High Optical Kerr Nonlinearity of PdSe2 Dichalcogenide 2D Films for Nonlinear Photonic Chips

As a novel layered noble metal dichalcogenide material, palladium diselenide (PdSe 2 ) has attracted wide interest due to its excellent optical and electronic properties. In this work, a strong third-order nonlinear optical response of 2D PdSe 2 lms is reported. We conduct both open-aperture (OA) and closed-aperture (CA) Z-scan measurements 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. In addition, the variation of n 2 as a function of laser intensity is also characterized, with n 2 decreasing in magnitude when increasing incident laser intensity, becoming saturated at n 2 = -9.96×10 − 16 m 2 /W at high intensities. Our results show that the extraordinary third-order nonlinear optical properties of PdSe 2 have strong potential for high-performance nonlinear photonic devices.


Introduction
Two-dimensional (2D) layered materials such as graphene, [1][2][3] graphene oxide (GO), [4][5][6][7][8][9] transition metal dichalcogenides (TMDCs), [10][11][12] and black phosphorus (BP) [13,14] have attracted a great deal of interest, enabling diverse nonlinear photonic devices with vastly superior performance compared to bulk materials. Amongst them, TMDCs (MX 2 , M = transition metal and X = chalcogen), with bandgaps in the near infrared to the visible region, have opened up promising new avenues for photonic and optoelectronic devices. [2,15,16] For instance, a few mono-layers of MoS 2 and WS 2 have been used as broadband, fast-recovery saturable absorbers for mode locking in pulsed ber lasers. [2,15] Nonlinear optical modulators and polarization dependent all-optical switching devices have been realized based on ReSe 2 [16] and SnSe. [17] As a new 2D noble metal dichalcogenide in the TMDC family, PdSe 2 has recently attracted signi cant interest. [18][19][20][21] 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. Due to this low-symmetry structure, PdSe 2 possesses unique in-plane anisotropic optical and electronic properties, [18,19] featuring an in-plane noncentrosymmetric structure, in contrast to its cousin PtSe 2 . Further, PdSe 2 has a layer-dependent bandgap, 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. Moreover, different to BP which degrades rapidly under ambient conditions, PdSe 2 is highly air-stable, indicating its robustness and potential for practical applications. The high carrier mobility and anisotropic Raman spectroscopy of 2D PdSe 2 layers have been investigated [18,20] as well as highly-sensitive photodetectors from the visible to mid-infrared wavelengths. [22,23] Recently, the optical nonlinear absorption of PdSe 2 nanosheets has also been reported in the context of modelocked laser applications. [24,25] To date, however, its optical Kerr nonlinearity has not been investigated.
Here, we characterize the third-order nonlinear optical properties of PdSe 2 multilayer lms via Z-scan technique with femtosecond optical pulses at 800 nm. Both OA and CA measurements are performed to investigate the nonlinear absorption and nonlinear refraction of PdSe 2 . Experimental results show that PdSe 2 lms exhibit a large and negative (self-defocusing) Kerr nonlinearity (n 2 ) of ∼ -1.33×10 − 15 m 2 /W, two orders of magnitude larger than bulk silicon. In the OA measurement, we observe 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. These results verify the large third-order nonlinear optical response of PdSe 2 as well as its strong potential for high-performance nonlinear photonic devices.

Material Preparation And Characterization
The atomic structure of PdSe 2 crystals is shown in Fig. 1(a). PdSe 2 exhibits a unique puckered pentagonal structure, different to other TMDCs like MoS 2 and WS 2 . The Se-Pd-Se layers stack with weak van der Waals interactions to form a layered structure. [18,19] 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 . More importantly, unlike the rapid degradation of BP under ambient conditions, PdSe 2 has signi cantly better air-stability. [22,23] Together, these properties of PdSe 2 make it promising for high performance photonic and optoelectronic applications.
Here, we investigate large-area multilayer PdSe 2 lms deposited on transparent sapphire substrates. The PdSe 2 lms were synthesized via Chemical vapor deposition (CVD). [26] 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., noncentrosymmetric) 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 the photography of the prepared PdSe 2 lm. 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 . [19,26] Raman spectrum of the prepared PdSe 2 lm excited with a laser at 514 nm is shown in Fig. 2(a). Three representative phonon modes can be observed, including the A g 1 (∼145.5 cm − 1 ) and B 1g 2 (∼222.5 cm − 1 ) 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. [20,26] 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 ~ 342.2 eV and ~ 336.9 eV are attributed to the Pd 3d 3/2 and Pd 3d 5/2 , respectively, whereas the peaks at ~ 55.7 eV and ~ 54.9 eV correspond to Se 3d 3/2 and 3d 5/2 , respectively. [20,26] 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 Fig. 2(c). The inset of Fig. 2(c) shows the Tauc plot extracted from the linear absorption spectrum, where the optical bandgap of the PdSe 2 lm is estimated to be ~ 0.7 eV. 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).
The refractive index rst increases dramatically with wavelength to reach a peak at ~ 700 nm and then decreases more gradually at longer wavelengths. 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).

Z-scan Measurements
To investigate the third-order nonlinear optical properties of PdSe 2 , we characterized the nonlinear absorption and refraction of the prepared PdSe 2 lms via the Z-scan technique, [27][28][29] 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. sample was moved through the focal point. We measured the response of pure sapphire substrate and did not observe any signi cant nonlinear absorption, indicating that the observed optical limiting response was induced by the PdSe 2 lm. We also note that the transmittance dip of the OA curve decreased when the incident laser intensity was increased. In principle, the optical limiting behaviour can be induced by several mechanisms such as nonlinear light scattering (NLS), reverse saturable absorption (RSA), two-photon absorption (TPA) and multi-photon absorption (MPA). [30,31] However, apart from the basic condition that the total energy of the photons involved in each process (eg., two photons, for TPA, one photon for SA etc.) must be larger than the bandgap, there is no a-priori reason for any particular process to dominate. For thin PdSe 2 lm in our case, though, we rst exclude the NLS effect since it usually dominates for dispersion or solution samples with laser-induced microbubbles. [30,31] According to the UV-vis spectra, the bandgap of the few-layer PdSe 2 lm is estimated to be 0.7 eV, which is lower than a single photon energy of the incident laser at 800 nm. Therefore, all the above processes can occur. While SA at low laser intensities and RSA at high laser intensities might be expected for the Z-scan measurements, we did not observe this. This could possibly be because the single photon transition is ine cient under 800-nm femtosecond laser excitation due to the indirect band structure of the few-layer 8-nm-thick PdSe 2 lms, or possibly parallel band absorption effects. [31] Considering this, RSA is unlikely to dominate the nonlinear absorption in PdSe 2 lms due to its one photon process. Given the high peak power of the incident femtosecond pulses, TPA is likely to account for the optical limiting behaviour observed in our Z-scan measurements.
To extract the TPA coe cient β of PdSe 2 , we t the measured OA results with the well-established theory. [27,28] The TPA coe cient β for the PdSe 2 lm is shown in Figure 3(b) at different laser intensities. A large β = 3.26 ×10 -8 m/W is observed, which is comparable to the reported values of graphene, and higher than that of WS 2 , highlighting the strong optical limiting effect in PdSe 2 lm. In addition, the TPA coe cient β is relatively constant with incident laser intensity, re ecting the fact that we are working in an intensity regime where the material properties of the PdSe 2 lms are not changing much. The slight uctuation in β with laser intensity may arise from light scattering in the PdSe 2 lm surface.
To further investigate the nonlinear absorption of the PdSe 2 lm, we measured the minimum transmittance with the sample at the focal point of the Z scan setup, for different incident laser intensities. Figure 3(c) shows the transmittance of PdSe 2 at the focal point as a function of laser intensity, where the transmittance uctuates around a relatively constant value at low intensities and then decreases signi cantly as the laser intensity increased. The experimental data ts the theory well, [31] verifying our assumption of TPA being the dominant process for nonlinear absorption in the PdSe 2 lm.
The order of the observed nonlinear absorption can also be con rmed by examining the relation between ln(1-T OA ) versus ln(I 0 ): [32] 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. [32] We obtain a slope of 1.18 (Figure 3(d)), 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. Figure 4(a) shows a representative CA result for PdSe 2 at a laser intensity of 17.15 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. The noise in the CA data is mainly induced by the light scattering in the PdSe 2 lm surface. By improving the lm uniformity, such noise can be further reduced. 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 TPA-induced free carrier nonlinear refraction and interband blocking. [33,34] Figure 4(b) shows the measured Kerr coe cient n 2 of PdSe 2 versus laser intensity, showing a large n 2 of -1.33×10 -15 m 2 /W. 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. [35,36] 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. [37] Another application of a negative Kerr nonlinearity is mode locking of lasers using the Kerr mode-locking technique [35,38] as well as the possibility of achieving net parametric modulational instability gain under normal dispersion conditions. [35,39] In addition, as shown in Figure 4(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 free-carrier and bound-electron nonlinearities. [33,[40][41][42][43][44] We assume that the two mechanisms co-exist in the PdSe 2 lm. It has been shown that, near the half-bandgap the two-photon resonance typically yields a positive n 2 . However, at higher photon energies, the bound-electron contribution to the n 2 nonlinearity becomes negative, while the free-carrier nonlinearity is usually also negative. [33,44] We therefore infer that either, or both, processes contribute to the nonlinearity since we observed a negative Kerr nonlinearity for the PdSe 2 lm. This is further complicated by the fact that PdSe 2 is an indirect bandgap material. The Kerr nonlinearity is dominated by direct transitions at all energies, whereas the nonlinear absorption is dominated by indirect transitions in energy regions where the direct transitions are not allowed (eg., below half of the direct bandgap for TPA). [45] 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. [33] 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.

Conclusion
In summary, we report a large third-order nonlinear optical response of PdSe 2 lms measured with the Zscan technique. Experimental results show that PdSe 2 has a strong TPA response with a large β of ~ 3.26 ×10 − 8 m/W. The Kerr nonlinearity (n 2 ) of PdSe 2 is also investigated. We nd that n 2 is negative, and with an absolute magnitude that is more than two orders of magnitude larger than bulk silicon. Furthermore, we characterize the variation in n 2 of PdSe 2 with laser intensity, nding that n 2 initially increases (decreasing in absolute magnitude) with incident laser intensity and then saturates at higher intensities.