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Physical Review A

Dynamic Lamb-dip effects in gas lasers with inhomogeneously broadened saturable absorbers

Carlos R. de Carvalho, L. Davidovich

Published May 1, 1992• 2 citations
Publisher

Abstract

We show, through a simple model, that as one changes the detuning of a standing-wave single-mode gas laser containing an inhomogeneously broadened saturable absorber, a Lamb-dip generated stability window may appear in the instability region. The width of this window is of the order of the homogeneous linewidth of the absorber, and it is not affected by power broadening.

DOI
10.1103/physreva.45.6748

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We show, through a simple model, that as one changes the detuning of a standing-wave single-mode gas laser containing an inhomogeneously broadened saturable absorber, a Lamb-dip generated stability window may appear in the instability region. The width of this window is of the order of the homogeneous linewidth of the absorber, and it is not affected by power broadening.
The structure of the Lamb dip may permit a standing-wave gas laser containing a saturable absorber (LSA) to exhibit frequency tristability while oscillating in a single spatial mode. This is concluded from the steady-state and stability analyses of a plane-wave gas-laser model in which the atomic populations are taken as homogeneous. Conditions for this behavior are investigated, and it is concluded that very high pump excitations are needed, which is in contrast to previously reported predictions of frequency multistability for LSA’s containing homogeneously broadened media.
The optical spectra corresponding to complex intensity pulsation patterns near line-center tuning of single-mode, standing-wave gas lasers contain some simple indicators of the origins of their complexity. Heterodyne measurements show that on detuning of the laser the power density in each component of the optical spectrum undergoes a Lamb-dip-like reduction as it passes through resonance with the zero-velocity atoms. These observations help to explain the sensitive dependence of the dynamics of standing-wave gas lasers on detuning within the Lamp dip and distortions of the Lamb-dip shapes when the lasers are unstable.
When a tuned standing-wave gas laser operates on-resonance, neighboring frequencies experience gain in accordance with the Lamb dip. Bennett1 showed that it is possible for certain of these frequencies also to satisfy the phase-matching condition required by the dispersion relation. In such cases, gas lasers possess three possible steady states—one on-resonance state and two frequency-pushed ones. Bennett suggested that this effect could give rise to bistability and hysteresis in the frequency vs detuning characteristics.
An analysis is made of the operation of a laser with a saturable absorber and dominant inhomogeneous line broadening. A four-level model is used to determine the characteristics of mode intensities and conditions for the appearance of an optical bistability. By analogy with a two-level model, the results obtained demonstrate that in single-mode operation this bistability appears only if the relaxation coefficients of the upper levels of atomic or molecular systems are different in the amplifying and absorbing parts of a laser. Moreover, a change in the inhomogeneous broadening alters greatly the optical bistability interval. The calculation method used in the present study can be readily extended to analyze a multimode laser.
This paper discusses the case of a Doppler-broadened gas laser with a saturable intracavity absorber gas. The semiclassical equations governing the field intensities and the atomic density-matrix elements are set up. The latter are written as Fourier series, the components of which are shown to obey coupled difference equations. In this paper the exact steady-state solution in single-mode operation is obtained. The lowest approximation (rate-equation approximation) is used to compute detailed characteristics of the system. In particular, the influence of the pumping rates in the two cells are investigated and displayed in the figures. The regions of bistable operation are determined and conditions for the occurrence of an inverted Lamb dip are given. The effect of a slow modulation of the pumping rates is discussed. The range of validity of the lowest approximation is investigated both analytically and numerically. Finally, there is a brief discussion of the influence of pressure on the parameters of the theory.
The domain of the third-order theory of the single-mode laser is usually defined by the condition nB/A ≪ 1, where n is the photon number in the cavity, and A and B are the gain and saturation coefficients. When the laser cavity is detuned from line center by Δω ≡ ηγ, where γ is the natural linewidth of the atomic transition, A and B change in the prescribed manner given by the Lamb theory, and it is usually taken for granted that the theory is valid both for small and large detunings η. By examining the relationships between various parameters we show that the limits on the domain of the third-order laser theory effectively limit the allowed detuning in many common lasers to one natural linewidth (η ≈ 1).