The Talbot effect: recent advances in classical optics, nonlinear optics, and quantum optics

TLDR

The Talbot effect, a self‑imaging phenomenon where periodic planar field distributions repeat, is applied in optics, acoustics, electron microscopy, plasmonics, X‑ray, and Bose–Einstein condensate research, and is explored for image processing, spatial‑frequency filtering, and optical metrology, with further advances anticipated. This article reviews recent advances of the Talbot effect across classical, nonlinear, and quantum optics. The review presents the physical aspects of self‑imaging, distilling mathematical formulations to the essential ones. Readers preferring strict mathematical treatments should consult the extensive reference list.

Abstract

The Talbot effect, also referred to as self-imaging or lensless imaging, is of the phenomena manifested by a periodic repetition of planar field distributions in certain types of wave fields. This phenomenon is finding applications not only in optics, but also in a variety of research fields, such as acoustics, electron microscopy, plasmonics, x ray, and Bose–Einstein condensates. In optics, self-imaging is being explored particularly in image processing, in the production of spatial-frequency filters, and in optical metrology. In this article, we give an overview of recent advances on the effect from classical optics to nonlinear optics and quantum optics. Throughout this review article there is an effort to clearly present the physical aspects of the self-imaging phenomenon. Mathematical formulations are reduced to the indispensable ones. Readers who prefer strict mathematical treatments should resort to the extensive list of references. Despite the rapid progress on the subject, new ideas and applications of Talbot self-imaging are still expected in the future.