Depolarization

Calculate depolarization effects via Mueller matrix model or spectral averaging.

depolarizer: M = diag(1, d, d, d), physical for −1/3 ≤ d ≤ 1; DOP_out = |d| · DOP_in

broadband light through a retarder: ⟨e^iΓ⟩ = V e^iΓ₀, flat in wavenumber V = sinc(π R_g Δσ), Gaussian V = exp(−(π R_g Δσ)² / (4 ln 2))

R_g = d (Δn − λ dΔn/dλ), Δσ = 1/(λ₀ − Δλ/2) − 1/(λ₀ + Δλ/2)

Depolarizer d (DOP scales by |d|)0.5

-0.333–1

Physical for d from −1/3 (the slider stops at −0.333) to 1: d = 1 passes the light unchanged, d = 0 is an ideal depolarizer, and d < 0 also turns the polarized part into the orthogonal state.

Input Stokes vector

S₀S₁S₂S₃

Output Stokes vector

(1.0000, 0.0000, 0.5000, 0.0000)

Degree of polarization

1.0000 → 0.5000

Output DOP against d

Output DOP of the input above for every physical d; the marker is the current d.

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Depolarizer diag(1, d, d, d), or a retarder in a band flat in wavenumber or Gaussian: V = Fourier transform of the spectrum at the group retardance (retardance linear in σ). |V| error < 0.03 for Δλ ≤ 0.5λ₀ in quartz.

Goldstein D. H. (2011). Polarized Light, 3rd ed., ch. Mueller Matrices for Polarizing Components, pp. 93–115. CRC Press. doi:10.1201/b10436
Cloude S. R. (1986). Group theory and polarisation algebra. Optik 75, 26–36: a Mueller matrix is physical when its coherency matrix has no negative eigenvalue.
Born M., Wolf E. (1999). Principles of Optics, 7th ed., ch. 7 Elements of the theory of interference and interferometers, pp. 286–411, and ch. 10 Interference and diffraction with partially coherent light, pp. 554–632. Cambridge University Press. doi:10.1017/CBO9781139644181.016
Ghosh G. (1999). Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals. Opt. Commun. 163, 95–102. doi:10.1016/S0030-4018(99)00091-7
Dodge M. J. (1984). Refractive properties of magnesium fluoride. Appl. Opt. 23, 1980–1985. doi:10.1364/AO.23.001980
Malitson I. H., Dodge M. J. (1972). Refractive index and birefringence of synthetic sapphire. J. Opt. Soc. Am. 62, 1405 (abstract); formula in Dodge M. J. (1986), Handbook of Laser Science and Technology vol. IV, part 2, p. 30, CRC Press.
Lomheim T. S., DeShazer L. G. (1978). Optical-absorption intensities of trivalent neodymium in the uniaxial crystal yttrium orthovanadate. J. Appl. Phys. 49, 5517–5522: YVO₄ dispersion formula. doi:10.1063/1.324471
Zelmon D. E., Small D. L., Jundt D. (1997). Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol% magnesium oxide-doped lithium niobate. J. Opt. Soc. Am. B 14, 3319–3322. doi:10.1364/JOSAB.14.003319
DeVore J. R. (1951). Refractive indices of rutile and sphalerite. J. Opt. Soc. Am. 41, 416–419. doi:10.1364/JOSA.41.000416

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