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Topical Meeting on Optical Bistability (OB)

Intrinsic Instabilities in Homogeneously Broadened Lasers

Lloyd W. Hillman, Robert W. Boyd, Jerzy S. Krasiński, Carlos R. Stroud

Published Jan 1, 1983• 1 citation
Publisher

Abstract

Experimental observation has shown that it is no simple matter to make a homogeneously broadened laser operate in a single longitudinal mode. However, elementary theoretical treatments of homogeneously broadening predict that such lasers can operate in only a single mode, because all of the atoms constituting the gain medium experience identical degrees of saturation.

DOI
10.1364/obi.1983.thb12

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Single-mode and multimode operation in inhomogeneously broadened lasers

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Homogeneously broadened lasers are considered as intrinsically single mode monostable devices [1] where intensity and frequency are defined by the cavity mode that lies nearest to the center of the atomic line. Here we show theoretically and experimentally that this heuristic picture falls when the interaction between different cavity modes becomes relevant. In fact, for sufficiently high detuning between cavity and atomic resonance frequencies (δAC), self pulsing of the laser arise from the simultaneous operation in two modes (phase instability) even if it is operating near threshold (C ⪯ 1) and in the so-called good cavity limit (k ≪ γ⊥, γ‖). Using parameter values which are typical of many solid state and molecular gas lasers (γ‖, k ≪ γ⊥), the theory predicts a bistable behavior in both the output intensity and frequency, as δAC is varied (Fig. 1). These theoretical results have been confirmed by experiments carried out on a CO2 laser where the distance between modes was controlled by changing the losses inside the cavity and the detuning δAC was varied by a fine tuning of the distance between mirrors. The output intensity versus δAC is shown in Fig. 2 for two different values of losses and gas pressure. Direct comparison between Fig. 2b) and Fig. 1 shows a good qualitative agreement. Measurements of the transients during the jump of Fig.2b) confirmed the mode-mode competition interpretation.

Topical Meeting on Optical Bistability (OB)•Jan 1, 1985•0 citations
Experimental observation has shown that it is no simple matter to make a homogeneously broadened laser operate in a single longitudinal mode. However, elementary theoretical treatments of homogeneously broadening predict that such lasers can operate in only a single mode, because all of the atoms constituting the gain medium experience identical degrees of saturation.
The instabilities in homogeneously broadened lasers, which we described in the previous chapter, have a paradigmatic importance because they arise in models which allow one to perform the linear-stability analysis in a simple analytic form. The treatment of the corresponding instabilities in the case of in homogeneously broadened lasers is substantially more complex in general. However, it is very interesting because, as we shall see, the instabilities arise in parametric domains that are much more accessible from the experimental viewpoint. A related issue is that of the possibility of multimodal emission in a laser. It is common knowledge that in order to attain multimode emission it is necessary to have a sort of in homogeneity in the gain medium, because in a completely homogeneous configuration all modes interact with all atoms, and the arising competition among modes implies that only one of them survives. There are basically two main kinds of in homogeneity, the first is of spatial nature and the other is of spectral nature. The first kind is realized in Fabry–Perot lasers, because different cavity modes interact with atoms at different spatial positions in the cavity thanks to the standing-wave configuration of the field and to the consequent phenomenon of spatial hole- burning (see Section 14.2 and Fig. 14.1). This circumstance is capable of weakening the mode–mode competition and allowing multimode operation. In unidirectional ring lasers, on the other hand, there is an “inhomogeneous” configuration in the case of inhomogeneous broadening, because different groups of atoms have different transition frequencies and therefore interact with different modes thanks to the spectral hole-burning (see Section 15.2 and Fig. 15.3). Again, this weakens the mode–mode competition and allows multimode operation. However, these are qualitative considerations, and the only reliable and quantitative method to determine the possibility of multimodal operation is the linear-stability analysis of the single-mode stationary solutions.
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.
The theory of small-signal laser amplification is developed for homogeneously broadened systems in which the three main decay rates, for the collective atomic dipole moment, the population inversion, and the field in the laser cavity, have arbitrary relative magnitudes. The calculations extend previous work on class-AAA and -BBB lasers, where the dipole decay rate greatly exceeds the other two rates, to class-CCC lasers, where the dipole decay rate is comparable to the others. The free-running laser is assumed to excite a single longitudinal mode of the cavity, whose frequency generally differs from that of the coupled atomic transition. The linear gains of the laser are derived for input signals whose frequencies are close to that of the lasing mode or to one of its adjacent nonlasing longitudinal modes. Divergences in the gain that occur for these two arrangements are associated with the previously studied single-mode and multimode instabilities of the free-running laser, respectively.
Homogeneously broadened lasers are considered as intrinsically single mode monostable devices [1] where intensity and frequency are defined by the cavity mode that lies nearest to the center of the atomic line. Here we show theoretically and experimentally that this heuristic picture falls when the interaction between different cavity modes becomes relevant. In fact, for sufficiently high detuning between cavity and atomic resonance frequencies (δAC), self pulsing of the laser arise from the simultaneous operation in two modes (phase instability) even if it is operating near threshold (C ⪯ 1) and in the so-called good cavity limit (k ≪ γ⊥, γ‖). Using parameter values which are typical of many solid state and molecular gas lasers (γ‖, k ≪ γ⊥), the theory predicts a bistable behavior in both the output intensity and frequency, as δAC is varied (Fig. 1). These theoretical results have been confirmed by experiments carried out on a CO2 laser where the distance between modes was controlled by changing the losses inside the cavity and the detuning δAC was varied by a fine tuning of the distance between mirrors. The output intensity versus δAC is shown in Fig. 2 for two different values of losses and gas pressure. Direct comparison between Fig. 2b) and Fig. 1 shows a good qualitative agreement. Measurements of the transients during the jump of Fig.2b) confirmed the mode-mode competition interpretation.