Three-dimensional arbitrary electromagnetic fields and temporal propagation

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 focusing lens to create the 3D field can be found by finding the time-variation and finding the wavepacket needed to input into a focusing lens.