Interaction of Atomic Hydrogen with Pico- and Femtosecond Laser Pulses

by

Jonathan Parker
(1990)

This thesis presents a theoretical study of the interaction of atomic hydrogen with coherent laser pulses in the 5 femtosecond to 10 picosecond range, in the weak-field limit, and in intense fields. We approach the problem in the weak-field limit by studying the relationship between the Fourier relation of the laser pulse (ΔωΔt) and the ΔEΔt relation of the atomic Rydberg wave packet generated by the laser pulse. A derivation of the wave packet based on the WKB approximation is given, permitting the quantity Δt to be derived for the quantum state, with the conclusion that under certain circumstances a transform-limited laser pulse (satisfying ΔωΔt = 1/2) can generate a transform-limited electron (satisfying ΔEΔt/ = 1/2).

The interaction of hydrogen with femtosecond pulses is studied at field intensities as high as 2.2×10¹⁴W/cm². The full three-dimensional Schrodinger equation is numerically integrated at intensities of this order as a guide to the development of theory. In terms of the Fermi golden rule (FGR) formulation of ionization, the results may be summarized as follows: just about every approximation employed in the derivation of FGR breaks down at 10¹⁴W/cm². Nevertheless, it was possible to provide straightforward non-perturbative methods to replace the approximations and perturbative methods employed FGR.

A population-trapping effect is found numerically and modeled theoretically. Despite the high field intensities, population representing the excited electron is recaptured from the ionization continuum by bound states during the excitation. Population returns to the atom with just the right phase to strongly inhibit ionization. A theory is presented that models this effect for a variety of laser pulse shapes, with and without the rotating-wave approximation.

The numerical integration reveals that a certain amount of above-threshold ionization (ATI) occurs. A theory similar to the Keldysh-type theories of ATI is developed. The theory differs from the Keldysh theories in that, like Schrodinger's equation, it is invariant under certain gauge transformations. The proposed theory gives far superior agreement with the numerical integration than Keldysh theory.

Classical ionization at 2.2×10¹⁴W/cm² is studied by numerically integrating Newton's equation on a Monte Carlo ensemble constructed to correspond to the above examples.

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Last modified 13 September 2006