Analytical modeling of thermal processes during femtosecond laser pulse action on metallic nanoparticle

doi:10.1016/j.photonics.2021.100974

Photonics and Nanostructures - Fundamentals and Applications

Volume 47, December 2021, 100974

https://doi.org/10.1016/j.photonics.2021.100974 Get rights and content

Highlights

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Analytical approach is used for thermal femtosecond pulse - nanoparticle interaction.
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Temperature dependences of metal electron-phonon coupling is taken into account.
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This model is used for estimations of femtosecond laser and nanoparticle parameters.

Abstract

The analytical approach has been proposed for the modeling of the thermal processes during the action of femtosecond laser pulse on metallic (gold) nanoparticle with allowance for the temperature dependences of the electron heat capacity and the electron-phonon coupling factor of gold based on thermal excitation of electron density. This leads to novel dependence of the electron-phonon equal temperature and the coupling factor on the maximal electron temperature. Whole process of femtosecond nanoparticle action has been divided into three stages which include firstly the heating of electron system by pulse, secondly the electron-phonon energy exchange and the establishment of the equal temperature of electrons with lattice, and thirdly the nanoparticle cooling with the corresponding analytical description of each stage. The satisfactory agreement with the computer results for femtosecond pulses validates of used analytical approach. This model can be used for the estimation of laser and nanoparticle parameters in the fields of the applications of femtosecond laser pulses.

Introduction

During the past decade, metallic nanoparticles (NPs) have found numerous applications in laser nanotechnology [1], [2], [3], chemistry and medicine [4], [5], [6], [7], [8], especially for cancer treatment [8], [9]. The unique plasmonic properties of the metallic NPs together with last achievements in the development of lasers make them particularly suitable for these applications. Constantly growing number of modern applications are based on the interactions of femtosecond laser pulses with metallic NPs for the treatment of NPs [1], [10], [11], [12], [13], [14], nanobubble formation around NPs [15], [16], [17] including the application of nanobubbles in laser medicine [18], [19]. Femtosecond laser−particle interactions induce a significant rise of temperature both in the particle and around it triggering several key processes and effects. Particle temperature can reach and overcome the melting or the boiling temperatures of NP metal, leading to thermal NP melting, evaporation and/or fragmentation if laser fluence is sufficiently high [1], [10], [11], [12], [13], [14].

Free electrons are the first agents to interact with laser pulses action on metallic NPs. In the case of action of femtosecond laser pulses with characteristic duration of about 10–100 fs the electron gas will be oscillated under action of an electric field and a nonthermal distribution of the hot electron is produced. It should be noted that the hot electrons in metallic NPs are of great interest for photonics and electronics [20], [21]. Electron-electron scattering and electron collisions with NP surface are leading to a thermalization of electron system at an elevated electron temperature [22]. The electrons can achieve tens of thousands of Kelvins and after electron-phonon exchange the lattice temperature can achieve of thousands of Kelvins accordingly. The absorption, the electron-phonon coupling and the heating of NPs under action of ultrashort laser pulses and their cooling after the termination of laser action usually have nonlinear character [22], [23], [24], [25], [26], [27], [28]. Such metallic NP characteristics as the parameter of electron-phonon coupling and the electron heat capacity depend on the electron temperature. It is very important to take into account these temperature dependences of NP parameters during femtosecond laser action that leads to their significant influence and novel results of the laser action.

A few computer calculations have been carried out to describe the processes of femtosecond laser pulse action on metal NP [24], [25], [27], [28], [29], [30]. On the other hand, it is interesting to get simple but more useful analytical description of these processes by taking into account the possible applications of femtosecond pulse action on metallic (gold) NPs and hot electrons. This attempt has been undertaken in article.

Section snippets

Methods and results

General system of equations describing the thermal processes of femtosecond laser pulse action on metal NP has the form [23], [24], [25], [26], [27], [28], [29], [30] of: $C_{e} (T_{e}) \frac{d T_{e}}{d t} = - G (T_{e}) (T_{e} - T_{i}) + q_{a b s}$ $C_{i} (T_{i}) \frac{d T_{i}}{d t} = G (T_{e}) (T_{e} - T_{i}) - q_{C}$ $с_{0} ρ_{0} V_{0} \frac{d T_{0}}{d t} = - q_{C}$ $C_{m} (T_{m}) \frac{d T_{m}}{d t} = N_{0} q_{C}$ with the initial condition:T_e (t = 0) = T_i (t = 0)= T₀ (t = 0) = T_m(t = 0) = T_∞where C_e, C_i and C_m are the heat capacities of electron, lattice and surrounding medium accordingly, T_e, T_i and T_m are the temperatures of electronic, lattice and

Conclusions

Femtosecond pulse interaction with metallic NPs is widely used in photonics, photochemistry, laser nanomedicine. The computer and analytical investigations of mentioned processes can be applied for the description and estimation of laser and NPs parameters. It is used the possibility to satisfactory describe the process of femtosecond pulse action on NP by analytical approach in contrast with computer calculations that is useful for simple estimations of main process parameters.

Whole process of

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Citation Excerpt :
The mechanism of NP fragmentation can be different when a femtosecond laser pulse is used instead of the nanosecond and picosecond pulses under study. When a metal particle is exposed to a femtosecond laser pulse, a two-temperature state arises with an electron temperature much higher than the ion temperature, despite its transitional nature, which can significantly affect the further dynamics [26,27]. However, for nanosecond (picosecond) pulses the thermal electron-lattice equilibrium approach can be used with good accuracy.
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View full text

Analytical modeling of thermal processes during femtosecond laser pulse action on metallic nanoparticle

Highlights

Abstract

Introduction

Section snippets

Methods and results

Conclusions

Declaration of Competing Interest

Opt. Laser Techn.

Appl. Surf. Sci.

Chem. Phys.

Ultrafast photoemission electron microscopy: imaging plasmons in space and time

Chem. Rev.

Thermo-plasmonics: using metallic nanostructures as nano-sources of heat

Laser Photonics Rev.

Special issue

Taking the heat off of plasmonic chemistry

J. Phys. Chem. C

Nanochemistry and nanomedicine for nanoparticle-based diagnostics and therapy

Chem. Rev.

Applications and challenges of thermoplasmonics

Nat. Mater.

Active targeting of gold nanoparticles as cancer therapeutics

Chem. Soc. Rev.

Femtosecond laser irradiation of plasmonic nanoparticles in polymer matrix: implications for photothermal and photochemical material alteration

Micromachines

Fragmentation of colloidal nanoparticles by femtosecond laser-induced supercontinuum generation

Appl. Phys. Lett.

Effect of single femtosecond pulses on gold nanoparticles

J. Phys. Chem. C

Near-field-induced femtosecond breakdown of plasmonic nanoparticles

Plasmonics

From thermo- to plasma-mediated ultrafast laser-induced plasmonic nanobubbles

Appl. Phys. A

Cavitation dynamics on the nanoscale

Appl. Phys. Lett.

Model for estimations of laser threshold fluencies for photothermal bubble generation around nanoparticles

Appl. Phys. A