Steady-state Ab Initio Laser Theory and its Applications in Random and Complex Media

Steady-state Ab Initio Laser Theory and its Applications in Random and Complex Media Li Ge 2010 A semiclassical theory of single and multimode lasing, the Steady-state Ab Initio Laser Theory (SALT), is presented in this thesis. It is a generalization of the previous work by Türeci et al which determines the steady-state solutions of the Maxwell-Bloch (MB) equations, based on a set of self-consistent equations for the modal fields and frequencies expressed as expansion coefficients in the basis of the constant-flux (CF) states. Multiple techniques to calculate the CF states in 1D and 2D are discussed. Stable algorithms for the SALT based on the CF states are developed, which generate all the stationary lasing properties in the multimode regime (frequencies, thresholds, internal and external fields, output power and emission pattern) from simple inputs: the dielectric function of the passive cavity, the atomic transition frequency, and the transverse relaxation time of the lasing transition. We find that the SALT gives excellent quantitative agreement with full time-dependent simulations of the Maxwell-Bloch equations after it has been generalized to drop the slowly-varying envelope approximation. The SALT is infinite order in the non-linear hole-burning interaction; the widely used third order approximation is shown to fail badly. Using the SALT we investigate various lasers including the asymmetric resonance cavity (ARC) lasers and random lasers. The mode selection and the quasiexponential power growth observed in quadrupole lasers by Gmachl et al are qualitatively reproduced, and strong modal interaction in random lasers is discussed. Lasers with a spatial inhomogeneous gain profile are considered, and new modes due to the scattering from the gain boundaries are analyzed in 1D cavities. Steady-state Ab Initio Laser Theory and its Applications in Random and Complex Media A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy