Matrix algebra for all-fiber optical resonators

A method for calculating the output intensities of passive optical resonators including fiber couplers is presented. The method is based on matrix algebra and is sufficiently general to consider cavities using several couplers. A 4×4 format is used which incorporates matrices for the action on the fields of both the coupler and the geometry developed around the coupler. The validity of this method is first tested on two well-known optical fiber devices. Then a double Fox-Smith resonator is investigated, and the results exhibit both high-frequency selectivity and high finesse. A potential application to single-longitudinal-mode operation of rare-earth-doped fiber lasers is also discussed