0
$\begingroup$

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)

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ 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? $\endgroup$
    – MarcoB
    May 30, 2016 at 16:27
  • $\begingroup$ ParametricPlot3D may be useful. $\endgroup$
    – xslittlegrass
    May 30, 2016 at 16:28
  • $\begingroup$ @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! $\endgroup$
    – guest314159
    May 30, 2016 at 17:10

1 Answer 1

Reset to default
2
$\begingroup$

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}]

I just added some additional parameters. Eventually I got
enter image description here

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.