Talbot effect in cylindrical coordinate systems

Abstract

The Talbot effect is a near-field self-imaging phenomenon, where the propagation of a laterally periodic field results in an image of the initial field at a certain propagation distance defined as the Talbot length. The effect is named after Henry Fox Talbot, who first discovered the effect. Cylindrical coordinate systems have been proposed to allow for almost perfect self- and fractional images related to the Talbot effect for angularly periodic fields, thanks to the cyclic nature of the angular periodicity. The task of this bachelor’s thesis is to investigate the propagation of an angularly periodic light field in cylindrical coordinate systems. The behaviour of the field is investigated theoretically in a cylinder surface geometry, and in a ring-core fiber by simulation. The theoretical part is based on literature and scientific articles, and the simulations are done using the split-step beam propagation method with MATLAB. The objective of the research is to observe the Talbot effect in a ring-core fiber, and to specify the properties of a ring-core fiber suitable for experimental research of the effect. This thesis focuses on the interference patterns and self- and fractional images of 2π-periodic input fields, which could be used, for example, to build a novel beam splitter. Beam splitters using the cylindrical Talbot effect could, in theory, split a single input beam to an arbitrary number of output beams of equal intensity. The number of output beams in a beam splitter like this would be limited only by the resolution of the system. In this work, the interference pattern typical to the Talbot effect was seen to be almost perfectly similar in a ring-core fiber as in a planar geometry. In a ring-core fiber, the interference pattern was observed to be somewhat longitudinally stretched due to the ring thickness, but the observed Talbot lengths are very precise regardless. As a result of the simulations, we were able to specify the properties of a ring-core fiber suitable for experimental research regarding the cylindrical Talbot effect. The applicable ring-core fiber is specified to have an inner radius of 20–50 μm, and a ring thickness of 1.5–3.0 μm. In this work, we also estimated that the interference pattern is fairly stable under thermal instability, and the observation of the Talbot effect in the fiber will most probably not need great measures of thermal stabilization. The results of this work suggest that it would be worthwhile to continue the research of the cylindrical Talbot effect experimentally, and that the cylindrical Talbot effect shows a lot of potential in terms of applicability.