Mode confinement and gain in junction lasers

Abstract

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\alpha = \frac{\alpha_{1} + P\alpha_{3}/nR + f\alpha_{2}}{g}</tex> , where the α <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> 's are the attenuation (or gain) constants associated with the various regions of the junction structure. Curves of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P/nR</tex> , <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</tex> 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.