Sample Stokes vectors for the various polarization states of electromagnetic radiation (ER) are shown below for: unpolarized light, linearly polarized light, elliptically polarized light, and circularly polarized light.
Unpolarized ER (<a> is the average wave amplitude in a reference plane):
Linearly polarized ER (0 ≤ γ ≤ 180° is the orientation angle of the polarization direction, a is the wave amplitude):
| linearly polarized light, arbitrary γ
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(2)
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| linear polarization, a = 1, γ = 0°;
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(3)
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| linear polarization, a = 1, γ = 90°;
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(4)
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| linear polarization, a = 1, γ = 45°;
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(5)
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| linear polarization, a = 1, γ = 135°;
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(6)
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Elliptically polarized ER, the most general expressions of the Stokes vector elements (0 ≤ γ ≤ 180° is the orientation angle of the major axis of the polarization ellipse, -45° ≤ η ≤ 45° is the ellipticity measure, defined as |tanη| = b/a, with a and b being the major and minor half-axes of the ellipse respectively, c2 = a2 + b2; ER is right-handed if the polarization ellipse is traced by the electric vector of the wave in the clockwise sense when the observer is looking at the light source, η is positive in that case, see, for example, Bohren and Huffman 1983, for a discussion of other conventions):
| elliptically polarized light, arbitrary γ, η
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c2 |
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c2 cos 2η cos 2γ |
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c2 cos 2η sin 2γ |
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c2 sin 2η |
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(7)
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Circularly polarized ER (a is the wave amplitude):
| right circularly polarized light, arbitrary a
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(8)
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| left circularly polarized light, arbitrary a
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(9)
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