e., coupling between the two modes will exist, showing the potential for sensing applications.
To better compare the results shown in Fig. 3c–h, the numerical results of the magnitude of the electric field on the xy plane for the SPP mode calculated at λ0 = 1.55 µm using a top dielectric of n2 = 1.25 are shown in Fig. 4a along with the magnitude of the electric field along the y axis (at x = 0). As observed, the SPP mode is mainly bounded in the region n2-MXene-cladding, corroborating the assumption used for the analytical calculations, as schematically shown in Fig. 3b. Regarding the core mode, the distribution of the magnitude of the electric field for the x and y polarized modes are shown in Fig. 4b, c along with the values along the y axis (at x = 0). As observed, no coupling with the MXene is obtained for the x polarized core mode, given that the electric field is parallel to the thin films, meaning that this polarization will not be feasible for a sensing device. However, coupling is obtained for the y-polarized mode, as described before. For the sake of completeness, the numerical results of the magnitude of the electric field on the xy plane and along the y axis at x = 0 for the case with a reduced d = 0.2 µm are shown in Fig. 4d–f, demonstrating how the coupling of SPPs to the MXene is increased, as expected.
Fig. 4 Field distributions for the SPP-fiber sensor using MXenes.
a–c Numerical results of the magnitude of the electric field on the xy plane for the SPP, x and y polarized core modes, respectively, considering an optical fiber as in Fig. 3a when the MXene with height a = 75 µm is placed at a distance d = 2 µm from the core. The bottom panels show the electric field distribution along the y axis at x = 0. The top dielectric has a refractive index of n2 = 1.25. d–f, Same configuration as in (a–c) but with a distance d = 0.2 µmTo further study the potential of MXenes for SPP-based sensing, the optical fiber from Figs. 3 and 4 was studied as a full 3D structure using the transient solver of the commercial software CST Studio Suite®, see details in the methods section. Three different materials for the top semi-infinite dielectric are considered n2 = 1.17, n2 = 1.23 and n2 = 1.28 while the rest of the parameters are the same as those from Figs. 3 and 4. The reflection coefficient was recorded for the mode shown in Fig. 4c at λ0 = 1.55 µm. In this context, the excitation of the SPP mode can be mapped by considering the spectral regions with small values of reflection. i.e., the y polarized core mode is coupled into the SPP mode. (note that the x polarized core mode is not used in this case as it will not couple to the MXene and hence coupling with the SPP mode will be negligible). The numerical results of the reflection coefficient within the spectral range under study for telecom sensing are shown in Fig. 3i. As it can be observed, a deep of reflection is achieved at λ0_sim = 1.463 µm, 1.503 µm and 1.567 µm when n2 1.17, n2 = 1.23 and n2 = 1.28, respectively. Note that this shifting towards longer wavelengths for larger n2 is in agreement with the discussion provided in Fig. 3c–h where the coupling of the y polarized core mode with the SPP mode was also red shifted.
For completeness, we carried out analytical calculations as in Fig. 3c–h considering top dielectrics with refractive index ranging from 1.12 to 1.29. The wavelength at which the effective refractive index of the y-polarized matches the SPP mode was recorded (Re{nSPP} = neff) and the results are shown as solid black line in Fig. 3j. Moreover, the numerical results of λ0_sim (deep of reflection coefficient) for different materials for the top of the MXene are shown as green squares in the same panel. From these results, one can corroborate how the spectral response is red shifted, as described before, with good agreement between the numerical and analytical values, demonstrating the potential of MXenes for SPP-based sensing at telecom wavelengths. These proof-of-concept simulations demonstrate the potential for MXene based optical fiber surface plasmon resonator devices. However, it should be noted that the large array of 'tunable' MXenes provide an enormous degree of freedom for device design. Our simplified effective index approach will provide a simple route to exploring this vast parameter space.
The proposed MXene-based structures for SPP-based devices at telecom wavelengths could be fabricated by the Langmuir-Blodgett (LB) technique. In this technique nanosheets can be suspended on a liquid subphase while a thinned fiber surface is passed through the liquid-air interface depositing as well-tiled monolayer. LB has been demonstrated experimentally for Ti3C2Tx recently by pH controlled water to prevent loss to the subphase33. Another study, instead, used a liquid-liquid interface with chloroform on a water subphase to drive monolayer formation34. Multiple LB layers can then be deposited sequentially to create MXene adlayers with the desired thickness.