This thesis presents an investigation of the modal gain characteristics of Vertical Cavity Surface Emitting Lasers (VCSELs). This is motivated by the experimental observations which tend to indicate fundamental mode operation at just above lasing threshold and multi-transverse mode operation at higher injection current levels. The complete mode spectrum of the cylindrical cavity is first analysed to illustrate that the original expectations that single (wavelength) mode operation solely due to the large wavelength separation created by short device lengths may not be realisable. The modal gains of different modes are calculated to demonstrate that mainly the difference between the modal gains, and not the separation between the resonances, provides a more satisfactory explanation of the fundamental mode operation at just above lasing threshold. At higher injection current levels, the increase in the modal gains of the higher order transverse modes (due to spatial hole burning) explains the excitation of higher order transverse lasing modes.
The model relies on calculating the modes of a cylindrical dielectric resonator and the the corresponding modal gains are obtained from a perturbation analysis which takes into account the gain profile due to the injected inversion population distribution. A self consistent evaluation of the inversion population distribution (which provides the required local gain profile) is derived from the corresponding diffusion equation for the injected carriers in the active layer of the device. The development for obtaining the above lasing threshold inversion population distribution (which includes radial and azimuthal variation) has been done hierarchically such that the numerical procedures developed in the simpler stages of the model directly apply to solve a part of the next level of sophistication. This hierarchy has helped to provide a very efficient and compact numerical procedure and may be seen as an important aspect of the work done in the thesis. Further refinements include the evaluation of the injection current profile dependence on injection contact geometry and current spreading.
|Date of Award