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Single-mode optical fiber ring (or loop) resonator utilizing degenerate two-wave mixing is proposed. The degenerate two-wave mixing can bring the fiber ring into full resonance and enhance the finesse or amplify the output intensity and change its characteristic from being of the channel-blocking to channel-passing type.

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The theory of optical fiber loop and ring resonators with multiple couplers is generalized. In Part 1 of the paper, general expressions for the circulating (resonant) and output fields and intensities of various configurations of such fiber loop and ring resonators are derived and tabulated. Computed results are presented as graphs. Special characteristics and possible applications of these loop and ring resonators are discussed. For example, they can be used as frequency selective beam splitters. Performance parameters of these loops and rings such as finesses, peak transmission, and contrast, etc. are treated in Part 2 of the paper.