# How to plot time-dependent vector field?

My problem is:
plot the motion of the top of the vector $E$ (electric field) on the plane $$(k_1 - k_2)z = 0.25 \pi$$. Vector components are $$E_x = \cos(\omega t - 0.5(k_1 + k_2)z - 0.5(k_1-k_2)z)$$ $$E_y = \cos(\omega t - 0.5(k_1 + k_2)z + 0.5(k_1-k_2)z)$$ where $0\le t \le \dfrac{2 \pi}{\omega}$.
It should looks like the light is elliptically polarized.
Which function should I use for this? You can just say me suitable function. Thank you)

• Have you tried anything? Can you at least present your equations in Mathematica syntax as well, so anybody interested in helping you can copy / paste them, rather than having to retype them? – MarcoB May 30 '16 at 16:27
• ParametricPlot3D may be useful. – xslittlegrass May 30 '16 at 16:28
• @xslittlegrass ParametricPlot is perfect. Thank you very much. I used 2D version because I have only 2 space coordinates. But anyway your advice is a super helpful! – guest314159 May 30 '16 at 17:10

Ok, thanks to @xslittlegrass for the hint.
So, the solution

omega = 2 Pi;
a = 0.1;
b = 0.2;
c = 300;
n1 = 10^(-4); n2 = 10^(-7);
k1 = n1 omega/c; k2 = n2 omega/c;
r = 0.25; z = r Pi/ (k1 - k2);
s = 10;
ParametricPlot[{2 a Cos[omega t - 0.5 (k1 + k2) z - 0.5 (k1 - k2) z] ,
2 b Cos[omega t - 0.5 (k1 + k2) z + 0.5 (k1 - k2) z] }, {t, 0,
2 Pi/omega}]