Spatial transformation of coherent optical waves with orbital morphologies

We theoretically verify that converting the Hermite-Gaussian modes into the Laguerre-Gaussian can lead to the spatial morphologies of the two-dimensional (2D) coherent states to be transformed from Lissajous figures to trochoidal curves. With this transformational relationship, we experimentally generate various structured light beams by exploiting a cylindrical-lens mode converter to transform the optical Lissajous modes. The present investigation manifests a notable method to generate optical coherent waves with various orbital spatial morphologies.