Modal properties and modal control in vertically emitting annular Bragg lasers.

The modal properties, including the resonant vertical radiation, of a type of laser structures based on the annular Bragg resonance (ABR) are studied in detail. The modal threshold gains and the resonance frequencies of such lasers are obtained from the derived governing characteristic equation. Two kinds of ABR lasers, one with a pi/2 phase shift in the outer grating and the other without, are analyzed. It is numerically demonstrated that, it's possible to get a large-area, high-efficiency, single defect mode lasing in ABR lasers if we choose the kind without a pi/2 phase shift in the outer grating and also a device size smaller than a critical value.