Comparison of Exactness of Scalar and Vectorial Optical Methods Used to Model a VCSEL Operation

In the paper, a comparison between results of the optical scalar and vectorial optical methods, using the scalar effective frequency method and the vectorial method of lines, respectively, as their typical examples, applied for simulating an operation of vertical-cavity surface-emitting diode lasers (VCSELs) is presented. Both optical approaches has been applied to simulate an operation of the standard 1.3-mum GaAs-based oxide-confined GaInAsN double quantum-well VCSEL, but comparison conclusions seem to be more general and concerns all VCSELs. Validity limits of the simplified scalar approach have been determined by comparing its approximate results with more exact ones obtained with the aid of the accurate vectorial model. The scalar model has been found to be quite exact in the case of a determination of the wavelength of emitted radiation, whereas its exactness in the lasing threshold analysis is much worse, especially in the case of higher order modes, smaller aperture diameters and/or weak radial optical guidance. Our analysis leads also to more general designing conclusions concerning the optimal position and the thickness of the oxide layer assuring, respectively, the stable single mode operation and the lowest threshold gain