Field Guide to Polarization (SPIE Vol. FG05) by Edward Collett

By Edward Collett

The polarization of sunshine is likely one of the so much awesome phenomena in nature and has ended in various discoveries and purposes. the character and mathematical formula of unpolarized mild and partly polarized gentle weren't without difficulty drawing close till the Fifties, while questions on polarized gentle and the mathematical instruments to house it all started to be addressed in earnest. consequently, there's a first-class knowing of polarized mild today.The basic target of this consultant is to supply an advent to the advancements in polarized gentle that experience taken position over the last half-century, and current the main salient subject matters of the subject material corresponding to Mueller matrices, Stokes polarization parameters, and Jones matrices.

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However, by placing a wave plate with its fast axis at +45° between a pair of crossed polarizers and varying the phase of the wave plate the intensity of the light that emerges from the second polarizer can be controlled. Polarization 26 Mueller Matrix Applications – The Optical Shutter 45° Input beam Output beam Horizontal polarizer Wave plate Vertical polarizer The shutter configuration is shown in the following figure. The Mueller matrix for the variable-phase wave plate with its fast axis at +45° is 0 ⎛1 ⎜ 0 cos φ M WP (45°) = ⎜ ⎜0 0 ⎜ ⎝ 0 − sin φ 0 0 ⎞ ⎟ 0 sin φ ⎟ .

60 from i = 0° to 90°. 40 Incident angle Polarization 52 Pile of Polarizing Dielectric Plates The transmitted beam is always partially polarized. An increase in the DOP can be obtained using a configuration known as a pile of polarizing plates. The plates are separated in A configuration of 6 dielectric plates. order to reduce the effects of reflection. The Mueller matrix equation and the Stokes vector for a beam transmitted through m dielectric plates are Input beam Output beam ST m = M T 2m ⋅ S , ⎛ (cos4 m α − + 1)S0 + (cos4m α − − 1)S1 ⎞ ⎜ ⎟ 1 ⎡ sin 2i sin 2r ⎤ ⎜ (cos4 m α − − 1)S0 + (cos4 m α − + 1)S1 ⎟ m ST = ⎢ .

Polarizing element(s) Input beam Output beam The input beam is characterized by a Stokes vector S and the output beam by S′. The assumption is made that S and S′ are linearly related by a 4 × 4 transformation matrix known as the Mueller matrix, which represents the polarizing element(s): ⎛S ′ ⎞ ⎜ 0 ⎟ ⎛ m00 ⎜S ′ ⎟ ⎜m ⎜ 1 ⎟ = ⎜ 10 ⎜ S ′ ⎟ ⎜ m20 ⎜ 2 ⎟ ⎜⎜ m ⎜ S ′ ⎟ ⎝ 30 ⎝ 3 ⎠ m01 m11 m21 m31 m02 m12 m22 m32 m03 ⎞ ⎛ S0 ⎞ ⎟⎜ ⎟ m13 ⎟ ⎜ S1 ⎟ . m23 ⎟ ⎜ S2 ⎟ ⎟⎜ ⎟ m33 ⎠⎟ ⎝⎜ S3 ⎠⎟ All the elements in the 4 × 4 Mueller matrix are real quantities.

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