Unraveling the vector nature of generalized space-fractional Bessel beams

We introduce an exact analytical solution of the homogeneous space-fractional Helmholtz equation in cylindrical coordinates. This solution, called vector Space-Fractional Bessel Beam (SFBB), has been established from Lorenz' gauge condition and Hertz transformations. perform scalar wave analysis focusing on electromagnetics applications, especially cases where dimensions beam are comparable to its wavelength $(k_r \approx k)$. The propagation characteristics such as diffraction self-healing properties have explored with particular emphasis polarization states transverse modes. Due continuous order orbital angular momentum dependence, this can serve a bridge between ordinary integer fractional and, thus, be considered generalized that is applicable both dimensional spaces. proposed SFBBs provide better control over readily generated using Digital Micromirror Devices (DMDs), Spatial Light Modulators (SLMs), metasurfaces, or spiral phase plates. Our findings offer new insights electromagnetic propagation, thus paving route towards novel applications optical tweezers, refractive index sensing, trapping, communications.