# Is Poincaire Sphere inverted if the direction of propogation of TEM wave is reversed?

1. Jun 13, 2010

My doubt arises because I couldn't understand how a Poincaire Sphere gives us info about direction of propagation of wave. Now as we know Poincaire sphere is a neat way of showing the polarization state of an TEM wave. Now ,let me give an example to illustrate my doubt : -

Let us take a uniform plane TEM wave travelling in +z direction which is composed of two linearly polarised TEM waves , one whose electric field lies in X direction , the other whose electric field lies in Y direction . Let us take the case of circular polarisation
so we take ,

Ex = E0 cos($$\omega$$ t - $$\beta$$ z) ax
Ey = E0 cos($$\omega$$ t - $$\beta$$ z + $$\pi$$\2) ay

Now the resultant TEM wave has the Electric field vector left handed circularly polarised .
On the Poincaire Sphere this will be given by the north pole point.

Suppose we had same wave but travelling in -ve z direction.
Ex = E0 cos($$\omega$$ t + $$\beta$$ z) ax
Ey = E0 cos($$\omega$$ t + $$\beta$$ z + $$\pi$$\2) ay
So the wave should be right handed circularly polarised(I hope I am right here ) . Now as far as I know , while plotting the polarisation state on the Poincaire sphere we simply take the Phase difference between the two waves and the ratio of their magnitudes into consideration .So according to me , this wave will also be plotted on the north pole point.

Isn't this a discrepancy (maybe of my understanding) that a right handed circular polarised wave is getting plotted to north pole. So do we invert the Poincaire sphere if we reverse direction of propagation of wave?

My doubt basically boils down to this - while plotting Polarisation state of a TEM wave on a Poincaire sphere , how is the direction of propagation of the TEM wave taken into account ?

2. Jun 14, 2010