How are plane waves, $p$-forms, and Maxwell's equations related?

I am very new to the concepts of $p$-forms and trying to get a better grasp of physicist use them to state Maxwell's equations.

Wikipedia has a picture of a plane wave http://en.m.wikipedia.org/wiki/Plane_wave

I presume this is used to represent for example electromagnetic radiation moving through space.

Here's my question: That picture of a plane wave looks like a 1-form. Does this similarity have anything to do with how physicists think about formulating Maxwell's equations in (what I think is called) covariant terms?

In other words, I am trying to see if the visual similarities can help me better understand these more advanced forms of the Maxwell equations beyond mere vector calculus.