# Linear polarized 3D glasses and the physical shape of light waves

Looking into how linear polarized 3D glasses work, I keep getting explanations that boil down to this:

However, I always assumed that a light wave was depicted in diagrams like this...

...to more easily plot on paper its properties like frequency and amplitude. I never thought that light waves would physically actually look like that. I always imagined light waves being emitted in the form of a sphere centered at its source just like sound:

If the latter is correct, then this explanation for polarized filters doesn't really make sense; or do I have some major misconceptions about the nature of waves?

Light waves are emitted spherically, however electromagnetic waves nevertheless have polarization.

The Maxwell equations that the electromagnetic field satisfies are $$\begin{array}{rlcrl} \nabla\cdot \vec E ~=& c\rho &~~& \nabla\times \vec E ~=& -\dot {\vec B}\\ \nabla\cdot \vec B ~=& 0 &~~& \nabla\times \vec B ~=& \vec J + \dot {\vec E}\\ \end{array}$$where the dots are $c^{-1}\partial/\partial t$ operators. Both $\vec B$ and $\vec E$ are vector fields; at every position they point in a certain direction.

If $\rho = 0$ and $\vec J = \vec 0$ as in vacuum then these equations become nicely symmetric and one can use the identity that $\nabla\times(\nabla \times X) = \nabla(\nabla\cdot X) - \nabla^2 X$ to artificially decouple them, getting the wave equations $\nabla^2 E= \ddot E,\; \nabla^2 B = \ddot B.$ Each of these equations has a very general solution; any superposition of vector fields $\vec F(\vec r - c t \hat v)$ works for any field $\vec F$ and any direction $\hat v.$

It is helpful to limit ourselves to monochromatic plane waves, whence we find for example that $$\vec E = E_0 ~\hat y~\cos(\omega ~(x - c t))\\\vec B = E_0~\hat z~\cos(\omega~(x - c t))$$obey the Maxwell equations in vacuum, if you take them together. We call this $y$-polarized coherent light in the $x$-direction, I believe: the polarization direction is customarily the direction that the electric field points.

Now how does a polarizer work? The easiest example is a wire-grid polarizer, a set of parallel wires next to each other. If those wires go along the $y$-direction, then the $\vec E$ field behaves like it just hit a metal, inducing currents up and down the wires. Metals reflect electromagnetic waves, and so the electromagnetic wave reflects off of the wires. But if the wires go along the $z$-direction, then the $\vec E$ field can't move electrons very far at all before they run into the side of the wire! So no big currents are made and the polarizer does not conduct in that direction -- the $\vec E$ field passes right through.

As for the general case of light being emitted, it is worthwhile to first look at the pretty pictures of a dipole antenna and look at the dipole radiation there. You can then think of thermal radiation like the Sun's light as taking this dipole and averaging out over all orientations of the dipole, as thermal electrons are randomly bouncing around in all directions. You can do this with impunity because the Maxwell equations above are linear and therefore the superposition of a bunch of solutions is another solution.

Substantial difference between light and sound is: light is transverse wave and can be polarised; sound wave in gas is longitudal wave and cannot be polarised.

Any electromagnetic radiation - and in special case light as a small and visible for us part of EM radiation - is composed of photons. This is right for the process of emission as well as for the absorption of EM radiation. Any photon has a electric E and a magnetic B field component, both perpendicular to each other and to the direction of propagation v (strictly right only for vacuum). The field components are oscillating during their propagation. In the following graphics this is visualised by the sequence of the red and the blue arrows:

Usually the source emits EM radiation with equal distributed directions of the field components, means, the electric field component for all the photons is directed all over the 360° in any plane perpendicular to the direction of propagation. And you are right for bulbs; the light will be distributed all around spherical. Strictly speaking it depends from the geometry of the source (like for a bell or like for a loudspeaker for example).

As long as this EM radiation is not modulated you will not be able to detect any wave characteristics. The emission from an antenna rod is an example for modulated radiation:

How we can polarize EM radiation? Empirical it is known, how wide the spaces between the edges of the grid have to be to let through photons from the needed wavelengths. The electric field component of the photon is able to interact with the edges of a grid. A well designed grid let through approx. 50% of the light; all this photons have nearly the same direction of oscillation of the electric field component.

So what is visualized in your diagram is usualy the oscillation of a field component of the elementary particle (the photon) of the EM radiation. Otherwise it shows a field component of a modulated radiation (radio wave).

When trying to understand light, there are two components to consider: the amplitude, and the polarization, and you can assign both these properties to all points in space. This is very difficult to visualize, so most of these images trying to visualize light are bound to be inaccurate. The first image you show in your post is accurate in showing how the polarization and amplitude vary together, while your second image is more accurate in showing how light spreads out from a source.

A more realistic way of plotting light is in something called a vector field plot. These plots use arrows to show the direction of polarization at different points in space, while using color or arrow length to represent the field intensity.

Here's an animation of a more realistic source, called dipole radiation. The polarization isn't plotted, but follows the plotted contours to a large degree. The source produces linearly polarized light, but the polarization direction is kind of curved to follow the contour of a sphere.

And here's another image of the same kind of radiation, but field direction plotted more explicitly.

I hope this gives you a sense of how both your ideas of light fit together.