SINGLE-MODE BEHAVIOR OF A CIRCULAR GRATING FOR POTENTIAL DISK-SHAPED DFB LASERS

The reflectivity and the resonance condition of a circular grating for a proposed disk-shaped DFB laser have been calculated. The periodicity and the position of the grating is so chosen that all of the reflections from each refractive index step are superimposed in-phase so as to be consistent with the resonant behavior of the fundamental mode wave. The resonant frequencies for several circular higher order modes (m=0, 2, 4) are almost the same as that of the fundamental mode and the peak height of the resonance of the higher order modes (m = 2, 4) are a few percent lower than that of the fundamental one. The resonant peaks completely disappear for still higher order modes (m ≥ 6) because the reflection from a single index step near the center is many orders of magnitude stronger for the higher order modes so that it completely dominates the reflection, and the resonance is destroyed. Such a peculiarity is explained by the fact that higher order modes reach a nearly cutoff state near the center of the circular grating. This effect corresponds to the cutoff condition of a rectangular waveguide. The calculated wave impedance (EIH) is almost purely imaginary in the central region of the grating for the higher order modes. © 1990 IEEE