Analysis of hyperboloidal ray envelopes in Herriott cells and their use in laser resonators

By the use of geometric optics and matrix methods an analysis of the spherical mirror Herriott cell is presented. The hyperboloidal beam envelope inside the cell is derived, and equations are given for the position and magnitude of its waist with respect to design parameters. The analysis is then repeated for the cell within a Fabry-Perot resonator. Here the stability condition is derived, and its region of validity is investigated for a range of parameters. Finally a theoretical study of the beam radius distribution at the optics is presented.