用于纳米/微米尺寸金属颗粒与阿秒激光脉冲相互作用的热非线性克莱因-戈登方程。
Thermal Nonlinear Klein-Gordon Equation for Nano-/Micro-Sized Metallic Particle-Attosecond Laser Pulse Interaction.
作者信息
Oane Mihai, Mahmood Muhammad Arif, Popescu Andrei C, Bănică Alexandra, Ristoscu Carmen, Mihăilescu Ion N
机构信息
Electrons Accelerators Laboratory, National Institute for Laser, Plasma and Radiation Physics (INFLPR), 077125 Magurele-Ilfov, Romania.
Laser Department, National Institute for Laser, Plasma and Radiation Physics (INFLPR), 077125 Magurele-Ilfov, Romania.
出版信息
Materials (Basel). 2021 Feb 10;14(4):857. doi: 10.3390/ma14040857.
In this study, a rigorous analytical solution to the thermal nonlinear Klein-Gordon equation in the Kozłowski version is provided. The Klein-Gordon heat equation is solved via the Zhukovsky "state-of-the-art" mathematical techniques. Our study can be regarded as an initial approximation of attosecond laser-particle interaction when the prevalent phenomenon is photon-electron interaction. The electrons interact with the laser beam, which means that the nucleus does not play a significant role in temperature distribution. The particle is supposed to be homogenous with respect to thermophysical properties. This theoretical approach could prove useful for the study of metallic nano-/micro-particles interacting with attosecond laser pulses. Specific applications for Au "nano" particles with a 50 nm radius and "micro" particles with 110, 130, 150, and 1000 nm radii under 100 attosecond laser pulse irradiation are considered. First, the cross-section is supposed to be proportional to the area of the particle, which is assumed to be a perfect sphere of radius R or a rotation ellipsoid. Second, the absorption coefficient is calculated using a semiclassical approach, taking into account the number of atoms per unit volume, the classical electron radius, the laser wavelength, and the atomic scattering factor (10 in case of Au), which cover all the basic aspects for the interaction between the attosecond laser and a nanoparticle. The model is applicable within the 100-2000 nm range. The main conclusion of the model is that for a range inferior to 1000 nm, a competition between ballistic and thermal phenomena occurs. For values in excess of 1000 nm, our study suggests that the thermal phenomena are dominant. Contrastingly, during the irradiation with fs pulses, this value is of the order of 100 nm. This theoretical model's predictions could be soon confirmed with the new EU-ELI facilities in progress, which will generate pulses of 100 as at a 30 nm wavelength.
在本研究中,给出了Kozłowski版本热非线性克莱因 - 戈登方程的严格解析解。通过茹科夫斯基“最先进”的数学技术求解克莱因 - 戈登热方程。当主要现象是光子 - 电子相互作用时,我们的研究可被视为阿秒激光 - 粒子相互作用的初始近似。电子与激光束相互作用,这意味着原子核在温度分布中不起重要作用。假定粒子在热物理性质方面是均匀的。这种理论方法可能对研究与阿秒激光脉冲相互作用的金属纳米/微米粒子有用。考虑了半径为50nm的金“纳米”粒子以及半径为110、130、150和1000nm的“微米”粒子在100阿秒激光脉冲照射下的具体应用。首先,假定横截面与粒子面积成正比,粒子被假定为半径为R的完美球体或旋转椭球体。其次,使用半经典方法计算吸收系数,考虑单位体积内的原子数、经典电子半径、激光波长和原子散射因子(金的情况下为10),这些涵盖了阿秒激光与纳米粒子相互作用的所有基本方面。该模型适用于100 - 2000nm范围。该模型的主要结论是,对于小于1000nm的范围,弹道现象和热现象之间存在竞争。对于超过1000nm的值,我们的研究表明热现象占主导。相比之下,在用飞秒脉冲照射期间,该值约为100nm。正在建设的新的欧盟 - ELI设施将很快证实该理论模型的预测,该设施将产生波长为30nm的100阿秒脉冲。