Characteristics of fork-shaped fringes formed by off-axis interference of two vortex beams

Fork-shaped fringes are formed for off-axis interference between two oblique-incident vortex beams. New formulas considering various parameters [such as the angles between two vortex beams and their topological charges (TCs)] are established to describe all kinds of fork-shaped fringes. An improved Mach–Zehnder interferometer is employed to investigate these interference fringes. Experimental measurements are consistent with numerical simulations by using our formulas. Our results broaden the understanding of the off-axis interference between two vortex beams, and can be applied to detect the TCs’ sign and value of an unknown vortex beam, especially large-value TCs.