On formation of a partially coherent beam in a stable-resonator laser

A new method involving the expansion of the field coherence function in partially coherent modes — the eigensolutions of the problem for the second-order coherence function in a stable resonator — is proposed for the theoretical description of the process of multimode laser beam formation. The method for solving the problem for arbitrary partially coherent modes is formulated and the expressions for these modes are derived in the general form. The characteristics of the fundamental partially coherent mode, which coincides with the coherence function of a Gaussian partially coherent beam, are analysed in detail. The partially coherent modes are shown to possess two spatial scales — the effective radius and the coherence radius, which makes them a convenient tool for solving the problem of generation of a partially coherent beam. It is found that the unambiguous relation between the characteristics of partially coherent modes and the stable-resonator parameters is achieved by involving into consideration not only the process of the beam formation by the resonator mirrors but also the process of interaction of radiation with the active laser medium.