We have considered a new type of singular beams called as optical quarks. They have fractional topological charges being equal to half an integer and they possess rather unique properties. There are four types of optical quarks, even and odd ones, which reveal the opposite signs of topological charges. The sums or differences of the even and odd quarks form standard vortex or non-vortex beams with the topological charges of integer order. All the quarks in the same beam annihilate and the beam vanishes. We conducted an analysis of all possible combinations of even and odd optical quarks with different charges. What provided an opportunity to explore what interactions correspond to their "sum" and "difference."