Physical wavelets and their sources: Real physics in complex spacetime

TL;DR

This paper introduces complete source distributions for acoustic and electromagnetic wavelets in spacetime and Fourier space, revealing simple Fourier sources and potential for FFT-based analysis algorithms.

Contribution

It defines and computes source distributions for wavelets in both spacetime and Fourier space, highlighting their simplicity and potential applications in wave analysis.

Findings

Fourier sources are simpler than spacetime expressions.

Complete source distributions are now defined for wavelets.

Potential for FFT-based pulsed-beam analysis algorithms.

Abstract

For the first time, complete source distributions for the emission and absorption of acoustic and electromagnetic wavelets are defined and computed, both in spacetime and Fourier space. The biggest surprise is the great simplicity of the Fourier sources as compared to the rather convoluted spacetime expressions obtained from the original wavelets. This suggests that the associated pulsed-beam propagators may play a fundamental role in emission and absorption processes including focus or "directivity." It also opens the way to constructing FFT-based algorithms for pulsed-beam analyses of acoustic and electromagnetic waves.