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Journal of the Optical Society of America B

Resonant radiation of an atom in laser pulse train

Weiping Zhang, Weihan Tan

Published Nov 1, 1987• 1 citation
Publisher

Abstract

We discuss the solutions of the Bloch equations of a two-level atom that resonantly interacts with a laser pulse train. In terms of solutions, we calculate the radiation spectrum of the two-level atom driven by the laser pulse train and obtain the multipeak structure. The appearance of the multipeak structure in the radiation spectrum depends both on the coupling strength of the atom with the side frequencies of the laser pulse train and on the pulse duration.

DOI
10.1364/josab.4.001885

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We discuss the solutions of the Bloch equations of a two-level atom that resonantly interacts with a laser pulse train. In terms of solutions, we calculate the radiation spectrum of the two-level atom driven by the laser pulse train and obtain the multipeak structure. The appearance of the multipeak structure in the radiation spectrum depends both on the coupling strength of the atom with the side frequencies of the laser pulse train and on the pulse duration.
This paper discussed the solution of the Bloch equations of a two-level atom resonantly interacting with laser pulse trains in detail. In terms of the solution, we calculate the radiation spectrum of the two-level atom excited by the laser pulse trains and obtain the following conclusions: (1) for the atoms satisfying the condition K1/K = 1 (such as gas atoms broadened by spontaneous emission), the laser pulse trains are almost equivalent to a CW laser; (2) for the atoms K1/K《1, saying, some solid atoms like ruby, the radiation spectrum of the atom exhibits the multipeak structure induced by the strong interaction of the atom with the side frequency components of the laser pulse trains.
The problem of a two-level atom interacting with a nonmonochromatic radiation pulse is studied both with and without the resonant approximation. Using the time-dependent perturbation theory, the analytical expressions for transition probability of the atom are obtained. It is shown how, depending on the value of the field strength, the atom's excitation probability can be obtained with the needed accuracy. It is shown that the upper level population of the atom exhibits oscillations which are absent in the resonant approximation. It is shown that absorption probability and dipole moment spectrum are governed by interference between the spectral components of a non- monochromatic radiation involved in nonlinear interaction process. Spectral distribution symmetry with respect to the resonance frequency being destroyed, the atom can be excited even if there is no resonant component in the pulse spectrum.
A general, analytic theory is presented of the excitation of a two-level atom by a series of short optical laser pulses. The atom is assumed to be isolated (collisionless) with radiative decay from upper to lower state at rate γ. The laser pulses are assumed to have a duration tp such that γtp ≪ 1 (the transient regime), and the spacing between pulses tr is such that tr ≫ tp. In this regime the atomic density matrix is calculated as a function of time during each optical pulse. An analytic expression for the atomic state (Bloch vector) after n optical pulses is also derived. For large n the atomic state converges to a repeating (steady state) cycle of pump excitation followed by radiative decay. The excited-state population in the steady state can be large but only if the spacing between pulses tr is small so that γtr ≲ 0.5. These results indicate that lasers that produce trains of pulses, such as mode-locked conventional lasers and free-electron lasers, can be effective in optical pumping of atoms.
Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width $\ensuremath{\gamma}$ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time ttt, $\ensuremath{\Phi}(t)$. Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: $\ensuremath{\Phi}(t)\ensuremath{\approx}sin\ensuremath{\Phi}(t)$ and $\ensuremath{\Omega}(t)>\ensuremath{\gamma}$, where $\ensuremath{\Omega}(t)$ is the resonance Rabi frequency. The generalization of the two-level atom results to the NNN-level atom is discussed.