Elliptical-ring-shaped Talbot effect in uniaxial crystals

In this paper, we propose a type of anisotropic elliptical-ring-shaped Talbot effect occurring in uniaxial crystals. The effect is realized by propagating a phase-only periodic elliptical-ring structure in the uniaxial crystal, orthogonal to the optical axis. Both phenomena of self-imaging at the Talbot distance and N-rings to one-ring convergence at the fractional Talbot distance were discussed. Numerical simulations were performed to demonstrate the correctness of theoretical derivation and the existence of the elliptical-ring-shaped Talbot effect. With the specific phase distribution, the N series of periodic elliptical rings of the incident plane will converge to one series of elliptical rings equally spaced at the fractional Talbot distance, where N is an even integer.