Periodic instabilities which occur in the output beam of a ring cavity containing a short cell of passive homogeneously broadened two-level atoms are studied as a function of the atomic detuning and the mode spacing in a high-finesse cavity. The output characteristics are found to be very sensitive to the round-trip time of the light through the cavity and to the refractive index. Conditions for the occurrence of large-amplitude self-oscillation are given in terms of these two parameters.>
Periodic instabilities which occur in the output beam of a ring cavity containing a short cell of passive homogeneously broadened two-level atoms are studied as a function of the atomic detuning and the mode spacing in a high-finesse cavity. The output characteristics are found to be very sensitive to the round-trip time of the light through the cavity and to the refractive index. Conditions for the occurrence of large-amplitude self-oscillation are given in terms of these two parameters.>
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 instabilities of a nonlinear optical medium with induced absorption in a ring cavity are theoretically analyzed. Stable, bistable, and unstable stationary solutions are found for various values of incident intensity and detuning. The dynamic treatment yields, in the unstable regime, oscillations of the transmitted intensity in various modes for constant incident intensity. If the medium relaxation time is short compared with the round-trip time, oscillatory solutions are obtained, which show strong locking of the oscillation frequency to multiples of the inverse round-trip time. If the round-trip time is comparable with the medium relaxation time, numerical integrations yield periodic solutions with substructures because of the mismatch of the two characteristic times.
We solve numerically the time-dependent equations of motion for an inhomogeneously broadened single-mode ring laser. As expected from the linear stability analysis, pulsations develop in the output of the laser for appropriate values of the gain parameter. Under resonant conditions, the tendency is for the system to slip from a periodic regime into irregular oscillations; out of resonance, however, periodic oscillations and period-doubling bifurcations are more typical over a large range of gain values. We find that, as the ratio of the population-to-polarization decay rates varies from a value of two (radiative limit) to smaller values, the periodic oscillations turn into a train of well-separated pulses whose peak intensity scales approximately as the square of the atomic density.
We study the five semiclassical laser equations in the mean-field limit for the simple model of two-level atoms with homogeneous broadening in a single-mode unidirectional ring cavity, taking into account detuning between atomic and cavity frequencies. Our analysis concentrates on the properties of the laser at and beyond the second thresh-old in the bad-cavity case. We first show that the position of the second threshold depends on the excitation mechanism: When the pump parameter is increased either adiabatically or abruptly, two different thresholds occur. The sequence of periodic and chaotic solutions beyond the second threshold is then discussed as a function of the detuning and the pump parameter.
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.
We review and extend the theory of instabilities in absorptive optical bistability for ring cavities containing homogeneously broadened two-level media. The instabilities occur in the high-transmission branch and result in either a precipitation to the low-transmission branch or in pulsed multimode operation. Two numerical approaches are used to predict operation away from the simple mean-field limit. First, an iterative method is used to solve the general field eigenvalue equation for cavity modes with frequencies displaced from the input frequency. This work shows that the instability region decreases in size as the mirror transmission increases. These calculations are confirmed by the second numerical technique, consisting of direct integrations of the coupled Maxwell-Bloch equations. This second approach also provides time histories of the instability evolutions, and divides the instability range into a precipitation regime and a self-pulsing regime. The results are discussed in terms of first- and second-order phase transitions, and agree with the analytical results obtained within the dressed-mode description of optical bistability. They show that when the incident field is adiabatically decreased along the high-transmission branch, the spiking behavior always appears abruptly. By further decreasing the incident intensity, the self-pulsing disappears either continuously if the system remains in the high-transmission branch, or discontinuously if the system precipitates to the low-transmission branch. Connection is made with induced probe gain known in the saturation spectroscopy of absorbers (uninverted media), in which population pulsations transfer energy from a saturating wave to the probe waves. The very close relationship with multimode operation in homogeneously broadened unidirectional ring lasers is also established.