Experimental demonstration of optical Mathieu beams

The observation of Mathieu beams that are propagation-invariant optical fields (PIOF) of the Helmholtz equation in elliptic coordinates was reported. The intensity pattern of the zero-order mode was highly localized in one transverse direction, in contrast with the J sub(0) - Bessel beams which was circularly symmetric. However, the physics of Mathieu beams was also based on the superposition of a set of plane waves whose wave vectors line on a cone.