Hamilton's Principle and the Maximum-Emission Coincidence

Self-locking of frequencies in laser oscillators is considered. The equations of motion for the cavity fields are restated as an extremum principle, which is a modified form of Hamilton's principle. This extremum condition is then compared with the ``maximum-emission'' condition hypothesized by Tang and Statz. It is found that the latter is not derivable from the former, unless one assumes infinitely fast-population relaxation of the laser medium and central tuning of laser modes with respect to the atomic resonance, and performs calculations by means of third-order perturbation theory. If the requirement of third-order perturbation calculations is relaxed, the maximum-emission hypothesis leads to a statement which is different from that of Hamilton's principle, but which coincidentally has the same solutions. If either of the other two assumptions is relaxed, the maximum-emission hypothesis not only gives a statement different from that of Hamilton's principle but leads to incorrect results.