Abstract

Surface-emitting lasers have been attracting people’s interest over the past two decades because of their salient features such as low-threshold current, single-mode operation, and wafer-scale integration (Iga, 2000). Their low-divergence surface-normal emission also facilitates output coupling and packaging. Although Vertical Cavity Surface Emitting Lasers (VCSELs) have already been commercially available, their single-modedness and good emission pattern are guaranteed only for devices with a small mode area (diameter of ~μm). Attempts of further increase in the emission aperture have failed mostly because of the contradictory requirements of large-area emitting aperture and single modedness, which casts a shadow over the usefulness of VCSELs in high-power applications. A highly desirable semiconductor laser will consist of a large aperture (say, diameter larger than 20 μm) emitting vertically (i.e., perpendicularly to the plane of the laser). It should possess the high efficiency typical of current-pumped, edge-emitting semiconductor lasers and, crucially, be single-moded. Taking a clue from the traditional edge-emitting distributed feedback (DFB) semiconductor laser, we proposed employing transverse circular Bragg confinement mechanism to achieve the goals and those lasers are accordingly referred to as “circular Bragg lasers.” There have been intensive research activities in planar circular grating lasers since early 1990s. Erdogan and Hall were the first to analyze their modal behavior with a coupledmode theory (Erdogan & Hall, 1990, 1992). Wu et al. were the first to experimentally realize such lasers in semiconductors (Wu et al., 1991; Wu et al., 1992). With a more rigorous theoretical framework, Shams-Zadeh-Amiri et al. analyzed their above-threshold properties and radiation fields (Shams-Zadeh-Amiri et al., 2000, 2003). More recently, organic polymers are also used as the gain medium for these lasers due to their low fabrication cost (Jebali et al., 2004; Turnbull et al., 2005; Chen et al., 2007). The circular gratings in the above-referenced work are designed radially periodic. In 2003 we proposed using Hankel-phased, i.e., radially chirped, gratings to achieve optimal interaction with the optical fields (Scheuer & Yariv, 2003), since the eigenmodes of the wave equation in cylindrical coordinates are Hankel functions. With their grating designed to follow the phases of Hankel functions, these circular Bragg lasers usually take three

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