MASTER EQUATION FOR SPATIOTEMPORAL BEAM-PROPAGATION AND KERR LENS MODE-LOCKING

We present a novel spatio-temporal master equation (ME) for describing the evolution of optical fields in laser cavities. Our ME introduces a new type of propagation operator explicitly dependent on the ABCD el ements of the cavity. We derive this and show that it correctly reprod uces the cavity mode structure in the linear limit. We apply our ME to the problem of Kerr lens mode-locking (KLM) and show that our numeric al results, in one dimension (x), are in excellent agreement with thos e found using the more conventional Huygens' integral method. Dispersi on and other fast-time effects are then added to give a full spatio-te mporal ME. Again this is applied to KLM and we show that stable solito n-like pulses result.