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Quantum Electronics and Laser Science Conference

Dynamic gain profiling in self-pulsing lasers

Belkacem Meziane

Published Jan 20, 2003• 0 citations
Publisher

Abstract

Summary form only given. Despite the large number of reports that were devoted to the investigation of the dynamic properties of single-mode inhomogeneously broadened (SMIB) lasers, some of their operative characteristics still demand further investigation. In connection with physical understanding of laser instabilities, we demonstrate that the sideband approach is insufficient to explain the distortion that occurs in the (initially) Gaussian profile when the output field undergoes large departures from stable operation. The report focuses on both numerical and analytical handling of the integro-differential 'Maxwell-Bloch' equations. An original approach, presented for the first time, consists in tracking the gain contour when a self-pulsing regime sets in. We demonstrate the occurrence of a lateral hole-burning effect that has never been revealed before. These findings lend themselves to the recognition of the fact that the unstable state initiates lateral saturation (an effect that has always been ignored in the treatment of SMIB laser dynamics). We show that lateral hole-burning cannot be described with the usual small-sideband analysis. In addition, we prove that, to first order, the role of population pulsations is masked by a DC component, distinct from the steady-state value, and responsible for the gain distortion. Leaning on obvious hints related to the occurrence of an amplitude field-switching around a zero mean-value, we derive analytical expressions that give a remarkably good account of the dynamic profiles, obtained likewise by numerical integration of the integro-differential equations.

DOI
10.1109/qels.1999.807583

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Physical Review A•Dec 1, 1982•51 citations
Summary form only given. Despite the large number of reports that were devoted to the investigation of the dynamic properties of single-mode inhomogeneously broadened (SMIB) lasers, some of their operative characteristics still demand further investigation. In connection with physical understanding of laser instabilities, we demonstrate that the sideband approach is insufficient to explain the distortion that occurs in the (initially) Gaussian profile when the output field undergoes large departures from stable operation. The report focuses on both numerical and analytical handling of the integro-differential 'Maxwell-Bloch' equations. An original approach, presented for the first time, consists in tracking the gain contour when a self-pulsing regime sets in. We demonstrate the occurrence of a lateral hole-burning effect that has never been revealed before. These findings lend themselves to the recognition of the fact that the unstable state initiates lateral saturation (an effect that has always been ignored in the treatment of SMIB laser dynamics). We show that lateral hole-burning cannot be described with the usual small-sideband analysis. In addition, we prove that, to first order, the role of population pulsations is masked by a DC component, distinct from the steady-state value, and responsible for the gain distortion. Leaning on obvious hints related to the occurrence of an amplitude field-switching around a zero mean-value, we derive analytical expressions that give a remarkably good account of the dynamic profiles, obtained likewise by numerical integration of the integro-differential equations.
This paper aims at demonstrating that the dynamic gain contour of an inhomogeneously broadened laser tuned to line center undergoes a lateral saturation effect in its unstable regime of operation. Such an effect is shown to be contained in the numerical solutions of the integro-differential Maxwell-Bloch equations that describe the system. After delimiting the domain of applicability of the usual small-sideband approach in describing dynamic gain profiling, we apply a strong harmonic-expansion method to these same equations to obtain an analytical expression that shows an excellent fit with the results of the numerical simulations.
This paper gives a full account of the dynamical properties of single-mode inhomogeneously broadened lasers. The study divides itself into two parts. First, the integro-differential ``Maxwell-Bloch'' equations, which describe such systems, are numerically solved for a large scan of values of the various control parameters that govern the dynamical evolution of self-pulsing lasers. The instability hierarchies, delimited with respect to the excitation parameter, reveal that, along with the various decay rates of the interacting variables, the chosen number of velocity components, which divides the polarization integral into discrete intervals, also plays an important role in the dynamical evolution of the system, especially in the self-pulsing regime of operation. The second part of this paper concerns another approach to modeling single-mode inhomogeneously broadened laser dynamics that largely circumvents the infinite-dimensional complexity of the medium's polarization. A hierarchy of low-dimensional models, with increasing accuracy with respect to the infinite-dimensional ``Maxwell-Bloch'' equations, is constructed and adapted to describe correctly most of the properties of single-mode inhomogeneously broadened lasers.
We study numerically the effects of local-field corrections originating from near dipole—dipole interactions on the dynamics of a single mode, inhomogeneously broadened laser. Our analysis is based on a set of generalized Maxwell–Bloch equations in which the inhomogeneous nature of gain broadening is accounted for by introducing two new dynamical variables and a single parameter that governs the extent of inhomogeneous broadening. Our results show that local-field effects occurring in a dense gain medium reduce the range of continuous wave operation and lead to instabilities and chaos at much lower pumping levels.
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.
Pattern formation in large-aspect-ratio single-mode inhomogeneously broadened lasers is studied by means of the integro-differential Maxwell-Bloch equations. As the inhomogeneous linewidth increases, the neutral stability curve shows a relaxation in the traveling wave selection allowing structures with different sizes to grow. We have performed numerical simulations with a simplified model based on a few discrete groups of atoms at different resonant frequencies to observe transverse dynamics above threshold for good and bad cavity configurations. We obtain, in general, that close to threshold the inhomogeneous broadening leads to a more complex pattern in comparison to the homogeneous broadening case. At higher pumpings, a stabilization in the number of spatial frequencies taking part in the transverse pattern is found. The influence of the laser aperture on temporal dynamics is also studied. It is shown how the typical self-pulsing regime present in single-mode inhomogeneously broadened lasers is destroyed for a wide enough aperture.
Self-pulsing of a single-mode laser has been studied with the use of the inhomogeneously broadened 3.51-\ensuremath{\mu}m transition in xenon. Time-averaged intensity power spectra, average power output, and real-time observations of intensity fluctuations have been recorded for various detunings of the Fabry-Perot cavity. Two forms of self-pulsing have been observed, both of which can be explained in terms of the phase locking of several frequencies which simultaneously exist in the same spatial mode, made possible by the rapid variations of the index of refraction in the high-gain medium. One form of such mode splitting occurs in the wings of the atomic response due to the variations in the inhomogeneously broadened anomalous dispersion. The second form can occur anywhere in the tuning range of the laser as it is caused by distortions induced in the dispersion by the hole-burning effects of the oscillating mode. The pulsation frequency of this induced mode splitting varies with cavity tuning, shows a dip at the atomic line center, and may be absent for detuning of one or two homogeneous linewidths away from center. The instabilities have shown subharmonic bifurcations of the pulsation frequencies. Both high-QQQ pulsation frequencies and broad bands of frequencies in the power spectra have been observed for various operating conditions.