CIRCULARLY SYMMETRICAL DISTRIBUTED FEEDBACK LASER - COUPLED MODE TREATMENT OF TE VECTOR-FIELDS

This paper carefully treats the vector orientation of transverse electric (TE) fields in deriving coupled mode equations for radially outward- and inward-going modes in a circular waveguide diffraction grating. The equations are first derived for cylindrical waves in a system that is translationally invariant along the cylinder axis; the derivation is then extended to the waveguide geometry. The coupled mode equations are used to describe the operation of the circularly symmetric distributed feedback (DFB) laser. While predicting a similar dependence of laser threshold gain on an azimuthal mode order to that found by a simpler, scalar-field treatment, the vector-field treatment predicts a fundamental difference in the location of the cavity resonances. The circular DFB laser is expected to lase in multiple azimuthal modes but maintain a relatively narrow overall spectral width.