Right and left-circularly polarized wave forms

Left part of the image:

The left-handed yellow wave helix shows the wave form for fixed time t and variable x. This wave form is said to have negative 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. The set of green vectors shows how a vector at x=0 would rotate with varying t.

Right part of the image:

This side is the mirror image of the left part of the image. The mirror is indicated by the light blue line. 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 view.

[ GA with Cinderella ]

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