Modeling nanogratings erasure at high repetition rate in commercial optical glasses

Volume nanogratings (NGs) imprinted by infrared femtosecond laser in commercial optical glasses take the form of orientable subwavelength birefringent nanostructures, being composed of an assembly of nanopores. The existence of NGs strongly depends on the laser parameters and glass composition. Therefore, in this work, we tentatively model the erasure threshold of NGs in a pulse energy - repetition rate processing window. For this purpose, we combine i) a heat diffusion model to simulate the thermal treatment experienced by the glass upon laser irradiation, and ii) the Rayleigh-Plesset equation to take into account the evolution of a nanopore size during laser processing. We first determine a criterion for nanopores erasure, falling within a typical characteristic time of few tens of ns, for which the cooling of the last laser pulse absorbed by the material is progressively cooled. Then, considering a multipulse regime, and the dependence of the deposited pulse number on the thermal treatment experienced by the glass, the modeled NGs erasure threshold follows the experimental trend. Finally, by using a steady state regime for various repetition rates and adjusting the energy deposition (absorption coefficient or beam waist) as a function of the pulse energy, the NGs existence window can perfectly match the experimental values.