The Jones Vector is a method of describing the direction of polarization of light. It uses a two element matrix for the complex amplitude of the polarized wave. The polarization of a light wave can be described in a two dimensional plane as the cross section of the light wave. The two elements in the Jones Vector are a function of the angle that the wave makes in the two dimensional cross section plane of the wave as well as the amplitude of the wave.

The amplitude may be separated from the ‘mode’ of the vector. The mode of the vector describes only the direction of polarization. Below is a first example with a linear polarization in the y direction.

Using the Jones Vector the mode can be calculated for any angle. See calculations below:

The phase differences of the Jones Vector are plotted for a visual representation of the mode. If both components of the differ in phase, the plot depict a circular or oval pattern that intersects both components of the mode on a two dimensional plot. The simplest of plots to understand is a polarization of 90 degree phase difference. In this case, both magnitudes of the components of the mode will be 1 and a full circle is drawn to connect these points of the mode. In the case of a zero phase difference, this is demonstrated at 45 degrees where both sin(45deg) and cos(45deg) equal 0.707. In this case, the phase difference is plotted as a straight line, indicating that polarization is of equal phase from each axis of the phase difference plot.