Aberration-like cusped focusing in the post-paraxial Talbot effect

Abstract

We present an analysis of self-imaging in a regime beyond the paraxial, where\ndeviation from simple paraxial propagation causes apparent self-imaging\naberrations. The resulting structures are examples of aberration without rays\nand are described analytically using post-paraxial theory. They are shown to\nrelate to, but surprisingly do not precisely replicate, a standard integral\nrepresentation of a diffraction cusp. Beyond the Talbot effect, this result is\nsignificant as it illustrates that the effect of aberration -- as manifested in\nthe replacement of a perfect focus with a cusp-like pattern -- can occur as a\nconsequence of improving the paraxial approximation, rather than due to\nimperfections in the optical system.\n