Semiconductor Lasers

  • Alan Rolf Mickelson


In the last chapter, we considered a model for a two-level system in a resonator and derived the following set of dynamical equations for the system’s time evolution:
$$\frac{{d{{b}_{\lambda }}}}{{dt}} = ( - i{{\omega }_{\lambda }} - {{k}_{\lambda }} - i\sum\limits_{\mu } {g_{{\mu \lambda }}^{*}{{\alpha }_{\mu }} + {{F}_{\lambda }}(t)}$$
$$\frac{{d{{\alpha }_{\mu }}}}{{2dt}} = ( - i\omega - \gamma ){{\alpha }_{\mu }} + i\sum\limits_{\lambda } {{{g}_{{\mu \lambda }}}{{b}_{\lambda }}{{d}_{\mu }} + {{\Gamma }_{{\mu - }}}} \left( t \right)$$
$$\frac{{d{{d}_{\mu }}}}{{dt}} = \frac{{{{d}_{0}} - {{d}_{\mu }}}}{{{{\tau }_{d}}}} + 2i\sum\limits_{\lambda } {\left( {g_{{\mu \lambda }}^{*}b_{\lambda }^{*}\alpha _{\mu }^{*}} \right) + {{\Gamma }_{d}}\left( t \right)}$$
To apply such a set of equations to any problem, however, it is necessary to know the parameters ω λ ,κ λ ,g μλ ,ω,γ,and τ d with some accuracy as well as to understand the pump mechanism well enough to be able to calculate in some detail the dynamic behavior of d 0 with the external pump. An additional problem arises with semiconductors in that one cannot consider individual atoms in the material as the electrons are not localized in the lattice. Therefore, the index μ is no longer a valid index on which to sum. These issues will be taken up sequentially in the sections of this chapter. In the first section of the effective index method, calculation of ω λ ,κ λ ,and the mode patterns u λ (r) will be considered in some detail. The second section will deal with a very simple model of band structure for the purpose of describing how one can replace the atomic coordinate µ with the electron wave vector k. The third section will discuss the concepts of Fermi levels and quasi-Fermi levels with attention directed toward elucidating the meaning of the time constants τ d and τ α = 1/γ, as well as finding a dynamical model for the d 0 in terms of measurable parameters. The fourth section of the chapter will cast the Maxwell-Bloch equations in their normal semiconductor rate equation form while giving some discussion of the polarizability χ in the equations. The fifth and concluding section of the chapter will discuss something about laser structure and doping profile.


Recombination Milling GaAs Sine Refraction 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abramowitz, M. and Stegun, I., 1965. Handbook of Mathematical Functions. Dover Publications, Inc., New York.Google Scholar
  2. Brillouin, L., 1960. Wave Propagation and Group Velocity. Academic Press, New York.MATHGoogle Scholar
  3. Goell, J.E., 1969. “A Circular-Harmonic Computer Analysis of Rectangular Dielectric Waveguides.” Bell Sys. Tech. J., 48, pp. 2133–2160.Google Scholar
  4. Knox, R.M. and Toulios, P.P., 1970. “Integrated Circuits for the Millimeter Through the Optical Frequency Range.” Proceedings of the Symposium on Sub-millimeter Waves,Polytechnic Institute of Brooklyn (March 31 -April 2, 1970), p. 497.Google Scholar
  5. Kittel, C., 1971. Introduction to Solid State Physics, Fourth Edition. John Wiley & Sons, New York.Google Scholar
  6. Maliuzhinetz, G.D., 1958. “Excitation, Reflection, and Emission of Surface Waves from a Wedge with Given Face Impedances.” DokL Akad. Nauk SSSR, 121, pp. 436–439.MathSciNetGoogle Scholar
  7. Marcatilli, E.A.J., 1969. “Dielectric Rectangular Waveguide and Directional Coupler for Integrated Optics.” Bell Sys. Tech. J., 48, pp. 2079–2102.Google Scholar
  8. Watson, G.N., 1966. A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge.MATHGoogle Scholar
  9. Yariv, A., 1989. Quantum Electronics, Third Edition. Holt, Rinehart & Winston, New York.Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Alan Rolf Mickelson
    • 1
  1. 1.Electrical and Computer EngineeringUniversity of Colorado at BoulderUSA

Personalised recommendations