Reduction of multi-photon ionization in dielectrics due to collisions

The collisional effect due to the multi-photon ionization process in dielectric material has been studied. We found that the breakdown threshold of fused silica is the same for both linearly and circularly polarized light at 55 fs and 100 fs, which we believe is an indication of the suppression of multi-photon ionization in solids. By numerically solving the time-dependent Schr6dinger equation with scattering, for the first time, we have observed substantial reduction of the multi-photon ionization rate in dielectrics due to collisions. PACS: 32.80.Rm; 77.32.Jp Multi-photon ionization (MPI) of free atoms is photoionization with photon energies smaller than the ionization potential. MPI has been uninterruptedly studied both experimentally and theoretically since its discovery in 1965 [1,2]. Experimentally, important results on ionization rate as a function of laser intensity were obtained in the 1970s [3]. The observation of ejected electrons with excessive photon energy than the minimum MPI required (termed as above-threshold ionization) widened the understanding of laser-atom interaction [4-6]. MuItiphoton Ionization of Atoms, edited by Chin and Lambropoulos and Atoms in Intense Laser Fields, edited by Gavrila have covered a great deal of the pursuit. In the theoretical studies of MPI, both analytical approximation and numerical methods have been employed. Keldysh studied the ionization probability of a hydrogen atom in an electromagnetic field, where the final state of the electron is described by the so-called Volkov states [7]. Depending on the adiabatic parameter, 7 = (Ui/2Up) t/2, where Ui is the ionization potential and Up = e2E2/4nm) 2 is the quiver energy of an electron in the electric field, the ionization is related to the tunneling effect for 7 < 1, or to multiphoton absorption when 7 >> 1. Keldysh's work was rediscovered and improved by Faisal and Reiss later and they are now known as the KFR theory [8, 9]. Numerical studies of the time-dependent Schr6dinger equation have also been done [10, 11]. By numerically integrating the time-dependent Schr6dinger equation, one can directly calculate the ionization of an atom in the electronmagnetic field. In both approaches, researchers were able to explain many of the observations of multi-photon processes. We would like to point out, however, that most of the experiments on MPI were done with low pressure gases where inter-atomic distance is larger than the electron excursion amplitude, hence collisional effect is negligible, and theoretical studies were also concentrated on single atoms interacting with the laser field. Recently, we performed a series of laser-induced breakdown (LIB) experiments with pulse widths ranging from 150 fs to 7 ns in wide-hand-gap dielectric materials [12]. The normally transparent dielectric material can be ionized by the intense laser radiation and absorbs the photon energy, resulting in a catastrophic breakdown of the material. The key factor in LIB is the free electron generation. Since the photon energy is much smaller than the energy gap of the material, the electron generation is through nonlinear processes. The main mechanisms for free electron generation are avalanche ionization and multi-photon ionization. Our findings show that avalanche ionization dominates the breakdown, and multiphoton ionization effect is small even at the short pulse width regime where one would expect that MPI is much stronger due to the high intensity of the laser field. It puzzles us and motivates us to further investigate the photoinization process in solids. In solids and dense gases, the excursion amplitude of a valence electron can become bigger than the inter-atomic distance when high intensity laser pulses are applied. Therefore, scattering of the electron off the neighboring atom is likely to occur during an optical cycle. Because of the high collision frequency inside solids, the periodic motion of electrons has been disturbed, and the electrons are dephased with respect to the driven field. Hence we believe that MPI will be suppressed in solids. In this paper we report our investigation on MPI in solids through laser-induced breakdown experiments and by numerical integration of the time-dependent Schr6dinger equation. We performed laser-induced breakdown