Near-Infrared Spatial Self-Phase Modulation in Ultrathin Niobium Carbide Nanosheets

Spatial self-phase modulation (SSPM) as a purely coherent non-linear optical effect (also known as Kerr effect) can support strong broadband phase modulation, which is essential for all-optical applications. Besides this, the increasing use of two-dimensional (2D) materials opens up new prospects in this field of research. In this work, we report a broadband SSPM response from 2D transition metal carbonitrides (MXenes) and Nb2C, arising in the near-infrared (1,550 nm) range. Based on the SSPM measurements of few-layer Nb2C nanosheets, the third-order non-linear optical parameters of Nb2C, including the non-linear refractive index n2 and susceptibility χ(3), were determined at 400, 800, 1,300, and 1,550 nm. Moreover, the physics mechanism of the dynamic formation process of SSPM diffraction rings was exploited. The formation time of SSPM diffraction rings can be divided into two typical parts which correspond to the polarization and reorientation of 2D Nb2C nanosheets. As a proof of concept, we demonstrate the nonreciprocal light propagation at wavelengths of 1,300 and 1,550 nm by constructing an Nb2C/water hybrid structure. Our results reveal strong optical phase modulation of Nb2C in the infrared region, thus showing the great potential of MXene materials for use in passive photonic devices.

Intrinsically, 2D materials are attracting increasing attention due to their unique optical modulation in a visible region; however, experimental evidence of the infrared light response of the SSPM in 2D materials has been rarely reported so far [31]. In particular, the SSPM patterns of black phosphorus were successfully acquired by our group at a wavelength of 1,160 nm [32]. Very recently, the use of SSPM technique allowed one to measure the third-order non-linear susceptibility of Ti 3 C 2 T x MXene within a visible-to-near-infrared (Vis-NIR) range (400-1,064 nm) [33]. The near-infrared region, especially presented by the optical communication band, is essential for all-optical modulation applications of the SSPM as it ensures the low-loss characteristics of the optical fiber communications.
Belonging to a class of two-dimensional (2D) inorganic compounds such as transition-metal carbides, nitrides, and carbonitrides, MXenes share a general formula of M n+1 X n (n = 1-3), where M is an early transition metal (e.g., Ti, Zr, V, Nb, Ta, and Mo), and X is a C or N. As a new member of the MXene family, Nb 2 C has attracted great attention due to its excellent performance in the fields of energy storage [34], electrochemical catalytic [35], and biomedicine [36]. Being semimetals with fascinating electrical properties, few-layer Nb 2 C nanosheets exhibit a narrow optical bandgap which favors the infrared optical response. Moreover, their superior photothermal conversion efficiency in the infrared region has even been proven in photothermal cancer therapy [36].
In this work, we investigate the near-infrared SSPM response of few-layer Nb 2 C nanosheets and expand SSPM response of 2D material to the communication band which cover 1,550 nm wavelength. The third-order non-linear susceptibility and the non-linear refractive index of Nb 2 C were measured within a broadband range from 400 to 1,550 nm. Moreover, to understand the physics mechanism behind this, we exploited the dynamic formation process of SSPM diffraction rings. Based on the time of the rings formation, the dynamic formation process of SSPM diffraction rings can be divided into two typical time stages which correspond to the polarization and reorientation of 2D Nb 2 C nanosheets. Further, we demonstrate the proof-of-concept Nb 2 C non-reciprocal light propagation. During the exploitation of a passive photonic device, water was used instead of reverse saturable absorption materials [17,27] to construct a Nb 2 C/water asymmetric hybrid structure. This enabled us to achieve the non-reciprocal light propagation in the near-infrared region by a facile way.

Synthesis of Nb 2 C Nanosheets
The Nb 2 AlC was purchased from 11 Technology Company Limited, the size of which is about 400 mesh. Ten grams of the bulk Nb 2 AlC powder was added into 80 ml of a 40% HF solution (Macklin Incorporation). The suspension was then vigorously stirred for 48 h at 25 • C. After that, the HF solution was removed and the multilayer Nb 2 C was washed with water by centrifugation until the pH of water was about 5. The tetrapropylammonium hydroxide (TPAOH) was then poured into Nb 2 C and stirred for 72 h. Finally, the selected few-layer Nb 2 C nanosheets were collected by centrifugation.

SSPM Measurements
The experimental setup is shown in Figure 2A. The light source is a mode-locked Ti:sapphire regenerative amplifier system (Spectra-Physics, Spitfire ACE-35F-2KXP, Maitai SP, and Empower 30). Femtosecond laser pulse has a very short action time with materials, which cause a small thermal effect compared with continuous laser and long pulse laser (ns, ms). The transmitted light was captured by a charge coupled device (CCD) detector (LBP2-VIS2 was applied at wavelengths of 400, 800, and 1,300 nm; and LBP2-HR-IR2 at 1,550 nm).

Sample Characterization
The scanning electron microscope (SEM) images were captured by field-emission Magellan 400 microscope (FEI Company). The transmission electron microscopy (TEM), high-angle annular dark field (HAADF), and energy dispersive X-ray spectroscopy (EDS) data were acquired on a JEM-3,100 (FEI Talos S-FEG) transmission electron microscope. The X-ray diffraction (XRD) patterns were recorded using a BRUKER D8 ADVANCE XRD system. The Ultraviolet-Visible-Near Infrared Rage (UV-Vis-NIR) absorption spectra from 200 to 1,600 nm of Nb 2 C were measured by a UV-vis spectrophotometer (Cary60, Agilent). Atomic Force Microscope (AFM) image was captured by CSPM 5,500.

RESULTS AND DISCUSSION
A typical two-step exfoliation strategy was employed to obtain Nb 2 C nanosheets (see Experimental section). Briefly, the Nb 2 AlC MAX phase was etched in hydrofluoric (HF) acid solution to remove the Al atoms. Ultrasound-assisted TPAOH co-intercalated exfoliation was effective to reduce the lateral size and the thickness of the obtained Nb 2 C nanosheet [12]. Figure 1A shows the SEM images of Nb 2 AlC powder. Before the HF etching, the MAX-phase Nb 2 AlC had the particle size of several or tens of micrometers along with a high interlayer bond strength. Inset in panel A is the zoom-in images of the single Nb 2 AlC particle which exhibits dense cross section. After the removal of Al atoms from the Nb 2 AlC, the multi-layer Nb 2 C was formed like an accordion pulled open, as shown in Figure 1B. As can be seen in Figure 1C, the AFM measurement of present few-layer Nb 2 C was performed to characterize its thickness of about 3-4 nm. Figure 1d1 depicts the TEM images of Nb 2 C nanosheets, revealing their transparent morphology and ultrathin structure. As shown in Figures 1d2-d4, HAADF and EDS mapping results of Nb 2 C nanosheets with clear boundaries confirm the coexistence of Nb and C elements, which provides evidence for the elemental composition of as-prepared 2D Nb 2 C nanosheets. Figure 1E displays the XRD patterns of samples. Two sharp peaks θ = 12.8 and 38.8 • are observed in the case of Nb 2 AlC, which is in good agreement with JCDS PDF#30-0033 for Nb 2 AlC. The disappearance of the peak at θ = 38.8 • indicates that the Al atoms have been successfully removed after etching in HF solution. The downshift of the peak at θ = 12.8 • and its broadening mean that MAX is converted into MXene. Figure 1F shows the UV-Vis-NIR absorption spectra of Nb 2 C (To note, the gap may attribute to be an error from instruments.) The abruptly enhanced near-IR absorption suggests a strong light-matter interaction within the near-infrared range.
The SSPM measurements of Nb 2 C nanosheets were carried out at four different wavelengths including the light communication band at 1,550 nm (Figure 2). The solvent we use is N-methyl pyrrolidone (NMP) which possessed low volatility, good thermal, and chemical stability. To exclude the influence of solvents to the formation of diffraction rings, the control group was set in which only the NMP solvent was contained for SSPM experiments. There are no diffraction rings for NMP at 400, 800, 1,300, and 1,550 nm. Figure 2A shows the experimental configuration used in the SSPM measurements. The typical SSPM diffraction patterns at different laser excitation wavelengths (from 400 to 1,550 nm) were captured by a CCD detector, as shown in Figures 2B-E. The distinguishable diffraction rings are observed at a wavelength of 1,550 nm, which indicates its potential versatility for optoelectronic applications within a range of a near-infrared telecom C band.
The quantitative information about the non-linear optical response of Nb 2 C is available from the third-order nonlinear optical parameters that can be evaluated by fitting the experimental results in the context of the non-linear optical theory. The number of rings N is plotted in Figure 2F as a function of incident intensity I, and the linear relationship between both parameters is evident. According to the Kerr law, the refractive index of Nb 2 C can be obtained as follows [1]: where n 0 = 1.47 (NMP) and n 2 are the linear and nonlinear refractive indexes, respectively, and I represents the laser beam intensity. When the laser beam passes through the Nb 2 C suspension, the phase shift ( Ψ ) can be expressed as follows [1]: where λ is the wavelength, L eff is the effective optical thickness, rǫ[0,∞) is the radial coordinate, and I(r, z) represent the radial intensity distribution of a focused laser beam. The total number of rings N is determined by the formula Ψ (0)-Ψ (∞) = 2Nπ [1]. As for the Gaussian beam, the intensity at the center of the beam (I 0 ) is twice the average intensity I, which can be found experimentally. Then the effective thickness of the cuvette L eff can be calculated from the following formula [1]: where L 1 and L 2 are the distances from the focal point to the back and front surfaces of the quartz cuvette respectively, and L = L 2 -L 1 is the thickness of the quartz cuvette. In our experiment, the focal length of the lens is f = 20 cm, L = 1 cm, and ω 0 is the waist radius of the laser beam. Therefore, the non-linear index n 2 can be defined as follows [37]: To gain insight into the intrinsic non-linear optical property of Nb 2 C nanosheets, the third-order non-linear susceptibility χ (3) total can be described by the equation below [37]: Then, χ monolayer of Nb 2 C can be obtained as follows [37]: The number of layers A eff can be found as [28], where ρ = 0.00286 mol/L is the Nb 2 C concentration, and V = 4 × 10 −3 L. The number of molecules in a single layer m = 1 × 4 cm 2 /(sin60 • ) × (6.302) 2 Å 2 = 1.83 × 10 16 . Hence the number of layers is A eff = 374. The experimentally measured non-linear optical parameters of different 2D materials are summarized in Table 1. The superior non-linear refractive response of Nb 2 C at 1,550 nm is a unique and attractive result. The intrinsic third-order non-linear optical susceptibility of an effective single layer reaches a value of 5.14 × 10 −9 e.s.u. at 1,300 nm and 3.73 × 10 −9 e.s.u. at 1,550 nm. As can be seen in Table 1, Nb 2 C possesses relatively high values of non-linear parameters within the near-infrared range. Using femtosecond laser pulses allows one to greatly suppress the thermal effects that may arise during the formation of the diffraction ring patterns due to spatial self-phase modulation [38,39]. Non-local electronic coherence is a common mechanism to explain spatial self-phase modulation, which is also known as wind-chime model. However, since the optical bandgap of fewlayer Nb 2 C nanosheets is found to be 0.81 eV [12], the singlephoton energy at 1,550 nm is not high enough to excite electronic transitions. The parallel-band absorption effects [40] induced two-photon absorption has been discovered in present metallic Nb 2 C nanosheets. Therefore, the two-photon SSPM is the most likely mechanism responsible for the emergence of the below-gap SSPM [28]. When the two-photon absorption establishes a new electric field polarization, the excited carriers will diffract with photons not only above but also below the bandgap [28].
After exploring the formation mechanism of the diffraction ring patterns within the near-infrared wavelength range, we were focused on the investigation of the dynamic formation process of Nb 2 C. Figures 3A-D depict the SSPM diffraction patterns acquired using a high-speed CCD detector at different time points and a laser excitation wavelength of 1,300 nm. First, the incidence of the laser beam on a sample leads to its self-focusing ( Figure 3A). Then the SSPM-induced diffraction rings appear ( Figure 3B). Their number increases rapidly until it becomes maximum. Finally, there is the downward collapse of the upper part of the pattern, forming a perpendicular (asymmetric) stable pattern. Maintaining the same beam incidence conditions, we also obtained the number of rings as a function of the dynamic formation time in Figures 3E-H. The time required for the diffraction ring formation is found to be almost independent of the incident beam wavelength. A schematic illustration of the time of the rings formation is shown in Figure 4. The first part is the polarization process (t 0 -t 1 in Figure 4) in which the electrons and holes of the nanosheets move in opposite directions when the laser passes through the sample, causing the nanosheets to be polarized [37]. Such a polarization process can be attributed to the nonlocal electron coherence when there is an interaction between 2D nanosheets and light-induced electromagnetic field. The second part is the reorientation process (t 1 -t 2 in Figure 4) in which the polarized fragments are rearranged under the force of an electric field. During the reorientation process, non-local electron coherence among the 2D nanosheets will be formed gradually. Such a non-local electron coherence-induced formation of typical SSPM diffraction rings have been observed in MoS 2 system previously [28]. In terms of the response time, the excited carriers generation and 2D nanosheets polarization will appear in the first part which corresponds to a timescale of about a picosecond or even a femtosecond. Considering the second part, there is typical interaction between polarized 2D nanosheets and Newton fluid with constant viscosity coefficient under the laser incidence. This process is a relatively slow one (about millisecond) and will be influenced by many parameters including viscosity coefficient of solvent, size of the 2D nanosheets, and incident laser power [28].
Taking into account the advantage of the SSPM response of Nb 2 C, non-reciprocal light propagation was designed as a proof-of-concept nanophotonic device. To construct asymmetric composite film system with non-reciprocal light transmission property, the composite films always contain a saturable absorption layer and a reverse saturable absorption material layer [41]. In the Kerr non-linearity-based, non-reciprocal light transmission work, the energy absorption of the incident light is the most important function of the reverse saturable absorption material layer [27]. We use the water to replace these reverse saturable absorption materials to construct an asymmetric composite film system. As we know, water has the advantages of stable physical and chemical properties and is environmentally friendly. Furthermore, water is low-cost and can be procured everywhere. When the laser beam passes forward (Nb 2 C/water), the SSPM diffraction rings will be excited due to a strong SSPM response of Nb 2 C caused by the Kerr effect. In other words, its large non-linear refractive index modulates the phase of the laser beam. Thereafter, water just reduces the intensity of the laser but makes no difference to the number of rings. Figures 5A-D display the SSPM patterns collected at the backward movement of the laser beam through the Nb 2 C/water hybrid structure at different beam intensities and a wavelength of 1,300 nm. However, when the laser passes backward, water reduces the incident light intensity that is small enough not to excite diffraction rings in the Nb 2 C layer due to its strong absorption in the near-infrared range. Figures 5E,F summarize the results of non-reciprocal light propagation for a Nb 2 C/water hybrid structure at wavelengths of 1,300 and 1,550 nm, where it easily observes the unidirectional excitation of the diffraction rings. This discovery not only enabled one to find a new medium for the non-reciprocal light propagation implementation, but also to broaden the insight into the non-linear optical devices operating within the near-infrared range (especially at 1,550 nm).

CONCLUSION
In summary, few-layer Nb 2 C nanosheets have been synthesized and their non-linear optical characteristics were measured via the SSPM technique within a near-infrared broadband range. The few-layer Nb 2 C nanosheets were shown to exhibit excellent nonlinear optical response and their non-linear refractive index was as high as 9.53 × 10-6 cm 2 /W at 1,550 nm. Moreover, in order to understand the physics mechanism behind it, dynamic formation process of SSPM diffraction rings was exploited. Based on the FIGURE 4 | Schematic illustration of the time required for the diffraction ring formation. The time can be divided into two parts. The t 0 indicates the laser start to incident on the medium. The polarization of 2D nanosheets finished in t 0 -t 1 region. The reorientation of 2D Nb 2 C occurs in t 1 -t 2 time zone. t 0 -t 2 time zone represents the time of the diffraction ring formation. t 2 diffraction rings become maximum. time of the rings formation, the dynamic formation process of SSPM diffraction rings can be divided into two typical time parts which correspond to the polarization and reorientation of 2D Nb 2 C nanosheets. Finally, the non-reciprocal light propagation was implemented through a Nb 2 C/water hybrid structure, giving a strong boost to research in the field of non-linear nanophotonic applications.

DATA AVAILABILITY STATEMENT
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.