Generalized axicon-based generation of nondiffracting beams

We generalize the well-known method of generating nondiffracting beams based on axicons by allowing phase modulations with azimuthal dependencies. This generalization includes the description of Bessel-like beams of zero order, higher orders and superpositions thereof. We present the enormous benefit of our approach for highly efficient and robust shaping of nondiffracting beams with arbitrary transverse profiles. The concept's versatility is demonstrated by discussing generation and propagation of various nondiffracting beams with potential regarding laser materials processing.