Abstract

The differential Mueller matrix expresses the local action of an optical medium on the evolution of a propagating electromagnetic field, including partially coherent and partially polarized waves. Here, we present a derivation of the differential Mueller matrix from the canonical form of Type I Mueller matrices without making use of the exponential generators of uniform media. We demonstrate how to practically obtain this parameterization numerically using an eigenvalue decomposition and find validity criteria to ensure that the matrix satisfies the constraints of a physical system. This provides a convenient tool-set to investigate depolarization effects and extends previous treatments of the differential Mueller matrix formalism.

© 2014 Optical Society of America

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References

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  1. R. Azzam, J. Opt. Soc. Am. 68, 1756 (1978).
    [CrossRef]
  2. N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 1942 (2011).
    [CrossRef]
  3. N. Ortega-Quijano and J. L. Arce-Diego, Opt. Lett. 36, 2429 (2011).
    [CrossRef]
  4. R. Ossikovski, Opt. Lett. 36, 2330 (2011).
    [CrossRef]
  5. T. A. Germer, Opt. Lett. 37, 921 (2012).
    [CrossRef]
  6. V. Devlaminck, P. Terrier, and J.-M. Charbois, Opt. Lett. 38, 1497 (2013).
    [CrossRef]
  7. V. Devlaminck, P. Terrier, and J.-M. Charbois, Opt. Lett. 38, 1410 (2013).
    [CrossRef]
  8. V. Devlaminck, J. Opt. Soc. Am. A 30, 2196 (2013).
    [CrossRef]
  9. R. Ossikovski and V. Devlaminck, Opt. Lett. 39, 1216 (2014).
    [CrossRef]
  10. A. V. G. Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).
    [CrossRef]
  11. B. N. Simon, S. Simon, N. Mukunda, F. Gori, M. Santarsiero, R. Borghi, and R. Simon, J. Opt. Soc. Am. A 27, 188 (2010).
    [CrossRef]

2014 (1)

2013 (3)

2012 (1)

2011 (3)

2010 (1)

1998 (1)

A. V. G. Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).
[CrossRef]

1978 (1)

Arce-Diego, J. L.

Azzam, R.

Borghi, R.

Charbois, J.-M.

Devlaminck, V.

Germer, T. A.

Gori, F.

Mallesh, K. S.

A. V. G. Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).
[CrossRef]

Mukunda, N.

Ortega-Quijano, N.

Ossikovski, R.

Rao, A. V. G.

A. V. G. Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).
[CrossRef]

Santarsiero, M.

Simon, B. N.

Simon, R.

Simon, S.

Sudha,

A. V. G. Rao, K. S. Mallesh, and Sudha, J. Mod. Opt. 45, 955 (1998).
[CrossRef]

Terrier, P.

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Figures (2)

Fig. 1.
Fig. 1.

Variation of the DOP with (a) and (c) depth dDOP/dz, and (b) and (d) angle φ between input and differential Stokes vector for a (a) and (b) symmetric and a (c) and (d) general mdep. The symmetric case has an identical effect on Stokes vectors opposite from each other on the Poincaré sphere, whereas the general case displays a strong asymmetry, sparing input polarizations aligned along the specific direction defined by the parametric vector a, but depolarizing inputs along a (see text for details). 

Fig. 2.
Fig. 2.

dDOP/dz for the (a) symmetric and the (b) general cases, evaluated along the principle directions (rn indicates the nth column of the rotation matrix R). In the symmetric case, the depolarization depends linearly on the input DOP. The general case polarizes inputs aligned close to a for a DOPtanha and has unequal effect on opposite polarization states.

Equations (18)

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dSdz=m·S=dMdz·M1·S.
M=L2·K·L1,
[1111111111111111]·[K0K1K2K3]T0.
m=dL2dzL21+L2dKdzK1L21+L2KdL1dzM1.
m|z=0=dL20dz·L10+L20·dL10dzmdet+L20·dK0dz·L201mdep.
mdet=[0τ4τ5τ6τ40τ3τ2τ5τ30τ1τ6τ2τ10],mdep=[κ0ζ4ζ5ζ6ζ4κ1ζ3ζ2ζ5ζ3κ2ζ1ζ6ζ2ζ1κ3].
mdep=L·D·L1,
m=limΔz0M(Δz)IΔz.
G·NI+Δzm+G·ΔzmT·G=I+2Δzmdep=L·(I+2ΔzD)·L1.
[111111111]·[D1D2D3]T0.
LD=[coshaaTsinhaasinhaa·aT(cosha1)+I],LR=[100R],
mdep=LD·LR·D·LR1·LD1=LD·[D00T0X]·G·LD·G,
mdep·[coshaasinha]=D0[coshaasinha].
D0=0.009,[τ1τ2τ3]T=[0.3980.0080]T,[τ4τ5τ6]T=[0.1500.0060.004]T,aa=[0.00610.00190.0008]T,rr=[0.0300.0080.0093]T,[d1d2d3]T=[1.41510.97120.6726]T.
dDOPdz=S·G·dS/dzI2DOP+(1DOP2)dI/dzIDOP=[DOPsT]·mdep·[1DOPsT].
mdep=LR·D·LR1,
mdep=LR·D·LRT+[γ2ηγnTγnρ(n·aT+a·nT)ρ2ηa·aT],γ=sinha,ρ=cosha1,η=aT·R·diag(D1,D2,D3)·RT·a,n=R·diag(D1,D2,D3)·RT·a+ρηa.
mdep=LR·D·LRT+Dn[sinh2aaTsinhacoshaasinhacoshaa·aTsinh2a],

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