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A lateral current injection (LCI) design for AlGaN deep-ultraviolet edge-emitting laser diodes (LDs) on AlN substrates is presented. Two-dimensional optoelectronic simulation predicts lasing at a wavelength of 290 nm. Unlike vertical current injection designs, LCI designs can take advantage of narrow-bandgap p-type contact layers with minimal impact on the optical confinement factor through a partial decoupling of the problems of optical confinement and electrical injection. With polarization-charge-matched quantum well barriers, a large number of quantum wells can be used in LCI designs, which not only enhances the optical confinement factor but also distributes joule heating over a large volume. This is the first theoretical investigation of an LCI LD design in the III-V nitride material system.