Active-cavity vertical-cavity surface-emitting laser eigenmodes with simple analytic representation

Gain-guided eigenmodes in open vertical-cavity surface-emitting laser cavities are constructed by superposition of paraxial (i.e., Gauss–Laguerre) modes employing the unfolded-cavity hard-mirror equivalent to distributed Bragg reflectors. The round-trip matrix is obtained analytically for simple gain profiles, including finite-mirror-size losses, diffraction spreading, and gain-confinement effects. Diagonalization yields the full range of stable, unstable, and steady-state complex eigenmodes and gain eigenvalues, in terms of the cavity parameters. More importantly, it is demonstrated that in cases of interest the lower-order cavity eigenmodes can be approximated by pure Gauss–Laguerre modes with optimum waist size prescribed through a simple variational principle. The Gaussian nature of the cavity modes is confirmed by comparison with experiments. Finally, the new eigenmode properties self-consistently account for wavelength blueshifting and reduction in the mode waist with increasing bias current, without invoking index guiding.