Show for linear polarization I cos 6 sin 6 Jones vector Sol

Show for linear polarization I = [cos 6 sin 6] Jones vector

Solution

a convenient way for keeping track of polarization in terms of a two-dimensional vector, called a Jones vector. This vector contains the essential information regarding the field polarization; the overall field strength E_eff is set aside in the discussion of polarization. Also note that the phase of E_eff represents an overall phase shift that one can trivially adjust by moving the light source (a laser, say) forward or backward by a fraction of a wavelength. This is often unimportant. When writing the Jones vector, instead of using the standard xˆ and yˆ vector notation, we organize its components in a column vector for later use in matrix algebra. The general expression for the Jones vector is

                                                                                                            

A polarizer can be represented as a 2x 2 matrix that operates on Jones vectors. The function of a polarizer is to pass only the component of electric field that is oriented along the polarizer transmission axis (perpendicular to the polymer chains). Thus, if a polarizer is oriented with its transmission axis along the x -dimension, then only the x -component of polarization transmits; the y -component is killed. If the polarizer is oriented with its transmission axis along the y -dimension, then only the y -component of the field transmits, and the x -component is killed. These two scenarios can be represented with the following Jones matrices:

(polarizer with transmission along x -axis)

(polarizer with transmission along y -axis)

A product of Jones matrices can represent a sequence of polarizers (with varying orientations). The matrices operate on the Jones vector in the order that the light encounters the devices. Therefore, the matrix for the first device is written on the right, and so on until the last device encountered, which is written on the left, farthest from the Jones vector.

This rotation can be accomplished by multiplying the following matrix to the incident Jones vector:

CosE   sinE

- sineE cosE.                              (rotation of coordinates through an angle q )