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Journal of Physics B Atomic and Molecular Physics

Representation of the pulsed output from a mode-locked laser using quantum field theory and an application in multiphoton ionisation

Davıd L. Andrews

Published Aug 14, 1978• 7 citations
Publisher

Abstract

The pulsed output obtainable from a mode-locked laser has usually been described using classical radiation theory. A quantised-field representation is developed and utilised in a discussion of multiphoton ionisation. The assumptions made in deriving the results are critically examined, and a modification of the theory to deal with other kinds of pulsed radiation is indicated.

DOI
10.1088/0022-3700/11/15/014

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The pulsed output obtainable from a mode-locked laser has usually been described using classical radiation theory. A quantised-field representation is developed and utilised in a discussion of multiphoton ionisation. The assumptions made in deriving the results are critically examined, and a modification of the theory to deal with other kinds of pulsed radiation is indicated.
Previous results for the shift of the ionisation potential of an atom in a laser field are used to investigate the kinematics of multiphoton ionisation in either a laser beam or a laser pulse. Previous results for a laser beam show essentially no shifts of the 'above-threshold ionisation' peaks in the electron energy distribution and only small widths. Results for a laser pulse show the possibility of large shifts and widths growing as the pulse becomes shorter. Electrons which absorb a larger number of photons are predicted to show less shifted and narrower peaks.
Abstract In reporting and explaining the interactions of light with atoms and molecules, a photon-based description is not only appropriate but clearly essential when electronic or other kinds of quantum transition ensue. However, textbook treatments frequently go no further than the Planck relation, in representing the quantum nature of the light itself—often resorting to classical principles when discussing mechanism. Complete consistency and rigour can be achieved by treating both the matter and the radiation in a fully quantised form, which requires the electromagnetic fields to be cast in a quantum field representation. It proves possible to develop a rigorous approach to this theory that is simple to convey and apply, and which lends itself to a significantly enhanced level of appreciation of mechanism. This paper lays a concise foundation and exemplifies the application in three specific cases: absorption, emission and scattering. It is also shown how this formulation affords a basis for applications in higher-order, multiphoton and nonlinear optical processes.
A quantum theory for pulse-train from the mode-looked laser has been developed. In the theory the author uses superposition model, i. e. the atomic states are coherent after absorbed photons from different modes of a mode-locked laser. So the final atomic state should be coherently added. The resolvent operator and projector operation are used to derive the operator U. Considering the phase relationship between the modes, the light field are described by multi-mode coherent state. This method can be used to describe the resonant multi-photon processes that the pulse train from the mode locked laser interacting with atoms.
The author presents a theory of resonant multiphoton ionisation by multimode laser light. He investigates N photon resonant N+1 photon ionisation for a high order bound-bound transition with the resonance dominated by the Stark shift. Two aspects of the problem are considered. He studies the bandwidth dependence for the resonant ionisation probability, approximating the multimode laser light by a chaotic field. Secondly, he investigates the effects of finite mode numbers of the multimode laser. Finally, the theory is compared with the recent experimental results of Lompre et al (1981).