A review on propagation-invariant, quasi-propagation-invariant beams and coordinate axicons

Propagation-invariant and structurally-stable beams have attracted the attention of research communities for their distinct appearances and angular momentum contents, as well as their unique applications. These special kind of beams are mostly descripted by various forms of wave equation. However, the recently described fractional wave equation and fractional Schrodinger equation have added a new aspect to these beams, and supports the idea of Coordinate Axicons—the axicons that follows the shapes of corresponding coordinate system and able to produce quasi-propagation-invariant beams at far field. In this present communication we therefore revisit the theoretical aspects of such beams giving special thrust to the Coordinate Axicon concept.