Free-Carrier Theory

Abstract

A discussed in the previous two chapters, the laser field and the semiconductor gain medium are coupled by the gain and the carrier-induced refractive index, or equivalently by the induced complex susceptibility. To determine these quantities, we need to solve the quantum mechanical gain medium equations of motion for the polarization of the medium. The evolution of these equations is driven by the system Hamiltonian. Equation (2.114) gives the total quantum mechanical Hamiltonian for the semiconductor medium, aside from interactions between the carriers and phonons, and injection current pumping. It contains contributions from the kinetic energies, the many-body Coulomb interactions and the electric-dipole interaction between the carriers and the laser field. Since a complete theory using the full Hamiltonian is relatively complicated, one often makes approximations that allow one to begin with a tractable treatment that is reasonably accurate and hopefully contains the most important effects. By gradually eliminating the approximations, one can work toward increasing rigorous treatments. In this book, we take such an approach.