Single-mode behavior of a circular grating for potentialdisk-shaped DFB lasers

The reflectivity and the resonance condition of a circular grating for a disk-shaped distributed-feedback (DFB) laser are calculated. The periodicity and the position of the grating are 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 calculated wave impedance (E/H ) is almost purely imaginary in the central region of the grating for the higher modes