Large and negative self-defocusing optical Kerr nonlinearity in Palladium di-Selenide 2D lms

We report a large third-order nonlinear optical response of palladium diselenide (PdSe 2 ) lms – a two-dimensional (2D) noble metal dichalcogenide material. Both open-aperture (OA) and closed-aperture (CA) Z-scan measurements are performed with a femtosecond pulsed laser at 800 nm to investigate the nonlinear absorption and nonlinear refraction, respectively. In the OA experiment, we observe optical limiting behaviour originating from large two photo absorption (TPA) in the PdSe 2 lm of β = 3.26 ×10 − 8 m/W. In the CA experiment, we measure a peak-valley response corresponding to a large and negative Kerr nonlinearity of n 2 = -1.33×10 − 15 m 2 /W – two orders of magnitude larger than bulk silicon. We also characterize the variation of n 2 as a function of laser intensity, observing that n 2 decreases in magnitude with incident laser intensity, becoming saturated at n 2 = -9.96×10 − 16 m 2 /W at high intensities. These results verify the large third-order nonlinear optical response of 2D PdSe 2 as well as its strong potential for high performance nonlinear photonic devices.

Palladium diselenide (PdSe 2 ), a new 2D noble metal dichalcogenide in the TMDC family, has recently attracted signi cant interest [27][28][29][30][31]. Similar to the puckered structure of BP, it has a puckered pentagonal atomic structure − with one Pd atom bonding to four Se atoms and two adjacent Se atoms covalently bonding with each other. This low-symmetry structure makes PdSe 2 possess unique in-plane anisotropic optical and electronic properties [27,29], featuring an in-plane noncentrosymmetric structure, in contrast to its cousin PtSe 2 . Further, the bandgap of PdSe 2 is layer-dependent, varying from 0 eV (bulk) to 1.3 eV (monolayer) -a property well suited for photonic and optoelectronic applications -in particular, for wavelength tuneable devices [27,29,31]. Moreover, PdSe 2 is highly air-stable, indicating its robustness and potential for practical applications as compared with BP. The high carrier mobility and anisotropic Raman spectroscopy of 2D PdSe 2 layers have been investigated [27,30] as well as highly-sensitive photodetectors from the visible to mid-infrared wavelengths [31,32]. Recently, the optical nonlinear absorption of PdSe 2 nanosheets has also been reported in the context of mode-locked laser applications [33][34][35]. To date, however, its optical Kerr nonlinearity has not been investigated.
Here, we report measurements of the third-order nonlinear optical response of 2D PdSe 2 lms.
Experimental results using the Z-scan technique with femtosecond optical pulses at 800 nm show that PdSe 2 lms exhibit a large and negative (self-defocusing) Kerr nonlinearity (n 2 ) of ∼ -1.33×10 -15 m 2 /W, which is two orders of magnitude larger than bulk silicon. Further, we measure a large nonlinear absorption β of ~ 3.26 ×10 -8 m/W, which originates from TPA in the PdSe 2 lms. In addition, we investigate the intensity dependence of the nonlinear response of PdSe 2 , nding that the absolute magnitude of the Kerr nonlinearity n 2 initially decreases slightly with incident laser intensity, becoming saturated at higher intensities. Our results show that the extraordinary third-order nonlinear optical properties of PdSe 2 have strong potential for high-performance nonlinear photonic devices. interactions to form a layered structure [27,36,37]. In each monolayer, the pentagonal rings are formed with one Pd atom bonding to four Se atoms and two adjacent Se atoms covalently bonding with each other, which is similar to the puckered structure of BP, and yields both anisotropic and noncentrosymmetric properties of PdSe 2 [27,37]. More importantly, unlike the rapid degradation of BP under ambient conditions, PdSe 2 has signi cantly better air-stability [29][30][31]. Together, these properties of PdSe 2 make it promising for high performance photonic and optoelectronic applications.

Material Preparation And Characterization
Here, we investigated large-area multilayer PdSe 2 lms deposited on transparent sapphire substrates. The PdSe 2 lms were synthesized via Chemical vapor deposition (CVD) [30,38]. A three-zone tube furnace was used to grow the PdSe 2 lms with palladium chloride (PdCl 2 ) and selenium (Se) as precursors. Se and PdCl 2 powders were placed at Zone 1 with a heating temperature of 250 °C and Zone 2 heated up to 500 °C, respectively. The evaporated Se and Pd precursors were then transported by the carrier gas of Ar/H 2 to Zone 3 at a high temperature of 600 °C, in which the continuous PdSe 2 lms were synthesized on an atomically at sapphire substrate. The lms were polycrystalline, as is typical for CVD synthesized lms, with crystal sizes varying from 10's of nanometres up to 100 nm. Because of the polycrystalline nature of the lms, the inversion symmetry breaking properties (i.e., non-centrosymmetric) of the single PdSe 2 crystals could not be observed on optical wavelength scales in the macroscopic PdSe 2 continuous lms studied in this work. Figure 1(b) shows a photograph of the prepared sample, indicating a high uniformity over the whole substrate. The morphology image and height pro le of the prepared PdSe 2 lms were characterized by atomic force microscopy (AFM), as illustrated in Fig. 1(c). The lm thickness was measured to be ~ 8 nm, which corresponds to ~20 layers of PdSe 2 [27,30,36]. vibrational modes that correspond to the movement of Se atoms and the A g 3 (~ 258.8 cm −1 ) mode that relates to the relative movements between Pd and Se atoms [27,30,32]. To further characterize the lm quality, X-ray photoelectron spectroscopy (XPS) was employed to measure the binding energy of PdSe 2 . Figure 2 (b) shows the XPS results of Pd 3d and Se 3d core levels for the PdSe 2 . The peaks of the t at 3 42.2 eV and ~ 336.9 eV are attributed to the Pd 3d 3/2 and Pd 3d 5/2 , respectively, whereas the peaks at 5 5.7 eV and ~ 54.9 eV correspond to Se 3d 3/2 and 3d 5/2 , respectively. These results are consistent with previous reports [30,32] and demonstrate the high quality of our prepared PdSe 2 lms.
To characterize the linear absorption and optical bandgap, the optical absorption spectrum (from 400 nm to 2500 nm) of the PdSe 2 lm was measured with ultraviolet-visible (UV-vis) spectrometry, as shown in  [29,32].
We also characterize the in-plane (TE-polarized) refractive index (n) and extinction coe cient (k) of the PdSe 2 lm via spectral ellipsometry, as depicted in Fig. 2(d). For the thin PdSe 2 lm with a thickness of 8 nm, the out-of-plane (TM-polarized) response is much weaker. Thus, using spectral ellipsometry we could only measure the in-plane n and k of the PdSe 2 lm. It can be seen that the refractive index rst increases dramatically with wavelength to reach a peak at ~ 700 nm and then decreases more gradually at longer wavelengths. This trend is similar to that of PtSe 2 -another noble metal dichalcogenide of the TMDC family [40]. The extinction coe cient exhibits a signi cant decrease from 600 nm to 1200 nm, and then the rate of decrease slows down at longer wavelengths. This shows an agreement with the trend of the UV-vis absorption spectrum in Fig. 2 (c) and further con rms the validity of our ellipsometry measurement. These measurements indicate that the lms had a bandgap of about 0.7 eV, residing just below the telecommunications wavelength band.

Experimental setup
To investigate the third-order nonlinear optical properties of PdSe 2 , we characterized the nonlinear absorption and refraction of the prepared PdSe 2 lm via the Z-scan technique [14,41,42] (Fig. 3), where a femtosecond pulsed laser with a centre wavelength at ~800 nm and pulse duration of ~ 140 fs was used to excite the samples. A half-wave plate combined with a linear polarizer was employed to control the power of the incident light. A beam expansion system consisting of a 25-mm concave lens and 150-mm convex lens was used to expand the light beam, which was then focused by an objective lens (10 ×, 0.25 NA) to achieve a low beam waist with a focal spot size of ~1.6 µm. The prepared samples were oriented perpendicular to the beam axis and translated along the Z-axis with a linear motorized stage. A highde nition charge-coupled-device (CCD) imaging system was used to align the light beam to the target sample. Two photodetectors (PDs) were employed to detect the transmitted light power for the signal and reference arms.
The Z-scan measurements were performed in two stages [14,41] including an open-aperture (OA) and a closed aperture (CA) measurement. The OA measurement was used to characterize the nonlinear absorption of PdSe 2 lms where all light transmitted through the sample was collected by a PD. To extract the TPA (β) of PdSe 2 , we t the measured OA results in Fig. 4(a) with [41,43]: where T CA (z, ΔΦ 0 ) is the normalized optical transmittance of the CA measurement and ΔΦ 0 = 2πn 2 I 0 L eff / λ is the nonlinear phase shift, with λ denoting the center wavelength of the femtosecond laser. Therefore, the Kerr nonlinearity of the PdSe 2 lm could be extracted from the ratio of the CA result to the OA result in the usual manner [14,41,42].

Results and discussion
We measured the OA curves at different incident laser intensities ranging from 12.08 GW/cm 2 to 21.32 GW/cm 2 . Figure 4(a) shows the OA Z-scan results for the PdSe 2 lm at three representative intensities. A typical optical limiting behaviour was observed in the OA curves, with the transmission decreasing as the PdSe 2 sample was moved through the focal point. We also note that the transmittance dip of the OA curve decreased when the incident laser intensity was increased. Various mechanisms, including nonlinear scattering, reverse saturable absorption (RSA) and two-photon absorption (TPA), may contribute to the observed optical limiting behaviour. The nonlinear scattering mechanism is rst excluded since it usually depends on the laser induced microbubble formation for dispersion or solution samples [44,45]. Usually, RSA is the dominant mechanism for nonlinear absorption under resonant or near resonant excitation, while the TPA dominates under non-resonant excitation [46,47]. In our case, the incident laser of 800 nm is far from the resonant wavelength ( 1771 nm, corresponding to an optical bandgap of 0.7 eV) of the PdSe 2 lm. Therefore, the optical limiting behaviour is mainly attributed to TPA. At low laser intensities, the linear absorption is dominant, while as the laser intensity increases, increased photon population makes TPA possible, resulting in the excitation of electrons from the valence to conduction bands.
To extract the TPA coe cient β of PdSe 2 , we t the measured OA results with Equation (1). The TPA coe cient β for the PdSe 2 lm is shown in Fig. 4 where k is the slope showing the order of the nonlinear absorption and C is a constant. For pure TPA, the slope is equal to 1 [48,49]. We obtain a slope of 1.18 ( Fig. 5(b)), suggesting the observed nonlinear absorption is mainly attributed to TPA in the PdSe 2 lm.
We also performed CA Z-scan measurements to investigate the Kerr nonlinearity (n 2 ) of the PdSe 2 lms.
The values of n 2 for the PdSe 2 lm at different laser intensities were extracted by tting the measured CA results with Equation 2 [41,42]. Figure 6(a) shows a representative CA result for PdSe 2 at a laser intensity of 21.32 GW/cm 2 . The transmittance of the sample exhibited a transition from peak to valley when the sample passed through the focal plane. Such a peak-valley CA behaviour corresponds to a negative Kerr coe cient n 2 and indicates an optical self-defocusing effect in the PdSe 2 lm. As discussed above, TPA results in the transfer of electrons from valence band to conduction band, increasing the free carrier density in the lm. Therefore, the observed negative Kerr nonlinearity potentially originates from the TPAinduced free carrier nonlinear refraction and interband blocking [50][51][52].  Table 1 compares the β and n 2 of PdSe 2 with other 2D layered materials. As can be seen, the value of n 2 for PdSe 2 is lower than those of graphene and GO, but still more than two orders of magnitude higher than bulk silicon [53,54]. Such a high n 2 suggests that PdSe 2 is an extremely promising material for self-defocusing based nonlinear photonic applications. For example, a negative Kerr nonlinearity can be used to self-compress ultrashort pulses in the presence of positive group-velocity dispersion [55,56]. Another application of a negative Kerr nonlinearity is mode locking of lasers using the Kerr mode-locking technique [53,57] as well as the possibility of achieving net parametric modulational instability gain under normal dispersion conditions [53,58].
Moreover, as shown in Fig. 6(b), the absolute value of n 2 initially decreases with laser intensity and then saturates at higher intensities. In theory, the optical nonlinear refraction originates mainly from the freecarrier and bound-electron nonlinearities [51,59,60]. We assume that both mechanisms exist in PdSe 2 lms. The refractive index change in the PdSe 2 lm can be expressed by Δn = n 2 * I 0 + σ r N, where n 2 * is the nonlinear refraction related to bonding electrons, σ r is the free carrier refractive coe cient and N is the charge carrier density. [51] Therefore, the effective n 2 = Δn/I 0 = n 2 * + σ r N/I 0 , is an intensity dependent parameter, which can explain the n 2 variation as a function of laser intensity observed in our measurements. In contrasting the Kerr 3 rd order nonlinearity and TPA with other 3 rd order effects such as optical third harmonic generation (THG) [64][65][66][67][68][69] it is interesting to note that unlike THG, both the sign and phase of the Kerr nonlinearity are critically important. The concept of the nonlinear FOM was originally proposed purely in the context of a limitation for n 2 devices having a positive n 2 and TPA. Here, the fact that n 2 for PdSe 2 is negative means that the conventional importance of a large FOM is probably not applicable.
Further, TPA has been known to potentially have a positive impact on some signal processing functions [70][71][72] and so the large TPA of PdSe 2 is a potential advantage to this material. The combination of a large and negative n 2 with a very large TPA makes PdSe 2 a highly interesting material for novel nonlinear processes that can exploit self-defocusing effects. It is signi cantly different to graphene oxide [73][74][75][76][77][78][79][80][81][82][83] in terms of both the Kerr nonlinearity and nonlinear absorption. It may offer interesting advantages when combined with advanced SOI photonic circuits [84][85][86][87] to yield advanced nonlinear functions.

Conclusion
We report a large third-order nonlinear optical response of PdSe 2 lms measured with the Z-scan technique. Our results show that PdSe 2 has a strong TPA response with a large β of ~ 3.26 ×10 -8 m/W.
We also investigate the Kerr nonlinearity (n 2 ) of PdSe 2 nding that n 2 is negative, and with an absolute magnitude that is more than two orders of magnitude larger than bulk silicon. Furthermore, the variation in n 2 of PdSe 2 with laser intensity is characterized. We nd that n 2 initially increases (decreasing in absolute magnitude) with incident laser intensity and then saturates at higher intensities. These results verify PdSe 2 as a promising 2D material with prominent nonlinear optical properties.

Declarations
Competing interests: The authors declare no competing interests.

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