Theoretical interpretation of the enhanced single-mode stability in extended cavity VCSELs

Paraxial eigenmode analysis demonstrates that the extended cavity stability follows from the geometric scaling of the diffractive cavity losses; the same principle also explains the narrow aperture stability. Because diffraction losses scale as (L/b)² = (Lλ/πw_o²)², one can enhance diffraction to differentiate thresholds among modes either by shrinking the mode waist w_o (smaller aperture) or by extending the cavity length L. The second approach does not limit the vertical cavity semiconductor laser (VCSEL) output power. Our predictions agree with experimental trends, and suggest that diffraction limited modes apply to extended cavity VCSELs, since guided mode theory (effective index or thermal lensing) does not allow strong stability dependence on cavity length. The extended length stabilization holds when factors other than diffraction (such as mode wing clipping or aperture scattering) significantly contribute to cavity losses.