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If the [Electric] wave interfered destructively then wave crests would cancel each other out while wave bottoms remain the same amplitude.... you end up with a magnetic field

ScientificSorcerer: your idea won't work because what you think of as the electric field variation is the spatial derivative of four-potential, whilst the magnetic field variation is the time derivative. See ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN where you can read this: "the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field, is first order in time". To visualize this, imagine you're in a canoe in a flat calm ocean, and a single wave comes at you. This wave has no trough, it's just a "hump" of water. You go up the wave, and E relates to the slope of your canoe, whilst B relates to how fast it's tilting. At the top of the wave your canoe is momentarily horizontal and not tilting, so E and B are zero. Then you go down the other side, and your canoe tilts down, then the wave has passed, and your canoe is horizontal and not tilting again. Once you've got that, appreciate this: you can't have a situation where your canoe only tilts up.The diagram below shows the sinusoidal waveform which is the derivative of the "hump" of potential beneath.

Yes of course. Maxwell introduced the term, and drew the picture below showing convergence, curl, and both together. See page 7 of ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN isn't a bad little article. The curl or rotation associated with a charged particle is an "all round" rotation, but for a sinusoidal electromagnetic wave, it isn't.

can polarization occur at such high frequencies? do you think that this could also create an electric field along with the magnetic field?

The wave which I am trying to create looks like the wave depicted below in the attachment.