Efficiency and equivalence of homogeneously broadened lossy lasers

A one-dimensional model of a laser with homogeneously broadened saturable gain and distributed loss is used to calculate the recirculating power and extraction efficiency for the case in which the mirrors are lossless. Accurate numerical results show that optimized single-ended lasers, equivalent symmetric lasers, and optimized symmetric lasers have the same extraction efficiency when the gain is small, but not when it is large. The peak efficiency of the single-ended laser is known to decrease with increasing length of the gain cell at high gain. The efficiency of the symmetric laser is found to decrease much less, so the output power nearly scales linearly with length over the range investigated. Thus past assumptions about equivalences between lasers must be reexamined. An approximate analytic solution of the laser equation is shown to be useful from threshold to closed cavity over a wide range of values of the small signal gain, the distributed loss coefficient, and the length of the gain cell.