Following the Flux in diffracted fields – An efficient numerical method for tracing the Eikonal function

Abstract

We report on our recently developed method for tracing lines of flux in three-dimensional diffracted wavefields using an approach we call ’non-linear ray tracing’ but which can be more accurately described as tracing the lines of flux in the context of the Eikonal function. These ’rays’ navigate through the diffracted field guided by the derivative of the phase at a sequence of successive points. Our approach is based on the Angular Spectrum method, a numerical algorithm that accurately and efficiently calculates diffracted fields for numerical apertures <0.7. This is used to generate a three-dimensional grid of complex wavefield samples in the focal region, followed by tracing the flux through this volume. The ray propagates in a straight line between two consecutive planes within the volume; the phase derivative is calculated at each plane to direct the ray on the next step of its journey. We demonstrate the effectiveness of our approach by generating results for focused laser beams with TEM00 and TEM01 laser profiles. We also simulate the effects of optical aberrations, described by Zernike polynomials, on the three-dimensional focused wavefield. Our non-linear ray tracing method provides a powerful and efficient approach for tracing lines of flux through complex three-dimensional wavefields, offering an exciting new tool for understanding these complex systems.