Localized wave solutions of the scalar homogeneous wave equation and their optical implementation

TL;DR

This paper reviews localized wave solutions of the scalar wave equation, providing a unified Fourier-based description that enhances understanding and suggests methods for optical generation of these non-dispersive wave fields.

Contribution

It offers a comprehensive mathematical framework for localized wave solutions, integrating diverse theoretical results into a single Fourier-based representation.

Findings

Unified Fourier decomposition of localized waves

Enhanced physical understanding of non-dispersive wave propagation

Proposed optical methods for generating localized wave fields

Abstract

In recent years the topic of localized wave solutions of the homogeneous scalar wave equation, i.e., the wave fields that propagate without any appreciable spread or drop in intensity, has been discussed in many aspects in numerous publications. In this review the main results of this rather disperse theoretical material are presented in a single mathematical representation - the Fourier decomposition by means of angular spectrum of plane waves. This unified description is shown to lead to a transparent physical understanding of the phenomenon as such and yield the means of optical generation of such wave fields.