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Conference on Lasers and Electro-Optics

Quantum mechanical description of the dynamics of a laser with two-pulse/cavity round-trip

Andreas Schmitt-Sody, Ladan Arissian, Andreas U. Velten, Jean‐Claude Diels

Published May 1, 2008• 0 citations
Publisher

Abstract

The density matrix of a two-level system interacting with a near resonant field, corresponds to the circulating intensities (diagonal elements) and the beat signal of the interfering outputs (off-diagonal element) of a ring laser.
DOI
10.1109/cleo.2008.4552289

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The generalization of the area theorem is derived for the case of a pulse circulating inside a ring laser cavity. In contrast to the standard area theorem, which is valid for a single pass of a traveling pulse through a resonant medium, the obtained generalized area theorem takes into account the medium-assisted nonlinear self-action effects through the medium excitation left by the pulse at the previous round-trip in the cavity. The generalized area theorem was then applied to the theoretical description of the dynamics of a single-section ring-cavity laser and the steady solutions for the pulse area and for the medium parameters were found both in the limit of a lumped model and for a spatially extended system. The derived area theorem can be used for the convenient analytical description of different coherent photonic devices, such as coherently mode-locked lasers or pulse compressors, as well as for the analysis of the photon echo formation in cavity-based setups.
Cavity Ring Down Spectroscopy has become an important method in gas phase spectroscopy and its uses promise to expand. While previous investigators have considered the decay of the stored energy in the cavity ring down cell following short pulsed excitation, this paper considers the effects of pulse reshaping during cavity ring down. It is found that in order to properly model these effects, one must consider not only the mode dependent loss of the ring down cavity, but also dispersion that shifts the resonant modes of the cavity. Only by considering the latter effect does one get a "causal" result where the free induction decay signal of the absorber occurs after the excitation pulse. It is demonstrated that in the limit that the cavity round trip time is long compared to both the T 2 time of the intracavity absorber and the temporal width of the excitation pulse, the reshaping of the n'th pulse out of the ring down cavity is the same as the reshaping produced by free space propagation over a distance of (2 n + 1) L where L is the separation of the mirrors in the cell. However, when the absorber T 2 becomes comparable to or longer than the cavity round trip time, then discrete modes of the ring down cavity become important. A general expression for the output is given for the important case of a weak absorber, and changes in the output are computed for a single absorption line as a function of the ratio of T 2 to the cavity round trip time for several values of the optical thickness of the sample. Lastly, it is suggested that monitoring changes in the pulse shape of the cavity ring down signal provides a way to characterize an absorption spectrum on a frequency scale of the laser bandwidth down to the cavity free spectral range.
Two-round-trip-time modulation of the cavity field has been observed in a passive ring resonator, containing an ammonia cell, pumped by smooth 100-ns CO2{\mathrm{O}}_{2}O2​ laser pulses. The results are in excellent accord with the theory of Ikeda instability instability in a two-level system, which is generalized to include reservoir kinetics.