Usability limits of the scalar effective frequency method used to determine modes distributions in oxide-confined vertical-cavity surface-emitting diode lasers

摘要

The accuracy of the commercially used, simplified scalar optical effective frequency method (EFM) is verified by comparing its results with those obtained using more accurate vectorial models represented by the method of lines (MoL). Both EFM and MoL methods are applied to the modern telecommunication oriented GaAs-based oxide-confined vertical-cavity surface-emitting diode laser (VCSEL) emitting 1.3 mu m radiation from the InGaAsN/GaAs double quantum well active region. Although both methods are applied to the specific laser structure, the conclusion remains valid for a broad range of different VCSEL designs. The scalar EFM approach has been found to remain surprisingly often quite exact; nevertheless, it falls for structures violating its fundamental assumption of plane wave propagation within the laser cavity. Therefore, a noteworthy discrepancy between modes calculated with the aid of scalar and vectorial approaches occurs for weaker guidance, i.e. for higher-order modes, smaller aperture diameters, thinner oxidation layers and/or apertures shifted from the antinode position. These cases need an exclusive use of the more exact but also more time-consuming vectorial algorithms.