Modeling the effect of fs light delocalization in Si bulk

Abstract

Stimulated by the recently observed strong delocalization of fs radiation in c:Si bulk, the numerical study of fs laser beam propagation and photoexcitation of silicon material has been performed. Two fundamental aspects-dissipation of laser energy due to two-photon absorption (TPA) and nonlinear beam transformation-have been elaborated to clarify the nature of this effect.It has been found that for incident pulse energy 100 µJ and tight beam focusing onto a spot of 6.5 µm diameter, due to TPA only a small part of the laser pulse energy (<1%) could reach the focal plane inside the Si bulk. As a result, the laser-produced e-h plasma density did not exceed ∼10 19 cm −3 and the bulk material damage (permanent modification) threshold was never reached. Additionally, the e-h plasma defocusing has been shown to give a contribution to the light delocalization, significantly widening the pulse propagation path. The data obtained are quite consistent with the experimental results.

Two-photon–induced internal modification of silicon by erbium-doped fiber laser

“…The same conditions as used for the experiments in Ref. [17] have been evaluated by numerical simulations [22]. The simulations showed that less than one percent of the laser energy reached the focal plane for a 250 fs pulse with a pulse energy of 100 µJ and a wavelength of 1200 nm.…”

Pulse-duration dependence of laser-induced modifications inside silicon

“…The first recent successes in locally tailoring the properties of silicon (Si) with ultrashort pulses tightly focused below the surface [1][2][3][4][5] have revealed responses strongly deviating from those extensively studied in dielectrics during the last two decades [6,7]. Till now, the investigations for internal modification of silicon have been focused on the short-wave infrared region of the spectrum (SWIR) and very modest dependence to the wavelength parameter is found as long as multiphoton absorption initiates localized energy deposition near the focus in an originally transparent Si target [8,9]. This is very similar to how visible or near-infrared femtosecond pulses are used for 3D writing applications inside dielectrics.…”

“…It is also today used for more advanced processing with some optical and fluidic functionalities added to Si in this regime [15][16][17][18][19][20]. At the opposite, the shortest ultrashort pulses (sub-100 fs) usually fail in inducing permanent changes inside Si using conventional machining configurations [2,8,21,22]. One can also note contradictions in the intermediate picosecond regime where some argues that modification regimes are hardly achievable with pulses of few picosecond duration [5,23] while other have recently presented demonstration of waveguide writing in Si with sub-ps pulses and conditions very similar to those used in dielectric studies [3,4].…”

Crystal structure of laser-induced subsurface modifications in Si

“…For a fixed pulse energy, shorter pulses result in higher instantaneous powers of the laser beam. Excessive powers induce two-photon absorption above the focus [36,37], resulting in absorption of laser energy at undesired locations and plasma-induced defocussing of the laser beam [37]. Moreover, when a critical power threshold is exceeded, self-focussing due to the Kerr effect becomes an issue [16].…”