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

Abstract

This is a continuation of our previous work [Opt. Express 16, 9155 (2008)]. In this paper we investigate the effect of nonuniform pumping on the modal properties of surface-emitting chirped circular grating lasers. By numerically solving the coupled-mode equations and matching the boundaries we compare and discuss the threshold pump levels and frequency detuning factors for three pumping profiles: uniform, Gaussian, and annular. Depending on the overlap of the pumping and modal profiles, Gaussian pumping results in the lowest threshold pump levels except for the fundamental mode of ring Bragg resonator laser, and annular pumping provides larger threshold discrimination between the fundamental and firstorder modes of circular DFB and ring Bragg resonator lasers, which is favorable for single-mode operation in these lasers. We also study the farfield patterns of the fundamental modes of circular DFB, disk-, and ringBragg resonator lasers. Circular DFB and ring Bragg resonator lasers have the first-order dominating peak, while disk Bragg resonator laser exhibits the zeroth-order dominating peak.

Surface-emitting circular DFB, disk-, and ring-Bragg resonator lasers with chirped gratings III: gain saturation effects and above-threshold analysis

“…The laser structural parameters are assumed to be the same as those in [7] and [8]. In short, in grating regions h 1 = 0.0072 + 0.0108i and h 2 = 0.0601 while in no-grating regions both vanish.…”

“…For some simple g 0 profiles, P pump has analytical expressions [8], otherwise, numerical integration always remains a resort.…”

“…The lowest P th and the highest η ex are achieved with the Gaussian pump for circular DFB and disk Bragg resonator lasers and with the annular pump for ring Bragg resonator laser. Actually P th and η ex are both related to the overlap between pump profile and modal intensity distribution [8]. A larger overlap results in more efficient energy conversion in the gain medium which consequently leads to a lower P th and a higher η ex .…”

“…Including a second-order Fourier component, the gratings are able to provide in-plane feedback as well as couple laser emission out of the resonator plane. In previous parts of this paper series [7,8], we have solved the modes and compared the modal properties, by both analytical and numerical approaches, of the three types of lasers at threshold. Gain saturation effects in above-threshold operation were previously studied in both linear and circular DFB and DBR lasers [4,[9][10][11][12].…”

Surface-Emitting Circular Bragg Lasers – A Promising Next-Generation On-Chip Light Source for Optical Communications

“…Far-field intensity patterns of the fundamental mode of (a) circular DFB, (b) disk, and (c) ring Bragg lasers. After (Sun & Yariv, 2009a) 3.3 Single-mode range, quality factor, modal area, and internal emission efficiency In the previous subsections we have compared the modal properties for devices with a fixed exterior boundary radius x b = 200. In what follows we will vary the device size and investigate the size dependence of modal gains to determine the single-mode range for each laser type.…”