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

Gain-guided eigenmodes in open vertical-cavity surface-emitting laser cavit ies are constructed by superposition of paraxial (i.e., Gauss-Laguerre) mod es employing the unfolded-cavity hard-mirror equivalent to distributed Brag g reflectors. The round-trip matrix is obtained analytically for simple gai n 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 te rms 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 simp le variational principle. The Gaussian nature of the cavity modes is confir med by comparison with experiments. Finally, the new eigenmode properties s elf-consistently account for wavelength blueshifting and reduction in the m ode waist with increasing bias current, without invoking index guiding. (C) 2001 Optical Society of America.