The usual representation of a free electromagnetic wave in vacuum looks like this:
The blue parts are the local electric field, while the green parts are the local magnetic field.
The circularly polarized wave is also another standard representation of an EM travelling wave, but it is a bit less well known.
Here are the wave functions describing the above usual linearly polarized wave:
\begin{align} \vec{\boldsymbol{E}} &= \vec{\boldsymbol{a}} \sin{(k \, x - \omega \, t + \phi)}, \tag{1} \\[12pt] \vec{\boldsymbol{B}} &= \vec{\boldsymbol{b}} \sin{(k \, x - \omega \, t + \phi)}, \tag{2} \end{align} where $\vec{\boldsymbol{a}}$ and $\vec{\boldsymbol{b}}$ are two orthogonal constant polarisation vectors, transverse to the propagation (the $x$ axis here).
Now, I believe that I remember (I'm not sure!) that there's a special superposition of travelling waves that gives a non-standard representation of the travelling EM plane wave, with the magnetic parts shifted by a quarter of wavelength relative to the electric parts. I'm unable to find which superposition exactly can do this, but I know that this superposition (if it exists !) is actually very simple.
I'm NOT talking about standard standing wave here, and I'm not talking about the circularly polarized travelling wave neither. However, the superposition I'm looking for may be related to such waves, I don't know.
So somebody could tell which superposition of waves can shift the magnetic crests (as seen above) by one quarter of a wavelength, relative to the electric crests ?