I Electric field in two dimensions in an electromagnetic wave

[mister i]

TL;DR Summary

Do the oscillations of the electric field in an electromagnetic wave always occur in two dimensions?

In general, do the oscillations of the electric field in an electromagnetic wave always occur in two dimensions? (Even if they are circular, for example like a 2D sheet of paper that rotates.) Could we say that an electromagnetic wave encodes three-dimensional information of an electric field into two dimensions (somewhat similar to a hologram)? (The same applying to the magnetic field.)

 

[renormalize]

In general, do the oscillations of the electric field in an electromagnetic wave always occur in two dimensions?

Yes, for an EM wave that propagates in the $z$-direction and is linearly polarized in the $x$-direction, the oscillations of the electric field are confined to the 2D $xz$-plane.

Could we say that an electromagnetic wave encodes three-dimensional information of an electric field into two dimensions (somewhat similar to a hologram)?

Is there anything special about EM waves in this question? Here's a time-lapse photo of a standing-wave on a vibrating string (from here):

By analogy, would you then ask:
"Could we say that a mechanical wave on a string encodes three-dimensional information of a string vibration-amplitude field into two dimensions (somewhat similar to a hologram)?"
What does that even mean?

 

[Baluncore]

An EM wave has three, mutually orthogonal vector components, an electric field vector, a magnetic field vector, and the Poynting vector along which the energy propagates with time.

Circular polarisation can be analysed as the summation of two separate EM waves, propagating in the same direction, but with their electric fields being orthogonal, and phase shifted 90° in time.