Abstract
We employ a large-Fresnel-number laser system to demonstrate the three-dimensional optical coherent waves localized on Lissajous and trochoidal parametric surfaces with Lissajous and trochoidal transverse patterns in degenerate cavities. The coherent structured beams are verified to be composed of degenerate Hermite-Gaussian and Laguerre-Gaussian modes with different longitudinal indices resulted from longitudinal-transverse coupling. As well known, the Hermite- Gaussian modes can be converted into Laguerre-Gaussian modes possessing orbital angular momentum by use of a pair of cylindrical lens. Consequently, we make use of cylindrical lenses to transform the Lissajous structured beams superposed of degenerate Hermite-Gaussian modes into the intriguing trochoidal structured beam possessing optical orbital angular momentum.
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