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Journal of the Optical Society of America B

S-matrix theory of multiphoton ionization

Predrag Krstić, Marvin H. Mittleman

Published Apr 1, 1990• 9 citations
Publisher

Abstract

The general S-matrix theory of multiphoton ionization is presented. The freedom in the form of the S matrix is discussed and exploited to derive a form that uses the exact dressed state as the initial state of the process. This results in a new S-matrix form, which is then evaluated in an approximate form. The numerical result is identical with a previously obtained one but radically different from that obtained by using the Keldysh–Faisal–Reiss theories.

DOI
10.1364/josab.7.000587

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Physical Review A•Sep 1, 1989•11 citations
The general S-matrix theory of multiphoton ionization is presented. The freedom in the form of the S matrix is discussed and exploited to derive a form that uses the exact dressed state as the initial state of the process. This results in a new S-matrix form, which is then evaluated in an approximate form. The numerical result is identical with a previously obtained one but radically different from that obtained by using the Keldysh–Faisal–Reiss theories.
The Keldysh-Faisal-Reiss theory of nonresonant multiphoton ionization seems to give reasonably good agreement with experiments for production rates in the above-threshold-ionization peaks. The theory has some conceptual difficulties, since physically equivalent Hamiltonians give radically different results when treated by this method. An alternate form of the S matrix is used here in which approximation must be made upon the exact wave function evolving from the initial state rather than the time-reversed form used in the Keldysh-Reiss treatment. The exact initial state is approximated by an adiabatic form which results in an S matrix that eliminates the conceptual difficulties described above.
The rate parameters for double multiphoton ionization are obtained as functions of T matrices, which are derived from the S matrix by a generalization of the Fermi Golden Rule. The different T's appear, and are distinguished from each other as coefficients of different energy singularities, principal parts as well as delta functions, in S. These are connected to the rate parameters, which appear in threecoupled-rate equations. New terms are shown to contribute to the direct ionization process and new interference terms are also found to contribute to the direct ionization rate. A new interpretation of the shake-off term is given, and it is found to be a sequential process. {PACS Nos.: 32.80F, 32.80K}
The general theory of multiphoton ionization of hydrogen atoms by simultaneous absorption of several photons is discussed. In the nonrelativistic dipole approximation, the calculations lead to a recursion relationship concerning angular functions and involve radial matrix elements containing many summations over intermediate states. A general method for exactly evaluating several sums is described in detail and applied to the photo-ionization of atomic hydrogen in the ground state. Numerical results are presented as dispersion curves of the transition rate $\frac{{\ensuremath{\sigma}}_{n}}{{I}^{N\ensuremath{-}1}}$ for a range of wavelengths from 1000 up to 7200 \AA{}.
Multiphoton ionization of hydrogen atoms by a strong multimode field when several final continuum states are populated is treated theoretically within a model based on the S-matrix formalism. The field is taken in dipole approximation, with zero bandwidth. Field-dressed Coulomb wave functions are used for the electron final states. Ionization rates are calculated for different numbers of photons absorbed in excess of the minimum number required to go into the continuum. In general, the calculated quantities are in good qualitative agreement with the corresponding experimental observations.
The Keldysh approximation to treat the multiphoton ionization of atoms is reconsidered. It is shown that, if one consistently uses the hypothesis under which the approximation should be valid (essentially, that of a weak, short-range binding potential), a Keldysh-like term results as an approximation to the first term of a uniformly convergent series in powers of the binding potential. No cancellation occurs when higher-order terms are taken into account. This result allows one to consider the Keldysh approximation as a well-defined theoretical model, without implying, however, that it is adequate to describe multiphoton ionization of real atoms.