The recently proposed 1-N-way resonator based on beam splitting and beam combining effects in rectangular cross-sectional multimode waveguides offers a valuable way in which N low-power laser elements can be combined in a coherent fashion. We develop a theory of such resonators in the presence of perturbations in the N-element array. We demonstrate that despite the presence of perturbations there is only one possible mode of the resonator. The theory is used to provide an understanding of the effects of a number of possible perturbations that could arise as a result of manufacturing processes and operational effects. The results give scaling laws for the design tolerances on array element mirror tilt, array element optical path length control, and the effects of array element malfunction and their need for gain balance.
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