Gain of TE-TM modes in quantum-well lasers

Semiclassical laser theory is rigorously applied to semiconductor lasers in order to obtain both the complete TE and TM linear gain. The resulting expressions for the modal gain in heterostructure lasers differ in form from those conventionally accepted. In particular, the conventional modal gain written as the product of a confinement factor and a bulk gain is only an approximation of the true modal gain derived. The conventional expression relies on an explicit definition of the active region of the laser, which can be ambiguous when certain heterostructures, such as parabolic quantum wells, are to be treated. This ambiguity is eliminated by the gain expressions as a more natural active region defined by the product of electron and hole wave functions emerges. The relevant approximations which allow the newly derived gain equations to be written in forms similar to the conventional expressions for single quantum well, multiquantum well (MQW), and in wide active region lasers are explicitly shown