Theory of Transverse Cavity Mode Selection in Homojunction and Heterojunction Semiconductor Diode Lasers

Abstract

A discussion of the transverse electromagnetic modes in single and double heterojunction lasers is presented. Three basic structures are analyzed: a laser with single heterojunction and optical cavity defined by the (p+-p) heterojunction and p-n junction; a double heterojunction laser with the second heterojunction at the p-n junction; and another double heterojunction unit which can have a large range of optical cavities because the second heterojunction is in the n region spaced a controlled distance from the p-n junction. Since the dielectric discontinuity at a heterojunction is an order of magnitude larger than at a p-n junction, these double heterojunction lasers can have high-order transverse modes. To model the observed radiation fields and, in particular, the preference for high-order modes, the optical properties of the junction region are treated as a five-layer dielectric slab. The two outer regions are bulk p+ and n+ (AlGa)As in the double heterojunction structures and p+(AlGa)As and n+ GaAs in the single heterojunction structures. The section between the p+ heterojunction and the p-n junction, which is customarily treated as the active section of the laser, has here been partitioned into two regions: a gain region adjacent to the p-n junction where recombination occurs and a lower gain region adjacent to the p-p+ heterojunction. In fact the latter region may be absorbing. The width of the first gain region is associated with the electron diffusion length in heavily doped p-type GaAs. For a suitable partition the modal gain of the high-order modes becomes larger than for the low-order modes, resulting in the highest mode reaching threshold first. In contrast, were the region between the n-p junction and the p-p+ heterojunction uniformly inverted, the laser would operate in the fundamental mode, contrary to experimental observation. Machine calculations indicate that structures radiating high-order modes have a gain region narrower than 1 μm.