Beam motion in a multipass laser cell

Results are presented of a theoretical and experimental investigation of a multipass laser cell. The optical system of the cell comprises two plane mirrors and one spherical. The simplicity of the cell design enables analytic calculations to be made of the pattern of light spots on the mirrors. The calculations are made allowing for aberrations of the focusing mirror to within the third order with respect to small deflections of an arbitrary beam from the axial one. By utilizing the quasiperiodicity of the beam motion, it is possible to reduce the finite-difference equations for the beam motion to a Hamiltonian system of differential equations. The problem of motion of light spots over the mirror is reduced to an appropriate dynamic problem which is solved using perturbation theory. The theoretical and experimental results are compared. The coordinates of a spot can be accurately determined (to within the spot size) from its number using the equations derived.