GPhaseVisualization2.mp4

Visualization 2 shows an animation of summing two counter-rotating vectors (red & blue) and their sum vector (green) for two full turns of rotation (from ωt = 0 until ωt = 4π). As with Visualization 1, the two input vectors have amplitudes A1 = 1 and A2 = 0.7, and phase difference δ = 0. We see that the difference between the co-rotating and counter-rotating cases is that a zero phase difference in the co-rotating case leads to a uniform-amplitude sum vector (green circular path), but in the counter-rotating case leads to an ellipse. When δ = 0 as shown here, the major and minor axes of the ellipse will have lengths equal to (A1 + A2) and |A1 - A2| respectively. One thing to note from the animation is that the rate of rotation of the green vector is not constant --- as the green vector nears the ellipse's major axis, its rate of rotation approaches its slowest, and when near the minor axis, its rate is fastest. This exactly replicates the nonlinear behavior in the geometric phase shift.