Thermal Nonlinear Klein–Gordon Equation for Nano-/Micro-Sized Metallic Particle–Attosecond Laser Pulse Interaction
Abstract
:1. Introduction
2. Kozłowski Thermal Model
3. Zhukovsky Mathematical Model
4. The Generalized Lambert–Beer Law
5. Simulations Based on the Thermal Klein–Gordon Equation
6. Conclusion
- For demonstration, the analysis was conducted for Au particles in the nano (100 nm) to micro (220–2000) nm range. A computational system with the following specifications was used to plot electron temperature profiles: core i7, 4th generation, 16 Gb Ram. The electron temperature graphics were generated after 1 min of simulation.
- The results show that the electron temperature variation strongly depends on particle size, both in nano- and micro-regimes. Thus, the larger the particle size, the larger the maximum temperature value spreading inside the particle.
- Longer simulation times (a few to tens of fs) allowed for a more accurate thermal field prediction after a longer thermalization time.
- The simulations were conducted for nanoparticles under 100 attosecond pulse laser irradiation. We attempted to develop a coherent approach using (i) the Kozłowski theoretical models [4,5] to take into account quantum effects, (ii) the Zhukovsky mathematical apparatus [8,9] to be able to consider the minimal time of irradiation (100 as), and (iii) the Zavestovskaya–Kanavin hypothesis to generalize the Lambert–Beer law as close to reality as possible [10].
- The main physical conclusion at the nanoscale is that we observed a dominant ballistic phenomenon, while for values higher than 500 nm, the two mechanisms (ballistic and thermal) compete. The shorter the target and irradiation time, the higher the presence of ballistic phenomena [17]. Compared to fs-scale irradiation, where the two phenomena are present at 100 nm [18], the same behavior within the range of 500–1000 nm can be observed. Our study suggests that the thermal field becomes dominant in the range exceeding 1000 nm.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
References
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Oane, M.; Mahmood, M.A.; Popescu, A.C.; Bănică, A.; Ristoscu, C.; Mihăilescu, I.N. Thermal Nonlinear Klein–Gordon Equation for Nano-/Micro-Sized Metallic Particle–Attosecond Laser Pulse Interaction. Materials 2021, 14, 857. https://doi.org/10.3390/ma14040857
Oane M, Mahmood MA, Popescu AC, Bănică A, Ristoscu C, Mihăilescu IN. Thermal Nonlinear Klein–Gordon Equation for Nano-/Micro-Sized Metallic Particle–Attosecond Laser Pulse Interaction. Materials. 2021; 14(4):857. https://doi.org/10.3390/ma14040857
Chicago/Turabian StyleOane, Mihai, Muhammad Arif Mahmood, Andrei C. Popescu, Alexandra Bănică, Carmen Ristoscu, and Ion N. Mihăilescu. 2021. "Thermal Nonlinear Klein–Gordon Equation for Nano-/Micro-Sized Metallic Particle–Attosecond Laser Pulse Interaction" Materials 14, no. 4: 857. https://doi.org/10.3390/ma14040857
APA StyleOane, M., Mahmood, M. A., Popescu, A. C., Bănică, A., Ristoscu, C., & Mihăilescu, I. N. (2021). Thermal Nonlinear Klein–Gordon Equation for Nano-/Micro-Sized Metallic Particle–Attosecond Laser Pulse Interaction. Materials, 14(4), 857. https://doi.org/10.3390/ma14040857