Discrete wavelet structure and discrete energy of a classical plane light wave

TL;DR

This paper uses wavelet transform to analyze classical light waves, revealing their energy can be discrete and linked to wavelet structure, and demonstrates wave-particle duality through simulation.

Contribution

It introduces a novel approach to decompose light waves into discrete wavelets and relates their energy to quantum-like discrete values, connecting classical analysis with quantum concepts.

Findings

Light wave energy can be discrete and associated with wavelet structure.

Energy change of wave packets follows a quantized form consistent with Planck's theory.

Simulation of single-photon interference demonstrates wave-particle duality.

Abstract

In this letter, the wavelet transform is used to decompose the classical linearly polarized plane light wave into a series of discrete Morlet wavelets. It is found that the energy of the light wave can be discrete, associated with its discrete wavelet structure.It is also found that the changeable energy of a basic plane light wave packet or wave train of wave vector $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over k} $ and with discrete wavelet structure can be with the form of ${H_{0k}} = n{p_{0k}}\omega$ $(n = 1,2,3,...)$, where $n$ is the parameter of discrete wavelet structure, $\omega $ is the idler frequency of the light wave packet or wave train, and ${p_{0k}}$ is a constant to be determined.This is consistent with the energy division of $P$ portions in Planck radiation theory, where $P$ is an integer. Finally, the random light wave packets with $n=1$ are used to simulate the Mach-Zehnder interference of single photons, showing the wave-particle duality of light.