This work focuses on the effects of spatial hole-burning (SHB) on the modulation response of oxide-confined vertical-cavity surface-emitting lasers. The comprehensive laser diode simulator, Minilase, as well as a simple 1-D rate equation models are used as simulation tools in the studies. We demonstrate that, due to the non-uniform transverse optical intensity, carriers at different locations of the quantum well (QW) have different stimulated recombination rates, and therefore exhibit different dynamic responses under direct modulation. This non-uniformity is revealed to be responsible for an over-damping of the relaxation oscillation and the reduction of the modulation bandwidth. Due to the limit of this nonlinear effect, VCSELs with small oxide apertures show lower intrinsic maximum bandwidth compared with that of large aperture structures. Further simulations demonstrate that this damping effect can be greatly reduced by making the electrical aperture smaller than the optical aperture, thereby significantly improving the modulation response.
We propose a novel treatment that enhances the accuracy of the Effective Index Method (EIM) when used for gain-guided oxide-confined VCSELs. If a thin oxide is placed at or near a z-field null position, the diffraction caused by the oxide becomes negligible. Gain-guiding subsequently dominates and causes the EIM to break down. To circumvent this problem, we propose to use an artificial index-guided diffraction effect to simulate the gain-guided diffraction effect. This is achieved by increasing the oxide thickness and making a correction to the oxide index by taking a weighted sum between the original oxide index and the center region index at the oxide layer position. The weight is specifically chosen to be the mean z-field (normalized to its local z-field variation) at the position of the oxide. We show that this simple correction to the EIM successfully simulates the gain-guided diffraction effect and produces the correct transverse phase variation for oxide-apertured VCSELs when gain-guiding becomes the dominant mechanism. Therefore, the improved EIM is able to produce resonant wavelengths which are in excellent agreement to those of the vector Green's function method for the COST-268 VCSEL model, both in the gain-guided and index-guided regimes. Comparisons with an experimental model have also been made and excellent agreement is shown.