Mode confinement and gain in junction lasers

For a three layer dielectric sandwich, the center dielectric region must have a dielectric constant higher than the outer regions and some finite thickness for a wave to be "bound" to the center region. We have calculated the transverse propagation constants for even TE modes when the dielectric sandwich is unsymmetrical. The resultant field distributions are used to derive a formula for the gain of a junction laser of the form
\alpha = \frac{\alpha_{1} + P\alpha_{3}/nR + f\alpha_{2}}{g}
, where the α
n
's are the attenuation (or gain) constants associated with the various regions of the junction structure. Curves of
P/nR
,
f
, and
g
as a function of active region thickness are given from which the condition for laser oscillation or the net gain or loss per unit length of a given device may be found.