Left-circularly polarized wave form

The right-handed yellow wave helix shows the wave form for fixed time t and variable x. This wave form is said to have positive helicity. The geometric algebra expression for it is:

q_omega (x,t) = a_omega exp(i(omega t - kx)),

with a_omega the constant vector amplitude in the i-bivector plane.

You can change the wave length by dragging the end point of the yellow equilibrium x-axis and you can rotate the wave by dragging the other red interactive point along the blue circle. (The radius of the blue circle is unimportant.) The set of green vectors shows how a vector at x=0 would rotate with varying t.

Please enable Java for an interactive construction (with Cinderella).

Compare the animated version.

[ GA with Cinderella ]

Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).