Gain-frequency-current relation for Pb<inf>1-x</inf>Sn<inf>x</inf>Te double heterostructure lasers

Abstract

The active region gain expression for Pb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Sn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Te lasers is obtained from the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \cdot p</tex> model of the conduction and valence band extrema. Curves of gain versus frequency with current, temperature, and majority carrier concentration as parameters are calculated using published values of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \cdot p</tex> model parameters. In addition, threshold current versus temperature and threshold current versus majority carrier concentration curves are given. A simple expression is obtained for the conductivity effective mass for use in the equation for free-carrier absorption appropriate to the highly degenerate majority carrier concentrations typical of Pb <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> Sn <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> Te laser material.