Pulsed laser modification of transparent dielectrics: what can be foreseen and predicted by numerical simulations?

From random inhomogeneities to periodic nanostructures induced in bulk silica by ultrashort laser

“…where E is the electric field, H is the magnetic field, J D is current derived from the Drude model for the dispersive media, J Kerr is Kerr polarization current, and J pi is the multiphoton ionization term by using the finite-difference time-domain (FDTD) method for nonlinear and disperse media [34,35,[48][49][50][51]. At the edges of the grid, absorbing boundary conditions related to convolutional perfect matched layers (CPML) are set to avoid nonphysical reflections [65].…”

“…The electromagnetic field in these regions is modeled by resolving the same system of Eqs. (1)- (5) with a narrower electron band gap E g = 5.2 eV [49,71,79,88]. As long as the size of the inhomogeneity is considerably smaller than the irradiation wavelength, the initial plasma generation follows the Rayleigh scattering distribution [62].…”

“…The initial Gaussian electric field profile is considered as a focused beam source with the beam waist of w 0 = 3 μm and the numerical aperture NA = n sin( λ πw 0 ) < 0.2 for irradiation wavelength from λ = 400 nm up to λ = 1200 nm relatively not high, for which the paraxial approximation of the Gaussian beam's profile is still valid [35,49]. Pulse width at half maximum (FWHM) is varied from θ = 80 fs up to θ = 240 fs.…”

“…Some of them were based on the nonlinear Schrödinger equation (NLSE) [45][46][47], others used Maxwell's equations coupled with rate equation for free electron generation [34,35,41,[48][49][50][51]. However, the NLSE being an asymptotic parabolic approximation of Maxwell's equations, requires the unidirectionality of the light beam and cannot describe cases where dense electron plasma is generated causing light scattering to large angles [35,36].…”

“…None of the hypotheses presented above explained the whole physics of the phenomenon and very few attempts were made to prove or to invalidate any of them based on numerical calculations [35,36,41,48,49].…”