Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping

We employ the inhomogeneous Helmholtz equation to explore the influence of the fractional degeneracy and the pump distribution on the resonant lasing mode. Theoretical analyses clearly reveal the relationship between the fractional degeneracy and the emergence of the ray-wave duality. Furthermore, we perform thorough laser experiments to confirm the theoretical exploration that the resonant modes near the degenerate cavities are well localized on the ray trajectories under the condition of the off-axis pumping. We also exploit the derived wave functions to calculate the resonant strengths that can noticeably manifest the enhancements of the output powers in the degenerate cavities.