Graphical Representation of the Supermode Theory of a Waveguide Directional Coupler

A novel graphical representation of the supermode theory of a waveguide directional coupler based on phasor analysis is described. Following this approach, dependence of the magnitudes and phases of the output fields on the splitting ratio of a directional coupler is discussed. Both the cases of phase-matched (identical) and non-phase-matched (non-identical) waveguides constituting a directional coupler are investigated. This approach directly illustrates the fact that the phase shift suffered by the coupled light relative to the throughput light is π/2, regardless of the splitting ratio for identical guides, which is not the case for couplers with non-identical waveguides. It also yields additional information about the phases of the output fields of a directional coupler. The usefulness of this approach in the context of wavelength-flattened couplers, wavelength division multiplexing couplers, and polarization effects in directional couplers is also discussed. This approach should also be helpful in the analysis of guided wave interferometric devices such as wavelength interleave filters and modulators, based on concatenated directional couplers.