Evolution of Gaussian beams and pulse stimulated emission from lasers with unstable resonators

A recurrence formula is derived for the passage of a Gaussian beam across an unstable resonator and across a periodic optical system. An analysis is made of the position and size of a laser beam constriction in an arbitrary unstable resonator. The nature of the variation of the beam diameter on a mirror with its initial parameters and with the number of passes through the resonator is investigated. The evolution of offaxis Gaussian beams is discussed and a generalization of the Lagrange-Helmholtz theorem is given. The process of formation of the diffraction divergence of the output radiation of a laser is followed in the presence of a noncoherent component representing the residue of the original spontaneous radiation. The results are applied to transient processes in a superluminescent laser with an unstable resonator.