The polarization of an electromagnetic field is defined as the direction of its E field (electrostatic).

An electromagnetic field is a physical field produced by electrically charged objects. The field can be viewed as the combination of an electric field and a magnetic field. The electromagnetic field may be viewed in two distinct ways: a continuous structure or a discrete structure.

Not really. You could have both an electric field and a magnetic field occupying the same space at the same time but they wouldn't 'make the definition' of electromagnetic until they began to fluxuate in phase at a harmonized frequency.

The scientists measured the electromagnetic field.

Well one way to look at it is that a photon IS an electromagnetic field. The photon is the gauge particle for the electromagnetic force. Without photons there would be no electromagnetic interaction force, and therefore no electromagnetic fields.