Unidirectional decomposition method for obtaining exact localized waves solutions totally free of backward components

TL;DR

This paper introduces a unidirectional decomposition method that produces exact, localized wave pulses with superluminal and luminal velocities, free of backward components, making them more feasible for experimental realization.

Contribution

The paper presents a novel unidirectional decomposition technique that generates exact localized wave solutions without backward spectral components, simplifying experimental implementation.

Findings

Produces exact localized wave pulses free of backward components

Allows finite energy localized waves in closed form

Eliminates need for ultra-wideband spectra in solutions

Abstract

In this paper we use a unidirectional decomposition capable of furnishing localized wave pulses, with luminal and superluminal peak velocities, in exact form and totally free of backward components, which have been a chronic problem for such wave solutions. This decomposition is powerful enough for yielding not only ideal nondiffracting pulses but also their finite energy versions still in exact analytical closed form. Another advantage of the present approach is that, since the backward spectral components are absent, the frequency spectra of the pulses do not need to possess ultra-widebands, as it is required by the usual localized waves (LWs) solutions obtained by other methods. Finally, the present results bring the LW theory nearer to the real experimental possibilities of usual laboratories.