I would like to approximate a plane electromagnetic wave with a very large sum of the following. Let an infinite line, say the z axis, have a electric polarization on that line and perpendicular to that line, say the x direction to be specific given by, P(z,t) = pcos(kz-ωt). The polarization is a function of both space and time. Now let there be a uniform density of such lines in all space all parallel to one another, all in phase, and with them all polarized in the x direction. Will such a construction approximate the electric and magnetic fields of plane E&M wave? Thanks!