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This paper presents the characteristics of parabolic bow-tie laser arrays (PBTLAs) which are a novel category of laser diodes specially designed to achieve high power with high brightness at 980 nm. Output powers in excess of 2.8 W/facet have been measured from five-element PBTLAs with output beam less than twice the diffraction limit, achieving high brightness of 275 MWcm-2srad-1 at 3 A (pulsed) injection current (=22 times the threshold). Changes in the achievable brightness due to changes in the optical cavity geometry and in the lateral optical guiding strength are discussed in detail, using the coupled-mode theory to interpret the experimental results. At threshold all devices operate in the highest (double lobed) array mode. At higher currents the arrays of tapered lasers change to quasi-in-phase operation when the modal gain of the fundamental array mode dominates because of the combined effect of carrier hole burning and spatial filtering from the narrow stripe central section of the device. Similar trends have been observed under continuous-wave operation. The reduction of lateral optical guiding strength is deleterious for the operational characteristics of PBTLAs and linear bow-tie arrays, and it leads to filamentation in gain-guided devices even at low currents. Theoretical results presented in this paper show that scalability is in principle possible; however, changes in the lateral gain profile due to hole-burning can significantly increase the modal gain of higher order modes and, therefore, strongly influence the optical output profile.