Waveplate / Retarder
Polarization state transformation by a birefringent waveplate with variable retardance and fast-axis orientation.
Intensity
1.000
State
Left circular
Ellipticity angle χ
-45.0°
Orientation ψ
—
Stokes Parameters
1.000
0.000
0.000
-1.000
Convention (Goldstein): RCP = [1, i]/√2 turns clockwise as seen by the receiver; S₃ > 0 is right-handed.
Key Formulas
Jones matrix: R(−θ) · diag(1, e−iΓ) · R(θ), R(θ) = [[cos θ, sin θ], [−sin θ, cos θ]]
Γ = retardance, θ = fast axis angle
Stokes: S₀ = |Eₓ|² + |E_y|², S₁ = |Eₓ|² − |E_y|²
S₂ = 2 Re(Eₓ* E_y), S₃ = 2 Im(Eₓ* E_y)
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
Ideal lossless linear retarder R(−θ)·diag(1, e^(−iΓ))·R(θ) on linearly polarized light, Goldstein convention (S₃ > 0 is right-handed). Not modelled: dispersion of Γ, reflections, tilt.
- Goldstein D. H. (2011). Polarized Light, 3rd ed., ch. The Jones Matrix Formalism, pp. 201–231. CRC Press. doi:10.1201/b10436
- Jones R. C. (1941). A new calculus for the treatment of optical systems, I. Description and discussion of the calculus. J. Opt. Soc. Am. 31(7), 488–493. doi:10.1364/JOSA.31.000488