Poincaré Sphere

Interactive visualization of polarization states on the Poincaré sphere.

Model: Exact

Polarization Parameters

Orientation angle θ (°)

Ellipticity angle χ (°)

Amplitude

Stokes Vector

I1.0000

Q (S₁)0.0000

U (S₂)0.8660

V (S₃)0.5000

DOP1.0000

HandednessRight-handed elliptical

Jones Ex0.683-0.183i

Jones Ey0.683+0.183i

Convention (Goldstein): RCP = [1, i]/√2 turns clockwise as seen by the receiver; S₃ > 0 is right-handed.

Poincaré Sphere

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Polarization Ellipse

Model and references

Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers

A fully polarized state from azimuth ψ and ellipticity χ: S = I(1, cos 2χ cos 2ψ, cos 2χ sin 2ψ, sin 2χ), with Goldstein's Jones vector. χ > 0 is right-handed, clockwise as seen by the receiver.

Goldstein D. H. (2011). Polarized Light, 3rd ed., chs. The Polarization Ellipse, pp. 49–58, and Stokes Polarization Parameters, pp. 59–91. CRC Press. doi:10.1201/b10436
Collett E. (2005). Field Guide to Polarization, SPIE Field Guides FG05: the Stokes parameters and the Poincaré sphere. SPIE Press. doi:10.1117/3.626141

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