This work is devoted to the electron temperature variation in metals through interaction with femtosecond laser pulses. Our study was inspired by the last mathematical breakthroughs regarding the exact analytical solutions of the heat equation in the case of flash laser-matter interaction. To this purpose, the classical Anisimov’s two temperature model was extended via the 3D telegraph Zhukovsky equation. Based upon this new approach, the computational plots of electron thermal fields during the first laser pulse interaction with a gold surface were inferred. It is shown that relaxation times and coupling factors over electron thermal conductivities (g/K) govern the interaction between the laser pulse and metal sample during the first picoseconds. The lower the factor g/K, the higher the electron temperature becomes. In contrast, the lower the relaxation time, the lower the electron temperature.

A Multiple-Temperature Model is proposed to describe the flash laser irradiation of a single layer of graphene. Zhukovsky’s mathematical approach is applied to solve the Fourier heat equations based upon quantum concepts, including heat operators. Easy solutions were inferred with respect to classical mathematics. Thus, simple equations were set for the electrons and phonon temperatures in the case of flash laser treatment of a single layer of graphene. Our method avoids the difficulties and extensive time-consuming nonequilibrium green function method or quantum field theories when applied in a condensed matter. Simple expressions were deduced that could prove useful for researchers.

The investigation of the thermal field distribution in a material sample irradiated by a laser beam or an electron beam with the energy of a few MeV appears as a demand for all kinds of experiments that involve irradiation. When investigating the effects of accelerated electrons on a target, it is necessary to figure out the temperature rise in the target. "lso during irradiation with laser beams, it is important to know the thermal behavior of the target. " parallel between laser and electron beam irradiation is also made. The results are very interesting. "lso, a very interesting case of cluster nano-particles ª nm inserted in a Cu surface heated with a laser beam is tacking in to account.The present chapter is a review article type which comprises the expertise gathers around this domain during the past years within the institute NILPRP-Romania.