The intense femtosecond laser allows us to realize deterministic and sharp edge laser processing for dielectrics [1], invoking a potential to achieve high-value-added processing. An essential physics behind the laser processing is nonlinear optical absorption (NOA) due to the TW/cm² class intensity of the femtosecond laser, which triggers the whole process. However, strong nonlinearity makes it challenging to understand the elementary process clearly.

We employ time-dependent density functional theory (TDDFT), an atomistic quantum simulation, to evaluate NOA. TDDFT is one of the most feasible theoretical frameworks to describe nonequilibrium electron excitation far from electron ground state, from first-principles [2]. We solve the time-dependent Kohn-Sham equation, working equation of TDDFT, for the electronic excitation, with the vector potential associated with the electric field and effective one-body potential reflecting atomistic information of materials. One of the beggest advantages of the numerical solution of TDDFT is the capability for arbitrary temporal shape for the vector potential, not like monochromatic frequency or linear polarization in the Keldysh formula [3].

We perform TDDFT simulation for NOA of crystalline silicon under two-color laser mixing, inspired by a coherent control for the ionization rate of Krypton gas via two-color laser mixing [4]. In experiments, a sum of intensities of two color components via sum frequency generation is ideally kept to a constant. To imitate this situation in the simulation, the sum of the intensities of the fundamental photon energy ω = 1.55 eV/(h/2π) and of the double energy 2ω is kept to a constant value. For lower intensity sum 10¹⁰ W/cm² in the matter, our simulation shows trivial behavior for NOA that NOA reveals monotonic decrease by the 2ω-intensity increase. For higher intensity sum 10¹² W/cm², there is an optimal mixing ratio to maximize NOA. This simulation result invokes an efficient laser processing scheme by adding the double photon energy sources for the strong-field regime.

[1] B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann,

Applied Physics A 63, 109 (1996).

[2] S. A. Sato, K. Yabana, Y. Shinohara, T. Otobe, K.-M. Lee, and G. F. Bertsch, Phys. Rev. B 92 (2015) 205413.

[3] L.V. Keldysh, Sov. Phys.—JETP, 20 1307 (1965).

[4] H. G. Muller, P H Bucksbaum, D W Schumacher and A Zavriyev, J. Phys. B: At. Mol. Opt. Phys. 23, 2761 (1990).