In Chap. 2, we describe a simple model for semiconductor gain from a free (i.e., noninteracting) electron-hole plasma. While this model provides some useful insight to the elementary physics of a semiconductor gain medium, its inadequacies show up in analyses of high-quality samples and advanced laser structures, where one clearly sees signatures of the more subtle Coulomb interaction effects among carriers. This chapter, as well as the next one, discusses approaches towards a more realistic description of the gain medium, where one includes the Coulomb interaction between charge carriers. The Coulomb potential is attractive between electron and holes (interband attraction) and repulsive for carriers in the same band (intraband repulsion) Since Coulomb interaction processes always involve more than one carrier, the resulting effects are often called many-body effects, and quantum mechanical many-body techniques have to be used to analyze these phenomena.
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For more details on the semiconductor Bloch equations and for further references see
- Haug, H. (1988), Ed., Optical Nonlinearities and Instabilities in Semiconductors, Academic, New York (1988)Google Scholar
Discussions of the two-level Bloch equations can be found in
- Allen, L. and J. H. Eberly (1975), Optical Resonances and Two-Level Atoms, John Wiley, New York; reprinted (1987) with corrections by Dover, New York.Google Scholar
- Meystre, P. and M. Sargent III (1991), Elements of Quantum Optics, 2nd Ed., Springer-Verlag, Heidelberg.Google Scholar
- Sargent III, M., M. O. Scully, and W. E. Lamb (1977), Laser Physics, Addison Wesley, Reading, MA.Google Scholar
The classical theory of plasma screening is discussed in
General many-body theory and sum rules are discussed in
For the modifications of the plasmon-pole approximation in an electron-hole plasma see
For the Padé approximation, see
- Gaves-Morris, P. R. (1973), Ed., Padé Approximants and Their Application, Academic Press, N.Y.Google Scholar
We have used the integral tables in
- Gradshteyn, I. S. and I. M. Rhyzhik (1980), Tables of Integals, Series and Products, Academic Press, New York.Google Scholar