1. Thermal effects in laser-metals interaction using a
quantum two temperature model
G. Florescu1, M. Oane2, C. Oproiu2, I. N. Mihailescu2, N. Serban2
1SUBSIDIARY OF TECHNOLOGY AND ENGINEERING FOR NUCLEAR PROJECTS, STR. ATOMISTILOR 409, MAGURELE, ROMANIA
2NATIONAL INSTITUTE FOR LASER, PLASMA AND RADIATION PHYSICS, STR. ATOMISTILOR 409, MAGURELE, ROMANIA
ABSTRACT
In this paper, we present a new approach to build laser-metal thermal interaction model with consideration of solving the two temperatures: electron and phonon temperatures. Using only one Fourier equation, we can get information about 3D thermal fields, surface temperature, and steady state quantum effects temperature while laser shooting on a metal. In this work, we apply to the Anisimov [1] and Nolte [2] models the integral transform technique [3]. Like an example we simulate the surface temperature in laser-Au thin film interaction, when the laser yields multiple-nanosecond ablation of metals.
s: or
THE ANALYTICAL MODEL
The TTM has the following two coupled equations: and
Here, we have from solid state physics: In the most general form, we may write the “source term”:
, where is the laser transverse mode {m,n}, is the linear absorption
coefficient for the mode {m,n}, is the surface absorption coefficient for the mode {m,n}, and q.c. are quantum steady state corrections. H-is the step function and is the espouse time. Using the integral transform technique we have the solution :
Here: and with:
. We have also: where: , ( is the lattice cooling time and is the pulse time) .
The Au thin film has 1mm thick. We will consider [5]:
. We have taken:
E pulse=200 mJ, Ilaser=109 W/cm2 , ,
and Our simulations [Fig.1 and Fig.2] are
in very good agreement with experimental data
from reference [5].
RESULTS OF THE THEORETICAL MODEL
Fig. 1 The thermal field on Au thin film after one Fig. 2 The thermal field on Au thin film after 100
laser pulse interaction laser pulses interaction.
We have obtained a simple solution for the two model temperature. The solution can help to know the thermal effect in laser-metal interaction. The metals are in the category: Au, Cu, Ag, Al-in order to make our physical approximation valid. The temperature should be lower than the melting temperature. In order to present the “power” of the present model we show the 3D thermal distribution fields during irradiation of an Au thin field.
The present study could also be applied for very short time interactions, where quantum effects may be involved also. For instance, the model can take also into account quantum effects, such as multi-photons absorption or a high absorption coefficient at the sample surface. Choosing different values for the surface absorption coefficients, enables one to construct a detailed model in order to obtain the temperature fields for two pulses irradiation of metals, when the time between the two pulses is of the order of magnitude 10ns - 100ns. The model open a theoretical basis for developing an analytical expression for the surface absorption coefficient, in order to describe the thermal behaviour of a metallic sample when two heating laser pulses which are separated by a very short time [4].
[1]. S. I. Anisimov, B. L. Kapeliovich, T. L. Perelman, (1974), JETP Lett., 39, (2),
[2]. S. Nolte, C. Momma, H. Jacobs, A. Tunnermann, B. N. Chichkov, B. Wellegehaussen, and H. Welling, (1997),
Journal Optical Society of America B/Vol.14,Nr.10, ,
[3]. M. Oane and D. Sporea, (2001), Infrared Physics & Technology 42, 31-40,
[4]. M. Oane, M. Taca, S. L. Tsao, Lasers in Engineering, in press, (2011); Vol.21, Nr.5-6.
[5]. M. Stafe, C. Negutu, I. M. Popescu, (2006), Journal of Optoelectronics and Advanced Materials, 8,
CONCLUSIONS
REFERENCES
Acknowledgments: the authors acknowledge with thanks for the financial support of this work by contract NUCLEU/2011
Acknowledgments: the authors acknowledge with thanks for the financial support of this work by the contract NUCLEU/2011.