Abstract
The problem of determining the electromagnetic field in an open unstable telescopic resonator filled with an active medium at high Fresnel numbers in regimes close to the threshold for laser action is considered. The method of matching asymptotic expansions is used to solve the initial equations. The cases when L R 0 ⪡ 1 ( L is the distance between the mirrors and R 0 is the characteristic radius of curvature of the mirrors) and L R 0 ~ 1 are considered. When L R 0 ⪡ 1 , the effect of the edges of the mirrors is analysed analytically. The laser mode of operation is assumed to be the threshold mode. Simplified equations are obtained as a consequence of the asymptotic analysis together with effective boundary conditions on the edges of the mirrors for the amplitudes of the field and the conditions for stationary emission.
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