Generic representation of active cavity VCSEL eigenmodes by optimized waist Gauss-Laguerre modes

Gain-guided eigenmodes in open VCSEL cavities are constructed by superposition of paraxial (i.e., Gauss-Laguerre) (GL) modes, employing the effective cavity hard mirror equivalent for the DBRs. A generic round-trip matrix is obtained analytically for simple gain profiles, including finite mirror diameter losses, diffraction spreading and aperture scattering effects. Diagonalization yields the full range of stable, unstable, and steady-state complex eigenmodes and gain eigenvalues. More importantly, it is demonstrated that in cases of interest the lower order cavity eigenmodes can be approximated by pure GL modes with optimum waist size prescribed through a variational principle. A simple analytic relation is thus obtained for the mode waist for a variety of laterally open cavities. The theory is confirmed by comparison with experimental results. The GL eigenmode properties account for wavelength blue-shifting, increasing density threshold current and increasing differentiation in modal losses with decreasing current aperture. They also yield the correct aperture placement effects in the cavity standing wave. Diffraction and scattering losses are shown to dominate over mirror losses at small cavity apertures.