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Jones Matrix of a Linear Polarizer Rotated at Angle θ with the y‐Axis
ОглавлениеFigure (4.12) shows the (y‐z)‐coordinate system and also the (e1‐e2) ‐coordinate system rotated at an angle θ with respect to the y‐axis. The original polarizer, located in the (y‐z)‐coordinate system is described by the Jones matrix [J]; and the rotated polarizer at an angle θ is described as the rotated Jones matrix [Jrot(θ)]. The rotated polarizer is located in the (e1‐e2) coordinate system. The relation between the Jones matrix [J] of unrotated polarizer and Jones matrix [Jrot(θ)] of the rotated polarizer is obtained by the coordinate transformation through the rotation Jones matrix [Rθ(θ)] and the inverse rotation Jones matrix [Rθ(θ)]−1 = [Rθ(−θ)].
Figure (4.12) shows that the unit vectors of two coordinate systems are related through the following transformations:
(4.6.16)
The following rotation Jones matrix [Rθ(θ)] and its inverse [Rθ(−θ)] can be defined from the above relations that could be useful to transform the vectors from one co‐ordinated system to another:
Figure 4.12 The (y–z) and rotated (e1–e2) Coordinate systems.
The above rotation matrices are used to transform both the Jones vector and the Jones matrix from one to another coordinate system. The Jones matrix concept is applied to the polarizing system in two steps:
