Propagation of obstructed Bessel and Bessel-Gauss beams

The investigation into Bessel beams has been a topic of immense research during the past 20 years, due to the interesting properties they display. Bessel beams not only exhibit diffraction free propagation, but also reconstruction of the amplitude and phase of the beam after encountering an obstruction. Although this self reconstruction property has been previously modelled by numerous groups, the techniques involve rigorous, time-consuming computations. In this work we present an efficient method to accurately calculate the reconstruction of a Bessel beam after an arbitrary obstruction. Our method considers the well-known conical wave features of Bessel beams and looks at the projection of the obstruction in space as a result of the travelling conical waves that produce the Bessel beams.