# Wavelength-Dependent Nonlinear Absorption in Palladium Nanoparticles
## 1 Introduction  
When the light is not strong, the optical response of a material usually scales linearly with the amplitude of the optical electric field. However, at high optical powers, the optical properties of material are no longer linearly related to the intensity of the incident light. As a result, nonlinear optical effects will occur. Among various nonlinear effects, nonlinear absorption is of importance since the nonlinearities considerably change the propagation of intense light through the medium, which can induce novel applications in optoelectronics, optical switchers and limiters. Nonlinear absorption includes saturated absorption (SA) and reverse saturated absorption (RSA). The absorption with the absorption coefficient decreasing with the increase of incident light intensity is called SA. On the contrary, the absorption with the absorption coefficient increasing with the increase of incident light intensity is called RSA. The rapid development of nanoscience and nanotechnology has provided more opportunities for nonlinear optics than ever. A number of nanomaterials possessing remarkable nonlinear optical properties have been found, which promotes the design and fabrication of nano-scale optoelectronic and photonic devices. Specially, various metal nanoparticles have been considered as potential nonlinear optical materials. Among them, gold and silver nanoparticles have received special attention because they both show a broad surface plasmon resonance (SPR) absorption band in the visible region of the electromagnetic spectrum, which can substantially enhance their nonlinear optical properties [1, 2]. In the case of some transition metal nanoparticles such as platinum and palladium, although their SPR is in the ultraviolet region, they still show interesting nonlinear optical properties in the visible region. Correspondingly, many researches on the nonlinearity of platinum and palladium nanomaterials have been carried out [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. In 2002, [PERSON] et al. studied the optical properties of platinum nanoparticles (PtNPs) excited by a pulse of 8 ns and 532 nm. They found that PtNPs showed strong optical limiting properties and discussed the optical limiting mechanism in terms of the interband transition [3]. In2005, [PERSON] et al. studied the PVP-Pt nanospheres using open-aperture Z-scan under 532 nm nanosecond pulsed laser with relatively weak energy. They observed the transition of optical absorption from saturated absorption (SA) to reverse saturated absorption (RSA) and theoretically analyzed the effect using a proposed formula [4]. In 2009, [PERSON] et al. carried out a Z-scan measure of PtNPs using a 50 ps laser pulse with a wavelength of 1064 nm and realized mode-locking in the Nd laser using PtNPs [5]. In 2011, [PERSON] et al. prepared palladium nanoparticles (PdNPs) with particle size 2-6 nm by a photochemical decomposition method, and studied the nonlinear optical absorption of PdNPs under the excitation of 532 nm nanosecond laser pulse. They found that PdNPs showed SA at the lower light strength of \(3.28\times 10^{11}\) W/m\({}^{2}\), and RSA at the higher light strength of \(7.96\times 10^{11}\) W/m\({}^{2}\)[6]. In 2013, [PERSON] et al. investigated the nonlinear optical properties of palladium metal-organic complex by Z-scan using a nanosecond laser with a 532 nm wavelength at different excitation energies. They found that the sample had good optical power limiting characteristics which was caused by RSA [7; 8]. In 2016, [PERSON] et al. used 800 nm and 515 nm laser pulses to carry out Z-scan experiments. It was found that with the increase of hydrogen concentration, PdNPs changed from SA to RSA. SA was believed to be caused by single photon absorption between the d-band and conduction band of PdNPs, and RSA was caused by two-photon absorption (TPA) between the d-band and conduction band [9]. In 2019, in order to optimize the stable electrochemistry behavior of platinum and efficient plasma excitation of gold, [PERSON] et al.