Vectorial diffraction- and dispersionless pulsed “optical knife” beams with femtosecond duration

Abstract Mathieu beams are nondiffracting solutions of the wave equation in elliptical coordinate system and can be perceived as “Optical Knives” due to unique asymmetric transverse intensity profile. Width of these “Optical Knives” can be controlled due to extra degree of freedom – eccentricity parameter. Femtosecond pulsed beams are of significant interest due to their importance in material processing and growing applicability elsewhere. Here we derive vectorial Mathieu beams and superpose them to create femtosecond pulsed beams, where diffraction spreading and dispersive broadening is compensated by a given angular dispersion. Intensity profiles, durations and polarization states of different “optical knife” pulsed beams are discussed in detail.