Transverse mode competition in a CO2 laser.

Transverse patterns in lasers have been observed since the earliest days of laser physics, as, e.g., in 1964 when they were reported for the first time on the transverse structures of a HeNe laser @1#, but transverse dynamics studies developed only in the past decade. Two approaches have been followed, depending essentially on the number of transverse degrees of freedom of the system, i.e., on the Fresnel number. At low Fresnel number, it has been shown that modal expansion of the field on a suitable basis of empty cavity modes is well adapted to explain the main properties of the various stationary and dynamical regimes @2,3#. At high Fresnel number, Coullet et al. demonstrated theoretically the existence of optical turbulence induced by defects, also called optical vortices, and suggested describing complex spatiotemporal dynamics as a function of such vortices @4#. Unfortunately, although phase singularities similar to optical vortices are common in the transverse patterns of lasers, and may form complex disordered patterns @3,5‐8#, optical turbulence in lasers has not yet been experimentally evidenced. Complex patterns have also been observed in a liquid-crystal device with optical feedback @9#, and turbulence has been evidenced in optical oscillators with photorefractive gain @10#. In CO 2 lasers, the limiting factor of the experimental analysis is the detection, as there is no technical solution to record patterns at a cadence of 1 MHz or higher, which is the typical scale of the dynamics. Therefore, the observations on laser transverse patterns are limited to the time averaged intensity @8#. The preliminary results of @8# showed that among a wide variety of patterns, the transverse profile of the CO 2 laser could exhibit self-organization, even at Fresnel numbers as large as 40. We show in this paper that in this situation, it is still possible to describe experimentally the patterns as a function of the modes of the empty cavity. Such an analysis allows us to evidence that patterns are combinations of a few modes among those present in the gain profile. The selection mechanism is shown to be transverse spatial hole burning, in good agreement with recent theoretical studies @11#. These results provide an alternative interpretation of laser patterns to that given by Feng et al. in terms of standing waves @12#. The experimental setup is essentially the one described in @8#. The detection consists in phosphorescent plates and a video camera. Unfortunately, as this system has a low resolution and is nonlinear, it provides pattern intensity distributions with a typical uncertainty of 20%. Another important point is the presence in the cavity of Brewster windows introducing astigmatism. This induces that ~i! the cylindrical symmetry of the cavity is broken to a rectangular symmetry, so that the Hermite-Gauss basis TEM m,n becomes relevant, and ~ii! the frequency degeneracy of modes having the same q5m1n index is lifted. Pertinent parameters to characterize the cavity are the generalized Fresnel number N F and the ratio Rn of the free spectral range to the transverse mode spacing. The former is a measure of the transverse degrees of freedom and the latter rules the interactions between the transverse modes. In @8#, it was shown that for Rn’15 and values of N F up to 30, the laser exhibits ordered time averaged intensity patterns @Figs. 1~a! ‐~c! # with the following properties: ~i! patterns may be described as lattices of dark