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Physical Review A

Spectrotemporal dynamics of a two-coupled-mode laser

Éric Lacot, F. Stoeckel, D. Romanini, Alexander A. Kachanov

Published May 1, 1998• 7 citations
Publisher

Abstract

In their review about intracavity laser spectroscopy, P. E. Toschek and V. Baev [in Laser Spectroscopy and New Ideas, edited by W. M. Yen and M. D. Levenson, Springer Series in Optical Science (Springer, Berlin, 1987)] have shown that multimode lasers are needed to obtain a high sensitivity. In this paper we show that two modes is enough. We discuss first the ideal case where only the spontaneous emission limits the sensitivity. In a second part we take into account the spatial hole burning, which couples the two modes and has for effect a lower limitation of the sensitivity. Analytical expressions are given for the modified absorption coefficient and the time evolution of the intensity of the two modes is calculated by numerical integration.

DOI
10.1103/physreva.57.4019

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In their review about intracavity laser spectroscopy, P. E. Toschek and V. Baev [in Laser Spectroscopy and New Ideas, edited by W. M. Yen and M. D. Levenson, Springer Series in Optical Science (Springer, Berlin, 1987)] have shown that multimode lasers are needed to obtain a high sensitivity. In this paper we show that two modes is enough. We discuss first the ideal case where only the spontaneous emission limits the sensitivity. In a second part we take into account the spatial hole burning, which couples the two modes and has for effect a lower limitation of the sensitivity. Analytical expressions are given for the modified absorption coefficient and the time evolution of the intensity of the two modes is calculated by numerical integration.
The instabilities in homogeneously broadened lasers, which we described in the previous chapter, have a paradigmatic importance because they arise in models which allow one to perform the linear-stability analysis in a simple analytic form. The treatment of the corresponding instabilities in the case of in homogeneously broadened lasers is substantially more complex in general. However, it is very interesting because, as we shall see, the instabilities arise in parametric domains that are much more accessible from the experimental viewpoint. A related issue is that of the possibility of multimodal emission in a laser. It is common knowledge that in order to attain multimode emission it is necessary to have a sort of in homogeneity in the gain medium, because in a completely homogeneous configuration all modes interact with all atoms, and the arising competition among modes implies that only one of them survives. There are basically two main kinds of in homogeneity, the first is of spatial nature and the other is of spectral nature. The first kind is realized in Fabry–Perot lasers, because different cavity modes interact with atoms at different spatial positions in the cavity thanks to the standing-wave configuration of the field and to the consequent phenomenon of spatial hole- burning (see Section 14.2 and Fig. 14.1). This circumstance is capable of weakening the mode–mode competition and allowing multimode operation. In unidirectional ring lasers, on the other hand, there is an “inhomogeneous” configuration in the case of inhomogeneous broadening, because different groups of atoms have different transition frequencies and therefore interact with different modes thanks to the spectral hole-burning (see Section 15.2 and Fig. 15.3). Again, this weakens the mode–mode competition and allows multimode operation. However, these are qualitative considerations, and the only reliable and quantitative method to determine the possibility of multimodal operation is the linear-stability analysis of the single-mode stationary solutions.
I. V. F. Gamaliĭ, E. A. Sviridenkov, and D. D. Toptygin Stimulated emission spectrum of a laser with narrow-band intracavity absorption and temporal modulation of the gain [Sov. J. Quantum Electron. 18, 1541–1547 (December 1988)] II. S. A. Kovalenko and S. P. Semin Simultaneous influence of quantum fluctuations of the intensity and of spatial homogeneities on the emission dynamics of wide-band lasers and the sensitivity of intracavity spectroscopy [Sov. J. Quantum Electron. 19, 101–102 (January 1989)]
A stochastic, semiclassical model is developed for a multimode, homogeneously broadened laser with rapid dipole dephasing, appropriate for semiconductor, Ti:sapphire, or dye lasers. The theory self-consistently incorporates population dynamics including temporal beating effects and relaxation oscillations, spatial hole burning, coherent-wave mixing, and quantum noise. The model is valid for single- and compound-cavity lasers in which the mode frequencies are well defined. We pay particular attention to finding a useful mode basis in the case that the gain medium does not completely fill the cavity. This situation can lead to coupled-cavity effects. For typical systems the model is valid for pump rates up to several times threshold and is tractable for numerical simulations. The theoretical development described in this paper is applied to an experimental system in a companion paper (J. Opt. Soc. Am. B14, 180 (1997)].
To test the application of solid-state lasers to intracavity laser absorption spectroscopy (ICLAS), we studied a neodymium-doped glass laser, in the presence of extreme relaxation oscillations (up to 108{10}^{8}108 intensity contrast). The contrast of these oscillations could be varied by changing the Q-switch transition time. The recorded absorption spectra accurately follow the regular ICLAS behavior except when the intensity in the first relaxation oscillation minimum becomes too low. In such a case, we find that the ICLAS absorption spectrum accumulated during the first spike is ``forgotten'' by the system. Numerical simulations were done which accurately describe the observed transition to a regime of memory loss, when the number of photons circulating in each mode drops close to 1. These simulations show that the mechanism of memory loss is the prevailing of spontaneous over stimulated emission. This effect sets the fundamental limit of the sensitivity of an ICLAS spectrometer where the nonlinear mode interactions are negligible. This effect was observed before only in a diode laser system with high internal losses. In this paper we report an observation of ICLAS sensitivity saturation by spontaneous emission during relaxation oscillations in a laser with low cavity losses. \textcopyright{} 1996 The American Physical Society.