We know that in free space, a propagating electromagnetic wave is always transverse. However, along a dielectric waveguide, the propagating wave can have longitudinal components. The exist of the longitudinal component makes the group index of refraction not equal to the phase group of refraction of the waveguide.
My questions is can one by using some combinations of propagating waves from any direction (even from the perpendicular direction to the waveguide) to make the field purely transverse or longitudinal in presence of a cylindrical fiber waveguide?
I am highlighting these two words here, and define the waveguide/optical fiber axis direction as the longitudinal direction and the plane perpendicular to the waveguide axis is the transverse plane. So, if a combined field oscillating along the fiber axis, I treat this as a longitudinal local field. Without this definition, one would get confused if we allow the light incident from any directions.
To be clear, meanwhile, I am talking about the electromagnetic field at least on one/periodical crossing section(s) of the propagating field or at least on a line, not just one or two specific/trivial points in space or the entire space. Thanks.