Modal properties and modal control in vertically emitting annular Bragg lasers

Abstract

Abstract: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 π /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 π /2 phase shift in the outer grating and also a device size smaller than a critical value.

Surface-emitting circular DFB, disk- and ring- Bragg resonator lasers with chirped gratings: a unified theory and comparative study

“…The destructive interference of radiation fields at one of the bandgap edges is the mode selection mechanism [33]. Engineering of this modal selection method is key to designing high-efficiency single-mode ring Bragg resonator lasers [32].…”

“…[31] and [32]. The foundation for validity of the "resonance condition theory" is the continuity of the amplitudes of the cylindrical waves at the interfaces.…”

“…Devices implementing this design have demonstrated both a low threshold and a small modal volume [23,24]. A comprehensive coupled-mode theory, including the effects of vertical radiation, on the threshold gain and emission efficiency of such circular grating lasers has been derived and used for analyzing disk type Bragg resonator lasers [31] and ring type Bragg resonator lasers [32]. The threshold gains were obtained by solving characteristic equations.…”

Surface-emitting circular DFB, disk-, and ring-Bragg resonator lasers with chirped gratings II: nonuniform pumping and far-field patterns

“…The coupled-mode equations for the Hankel-phased circular gratings in active media were derived in [12] and [13] including the effect of resonant vertical radiation. By using the Green's function method, the contribution from vertical radiation is incorporated as a coefficient into the coupled in-plane wave equations, yielding a set of evolution equations for the amplitudes of the in-plane waves…”

A unified theory for surface emitting chirped circular grating lasers

“…Devices implementing this design have demonstrated both a low threshold and a small modal volume [5,6]. A comprehensive coupled-mode theory, including the effects of vertical radiation, of such circular grating lasers has been derived and used for analyzing disk and ring types Bragg resonator lasers [7,8]. The characteristic equations used for obtaining the threshold gains and detuning factors were derived by matching the electric fields and their first derivatives at all the interfaces between grating and no-grating regions.…”