## 1 Introduction  
Modeling light--metal interaction for ultrafast laser fields remains a challenging issue as the role of transient electronic response in the metal band structure is a dominant factor in optical properties. Intense photoexcitation in the femtosecond range for fluence near the ablation threshold, typically 0.2 J/cm\({}^{2}\) for most of transition metals, forces conduction electrons in metals to move around the lattice ions, enabling photon absorption through an inverse bremsstrahlung process [1]. Beyond this classical view, electrons undergo electron-electron and electron-phonon scattering, resulting in a photon absorption process as well as an internal thermalization [2, 3]. Throughout the laser-solid absorption, the electrons are redistributed within the density of states respecting the Pauli exclusion principle. This involves intraband and interband displacements of the electron population, followed by thermalization within the bands [4]. Screening effects determine a subsequent evolution of the bands themselves [5]. The evolution of optical properties relies directly on the transient electronic band structure. The prediction of optical properties thus requires an inaccessible kinetic description, challenging the rationalization of the collective processes. To interpret and predict the optical dynamics in time-dependent ultrashort laser--metal modeling, clarification and simplification of the absorption mechanisms are required. To achieve this, tractable models and simulation approaches capable of describing fast electron dynamics are formulated. For pure transition metals irradiated in IR-visible range, the absorption length corresponding to the optical skin depth is on a scale of a few tens of nanometers, and the optical properties are determined by the bulk properties. For irradiated quasi-flat and rough surfaces, this strong energy confinement is able to trigger a plethora of surface ultrafast phenomena at the nanoscale [6, 7]. The observed material reflectivity and thus the amount of laser energy absorbed in the skin depth is defined by the collective electronic response to the laser field through intraband and interband transitions in sub-bands of the crystal state [8; 9; 10; 11; 12]. The time-resolved complex refractive index of the laser-irradiated surface has been previously reported by a dual-angle reflectometry technique, which was applied to study the optical dynamics of \(d\)-band electrons in transition metals near the threshold fluence [13; 14; 15; 16]. To better determine the refractive index without Fresnel equations, a direct measurement of optical properties has been recently proposed by an ultrafast pump-probe method combining ellipsometry with reflectometry [17; 18]. Recent self-reflectivity measurements of femtosecond-laser-heated aluminum and tungsten also confirm the importance of the transient density of states for interpreting the experimental data [19]. Moreover, both time-resolved and integrated optical data showed a strongly increased optical coupling due to the fast variation of the optical properties during irradiation with ultrashort laser pulses. Fitting these optical properties on a relatively large spectrum is of great interest for spectroscopy, plasmonics, nanophotonics, and optical engineering, which requires dispersion models, such as Drude, Drude-Lorentz, Critical Points, or Partial-Fraction [20; 21; 22]. The goal of the present work is to propose a straightforward Drude-Lorentz model with electron-phonon nonequilibrium parameters that ultimately aims at being implemented into numerical models as Maxwell solvers. Our approach provides fitting values of optical properties during the nonequilibrium state lasting a few picoseconds when the lattice temperature remains undisturbed at 300 K, modifying the material primary response to the laser irradiation. A \"hot\" electron temperature range of 10,000-30,000 K was considered to obtain a non-negligible effect on permittivity and, at the same time, to work in the limits of material stability [23].