Do optical quarks exist in free space: scalar treatment?

Abstract: We have considered new type of singular beams with fractional topological charges that were called the optical quarks possessed rather unique properties, their topological charges being half of the integer order. There are four types of optical quarks: even and odd with opposite signs of the topological charges. The sums or difference of the even and odd quarks form the standard vortex (or non-vortex) beams with the integer order topological charges. All quarks in the same beam annihilate, the beam vanishes. The analysis of the quark angular spectra showed that the optical quarks are structurally unstable field forms under the free-space propagation. We have analyzed their propagation properties for different types of the beam envelope including the symmetric beam array with discrete optical quarks. We have discussed the properties of the possible structurally stable quark forms and medium capable to maintain optical quarks