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.

Spiral pattern is formed for coaxial interference between two vortex beams with different radii of wavefront curvatures and different topological charges (TCs). A theoretical model considering various parameters (such as phase difference, radius of wavefront curvature, and TCs) is established to predict all kinds of interference patterns. An improved Mach-Zehnder interferometer is set up in an experiment to generate different kinds of spiral patterns and verify the theoretical model. The number of spiral lobes is determined by the absolute value of TCs’ difference between two vortex beams, and the twist direction relates to the sign of TCs’ difference and the difference of reciprocals for the radii of wavefront curvature, clockwise for the same sign, and counterclockwise for the opposite signs. The twist direction of the spiral pattern reverses and the lobes direction near the core of the pattern changes obviously when the spherical wave changes from convergence to divergence.

Spiral phase plate (SPP) is the widely used method in the generation of vortex beam (VB) with fixed topological charges (TCs) for specific wavelength. Although VB with large TCs can be directly generated by using the SPP with high vortex order. The fabrication of high-quality SPPs with high vortex orders usually requires complex manufacturing process and high machining accuracy. An alternative method to generate VBs with large TCs is cascaded multiple SPPs with low order. In this study, we numerically calculate the transmitted light field of cascaded multiple SPPs according to the Huygens–Fresnel diffraction integral, and perform the experimental verifications. Based on cascading 6 SPPs (3 SPPs with TCs of 2, and 3 SPPs with TCs 4, respectively), an VB with TCs as high as 18 is generated. Furthermore, The TCs of the generated VB are detected by coaxial and off-axis interfering with fundamental Gaussian beam or its conjugate beam, respectively. The generated fork and spiral patterns allow us to distinguish the value and sign of TCs carried by the VB. The experimental results coincide well with the theoretical simulations. The fork pattern shows better resolution than the spiral one, and the petal pattern with small spiral allows us to distinguish large TCs with a higher resolution.

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