# Reason for the convention about polarization states

I'd like to know if there is a special reason for limiting convention of polarization state to waves that can be split in just two components of equal frequency.

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2. In homogeneous, linear, anisotropic media, the propagation direction of a plane wave is the $k$-vector, which is perpendicular to the electric and magnetic field directions. If we only consider the electric field, then it's vector will trace some shape in the plane perpendicular to the $k$-vector. Since the shape traced is in a plane, we only need two numbers (say x and y) to the electric field vector and any given time/spatial point. So the reason that we define the single frequency is because we think about plane waves usually, and the reason that the Jones formalism only uses two components is because in a lot of materials that we care about the electric field vector is always perpendicular to the $k$-vector.