Simple way for in-phase mode selection in laser with annular gain region A. P. Napartovich, N. N. Elkin, D. V. Vysotsky Troitsk Institute for Innovation and Fusion Research, Troitsk, 142092 Moscow region, Russia ABSTRACT Properties of laser cavity composed of two plane segmented mirrors placed at half-Talbot distance are considered theoretically in application to gas laser with annular active medium. Discrimination of in-phase mode against other supermodes is demonstrated. Keywords: Talbot effect, phase locking 1. INTRODUCTION An attractive feature of a gas laser with annular shape of gain region is its compactness at high power level. A particular simple situation takes place when radial propagation of the wave field is limited by waveguide walls like construction of diffusion cooled CO 2 laser with radio-frequency (RF) discharge excitation 1 . Construction difficulties inherent to its geometry are non-uniform plasma excitation and a large amount of axial modes lasing simultaneously. In the case of radio-frequency (RF) discharge the electrode voltage uniformity appears to be improved by sectioning electrodes 2 . But the problem still remains how to arrange single-mode laser operation. Angular propagation properties of radiation field in cavity considered are very similar to propagation of radiation in a cavity formed by infinite stripe mirrors Diffraction losses in angular direction are completely eliminated resulting in a plenty of modes with equal losses. In work 3 it was proposed to introduce mode discrimination by placing a spatial filter in front of one of mirrors absorbing radiation incident on it. This filter had a periodical in angular direction array of apertures. The length of the resonator L was coupled with distance between filter apertures Δ so that Talbot condition was producing L = Δ 2 /λ = L T /2, where L T is so-called Talbot distance where self- reproduction of periodical field takes place. Besides an external profile-modulated mirror was used to transform lasing out-of-phase mode with binary alternating phase (0, π) to the in-phase one (all beams with the same phase). Numerical simulations made in 4 have shown the existence of the field Talbot self-reproduction in such a resonator even without annular waveguide. In the work 5 the fractional Talbot effect (i.e. self-reproduction with image multiplication of the periodical field distribution at fractions of Talbot distance) was studied numerically in the guided Talbot resonator. It should be mentioned that the real field distribution of the in-phase mode of the resonator was replaced by combination of several axial modes of annular waveguide, while in the radial direction only the fundamental mode of the waveguide was taken into account. The inherent drawback of resonator geometry considered above results from the exact reproducing of two different supermodes of array in-phase and out-of-phase 6 . We propose and analyze numerically a new version of Talbot cavity when both plane reflectors are segmented with reflecting parts positioned periodically along the ring and supplementing each other (see Fig. 1). Distance between reflectors is also L T /2. Reflectors are identical except a turn around axis onto half a reflectance modulation period. Fill factor for reflection is ½. Numerical simulations of cavity modes including saturable gain medium were performed. The out-of-phase mode is eliminated completely having high losses in this construction. The in-phase mode has diffraction losses close to zero because of property of the periodical field to form an image identical to the origin but turned onto a half a period 6 . An additional benefit of this cavity is high laser extraction efficiency due to rather smooth intensity distribution of the in-phase mode in the middle of cavity