Strong field approximation (SFA) is the most important approximation
in the analytical theory of intense laser matter interaction. Based
on SFA many analytical theories have been developed such that a
broad spectrum of strong field physics phenomena can be described.
The central idea of SFA-based theories is to approximate the
electron propagation in the continuum by the Gordon-Volkov
wavefunction - a well studied analytical solution to the time-dependent Schr\"{o}dinger equation where the electron is driven by the
laser field only. This approximation captures some of the essential
features of strong-field physics, but at the same time causes several problems in the theory.
In this thesis a comprehensive study of the SFA has
been presented. We introduce the SFA in both the length gauge and the
velocity gauge. The adequacy of SFA has been discussed by comparing the theory to the numerical solution to
the time-dependent Schr\"{o}dinger equation (TDSE). The numerical method of solving TDSE is
presented as a separate chapter.
In order to obtain a better
understanding of the applicability of SFA-based theory, we tested the major approximations in the theory by using
three different models: the zero-range potential, the hydrogen atom and
the hydrogen molecular ion. The accuracy of the method of steepest descent (MSD)
and other major approximations in the analytical theory have
also been examined. Targeting at the generalization of
the SFA-based theories, several extensions and improvements of SFA
have been proposed. We will review them in detail and bring them
into unity.
One of the most successful aspect of the SFA-based theories is to
describe and decompose electron dynamics into components such that
identification of different physical processes becomes possible. For
instance, the direct ionization and non-sequential double ionization
bear clear definitions only within the SFA-based framework. The
physical interpretation becomes more straight forward due to the
fact that there is a close connection between the quantum orbital
and classical trajectory. The MSD is a
mathematical tool to bridge the quantum orbital and the classical
trajectory in an SFA-based theory. We will discuss MSD within a
systematic framework so that the higher order asymptotic expansion
terms can be obtained in a straight forward way.
After gaining substantial understanding of the SFA and the MSD we developed
a graphic user interface (GUI) software that is capable of
calculating strong field ionization rates, photo-electron spectra
and high harmonic generation spectra. The software interface and
algorithms have been presented in the thesis. Sample calculations
were done and compared with the previously obtained results.
In the last chapter of the thesis, we further developed the theory to
describe a two-laser ionization scheme where one laser is chosen
to be resonantly coupled two real states and the other is a strong
few-cycle laser pulse. We demonstrate the periodic dependence of the
total ionization on the appearance time of the strong few-cycle
laser pulse. In the case of few-cycle pulses with lower intensity,
we observed side-bands in the photoelectron spectrum, whose
intensity vary periodically with the appearance time of the pulse.
We show that our extended theory is able to explain these phenomena
adequately.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/6604 |
| Date | January 2012 |
| Creators | Long, Zijian |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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