Vortex beam interaction with a step

Abstract

In this work, we describe a technique to measure the height of a reflective single-step sample using the diffraction of a vortex beam behind a triangular aperture. When we scan the beam over the step, we simulated that it must acquire a phase ϕ_s apart from the azimuthal phase due to the intrinsic nature of the vortex' wavefront. Depending on the step height h, the diffraction can either be poorly structured or well-structured. To quantify our results, we plot the Structural Similarity (SSIM) index between a pattern generated from a vortex beam reflected by a flat surface (h = 0) and from a beam reflected by a step with a given height (h ≠ 0). We find that the SSIM value decreases as we increase the height up to h = 150 nm. As we increased h until ϕ_s returns to 2π, the SSIM index increases. In our simulations, we can measure height differences of h = λ/4. Moreover, we compare our results to a Gaussian beam. Unlike the vortex beam, the Gaussian beam is sensitive only to changes when the beam center is precisely at the step edge. This suggests that vortex beams can be used as a precise scanning method, as they display notable changes for all scanning points over the sample.