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Modern Semiconductor Laser Theory
Optical gain is probably one of the most important basic properties of semiconductor lasers. A free carrier model with a phenomenological damping is often used in an optical gain calculation for simplicity. This model provides some useful insight to the basic properties of a semiconductor laser. However, we need to include a Coulomb interaction between charged carriers for a more realistic description of the semiconductor laser. For example, many-body effects have been known to be very important in gallium nitride (GaN)-based lasers. Since Coulomb interaction processes involve more than one carrier, these effects are often called many-body effects. Coulomb interaction includes attractive interaction between electrons and holes (interband) and repulsive interaction between same carriers (intraband), and is the dominant contributor to optical damping. The optical gain and the refractive index spectra are significantly affected by these Coulomb interactions. That is, the spectral position of the optical gain and the refractive index spectra are shifted through bandgap renormalization, and their shapes are modified through Coulomb correlation effects.
We need quantum mechanical many-body techniques to analyze these Coulomb interaction processes. The equations of motion derived from the many-body Hamiltonian couple expectation values of products of two particle operators to those of the product of four particle operators, which, in turn, are coupled ...
