What are the traveling waves composing the Hermite-Gauss beams that make them structured wavefields?

To the best of our knowledge, at the present time there is no answer to the fundamental question stated in the title that provides a complete and satisfactory physical description of the structured nature of Hermite-Gauss beams. The purpose of this manuscript is to provide proper answers supported by a rigorous mathematical-physics framework that is physically consistent with the observed propagation of these beams under different circumstances. In the process we identify that the paraxial approximation introduces spurious effects in the solutions that are unphysical. By removing them and using the property of self-healing, that is characteristic to structured beams, we demonstrate that Hermite-Gaussian beams are constituted by the superposition of four traveling waves. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Automated summary

This study aims to establish a rigorous mathematical-physics framework to provide a complete and accurate description of the structured nature of Hermite-Gauss beams, and identifies spurious effects introduced by the paraxial approximation in the solutions. By utilizing the self-healing property of structured beams, it is demonstrated that Hermite-Gaussian beams are constituted by the superposition of four traveling waves.