Kenneth J. Schafer

Dynamics of short-pulse excitation, ionization and harmonic conversion

In recent years there have been very significant advances in short pulse, high intensity laser technology. Lasers with pulse lengths of 0.1–1 ps and wavelengths from 0.2–1 μm can be focused to produce intensities from 1012 to above 1018 W/cm2. One major use of these systems has been for studies of the response of atoms and molecules to such intense, well characterized electromagnetic fields. Because these pulses are very short, neutral atoms can survive to experience intensities where theoretical treatments based on the traditional perturbation expansion of the wave function in terms of the field-free states will fail completely to describe the dynamics of the system. An explicit, non-perturbative time-dependent calculation is one approach which can represent these strong field effects.

Optical harmonic generation in atomic and molecular hydrogen

Abstract We compare calculated optical harmonic spectra for the hydrogen molecule and the hydrogen atom in an intense, linearly polarized laser field. The hydrogen atom calculations use an exact, time-dependent method and the hydrogen molecule calculations are performed in a time-dependent Hartree-Fock approximation. In both cases, the laser-matter interaction is treated completely non-perturbatively. We show that if the H 2 bond length is stretched so that H 2 has the same ionization potential as H, both systems produce remarkably similar harmonic spectra when irradiated with a 1064 nm laser at 1 × 10 14 or 2 × 10 13 W/cm 2 .

NONLINEAR EFFECTS IN ELECTRON AND PHOTON EMISSION FROM ATOMS IN INTENSE LASER FIELDS

Atoms subject to intense laser fields are capable of absorbing many more photons than the minimum number needed to ionize. This leads to two striking nonlinear phenomena, above-threshold ionization, and high-order harmonic generation. We have used time-dependent methods to calculate both these processes nonperturbatively for realistic, three-dimensional atoms. This allows us to clarify the relationships between photon and electron emission rates in the strong field regime.

Understanding the dynamics of multiphoton processes in atoms and molecules

The dynamics of the high‐order, nonlinear processes in atoms and molecules induced by strong laser fields have been probed using techniques first introduced by Chris Bottcher and his collaborators. Our current understanding of the emission of electrons and photons from laser‐excited atoms and of laser‐induced molecular stabilization has been achieved by exploiting these ideas.

Harmonic Generation at High Intensities

Atomic electrons subject to intense laser fields can absorb many photons, leading either to multiphoton ionization or the emission of a single, energetic photon which can be a high multiple of the laser frequency. The latter process, high-order harmonic generation, has been observed experimentally using a range of laser wavelengths and intensities over the past several years.1»2 Harmonic generation spectra have a generic form: a steep decline for the low order harmonics, followed by a plateau extending to high harmonic order, and finally an abrupt cutoff beyond which no harmonics are discernible. During the plateau the harmonic production is a very weak function of the process order. Harmonic generation is a promising source of coherent, tunable radiation in the XUV to soft X-ray range which could have a variety of scientific and possibly technological applications. Its conversion from an interesting multiphoton phenomenon to a useful laboratory radiation source requires a complete understanding of both its microscopic and macroscopic aspects. By “microscopic” we mean the response a single atom to a pulse of intense laser radiation, while “macroscopic” refers to the spatial and temporal characteristics of the emitted radiation as it propagates through the nonlinear medium in which it is produced. In this article we focus on the response of a single atom to an intense, short pulse laser. The macroscopic aspects of harmonic generation are treated in detail elsewhere in this volume.3

High-order harmonic generation with short-pulse lasers

Recent progress in the understanding of high-order harmonic conversion from atoms and ions exposed to high-intensity, short-pulse optical lasers is reviewed. We find that ions can produce harmonics comparable in strength to those obtained from neutral atoms, and that the emission extends to much higher order. Simple scaling laws for the strength of the harmonic emission and the maximum observable harmonic are suggested. These results imply that the photoemission observed in recent experiments in helium and neon contains contributions from ions as well as neutrals.

Time-dependent studies of high-order harmonic generation (Invited Paper)

Experimental results have demonstrated very high order harmonic generation in rare gases exposed to intense laser fields. We use time-dependent methods to calculate the single atom emission spectrum in a number of systems. These spectra show many of the same features seen experimentally, e.g. a broad plateau that depends in intensity and extent on the ionization potential. To explain the observed spectra, we fold these single atom results into a full solution of the propagation equations for the nonlinear medium. This leads to impressive agreement between theory and the experiment for xenon, both in the absolute number of photons observed as well as the intensity dependence of all harmonics through the 21st. The use of time-dependent methods also facilitates a comparison between photon and electron emission processes.

Phase Effects in Two-Color Multiphoton Processes

There has been considerable interest over the past few years in the interactions of atoms and molecules with intense, short pulsed lasers. Measurements and calculations of ionization rates and photoemission rates have been reported for many wavelengths and intensities for single frequency laser fields. More recently, the effects of the presence of a second, intense laser field have been considered. Predictions that ionization dynamics can be controlled using two lasers with a fixed phase relationship between the them have been realized in experiments by Chen and Elliot1 and by Muller, et al.2 In both experiments the rate for multiphoton ionization was shown to depend on this phase. Muller, et al. also showed that the ATI (above threshold ionization) photoelectron energy distributions were also affected. Here we report calculations of the two-color ionization of hydrogen that reproduce these observed phase sensitive effects. We also present angular distributions for the photoelectrons and their variation with the relative phase between the lasers. In addition these calculactions address the question of the magnitude of the ponderomotive shift of the ionization potential caused by the combined laser fields.

Coherence in Strong Field Harmonic Generation

The high-order harmonics generated when an intense, short-pulsed laser is focused into an atomic gas provide not only a surprisingly strong source of short wavelength, coherent radiation, but also prove to be a sensitive probe of the dynamics of atoms in strong electromagnetic fields. The source of the harmonic radiation is the polarization induced in the atomic medium by the pump laser. This polarization results from the distortion of the electronic charge density in each individual atom, producing a time-dependent dipole moment whose phase is determined by the phase of the driving field at the atom. The Fourier transform of the atomic dipole is directly related to the strengths and phases of the harmonic emission from the individual atoms. Interference between the harmonic fields produced at different points in the medium can be constructive or destructive depending on the phases set by the incident field. The overall harmonic conversion efficiency can depend very strongly on these phase matching effects. Therefore, modelling strong-field harmonic conversion requires both the calculation of the single atom response and the solution of the propagation equations for the harmonic fields.

Time-Dependent Dynamics of an Atom in an Intense Laser Field

In recent years we have seen very rapid advances in the technology of short pulse, very high intensity lasers. Lasers with pulse lengths of 0.1–1 ps and wavelengths from 0.2–1 μm can be focused to produce intensities from 1012 to above 1018 W/cm2. One major use of these systems has been to study the response of atoms and molecules to such intense, well characterized electromagnetic fields. These pulses are short enough that neutral atoms survive to experience intensities where traditional perturbation expansions, based on the field-free states of the system, will fail completely to describe the dynamics of the system. Evidence for non-perturbative ionization can be found in the photoelectron energy spectra which contain numerous peaks separated by the photon energy. These peaks indicate a high probability of absorbing many more photons than the minimum required for ionization. This phenomenon, called above threshold ionization (ATI), has been observed in many experiments1 and is reproduced theoretically from an energy analysis of the final state wave function obtained from a time-dependent calculation.2 A second remarkable observation in high intensity experiments is the unexpectedly efficient production of very high-order harmonic radiation during the laser pulse. Harmonics up to the 109th order of a 140 fs Ti-sapphire (806nm) laser in neon have been reported.3 Again, the time-dependent wave function contains the information that explains this highly nonlinear, non-perturbative behavior. The Fourier transform of the dipole induced in the electronic charge distribution gives the spectrum of emitted radiation. For many atomic systems, the calculated spectra agree quantitatively with the observed harmonic emission.4