the Stokes parameters when looking down the beam towards the source (opposite the direction of light propagation) or looking down the beam away from the source (coincident with the direction of light propagation). These two conventions result in different signs for , and a convention must be chosen and adhered to. Examples Below are shown some Stokes vectors for common states of polarization of light. {| |- | || Linearly polarized (horizontal) |- | || Linearly polarized (vertical) |- | || Linearly polarized (+45°) |- | || Linearly polarized (−45°) |- | || Right-hand circularly polarized |- | || Left-hand circularly polarized |- | || Unpolarized |} Alternative explanation A monochromatic plane wave is specified by its propagation vector, , and the complex amplitudes of the electric field, and , in a basis . The pair is called a Jones vector. Alternatively, one may specify the propagation vector, the phase, , and the polarization state, , where is the curve traced out by the electric field as a function of time in a fixed plane. The most familiar polarization states are linear and circular, which are degenerate cases of the most general state, an ellipse. One way to describe polarization is by giving the semi-major and semi-minor axes of the polarization ellipse, its orientation, and the direction of rotation (See the above figure). The Stokes parameters , , , and , provide an alternative description of the polarization state which is experimentally convenient because each parameter corresponds to a sum or difference of measurable intensities. The next figure shows examples of the Stokes parameters in degenerate states. Definitions The Stokes parameters are defined by where the subscripts refer to three different bases of the space of Jones vectors: the standard Cartesian basis (), a Cartesian basis rotated by 45° (), and a circular basis (). The circular basis is defined so that , . The symbols ⟨⋅⟩ represent expectation values. The light can be viewed as a random variable taking values in the space C2 of Jones vectors . Any given measurement yields a specific wave (with a specific phase, polarization ellipse, and magnitude), but it keeps flickering and wobbling between different outcomes. The expectation values are various averages of these outcomes. Intense, but unpolarized light will have I > 0 but Q = U = V = 0, reflecting that no polarization type predominates. A convincing waveform is depicted