The effective frequency method in the analysis of vertical-cavity surface-emitting lasers

An effective index model for vertical-cavity surface-emitting lasers (VCSELs) is reexamined. In a systematic manner, the basic equations are derived. Instead of effective indices of plane reference waveguides, effective frequencies of plane reference resonators appear. Calculations of the threshold gain and lasing wavelength of a long-wavelength VCSEL show the usefulness of the method and clarify the waveguiding mechanisms in VCSELs, Both dispersion and waveguiding influence the lasing wavelength remarkably.