This thesis is an effort to address several issues in coherent beam combining. First, a mathematical formalism is developed to study cavity dependent properties, in particular, the modal response of complex laser systems. It is shown that the coherent beam combining in these common cavities is extremely sensitive to random path-length variations of the individual gain elements.
Next, a number of methods are explored to reduce this sensitivity to length variations without actively controlling the path-lengths. This thesis introduces several coherent beam combining architectures based on Michelson cavity in which the spatial and longitudinal supermodes of the common cavity are manipulated to decrease the path-length sensitivity. A set of experiments is designed to verify the role of spatial and longitudinal supermodes. The measured dominant eigenmode, eigenvalue and output power are in good agreements with the predictions of the modal analysis.
Finally, many applications prefer the output power to be concentrated in a small spot, whereas the supermodes of most complex cavities contain several lobes. This thesis describes a mode shaping technique, capable of converting any supermode to the desired distribution, with theoretically a 100\% efficiency. The technique employs two phase plates modifying the phases in Fourier conjugate planes to create a uniform beam (both in amplitude and phase), which directs all the power to the central lobe of the far-field. An experiment is performed to combine eleven in-phase beams, corresponding to the fundamental mode of the self-Fourier cavity, into a single-lobed far-field.