Does the E Vector of a Polarized EM Wave Trace an Ellipse in Space?

[ask_LXXXVI]

Let us consider the Electric field components of a polarized EM wave .
[PLAIN]http://www.cdeep.iitb.ac.in/nptel/Electrical%20&%20Comm%20Engg/Transmission%20Lines%20and%20EM%20Waves/graphics/CHAP%204__255.png.

Now if we fix the value of z (for convenience take z=0) and consider the locus of the Electric field vector over time, we get an ellipse in general. This is what is meant by elliptical polarization. Now this is the temporal aspect. That is - at a fixed location of space , the E vector keeps changing its direction with time (while staying in the plane perpendicular to direction of propagation)

My doubt is what is the behavior when we fix the value of t (let us take t=0 for convenience) and consider the locus of the Electric field vector with respect to the variation in z. Will we get a change in direction of Electric field vector as we change z?

My personal opinion is that it will vary with z also,as the cosine terms in the equation look similar if we suppress either z or t by keeping them fixed . I just want to have a confirmation.
It would be a great help if someone directs me to a website containing an applet which helps in visualizing this particular situation

 

[0xDEADBEEF]

If z is the direction of propagation, then changing z or changing -t is indeed the same.

 

[ask_LXXXVI]

If z is the direction of propagation, then changing z or changing -t is indeed the same.

yes z is the direction of propagation .


I guess the spatial variation of the E vector wasn't discussed in the course I took as Polarization deals with the temporal behavior of the fields and not the spatial.