“…For example, imprinting an azimuthally varying phase profile creates orbital angular momentum (OAM) states that possesses a helical wavefront and carry quantized OAM (Bazhenov et al, 1990 ; Allen et al, 1992 ); imprinting a cubic phase profile creates the Airy beams that possess a curved trajectory in free space and self-healing property whereby the beam appears to reconstruct itself in the presence of obstacles (Berry and Balazs, 1979 ); and imprinting a radial phase prepares the “non-diffractive” Bessel beams (Indebetouw, 1989 ). The enabling properties of structured light beams and the access to new degrees of freedom have brought forth a wide range of impactful applications in optical phenomenology and microscopy, high-bandwidth communication, manipulation of matter, and quantum science (Mair et al, 2001 ; Andersen et al, 2006 ; Marrucci et al, 2006 , 2011 ; Maurer et al, 2007 ; Padgett and Bowman, 2011 ; Wang et al, 2012 ; Ritsch-Marte, 2017 ; Sarenac et al, 2018 ; Schwarz et al, 2020 ; Cameron et al, 2021 ).…”