“Optical knives” design based on vector Mathieu beams

Laser micromachining of structures with dimensions comparable to the wavelength of incident light is among the hot topics of modern light-matter interaction, with long focal lines and small focal spot sizes (also known as “optical needles” [1]) being strongly desired in some specific areas. Nondiffracting Bessel beam is a common example of the optical field, which can be perceived as an optical needle. Mathieu beams are another example of the nondiffracting beams and are interesting in practical applications due to its asymmetrical cross-section [1]. Mathieu beams possess a rather complicated distribution of electric field which also has some practical applications [2]. Moreover, Mathieu beams have additional (in comparison to a Bessel beams) degree of freedom — an eccentricity parameter, which enables us to perceive them as “optical knives” of controllable width.