Three-dimensional Arbitrary Electromagnetic Fields and Temporal Propagation

TL;DR

This paper demonstrates that arbitrary 3D electromagnetic fields are transient solutions to Maxwell's equations, providing equations and algorithms for designing and generating such fields through phase optimization and wavepacket shaping.

Contribution

It introduces a simple equation for the temporal evolution of arbitrary 3D electromagnetic fields and phase optimization algorithms for their realization.

Findings

Arbitrary 3D electromagnetic fields are transient solutions to Maxwell's equations.

Phase optimization enables phase-only modulation for field realization.

A method to determine the input wavepacket for focusing lenses to generate desired 3D fields.

Abstract

We show that arbitrary 3D electromagnetic fields are transient solutions to Maxwell's equations and provide a simple equation to find how the field evolves over time. Multiple 3D fields can be realized at different times by superposing with an initial phase. Phase optimization algorithms allow for a phase-only modulated input signal. The necessary input wavepacket before a focus lens to create the 3D field can be found by finding the time-variation through a spatial plane. These results provide a way for designing arbitrary transient 3D waves and finding the wavepacket needed to input into a focusing lens.