= Closed-surface Poynting flux of a plane wave
For a real linearly polarized monochromatic vacuum <plane wave>, the local <Poynting vector> is proportional to $\cos^2(\mathbf k\cdot\mathbf r-\omega t)\widehat{\mathbf k}$. Its flux through a closed surface generally oscillates at $2\omega$, with zero cycle average, although particular volume geometries can cancel it identically. For a circularly polarized plane wave of constant amplitude the <Poynting vector> is spatially and temporally constant, so the net flux through every closed surface is exactly zero. A nonzero constant local energy flux must not be confused with the net closed-surface flux.
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