Improved effective index method for oxide-confined VCSEL mode analysis

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.