Imagine an electromagnetic wave (a monochromatic one for example). The electric field amplitude and its variations travel in the propagation direction.
So, if there really exists a propagation direction, what happens in other directions?
I mean, is there an oscillation in those other directions?
Does something (electric or magnetic field) move in those directions?
Does it's speed in those direction depends on frequency,or is this wave infinitely thin? Is it not covering any space in other directions?
I have seen many graphs showing that the field variation is not in the direction of propagation, that "means", based on polarization experiments that it's not a Longitudinal wave, It's a transverse wave.
If I accept that the field is not varying in the propagation direction (it just goes forward in that direction), then I could think it's varying in other directions, but in what direction?
Perhaps we can't say it's varying in any direction, it's not a spatial variable. I just can't imagine how the field variation is distributed in space.
EDIT
some options
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Electromagnetic waves just move in one single spatial propagation direction.. then all spatial concepts that take account other directions are wrong, like "polarization" and "transverse wave" definition
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Electromagnetic waves moves in others directions too, then speed of propagation in those other directions could depend on frequency, and thats weird, but who knows!
EDIT 2 (Add my comment as part of the question)
If there are infinite wave planes, then imagine a light that is turned OFF and then is turned ON, comparing the EM, first it is covering nothing, and then suddenly reach "infinity" (or at least very far..in fact any distance is enough), what is the speed of THAT propagation? because it is NOT a wave propagation, because is not in the direction of propagation, that infinite or very large field extends itself at infinite speed?
Best Answer
I am still not sure I understand your question but from what I gathered you are confused about the behavior of an EM wave (let's say monochromatic) so I'll discuss the properties of waves of increasing difficulty (eventually returning to EM).
EM waves are not easy to imagine because they are vectorial in nature. That is, in every point of the space there is an arrow describing the magnitude and direction of the $E$ field. Let's simplify this a imagine that at every point there is just a single value, say pressure, so we are be talking about sound waves. It's useful to consider the notion of a wave front. This is a collection of points that have the same phase (think of the circles that form if you throw a stone into the water). For a monochromatic wave $$ p = p_0 \exp(i\omega t - i{\mathbf k \cdot r})$$ (characterized by the wave-vector $\mathbf k$ and frequency $\omega$), it will be just a plane. You can imagine that plane moving at the speed of propagation $c = {\omega \over |{\mathbf k}|}$ into the direction given by $\mathbf k$. Let's emphasize that all points of that plane will oscillate in the same manner; which simplifies the picture by letting us consider just one point from that plane. We are left with the following image
Imagine that the direction of the propagation of the wave is the horizontal axis, the phase of the wave is carried out on the vertical axes and the plane is represented by any point of the curve (e.g. pick the top of the wave) that travels to the right.
Now, let's consider vector fields. These can be written as ${\mathbf E} = (E_x, E_y, E_z)$ and the previous discussion applies for every component of the field. So there are now three independent oscillations each with its own phase. Except that EM field is massless and so cannot oscillate in the direction of propagation (so called longitudinal polarization); this fact can be derived from Maxwell's equations. So this leaves us with two transversal polarizations $E_x$ and $E_y$ (taken as complex numbers because we also need to take account of their phases) by identifying the $\mathbf z$ axis with the direction of propagation $\mathbf k$. As in the previous case, for monochromatic wave the wavefront will be a plane. But now we have two independent polarization and instead of simple oscillation we will in general obtain an elliptical polarization
Again, single point on the curve represents a whole wavefront plane. Note that special cases include circular (when $E_y$ lags by $\pi /2$ behind $E_x$ but has equal magnitude) and linear polarizations (when $E_y$ and $E_x$ are in phase).
Notes
We haven't discussed the magnetic part of EM wave $\mathbf B$ because it's determined by just knowing the wave vector $\mathbf k$ and the $\mathbf E$ field. The important point being that it will be perpendicular to both. So the above discussion about the travel of wavefront applies also to $\mathbf B$ field.
The monochromatic waves are not realistic as you might imagine. They are infinite in extent (whole wavefront plane oscillates and it sweeps entire universe during its travel). In reality the waves travel as concentrated wave-packets. But the above discussion is still useful because we can use Fourier analysis to pass to the frequency image of the wave and decompose the packet into monochromatic waves.
If we are not in the vacuum then the picture is much more complex. The $\mathbf E$ and $\mathbf B$ fields need not be perpendicular to the $\mathbf k$ vector (because the photons gain effective mass in the medium thanks to refractive index), the energy travels in different direction than the wave itself and so on.