Ultra-large Optical Kerr Nonlinearity in 2D PdSe2 Dichalcogenide Thin Films for Integrated Nonlinear Photonics

As a novel layered noble metal dichalcogenide material, palladium diselenide (PdSe2) has attracted wide interest due to its excellent optical and electronic properties. In this work, a strong third-order nonlinear optical response of 2D PdSe2 films 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 PdSe2 film 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 n2 = -1.33×10-15 m2/W – two orders of magnitude larger than bulk silicon. In addition, the variation of n2 as a function of laser intensity is also characterized, with n2 decreasing in magnitude when increasing incident laser intensity, becoming saturated at n2 = -9.96×10-16 m2/W at high intensities. Our results show that the extraordinary third-order nonlinear optical properties of PdSe2 have strong potential for high-performance nonlinear photonic devices. Keywords: 2D materials, PdSe2 films, Z-scan technique, Kerr nonlinearity, nonlinear photonics.


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 (MX2, 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 MoS2 and WS2 have been used as broadband, fast-recovery saturable absorbers for mode locking in pulsed fiber lasers. [2,15] Nonlinear optical modulators and polarization dependent all-optical switching devices have been realized based on ReSe2 [16] and SnSe. [17] As a new 2D noble metal dichalcogenide in the TMDC family, PdSe2 has recently attracted significant 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, PdSe2 possesses unique in-plane anisotropic optical and electronic properties, [18,19] featuring an in-plane noncentrosymmetric structure, in contrast to its cousin PtSe2. Further, PdSe2 has a layer-dependent bandgap, varying from 0 eV (bulk) to 1.3 eV (monolayer) -a property well suited for photonic and optoelectronic applicationsin particular, for wavelength tuneable devices. Moreover, different to BP which degrades rapidly under ambient conditions, PdSe2 is highly air-stable, indicating its robustness and potential for practical applications. The high carrier mobility and anisotropic Raman spectroscopy of 2D PdSe2 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 PdSe2 nanosheets has also been reported in the context of mode-locked 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 PdSe2 multilayer films 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 PdSe2. Experimental results show that PdSe2 films exhibit a large and negative (selfdefocusing) Kerr nonlinearity (n2) 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 PdSe2 films. In addition, we investigate the intensity dependence of the nonlinear response of PdSe2, finding that the absolute magnitude of the Kerr nonlinearity n2 initially decreases slightly with incident laser intensity, becoming saturated at higher intensities. These results verify the large third-order nonlinear optical response of PdSe2 as well as its strong potential for high-performance nonlinear photonic devices.

MATERIAL PREPARATION AND CHARACTERIZATION
The atomic structure of PdSe2 crystals is shown in Figure 1(a). PdSe2 exhibits a unique puckered pentagonal structure, different to other TMDCs like MoS2 and WS2. 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 non-centrosymmetric properties of PdSe2. More importantly, unlike the rapid degradation of BP under ambient conditions, PdSe2 has significantly better air-stability. [22,23] Together, these properties of PdSe2 make it promising for high performance photonic and optoelectronic applications. Here, we investigate large-area multilayer PdSe2 films deposited on transparent sapphire substrates. The PdSe2 films were synthesized via Chemical vapor deposition (CVD). [26] The films were polycrystalline, as is typical for CVD synthesized films, with crystal sizes varying from 10's of nanometres up to 100 nm. Because of the polycrystalline nature of the films, the inversion symmetry breaking properties (i.e., non-centrosymmetric) of the single PdSe2 crystals could not be observed on optical wavelength scales in the macroscopic PdSe2 continuous films studied in this work. Figure 1(b) shows the photography of the prepared PdSe2 film. The morphology image and height profile of the prepared PdSe2 films were characterized by atomic force microscopy (AFM), as illustrated in Figure 1(c). The film thickness was measured to be ~ 8 nm, which corresponds to ~20 layers of PdSe2. [19,26]  Raman spectrum of the prepared PdSe2 film excited with a laser at 514 nm is shown in Figure 2(a). Three representative phonon modes can be observed, including the Ag 1 (∼145.5 cm −1 ) and B1g 2 (∼222.5 cm −1 ) vibrational modes that correspond to the movement of Se atoms and the Ag 3 (~ 258.8 cm −1 ) mode that relates to the relative movements between Pd and Se atoms. [20,26] To further characterize the film quality, X-ray photoelectron spectroscopy (XPS) was employed to measure the binding energy of PdSe2. Figure 2(b) shows the XPS results of Pd 3d and Se 3d core levels for the PdSe2. The peaks of the fit at ~ 342.2 eV and ~ 336.9 eV are attributed to the Pd 3d3/2 and Pd 3d5/2, respectively, whereas the peaks at ~ 55.7 eV and ~ 54.9 eV correspond to Se 3d3/2 and 3d5/2, respectively. [20,26] To characterize the linear absorption and optical bandgap, the optical absorption spectrum (from 400 nm to 2500 nm) of the PdSe2 film was measured with ultravioletvisible (UV-vis) spectrometry, as shown in Figure 2(c). The inset of Figure 2(c) shows the Tauc plot extracted from the linear absorption spectrum, where the optical bandgap of the PdSe2 film is estimated to be ~ 0.7 eV. We also characterize the in-plane (TE-polarized) refractive index (n) and extinction coefficient (k) of the PdSe2 film via spectral ellipsometry, as depicted in Figure 2(d). The refractive index first increases dramatically with wavelength to reach a peak at ~ 700 nm and then decreases more gradually at longer wavelengths. The extinction coefficient exhibits a significant 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 Figure 2(c).

Z-SCAN MEASUREMENTS
To investigate the third-order nonlinear optical properties of PdSe2, we characterized the nonlinear absorption and refraction of the prepared PdSe2 films 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 high-definition chargecoupled-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. Figure 3(a) shows the OA Z-scan results for the PdSe2 film at three representative intensities. A typical optical limiting behaviour was observed in the OA curves, with the transmission decreasing as the PdSe2 sample was moved through the focal point. We measured the response of pure sapphire substrate and did not observe any significant nonlinear absorption, indicating that the observed optical limiting response was induced by the PdSe2 film. 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), twophoton 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 PdSe2 film in our case, though, we first 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 PdSe2 film 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 inefficient under 800-nm femtosecond laser excitation due to the indirect band structure of the few-layer 8-nm-thick PdSe2 films, or possibly parallel band absorption effects. [31] Considering this, RSA is unlikely to dominate the nonlinear absorption in PdSe2 films 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 coefficient β of PdSe2, we fit the measured OA results with the well-established theory. [27,28] The TPA coefficient β for the PdSe2 film 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 WS2, highlighting the strong optical limiting effect in PdSe2 film. In addition, the TPA coefficient β is relatively constant with incident laser intensity, reflecting the fact that we are working in an intensity regime where the material properties of the PdSe2 films are not changing much. The slight fluctuation in β with laser intensity may arise from light scattering in the PdSe2 film surface. To further investigate the nonlinear absorption of the PdSe2 film, 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 PdSe2 at the focal point as a function of laser intensity, where the transmittance fluctuates around a relatively constant value at low intensities and then decreases significantly as the laser intensity increased. The experimental data fits the theory well, [31] verifying our assumption of TPA being the dominant process for nonlinear absorption in the PdSe2 film. The order of the observed nonlinear absorption can also be confirmed by examining the relation between ln(1-TOA) versus ln(I0): [32] ln(1 -T OA ) = kln(I 0 ) + C, (1) 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 PdSe2 film. We also performed CA Z-scan measurements to investigate the Kerr nonlinearity (n2) of the PdSe2 films. The values of n2 for the PdSe2 film at different laser intensities were extracted by fitting the measured CA results. Figure 4(a) shows a representative CA result for PdSe2 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 coefficient n2 and indicates an optical self-defocusing effect in the PdSe2 film. The noise in the CA data is mainly induced by the light scattering in the PdSe2 film surface. By improving the film 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 film. 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 coefficient n2 of PdSe2 versus laser intensity, showing a large n2 of -1.33×10 -15 m 2 /W. Table 1 compares the β and n2 of PdSe2 with other 2D layered materials. As can be seen, the value of n2 for PdSe2 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 n2 suggests that PdSe2 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 groupvelocity dispersion. [37] Another application of a negative Kerr nonlinearity is mode locking of lasers using the Kerr modelocking 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 n2 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 PdSe2 film. It has been shown that, near the half-bandgap the two-photon resonance typically yields a positive n2. However, at higher photon energies, the boundelectron contribution to the n2 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 PdSe2 film. This is further complicated by the fact that PdSe2 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 PdSe2 film can be expressed by Δn = n2 * I0 + σrN, where n2 * is the nonlinear refraction related to bonding electrons, σr is the free carrier refractive coefficient and N is the charge carrier density. [33] Therefore, the effective n2 = Δn/I0 = n2 * + σrN/I0, is an intensity dependent parameter, which can explain the n2 variation as a function of laser intensity observed in our measurements.

CONCLUSION
In summary, we report a large third-order nonlinear optical response of PdSe2 films measured with the Z-scan technique. Experimental results show that PdSe2 has a strong TPA response with a large β of ~ 3.26 ×10 -8 m/W. The Kerr nonlinearity (n2) of PdSe2 is also investigated. We find that n2 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 n2 of PdSe2 with laser intensity, finding that n2 initially increases (decreasing in absolute magnitude) with incident laser intensity and then saturates at higher intensities. Our results verify PdSe2 as a promising 2D material with prominent nonlinear optical properties.

ACKNOWLEDGEMENT
This work was supported by the Australian Research Council Discovery Projects Program (No. DP150102972 and DP190103186), and the Industrial Transformation Training Centres scheme (Grant No. IC180100005). We acknowledge Swinburne Nano Lab and Micro Nano Research Facility (MNRF) of RMIT University for the support in material characterization as well as Shenzhen Sixcarbon Technology for the PdSe2 film fabrication. We thank Dr. Yunyi Yang and Dr. Tania Moein for technical support, Dr. Deming Zhu for assisting in XPS characterization and Dr. Chenglong Xu for assisting in optical characterization.