The instability threshold characteristics are investigated for two different optical devices, the ring cavity and the feedback mirror, with passive weakly absorbing two-level atoms cell. The linear stability analysis of the ring cavity predicts emission of several conical shells, depending on the optical arrangement and the buffer gas pressure. In the case of pure vapor, each conical shell has its own frequency. All the cones display the same frequency in the case of large buffer gas pressure. The feedback mirror device displays very different instability characteristics, with only one frequency emitted along a unique cone, in agreement with the experiment. The self-oscillation is shown to be controlled by the reflectivity properties of the cell, which behaves at threshold as a mixture of ordinary mirror and phase conjugate mirror
The instability threshold characteristics are investigated for two different optical devices, the ring cavity and the feedback mirror, with passive weakly absorbing two-level atoms cell. The linear stability analysis of the ring cavity predicts emission of several conical shells, depending on the optical arrangement and the buffer gas pressure. In the case of pure vapor, each conical shell has its own frequency. All the cones display the same frequency in the case of large buffer gas pressure. The feedback mirror device displays very different instability characteristics, with only one frequency emitted along a unique cone, in agreement with the experiment. The self-oscillation is shown to be controlled by the reflectivity properties of the cell, which behaves at threshold as a mixture of ordinary mirror and phase conjugate mirror
The threshold characteristics of the static and periodic instability of the single feedback mirror device are investigated for a homogeneously broadened two-level medium as a function of the input intensity, the detuning, the buffer-gas pressure, the atomic concentration, and the round-trip time d, and compared with experimental results. For a large range of parameters that agrees with the experiment, the self-oscillation process is shown to be mainly induced by the longitudinal grating, which ensures a large instability domain, and controlled by the buffer-gas pressure, which must be low enough in order that the threshold period of the oscillation is constant on a doughnutlike transverse profile and nearly equal to 2d. This oscillation, called the 2d oscillation, is neither a result of pure phase-conjugate-mirror operation of the atomic medium nor a result of a Rabi sideband gain process. It is shown to take place through a mixture of phase-conjugate-mirror and ordinary mirror operations, which are both allowed by the specific optical arrangement of the device.
Spatiotemporal instabilities of a single-feedback-mirror device are investigated with the help of the linear stability analysis of the stationary regime for a saturable medium that has a complex nonlinear susceptibility; the outcome is compared with experimental results. The first striking result of the analysis is the occurrence of an oscillation with a period nearly twice the round-trip time, regardless of its value with respect to the atomic linewidth for given physical situations, when only longitudinal grating effects are considered. This result cannot be interpreted as a pure phase-conjugate resonator operation, which is expected to occur only when transverse grating effects are included. When such effects are included, the second striking feature is the prediction of the spontaneous breaking of the revolution symmetry; symmetry is broken by rotating light spots, with an instability threshold that depends on the number of spots; this prediction agrees with experiment.
The linear stability analysis of the plane wave stationary solution of the dispersive single-feedback mirror device displays a 2τR oscillation only if the phases of the stationary forward and backward field amplitudes are 2π shifted, δφ = 2kπ. The condition provides an instability boundary in the space of the atom field detuning and the input intensity, the shape of which agrees with experimental results. The 2τR oscillation is the signature of an instability which develops in a phase conjugate resonator, constituted of the atomic cell and a totally reflecting ordinary mirror. Thus, a stationary symmetric profile may undergo a 2τR Hopf bifurcation together with a spontaneous breaking of the cylindrical symmetry. The a-c profiles are constituted of spots located on a ring, as observed in the Tucson experiment [G. Giusfredi et al., J. Opt. Soc. Am. B 5, 1181 (1988)]. A mean phase δφp is defined, which results from an average of the grating, weighted with the mode TEM0, ±p. Therefore the system itself determines the number of spots in order that δφp fulfills the requirement δφ= 2kπ.
In this chapter we outline the general scenario for optical temporal instabilities, starting from the standard Maxwell–Bloch equations. With the exception of Section 22.7, in Part II we will always consider the ring-cavity configuration because only in the case of the ultrathin-medium case considered in Section 22.7 is the treatment of instabilities in Fabry–Perot cavities not substantially more complicated than that in the ring-cavity configuration. Some authors have introduced special approaches in order to study temporal optical instabilities, exploiting the concepts of gain and of dispersion, which are natural in optical systems and therefore help our intuition. In particular, a hint of the mechanism that produces instabilities in optical systems is offered by the so-called “weak-sideband” approach or “gain-feedback approach” [245–249], whose validity can be justified rigorously with the help of the linear-stability analysis [250]. The central point of this method is the response of the system to a weak probe passing through a collection of two-level atoms driven by a strong field [251–253]. If the strong signal with carrier frequency ω 0 saturates the medium, we can find regions of the frequency axis, which are far removed from the carrier frequency of the signal, where the weak probe can experience gain instead of absorption even if the medium has no population inversion. In this book we follow the approach of [250], which is rigorously rooted in the linear- stability analysis and, in addition, establishes a general, useful and, in a sense, surprising connection between single-mode and multimode instabilities. We classify as single-mode a temporal instability that involves the resonant mode only, and classify as multimode a temporal instability that involves only off-resonance cavity modes. The discussion in this chapter is mainly focussed on this connection. In Section 20.1 the multimodal equations derived in Section 12.2 are reformulated by introducing a modal expansion also for the atomic variables. In this way one obtains a complex hierarchy of equations that couple the modal amplitudes for the field and for the atomic variables.
We discuss a novel type of optical instability, which leads to the spontaneous formation of a stationary spatial structure, instead of to the onset of oscillations or pulsations. A passive system is contained in an optical cavity, to which we add two lateral mirrors. Under appropriate conditions, diffraction of radiation can induce the onset of a transverse-stripe structure in an initially uniform plane-wave field configuration. In this paper, we consider the case of a homogeneously broadened two-level system. The model on which our analysis is based is derived from the Maxwell-Bloch equations in the paraxial approximation, using the mean-field limit and assuming a large Fresnel number. We show that, with respect to the bistability parameter C, the threshold of the spatial instability coincides with the bistability threshold for absorptive, resonant optical bistability. The spatial instability requires, however, a detuned configuration and can arise both in the absence and presence of bistability. In the latter case, it can occur both in the lower and in the upper branch of the steady-state curve. The instability is caused by competition between different transverse modes, which realize a situation of spatial coexistence, different from the state of temporal coexistence which characterizes the spontaneous oscillations that arise from the previously known multimode instabilities. Finally, we discuss some points relevant for an experimental observation of this phenomenon.