Poynting Vector: a Plane EM Wave in 3D

A light wave is a braid of two fields: an electric field and a magnetic field, oscillating at right angles to each other and to the direction the wave travels. Their cross product, the Poynting vector S = E x B, points the way the energy flows and measures how much. For a wave travelling forward, E and B rise and fall together, so S is always positive: energy is carried steadily in one direction, never backward, even though the fields themselves keep flipping sign. Averaged over a cycle it settles to half the peak, which is exactly the intensity your eye or a solar panel feels. Twist the polarization into a circle and the fields trace helices of constant length, so the flow is perfectly smooth. Trap the wave between mirrors into a standing wave and something striking happens: E and B fall out of step, the Poynting vector sloshes back and forth, and the net energy transport drops to zero. The scene shows the E and B fields propagating with the energy-flow arrows; the diagnostic plots the three quantities and the time-averaged flow.