Generation of Mathieu beams using the method of 'combined axicon and amplitude modulation'

We introduce a novel method of non-diffractive Mathieu beams formation using a technique of 'combined axicon and amplitude modulation'. First, the theoretical mechanism of generating Mathieu beams is analytically derived in detail using the stationary-phase method. Subsequently, we experimentally generate several kinds of Mathieu beams using an amplitude-type spatial light modulation (SLM)-plus-axicon setup. The experimental results show that the proposed method for generation of Mathieu beams is simple and flexible, and thus it is particularly suitable for generating the family of all kinds of non-diffractive Mathieu beams.