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

Abstract

We present an analysis of the Talbot effect beyond the paraxial regime, where deviation from Fresnel propagation destroys perfect, periodic self-imaging. The resulting interference structures are examples of aberration without geometric optical rays, which we describe analytically using post-paraxial theory. They are similar to, but do not precisely replicate, a standard integral representation of a diffraction cusp (the Pearcey function). Beyond the Talbot effect, this result illustrates that aberration—as the replacement of a perfect focus with a cusp-like pattern—can occur as a consequence of improving the paraxial approximation, rather than due to imperfections in the optical system.