Modal Theory of Phase‐Modulated and Frequency‐Shifting Ring Cavities

A theoretical and experimental characterization of the optical modes of dispersionless ring cavities incorporating phase modulators (PM) and/or frequency shifters (FS) is presented. Using linear operator theory, the exact response of these cavities to arbitrary modulating waveforms and optical inputs is computed and shown to be a filtering process that selects a certain class of fields, invariant under multiple roundtrips, which are identified with the cavity's optical modes. The different types of PM/FS cavity modes are analyzed. This approach also leads to a representation of these cavities as unmodulated resonators preceded and followed by complementary phase modulations, which are linearly related to the imparted intracavity phase modulation or frequency shift. The theory is experimentally validated by the external injection of engineered phase and frequency modulated cavity modes in an Er:fiber PM fiber loop, and also compared with the emission modes of frequency modulated lasers and continuous wave (CW) frequency shifted feedback lasers. These results provide a unified view for the linear analysis of systems employing PM/FS active cavities or resonators, of interest in the field of photonic signal generation and processing.