By Edward Collett
The polarization of sunshine is without doubt one of the such a lot striking phenomena in nature and has ended in various discoveries and functions. the character and mathematical formula of unpolarized gentle and in part polarized gentle weren't easily drawing close till the Fifties, whilst questions about polarized gentle and the mathematical instruments to house it all started to be addressed in earnest. for that reason, there's a first-class knowing of polarized mild today.The basic target of this advisor is to supply an advent to the advancements in polarized gentle that experience taken position during the last half-century, and current the main salient issues of the subject material similar to Mueller matrices, Stokes polarization parameters, and Jones matrices.
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Extra info for Field Guide to Polarization (SPIE Vol. FG05)
Example text
Py Incident beam z px Output beam The Mueller matrix for a linear polarizer (the polarization matrix form used in the intensity domain) is found to be ⎛ px 2 + py2 ⎜ 2 2 1 ⎜ px − py M POL ( px , py ) = ⎜ 2⎜ 0 ⎜ 0 ⎝ px 2 − py2 2 px + py 0 2 0 0 2 px py 0 0 ⎞ ⎟ 0 ⎟ ⎟. 0 ⎟ 2 px py ⎟⎠ 0 For an ideal linear polarizer there is complete transmission along one axis and no transmission along the orthogonal axis. The Mueller matrix for an ideal linear polarizer with its transmission axis along the xaxis is px = 1 and py = 0.
In the direction of the optic axis, however, the ellipsoidal wave becomes spherical. For a uniaxial crystal with its optic axis in the z direction, v x = v y = v o [the ordinary wave (o)] and v z = v e [the extraordinary wave (e)]. Substituting these conditions into Fresnel’s equation, above, yields two solutions: v′2 = vo 2 , and v′′2 = vo 2 cos2 θ + ve 2 sin2 θ, where the angle θ is measured from the optics axis. Along the optic axis v ″ 2 = v o 2 , and perpendicular to the optic axis v ″ 2 = v e 2 .
The Stokes vector of a transmitted beam through a single surface of a dielectric (glass) for incident unpolarized light is ⎛ S0T ⎜ ⎜ S1T ⎜ S2T ⎜⎜ ⎝ S3T ⎞ ⎟ ⎟ = 1 sin 2i sin 2r ⎟ 2 (sin α cos α )2 + − ⎟⎟ ⎠ ⎛ cos2 2α − + 1 ⎞ ⎜ ⎟ 2 ⎜ cos 2α − − 1 ⎟ , ⎜ ⎟ 0 ⎜⎜ ⎟⎟ 0 ⎝ ⎠ and the DOP of the transmitted beam is P= S1 cos2 α − − 1 = . 5 Incident Angle i Polarization 46 Reflection and Transmission Stokes Parameters (cont’d) The transmitted light is always partially polarized, and the incident unpolarized light never becomes completely polarized using a single surface.
