Dynamics and mode competition in wave-chaotic dielectric cavity lasers

The interacting mode problem for 10-100 micron-scale lasers based on dielectric resonators, both cylindrical and deformed cylinders or the asymmetric resonant cavity lasers (ARCs). A non-linear lasing theory is studied with many modes interacting. An improved treatment is presented in which the modal expansion is in terms of linear amplifying states, which are solutions of the wave equation for piecewise constant (in space) complex (amplifying) index of refraction with real k, and satisfy somewhat more complicated orthogonality relations. Mode selection, shape sensitivity and power output in the many mode regime for circular as well as deformed lasers are studied. It is found that spatially selective pumping plays a key role in the selection of bow-tie modes but may not be crucial for obtaining a large power increase with deformation. Finally, the mode-locking aspects and the time-dynamics are discussed and is related to the point-group symmetries and the ray dynamics of the cavity.