  We develop an analytic theory for the recently demonstrated Josephson
Junction laser (Science 355, p. 939, 2017). By working in the time-domain
representation (rather than the frequency-domain) a single non-linear equation
is obtained for the dynamics of the device, which is fully solvable in some
regimes of operation. The nonlinear drive is seen to lead to mode-locked
output, with a period set by the round-trip time of the resonant cavity.
