How can someone determine from the surface current distribution the electric field polarization?
Great question! The answer has to do with the boundary conditions of Maxwell's Equations at interfaces.
See: https://en.wikipedia.org/wiki/Interface_conditions_for_electromagnetic_fields
Time varying surface current at an interface create a time varying magnetic field, which create a time varying electric field.
If the surface currents are constant, then you get a magnetic field but no electric field.
The magnetic field will be perpendicular to and in the same plane as the surface current. The electric field will be perpendicular to the magnetic field (essentially aligned with the surface current).