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Nov 12, 2017 at 7:29 vote accept JDoeDoe
Nov 8, 2017 at 20:43 comment added Emilio Pisanty @Kthaxt JDoeDoe's second suggestion hat $\mathbf E_0$ as a real vector field.
Nov 8, 2017 at 19:20 comment added kthaxt I think the direct answer to the question then is that JDoeDoe's second suggestion, that $\textbf{E}_0$ is a complex vector field, is correct. Each component can be a function of x, y, and z. But not time, time dependence has been separated to the $e^{-i \omega t}$ as we are assuming the time dependence is sinusoidal.
Nov 7, 2017 at 18:54 history edited Emilio Pisanty CC BY-SA 3.0
added 168 characters in body
Nov 7, 2017 at 18:35 history answered Emilio Pisanty CC BY-SA 3.0