The `diffusion' of light and angular distribution in the laser equipped with a multilobe mirror

The distribution of radiation is investigated for the modeless laser having a multilobe mirror with the lobes (planes) inclined by small angles to optical axis. It is shown that change of the direction resulting from many passages of a ray through the optical system including a multilobe mirror may be described as Brownian walk of a point along the plane or equivalently as a solution of the two-dimensional diffusion equation. Boundary conditions for the diffusion equation may be approximately formulated as null conditions at some angle which, if being reached during the walk, guarantees that the ray escape from the optical system. In the framework of this approximation an explicit formula for the distribution of the outgoing ray in different angles is derived. After many passages through the optical system the angular distribution tends to some universal function. In the case of the round mirror it may be presented by the Bessel function of order zero.