Stable propagation of non-Gaussian beams in a multiple-pass cell

To apply annular output beams emitted from an unstable resonator to a multiple-pass cell (MPC) for Raman conversion, we studied the mode-matching condition of non-Gaussian beams to a MPC using beam propagation analysis based on Laguerre-Gaussian functions. During transits of the MPC, the radial profile of an annular beam changes between annular and Airy patterns. Although such behavior indicates that it is impossible to achieve complete mode matching of an annular beam, we found a quasi-mode-matching condition under which the variation of beam size was minimized. The above theoretical analysis was verified experimentally using a CO(2) laser beam prepared for a para-hydrogen Raman laser.