Journal of Quantitative Spectroscopy & Radiative Transfer 252 (2020) 107066 Contents lists available at ScienceDirect Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt The thermal lens effect on laser heating of a metal nano-sphere particle immersed in oil I. Gurwich a,∗ , M. Spector b,1 a Photonics and Electro-Optics Engineering Unit, Ben-Gurion University, Beer-Sheva 8410501, Israel b Photonics and Electro-Optics Engineering Unit, Ben-Gurion University, Beer-Sheva 8410501, Israel a r t i c l e i n f o Article history: Received 23 February 2020 Revised 2 May 2020 Accepted 5 May 2020 a b s t r a c t In this work, we revise the model describing laser heating of a spherical metallic nanoparticle (NP) im- mersed in transparent oil. We study the generated temperature non-uniformity of the ambient medium and its effect on the propagation of the laser beam. Thus, the model describes the influence of thermal non-uniformity on scattering and absorption of light by the heated particle. Recently, different aspects of the heating of NPs by a laser beam have been actively researched. Some experimental works demon- strated an enigmatic dependence of the effective scattering cross-section of the heated particle on the intensity of the laser beam, illuminating it. The authors of these works labeled the observed effects as “saturation,” and “reverse saturation.” In this paper, we show that the propagation of the incident laser beam in a non-uniform oil can by itself be the source of both “saturation” and “reverse saturation” els effects. © 2020 Elsevier Ltd. All rights reserved. 1. Introduction The process of heating a metallic NP immersed in an ambi- ent medium by an incident laser beam involves different aspects of nonlinear optics. Such systems have been extensively studied in recent time, both theoretically and experimentally. In several such experiments, where the studied particles were immersed in an index matching oil, an interesting effect was dis- covered [1–5]. The authors measured the effective scattering cross- section, C sc,p , and realized that it exhibits nonlinear dependence on the intensity of the laser beam (and thus, on the temperature of the NP) under steady state conditions. This dependence (taken here from [1]) is depicted in Fig 1. The observed effects were labeled as scattering saturation, i.e., decreasing of C N (SS henceforth) and reverse scattering saturation, i.e., increasing again of C N (RSS henceforth). The authors tried to explain their result by linking it to the surface plasmon resonance (SPR). However, this explanation is not supported by the known models of the dielectric susceptibility of metals (see, e.g., [6]). An- other attempt to explain the data above was performed in [5]. This study took into account both the thermo-optical properties of the particle and the ambient medium. The authors in [5] performed ∗ Corresponding author. E-mail address: iosephg@gmail.com (I. Gurwich). 1 Equal contribution. their analysis for wavelengths being in the vicinity of resonance, as well as far from it. The results showed SS effect (decreasing of C sc ), but, significantly milder than that shown in Fig. 1. On the contrary to the experimental data, depicted in Fig 1, the RSS effect was not observed at all. We note that the model represented in [5] neglects the tem- perature spatial in-homogeneity of the ambient medium. Thus, the authors of [5] examined a NP only partly coupled with the ambient medium. Following the analysis above, we conclude that neither the SPR nor the thermo-optical properties of a metal particle can provide the cumbersome nonlinear dependence of the scattering cross- section on the beam intensity C sca (I L ) shown in Fig. 1). Moreover, as far as we know, the optical non-uniformity of the ambient medium appearing from its temperature non-uniformity was not analyzed in any of the experiments, dealing with the heat- ing of metallic NP immersed in an ambient medium [1–4]. This circumstance, in turn, leads to a lack of data regarding the various physical properties of the ambient medium. The reasons above stimulated our attempt to take into account the spatial non-uniformity of the temperature. The spatial non uni- formity of temperature (and the optical properties, as a result) affects the beam propagation, and thus, the heating of the par- ticle. Therefore, we deal not with the particle itself, but rather with a complicated system, including the particle immersed in the nonuniform medium. We show that the measured value of C N is not the scattering cross-section of the hot particle C sc,p , but rather https://doi.org/10.1016/j.jqsrt.2020.107066 0022-4073/© 2020 Elsevier Ltd. All rights reserved.