Surface-emitting circular DFB, disk-, and ring-Bragg resonator lasers with chirped gratings. III: gain saturation...

As Part III of this series, this paper focuses on an above-threshold modal analysis which includes gain saturation effects in the surface-emitting chirped circular grating lasers. We derive an exact energy relation which states that, in steady state, the net power generated in the gain medium is equal to the sum of peripheral leakage power and vertical emission power. This relation is particularly useful in checking the accuracy of numerical mode solving. Numerical simulations demonstrate the dependence of required pump level on the vertical emission power and compare the laser threshold and energy conversion efficiency under uniform, Gaussian, and annular pump profiles. A larger overlap between the pump profile and modal intensity distribution leads to a lower threshold and a higher energy conversion efficiency. Finally the dependence of required pump level on device sizes offers us new design guidelines of these lasers for single-mode, high-efficiency, high-power applications.