The polarization of light can be described by a Jones vector, which is of the form.

(1)By convention the first element of a Jones vector is chosen to be real. Thus the second element gives the relative phase between the x and y components of the electric field. In general we can write the a normalized Jones vector as.

(2)A table of useful Jones Vectors is given below.

Polarization | Jones Vector | Relative Phase |
---|---|---|

Horizontal (linear in x) | $\left(\begin{array}{c} 1\\ 0 \end{array} \right)$ | 0 |

Vertical (linear in y) | $\left(\begin{array}{c} 0\\1 \end{array} \right)$ | 0 |

Diagonal (linear at 45 degrees) | $\frac{1}{\sqrt{2}}\left(\begin{array}{c} 1\\ 1 \end{array} \right)$ | 0 |

Right Hand Circular | $\frac{1}{\sqrt{2}}\left(\begin{array}{c} 1\\ -i \end{array} \right)$ | $\frac{\pi}{2}$ |

Left Hand Circular | $\frac{1}{\sqrt{2}}\left(\begin{array}{c} 1\\ i \end{array} \right)$ | $-\frac{\pi}{2}$ |

The effect of an optical element on the polarization of light is given by the corresponding Jones matrices. The Jones matrix describing a waveplate with a phase restardance of $\phi_R$ is given by.

(3)If the waveplate is rotated about the optical axis by an angle $\theta$ then the Jones matrix is given by.

(4)Where, the rotation matrix is of the form.

(5)Thus we obtain the Jones matrix for a waveplate of arbitreaty phase retardance at an angle $\theta$ to the optical axis.

(6)