Multiring polygon super-geometric beam generation based on the quasi-frequency- degeneracy state of a multiaxial super-geometric mode laser

Novel structured modes with a multiring polygon shape are anticipated in the quasi-frequency-degenerate (QFD) cavity, and their counterpart modes are multiaxial super-geometric (MASG) modes in the frequency-degenerate (FD) cavity. The multiring polygon super-geometric modes are numerically constructed by extending their decomposed multiaxial geometric (MAG) modes in the FD state to the modes in the QFD state, implying that they are a kind of special transverse mode in the QFD laser cavity. Then, the characteristics of the multiring polygon super-geometric modes are investigated under different parameters. Studying the multiring polygonal-shaped optical modes may broaden the application areas of structured light, such as particle trapping and manipulation.