Abstract
We consider the effects of the cross-sectional shape on the quantum confinement energies in quantum wire lasers that have been prepared by epitaxial overgrowth on V-grooved and other patterned substrates. Analytic solutions allow some key conclusions to be drawn, while numerical solutions allow a closer approximation to the actual shapes generated experimentally. We are able to obtain the effect of varying the shapes, not only on the ground states but also on the separation of the excited states that might be induced to lase experimentally.