Lissajous structured beams emerging from a spherical laser cavity subject to the birefringent effect of the laser crystal are quantitatively analyzed. The analysis reveals that the birefringent effect leads to numerous frequency degeneracies at the cavity lengths near an ideal degenerate cavity. By using a diode-pumped Nd:GdVO laser, the emergence of Lissajous structured modes relevant to frequency degeneracies is precisely quantified by comparing experimental results with numerical analyses. The present quantitative analysis provides an important guideline for the generation of structured transverse modes related to the ray-wave correspondence.
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