Abstract
We propose a theoretical model to generate the resonant geometric modes localized on ray periodic trajectories with orbital angular momentum. Based on the numerical analysis, we realize resonant geometric modes in the off-axis pumped degenerate cavity ${\rm Nd}{:}{{\rm YVO}_4}$Nd:YVO4 lasers with an external mode converter. The experimental results reveal that laser output modes display the planar geometric modes when the off-axis displacement is sufficiently large, and the cavity length is set to satisfy the degenerate conditions. To generate the vortex beams, the planar geometric modes are transformed into circular geometric modes. Finally, the resonant geometric modes with large orbital angular momentum (OAM) can be generated from converting the circular geometric modes with an axicon lens. The experimental results are performed to approve the theoretical analyses.
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