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Physical Review A

Physical mechanism of asymmetric bistable and dynamically unstable emission with low second threshold in Raman lasers

Weiping Lu, Robert G. Harrison

Published Jun 1, 1990• 10 citations
Publisher

Abstract

Bistable and dynamically unstable emission from a single-mode homogeneously broadened Raman laser is shown to arise from laser- and pump-field induced distortion and displacement of the dispersion profile associated with the laser gain. These features occur for broad cavity tuning to the low-frequency side of gain center, the threshold for dynamical behavior, being as low as the first lasing threshold. Results of this analytic treatment are in exact agreement with earlier numerical analysis.

DOI
10.1103/physreva.41.6563

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Bistable and dynamically unstable emission from a single-mode homogeneously broadened Raman laser is shown to arise from laser- and pump-field induced distortion and displacement of the dispersion profile associated with the laser gain. These features occur for broad cavity tuning to the low-frequency side of gain center, the threshold for dynamical behavior, being as low as the first lasing threshold. Results of this analytic treatment are in exact agreement with earlier numerical analysis.
Detailed analysis of the steady-state and dynamical unstable behavior of single-mode, homogeneously broadened Raman lasers is presented. Bistable features of the Raman emission and its operating conditions are determined from steady-state analysis. Parametrization of the dynamical behavior shows instabilities to exist over a broad range of operation conditions and for broad cavity detuning to the low-frequency side of the gain center where the bistable emission also prevails. Notably, period-doubling routes to chaos and sustained oscillatory behavior in both intensity and phase are found to occur for both good and bad cavity conditions, the dynamics of the phase revealing additional temporal features to that of intensity.
We use the semiclassical strong-signal theory of the laser to predict and explain the onset of side-mode buildup in lasers with one oscillating mode. Two general categories are considered: one for which the side modes and the oscillating mode all have the same wavelength and the other for which they have different wavelengths. The treatments include an arbitrary amount of inhomogeneous broadening. Our approach unifies the treatments of the side-mode instabilities presented earlier and extends them to handle standing waves in addition to the previously treated running waves. We write the field and the population matrix elements as Fourier series in the adjacent-mode beat frequency. This approach has been used extensively in both multimode laser theory and saturation spectroscopy. This technique coincides with linear stability analyses used by others, provided that our beat frequency includes a contribution that is proportional to the complex side-mode gain. We give a solution that allows for detuned operation along with its simpler, centrally tuned special case. The connection with saturation spectroscopy clearly reveals that the side-mode instabilities require side-mode gain. For the single-wavelength case, nonlinear anomalous dispersion is also required. The side-mode gain and dispersion result from both inhomogeneous broadening and population pulsations. The lowest instability thresholds occur when both of these mechanisms play a role. The approach can also be used to treat instabilities in optical bistability by substituting the appropriate equation of state for the strong-mode intensity and by changing the sign of the absorption coefficient. In homogeneously broadened, standing-wave lasers, we show that multiwavelength instabilities depend strongly on the position of the medium in the cavity. We illustrate the theory by giving numerical results for the output pulsation frequency and for the instability threshold by using parameters that are appropriate for the He–Xe laser. These results correlate well with experimental observations.
Unstable and bistable behavior has been predicted recently in multimode homogeneously broadened lasers as a function of the detuning between the cavity and the atomic frequencies. As an example of a device for which most required physical conditions for the appearance of this instability are satisfied, we have analyzed the behavior of a low-pressure (10–20 Torr) CO2 laser. The operating parameters (relaxation rates for the population inversion, 104s−1, and for the polarization, 108s−1) restrict the accessible range of theoretically expected phenomena to a stable intensity output without evidence of stable self-pulsing. However, mode–mode competition is responsible for bistability in both the intensity and the operating frequency on varying the detuning parameter. This behavior is confirmed by additional observations of the transient that accompanies the jump between the two stable branches. We have also studied the effect of varying the cavity losses and discovered bistability also in the vicinity of the threshold for laser action. This kind of behavior is not predicted by the plane wave Maxwell-Bloch equations but can be explained in terms of a radial gain profile. Both effects—mode–mode competition and transverse—lead to a variety of bistable behaviors depending on gas pressure and discharge current.
Interaction of two coherent fields of arbitrary intensity with a general homogeneously broadened three-level molecular system for both an amplifier as well as a laser oscillator under general conditions of pumping is discussed. The amplifier solution is obtained through the time-averaged density-matrix formalism with two coherent fields treated classically. A detailed consideration of both real and imaginary parts of the electric susceptibility at pump and emission frequencies, corresponding to gain and dispersion in the active medium has been taken into account. The results obtained are used to study a number of situations for weak and strong pumping in the laser amplifier. Subsequently these are applied to a mode analysis of a unidirectional single-mode laser oscillator to determine the output characteristics of the laser and to establish conditions under which emission becomes dynamically unstable resulting in sustained oscillatory emission. The results obtained are found to be in good agreement with those of a full numerical analysis of the atomic and field coupled equations describing the system.
We provide a comprehensive analysis of the standard model of the bidirectional ring laser in which only one mode can be supported in each direction and in the limit that the polarization can be eliminated adiabatically. The interaction between the two counterpropagating modes can be derived and it is most naturally viewed as a coupling between them via scattering from a spatial grating formed in the population inversion. If the grating is a sufficiently small modulation of the spatial average of the population inversion, it can be approximated by a sinusoidal function. A systematic derivation of the model with only a sinusoidal grating for the homogeneously broadened case is presented that reveals and corrects errors in several previously published analyses. The stability of the steady-state solution is analyzed. The bidirectional steady-state solution is unstable and the unidirectional steady-state solutions may be stable or unstable depending on the parameters. The well-established result of bistability between the two modes when the cavity is tuned to resonance is recovered, a result that persists, in part, even when the losses between the two modes are different.With detuning, the unidirectional steady-state solutions can be destabilized, creating regions in the parameter space where only time-dependent solutions are found. For parameters characteristic of solid-state or molecular gas lasers, the instability can occur for very small detunings and even very close to the lasing threshold. Asymptotic limits of the instability boundaries for these parameters are presented. Additional results are derived formally for inhomogeneous broadening with a Lorentzian line shape and for arbitrary inhomogeneous linewidths. Explicit analytic results are presented in the limits of very small and very large inhomogeneous linewidths compared with the homogeneous linewidth. Time-dependent solutions in the homogeneously broadened case for relaxation rates appropriate to CO2{\mathrm{CO}}_{2}CO2​ lasers show that there are broad regions in the parameter space of gain and detuning for which the behavior is dynamically chaotic in the form of nearly ``square-wave'' alternation between the counterpropagating modes of the laser with irregular switching times. In other regions of that parameter space we find more irregular pulsations and pulse alternations. Regions of periodic pulsations also have been found.