Phase-alignment in EM-waves In a physics-book I read that "it should be noted that the [electric and magnetic] fields [in a moving EM-wave] alternate at first, 90 degrees out of phase with each other.  As they travel, they gradually come into phase". Is this true ??  I've never read or heard this before.
 A: Consulting the late J.D. Jackson's "Classical Electrodynamics, 3rd edition", page 411, we find the following expressions for the fields due to a sinusoidally excited, center-fed, linear antenna that is small compared to a wavelength:
$$\mathbf{H} = \frac{ck^2}{4\pi}\left(\mathbf{n} \times \mathbf{p}\right)\frac{e^{ikr}}{r}\left(1 - \frac{1}{ikr}\right)$$
$$\mathbf{E} = \frac{1}{4\pi\epsilon_0}\left\{k^2\left(\mathbf{n} \times \mathbf{p}\right)\times \mathbf{n}\frac{e^{ikr}}{r} + \left[3\mathbf{n}(\mathbf{n}\cdot \mathbf{p}) - \mathbf{p}\right]\left(\frac{1}{r^3} - \frac{ik}{r^2}\right)e^{ikr}\right\}$$
We note that there are magnetic and electric terms that decay as $1/r$ and $1/r^2$ as well as an electric term that decays as $1/r^3$ where $r$ is the distance from the antenna.
The $1/r$ terms are in phase (always) and thus transport energy away from the antenna; these are the radiation terms and they dominate in the far-field:
$$\mathbf{H} = \frac{ck^2}{4\pi}\left(\mathbf{n} \times \mathbf{p}\right)\frac{e^{ikr}}{r}$$
$$\mathbf{E} = \frac{1}{4\pi\epsilon_0}k^2\left(\mathbf{n} \times \mathbf{p}\right)\times \mathbf{n}\frac{e^{ikr}}{r} = Z_0 \mathbf{H} \times \mathbf{n}$$
In the region near the antenna (near-field), the dominant terms approach
$$\mathbf{H} = \frac{i \omega}{4\pi}\left(\mathbf{n} \times \mathbf{p}\right)\frac{1}{r^2}$$
$$\mathbf{E} = \frac{1}{4\pi\epsilon_0}\left[3\mathbf{n}(\mathbf{n}\cdot \mathbf{p}) - \mathbf{p}\right]\frac{1}{r^3}$$
which are out of phase (reactive) and thus energy flows back and forth between these fields and the antenna.
In summary, it is true that the dominant fields near the antenna are out of phase but these aren't the fields that propagate to the far-field since these fields decay as the inverse square and the inverse cube of the distance from the antenna.
A: The electric and magnetic fields in a linearly polarized sinusoidal plane electromagnetic wave in vacuum or in a simple dielectric are always in phase, but their planes of oscillation in space are orthogonal to each other. The mentioned statement "they gradually come into phase" seems not to hold for such a wave.  
