Abstract

We derive a more general version of the commonly known quasi-monochromatic Mueller matrix of a linearly birefringent single-mode optical fiber. In the matrix, the complex degree of self-coherence of the illuminating field is replaced by the normalized cross-correlation of a pair of any jointly stationary light disturbances associated with the eigenpolarization modes, where both modulus and phase of the cross correlation are included. This allows one to write polychromatic Mueller–Stokes equations of multisection systems transmitting any uniformly polarized stationary field. A way for handling arbitrary phase birefringence dispersion is also suggested.

© 2013 Optical Society of America

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  1. T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.
  2. T. Korteński and T. Eftimof, J. Mod. Opt. 37, 1413(1990).
    [CrossRef]
  3. A. W. Domański, Opto-Electron. Rev. 13, 171 (2005).
  4. P. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
    [CrossRef]
  5. R. Castañeda, Opt. Commun. 284, 4114 (2011).
    [CrossRef]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ., 1995).
  7. O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
    [CrossRef]
  8. B. Kanseri, S. Rath, and H. C. Kandpal, Opt. Commun. 282, 3059 (2009).
    [CrossRef]
  9. A. Loeber, J. Opt. Soc. Am. 72, 650 (1982).
    [CrossRef]
  10. P. L. Makowski, M. Z. Szymański, and A. W. Domański, Appl. Opt. 51, 626 (2012).
    [CrossRef]
  11. P. L. Makowski and A. W. Domański, Proc. SPIE 8697, 869703 (2012).
    [CrossRef]
  12. K. Mochizuki, Appl. Opt. 23, 3284 (1984).
    [CrossRef]
  13. R. Barakat, J. Opt. Soc. Am. 53, 317 (1963).
    [CrossRef]

2012 (2)

P. L. Makowski and A. W. Domański, Proc. SPIE 8697, 869703 (2012).
[CrossRef]

P. L. Makowski, M. Z. Szymański, and A. W. Domański, Appl. Opt. 51, 626 (2012).
[CrossRef]

2011 (2)

P. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
[CrossRef]

R. Castañeda, Opt. Commun. 284, 4114 (2011).
[CrossRef]

2009 (1)

B. Kanseri, S. Rath, and H. C. Kandpal, Opt. Commun. 282, 3059 (2009).
[CrossRef]

2005 (2)

A. W. Domański, Opto-Electron. Rev. 13, 171 (2005).

O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
[CrossRef]

1990 (1)

T. Korteński and T. Eftimof, J. Mod. Opt. 37, 1413(1990).
[CrossRef]

1984 (1)

1982 (1)

1963 (1)

Barakat, R.

Berghmans, F.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Castañeda, R.

R. Castañeda, Opt. Commun. 284, 4114 (2011).
[CrossRef]

Chah, K.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Chojetzki, C.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Domanski, A. W.

P. L. Makowski, M. Z. Szymański, and A. W. Domański, Appl. Opt. 51, 626 (2012).
[CrossRef]

P. L. Makowski and A. W. Domański, Proc. SPIE 8697, 869703 (2012).
[CrossRef]

A. W. Domański, Opto-Electron. Rev. 13, 171 (2005).

Eftimof, T.

T. Korteński and T. Eftimof, J. Mod. Opt. 37, 1413(1990).
[CrossRef]

Friberg, A. T.

P. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
[CrossRef]

Geernaert, T.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Golojuch, G.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Kandpal, H. C.

B. Kanseri, S. Rath, and H. C. Kandpal, Opt. Commun. 282, 3059 (2009).
[CrossRef]

Kanseri, B.

B. Kanseri, S. Rath, and H. C. Kandpal, Opt. Commun. 282, 3059 (2009).
[CrossRef]

Korotkova, O.

Kortenski, T.

T. Korteński and T. Eftimof, J. Mod. Opt. 37, 1413(1990).
[CrossRef]

Loeber, A.

Makara, M.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Makowski, P. L.

P. L. Makowski, M. Z. Szymański, and A. W. Domański, Appl. Opt. 51, 626 (2012).
[CrossRef]

P. L. Makowski and A. W. Domański, Proc. SPIE 8697, 869703 (2012).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ., 1995).

Martynkien, T.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Mergo, P.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Mochizuki, K.

Nasilowski, T.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Olszewski, J.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Rath, S.

B. Kanseri, S. Rath, and H. C. Kandpal, Opt. Commun. 282, 3059 (2009).
[CrossRef]

Réfrégier, P.

P. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
[CrossRef]

Setälä, T.

P. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
[CrossRef]

Statkiewicz, G.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Szpulak, M.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Szymanski, M. Z.

Thienpont, H.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Urbanczyk, W.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Van Erps, J.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Wojcik, J.

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

Wolf, E.

O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ., 1995).

Appl. Opt. (2)

J. Mod. Opt. (1)

T. Korteński and T. Eftimof, J. Mod. Opt. 37, 1413(1990).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Commun. (2)

B. Kanseri, S. Rath, and H. C. Kandpal, Opt. Commun. 282, 3059 (2009).
[CrossRef]

R. Castañeda, Opt. Commun. 284, 4114 (2011).
[CrossRef]

Opt. Lett. (1)

Opto-Electron. Rev. (1)

A. W. Domański, Opto-Electron. Rev. 13, 171 (2005).

Proc. SPIE (2)

P. Réfrégier, T. Setälä, and A. T. Friberg, Proc. SPIE 8171, 817102 (2011).
[CrossRef]

P. L. Makowski and A. W. Domański, Proc. SPIE 8697, 869703 (2012).
[CrossRef]

Other (2)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ., 1995).

T. Nasilowski, F. Berghmans, T. Geernaert, K. Chah, J. Van Erps, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, T. Martynkien, W. Urbanczyk, P. Mergo, M. Makara, J. Wojcik, C. Chojetzki, and H. Thienpont, in IEEE International Symposium on Intelligent Signal Processing (IEEE, 2007), pp. 1–6.

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Equations (19)

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M0(z)=[11|γ11|cos(Δβ0z)|γ11|sin(Δβ0z)|γ11|sin(Δβ0z)|γ11|cos(Δβ0z)],
γ11(z)=0+|v(ω)|2ei(ωω0)Δτgzdω0+|v(ω)|2dωeiΔβ0z.
Ej(t)=aj(t)eiω¯t+iΦj(t),(j=x,y),
S(z)=[Jxx(z)+Jyy(z)Jxx(z)Jyy(z)2R[Jxy(z)]2I[Jxy(z)]].
J(z)=[Γxx(0)Γxy(τz)Γyx(τz)Γyy(0)],
Γij(τ)=Ei*(t)Ej(t+τ),(i,j=x,y),
M(z)=[11M33M34M43M44]
S(z)=M(z)S(0).
E˜x(t)=eiω¯t0Ex(t),
Γ˜xy(τ)=eiω¯t0Γxy(τ),
S2(z)=R[Γ˜xy(τz)]=M33R[Γ˜xy(0)]+M34I[Γ˜xy(0)],
S3(z)=I[Γ˜xy(τz)]=M43R[Γ˜xy(0)]+M44I[Γ˜xy(0)],
R[Γxy(τz)]=M33R[Γxy(0)]+M34I[Γxy(0)],
I[Γxy(τz)]=M43R[Γxy(0)]+M44I[Γxy(0)].
M33=R[γxy(τz)γxy(0)],M34=I[γxy(τz)γxy(0)],
M43=M34,M44=M33.
M33=R[γ11(τz)],M34=I[γ11(τz)].
S2=M2(z2)T(θ)M1(z1)S0
Γij(z)=+Wij(ω)eiωτ(z;ω)dω,(i,j=x,y),

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