Jeremy R. Gulley

Ultrafast laser-induced damage and the influence of spectral effects

Abstract. Numerous studies have investigated the prerequisite role of photoionization in ultrafast laser-induced damage (LID) of bulk dielectrics. This study examines the role of spectral width and instantaneous laser frequency in LID using a frequency dependent multiphoton ionization (MPI) model and numerical simulation of initially 800 nm laser pulses propagating through fused silica. Assuming a band gap of 9 eV, MPI by an 800 nm field is a six-photon process, but when the instantaneous wavelength is greater than 827 nm an additional photon is required for photoionization, reducing the probability of the event by many orders of magnitude. Simulation results suggest that this frequency dependence can significantly impact the onset of LID and ultrashort pulse filamentation in solids.

Ultrashort-pulse propagation through free-carrier plasmas

The past decade has seen frequent use of a modified nonlinear Schroedinger equation to describe ultrashort pulse propagation in materials where free-carrier plasmas are present. The optical contribution from the resulting free-current densities in this equation is often described using a classical Drude model. However, the ultimate form of this contribution in the modified nonlinear Schroedinger equation is somewhat inconsistent in the literature. We clarify this ambiguity by deriving the modified nonlinear Schroedinger equation from the classical wave equation containing a free-current density contribution. The Drude model is then used to obtain an expression for the complex free-carrier current density envelope with temporal dispersion corrections for ultrashort laser pulses. These temporal dispersion corrections to the current-density term differ, to our knowledge, from all other models in the literature in that they depend more sensitively on the value of the Drude free-carrier collision time. These corrections reduce to the current models in the literature for limiting cases. Theoretical analysis and computer simulations show that these differences can significantly affect the dynamic interactions of plasma absorption and plasma defocusing for materials with free-carrier collision times on the order of one optical cycle (or less) of the applied field.

Simulation and analysis of ultrafast-laser-pulse-induced plasma generation in fused silica

Recent experiments on optical damage by ultrashort laser pulses have demonstrated that the temporal pulse shape can dramatically influence plasma generation in fused silica. We use a modified 3+1D nonlinear Schrodinger equation for the pulse propagation coupled to a rate equation for the plasma density in the dielectric material to simulate pulse propagation and plasma formation in fused silica. We use these simulations to analyze the influence of pulse shape and beam geometry on the formation of the electron plasma and hence modification in the bulk material. In particular, we simulate the effect of pulses reconstructed from experimental data. It is expected that a better understanding of the dynamics of laser-induced plasma generation will enable the accurate simulation of optical damage in a variety of dielectrics, ultimately leading to an enhanced control of optical damage to real materials and optical devices.

Time-frequency Control of Ultrafast Plasma Generation in Dielectrics

This paper examines ultrafast laser-induced plasma generation in dielectrics by modeling ionization and pulse propagation in glass. Photoionization models for solids predict that the multi-photon ionization rate should increase for near-UV frequencies when compared to those in the visible or near-IR. Conversely, the frequency dependence of a Drude-type absorption by free electrons can produce an increased ionization yield through avalanching for frequencies in the IR. The simulations presented in this paper reveal how such frequency-dependent models influence the plasma formation during nonlinear pulse propagation in fused silica. It is further shown by a multi-rate equation model that the contribution from avalanching, when properly delayed, is reduced by an order of magnitude at near-IR frequencies throughout the propagation. A modified multi-rate equation is then introduced to model combinations of ultrashort high-frequency and low-frequency pulses that can maximize plasma generation while operating at the lowest possible fluences.

Nonlinear space-time focusing and filamentation of annular femtosecond pulses in dielectrics

Filamentation during simultaneous space-time focusing in bulk fused silica is investigated numerically. We model the use of a pair of concentric gratings to transform a common femtosecond laser pulse with a Gaussian spatial profile into a radially chirped, annular beam shape that is focused into the bulk of silica by a lens. By varying the energy and/or time-chirp of the incident pulse, we capture the pulse dynamics and material response that yields material modification and damage in the nonlinear focus. The results show rich pulse dynamics, enhanced damage/modification site localization, and suggest novel approaches to laser machining of solids.

A split-step method to include electron-electron collisions via Monte Carlo in multiple rate equation simulations

A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron-phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron-electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron-electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.

Modeling Free-Carrier Absorption and Avalanching by Ultrashort Laser Pulses

In the past decade it was demonstrated experimentally that negatively-chirped laser pulses can lower the surface LIDT for wide band-gap materials by decreasing the number of photons required for photoionization on the leading edge of the pulse. Similarly, simulations have shown that positively-chirped pulses resulting from selffocusing and self-phase modulation in bulk dielectrics can alter the onset of laser-induced material modifications by increasing the number of photons required for photoionization on the leading edge of the pulse. However, the role of multi-chromatic effects in free-carrier absorption and avalanching has yet to be addressed. In this work a frequency-selective model of free-carrier dynamics is presented, based on a recently extended multi-rate equation for the distribution of electrons in the conduction band. In this model free-carriers gain energy from the field by single-photon absorption at the instantaneous frequency, which varies as a function of space and time. For cases of super-continuum generation it is shown that a Drude-type absorption can vary from 50% to over 200% the absorption rate as evaluated at the central pulse frequency only. Simulations applying this model to ultrafast laser-plasma interactions in fused silica explore how pulse chirps may be used as a distinguishing parameter for LID resulting from otherwise identical pulses.

Frequency dependence in the initiation of ultrafast laser-induced damage

Numerous studies have investigated the role of photoionization in ultrafast laser-induced damage of bulk dielectrics. This study examines the role of spectral width and instantaneous laser frequency in laser-induced damage using a frequency dependent multiphoton ionization model and numerical simulation of an 800 nm laser pulse propagating through fused silica. When the individual photon wavelengths are greater than 827 nm, an additional photon is required for photoionization, reducing the probability of the event by many orders of magnitude. Simulation results suggest that this frequency dependence may significantly affect the processes of laser-induced damage and filamentation.

Simulation and analysis of ultrafast laser pulse induced plasma generation in dielectric materials

Recent experiments on optical damage by ultrashort laser pulses have demonstrated that the temporal pulseshape can dramatically influence plasma generation in fused silica and sapphire. In this work a modified 3+1D nonlinear Schroedinger equation for the pulse propagation coupled to a rate equation for the plasma density in the dielectric material is used to simulate pulse propagation and plasma formation in a range of dielectric materials. We use these simulations to analyze the influence of pulse-width, pulse-shape and beam geometry on the formation of the electron plasma and hence damage in the bulk material. In particular, when possible, we simulate the effect of pulses reconstructed from experimental data. It is expected that a better understanding of the dynamics of laser-induced plasma generation will enable the accurate simulation of optical damage in a variety of dielectrics, ultimately leading to an enhanced control of optical damage to real materials and optical devices.

Self-consistent modeling of photoionization and the Kerr effect in bulk solids

In calculations of ultrafast laser-induced ionization the treatment of fundamental mechanisms such as photoionization and the Kerr effect are treated in isolation using monochromatic perturbative approaches. Such approaches are often questionable for pulses of ultrashort duration and multi-chromatic spectra. In this work we address this issue by solving the quantum optical Bloch equations in a 3D quasi-momentum space and show how to couple this model to ultrashort pulse propagation in dielectrics. This approach self-consistently couples a quantum calculation of the photoionization yield, the photoionization current, and the current from free-carriers with the traditional Kerr effect (self-focusing and self phase modulation) without resort to a perturbative treatment. The material band structure is taken in the tight binding limit and is periodic in the crystal momentum space. As this model makes no assumption about the pulse spectrum, we examine the laser-material interaction of strongly chirped pulses and multi-color multi-pulse schemes of laser-induced material modification. These results are compared to those predicted by standard treatments, such as the Keldysh model of photoionization, for pulses of ultrashort duration.