| This thesis focuses on theoretical and numerical investigation of the dynamics of coupled lasers and laser arrays, specifically through the avenue of two different systems of interest: 1) passive coherent beam combining of continuous-wave fiber laser arrays, and 2) passive coupling of mode-locked semiconductor lasers.;The coherent beam combining work contributes to understanding the phasing dynamics in externally-coupled fiber laser arrays (specifically here, a spatially-filtered, ring-oscillator combining geometry) by use of a multi-longitudinal-mode, dynamical model to study the system. The results show that the passive phasing and locking processes operate on a much faster timescale than that of the power and gain transients, and the system is able to recover its phase-locked state within just a few cavity roundtrips after a strong perturbation from steady-state; the results agree with previous experiments. The simulations also demonstrate that the non-resonant Kerr nonlinearity is detrimental to the system's combining efficiency and ability to coherently lock in phase, as determined by qualitative examination and quantitative assessment of the far-field output and its on-axis intensity. A physical explanation of the role of the nonlinearity and a comparison to 50:50 directionally-coupled arrays, both presented within the context of coincident mode theory, is provided to accompany the numerical results.;The mode-locked semiconductor lasers work examines the dynamics of two evanescently coupled, ring-cavity semiconductor lasers (with saturable absorbers) by use of a delay differential equation model (that is extended to incorporate the action of a directional coupler) and with the aid of numerical simulations and bifurcation analyses methods. The findings in this thesis include the following catalog of the variety of complex, interesting, and important phenomena in this system and their dependence on coupling, unsaturated gain, and linewidth enhancement factors: 1) symmetry-breaking effects that lead to strong modulations of and delayed synchronization between the two lasers' pulse trains; 2) the evolution of the coupled lasers from an initial unsynchronized state to nearly-perfect, in-phase synchronization; 3) a subharmonic mode-locked regime in which the two lasers pulsate in anti-synchrony (i.e. anti-phase) and, in the case of lasers with identical roundtrip times, at one half the solitary laser's fundamental mode-locked repetition rate; 4) fractional harmonic mode-locking regimes with repetition rates corresponding to three-halves and five-halves the fundamental mode-locking frequency of the solitary lasers; 5) a destabilization of mode-locking and continuous-wave operation; and 6) multistability between the different dynamical regimes and behaviors. These behaviors can be observed even in the presence of noise. |
