Abstract

An efficient simulation technique is proposed for computing propagation of uniformly polarized statistically stationary fields in linear nonimage-forming systems that includes dispersion of linear birefringence to all orders. The method is based on the discrete-time Fourier transformation of modified frequency profiles of the spectral Stokes parameters. It works under the condition that all (linearly) birefringent sections present in the system are described by the same phase birefringence dispersion curve, being a monotonic function of the optical frequency within the bandwidth of the light. We demonstrate the technique as a supplement for the Mueller–Stokes matrix formalism extended to any uniformly polarized polychromatic illumination. Accuracy of its numerical implementation has been verified by using parameters of a Lyot depolarizer made of a highly birefringent and dispersive monomode photonic crystal fiber.

© 2013 Optical Society of America

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  1. B. H. Billings, “A monochromatic depolarizer,” J. Opt. Soc. Am. 41, 966–968 (1951).
    [CrossRef]
  2. A. Loeber, “Depolarization of white light by a birefringent crystal. II. The Lyot depolarizer,” J. Opt. Soc. Am. 72, 650–656 (1982).
    [CrossRef]
  3. W. K. Burns, “Degree of polarization in the Lyot depolarizer,” J. Lightwave Technol. 1, 475–479 (1983).
    [CrossRef]
  4. K. Mochizuki, “Degree of polarization in jointed fibers: the Lyot depolarizer,” Appl. Opt. 23, 3284–3288 (1984).
    [CrossRef]
  5. P. L. Makowski, M. Z. Szymanski, and A. W. Domanski, “Lyot depolarizer in terms of the theory of coherence-description for light of any spectrum,” Appl. Opt. 51, 626–634 (2012).
    [CrossRef]
  6. E. I. Alekseev and E. N. Bazarov, “Theoretical basis of the method for reducing drift of the zero level of the output signal of a fiber-optic gyroscope with the aid of a Lyot depolarizer,” Sov. J. Quantum Electron. 22, 834–839 (1992).
    [CrossRef]
  7. R. Barakat, “Theory of the coherency matrix for light of arbitrary spectral bandwidth,” J. Opt. Soc. Am. 53, 317–322 (1963).
    [CrossRef]
  8. P. L. Makowski and A. W. Domanski, “Approach for modeling influence of birefringence dispersion on polarization properties of multi-section systems,” Proc. SPIE 8697, 869703 (2012).
    [CrossRef]
  9. P. Réfrégier, T. Setälä, and A. T. Friberg, “Temporal and spectral degrees of polarization of light,” Proc. SPIE 8171, 817102 (2011).
    [CrossRef]
  10. T. R. Woliński, “Polarimetric optical fibers and sensors,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2000), Vol. 40, pp. 1–75.
  11. 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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.
  12. D. J. Liu and Z. X. Zhou, “Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 54, 95–101 (2009).
    [CrossRef]
  13. R. C. Jones, “A new calculus for the treatment of optical systems. VII. Properties of the N-matrices,” J. Opt. Soc. Am. 38, 671–683 (1948).
    [CrossRef]
  14. N. Ortega-Quijano and J. L. Arce-Diego, “Generalized Jones matrices for anisotropic media,” Opt. Express 21, 6895–6900 (2013).
    [CrossRef]
  15. R. M. A. Azzam, “Propagation of partially polarized light through anisotropic media with or without depolarization: a differential 4×4 matrix calculus,” J. Opt. Soc. Am. 68, 1756–1767 (1978).
    [CrossRef]
  16. E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
    [CrossRef]
  17. F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, “Coherent-mode decomposition of partially polarized, partially coherent sources,” J. Opt. Soc. Am. A 20, 78–84 (2003).
    [CrossRef]
  18. J. Tervo, T. Setälä, and A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space-frequency domain,” J. Opt. Soc. Am. A 21, 2205–2215 (2004).
    [CrossRef]
  19. M. A. Alonso and E. Wolf, “The cross-spectral density matrix of a planar, electromagnetic stochastic source as a correlation matrix,” Opt. Commun. 281, 2393–2396 (2008).
    [CrossRef]
  20. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  21. P. L. Makowski and A. W. Domanski, “Extended Mueller–Stokes description of polarization-mode transformation in linearly birefringent single mode optical fibers,” Opt. Lett. 38, 1107–1109 (2013).
    [CrossRef]
  22. O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198–200 (2005).
    [CrossRef]
  23. A. Dogariu and G. Popescu, “Measuring the phase of spatially coherent polychromatic fields,” Phys. Rev. Lett. 89, 243902 (2002).
    [CrossRef]
  24. C. Brosseau, “Mueller matrix analysis of light depolarization by a linear optical medium,” Opt. Commun. 131, 229–235 (1996).
    [CrossRef]
  25. C. Tsao, Optical Fibre Waveguide Analysis (Oxford University, 1992).
  26. K. Böhm, K. Petermann, and E. Weidel, “Performance of Lyot depolarizers with birefringent single-mode fibers,” J. Lightwave Technol. 1, 71–74 (1983).
    [CrossRef]
  27. L. Zhang, T. Luo, Y. Yue, and A. E. Willner, “High group birefringence in photonic crystal fibers with both positive and negative phase birefringences,” Pure Appl. Opt. 10, 035004 (2008).
    [CrossRef]

2013

2012

P. L. Makowski, M. Z. Szymanski, and A. W. Domanski, “Lyot depolarizer in terms of the theory of coherence-description for light of any spectrum,” Appl. Opt. 51, 626–634 (2012).
[CrossRef]

P. L. Makowski and A. W. Domanski, “Approach for modeling influence of birefringence dispersion on polarization properties of multi-section systems,” Proc. SPIE 8697, 869703 (2012).
[CrossRef]

2011

P. Réfrégier, T. Setälä, and A. T. Friberg, “Temporal and spectral degrees of polarization of light,” Proc. SPIE 8171, 817102 (2011).
[CrossRef]

2009

D. J. Liu and Z. X. Zhou, “Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 54, 95–101 (2009).
[CrossRef]

2008

M. A. Alonso and E. Wolf, “The cross-spectral density matrix of a planar, electromagnetic stochastic source as a correlation matrix,” Opt. Commun. 281, 2393–2396 (2008).
[CrossRef]

L. Zhang, T. Luo, Y. Yue, and A. E. Willner, “High group birefringence in photonic crystal fibers with both positive and negative phase birefringences,” Pure Appl. Opt. 10, 035004 (2008).
[CrossRef]

2005

2004

2003

2002

A. Dogariu and G. Popescu, “Measuring the phase of spatially coherent polychromatic fields,” Phys. Rev. Lett. 89, 243902 (2002).
[CrossRef]

1996

C. Brosseau, “Mueller matrix analysis of light depolarization by a linear optical medium,” Opt. Commun. 131, 229–235 (1996).
[CrossRef]

1992

E. I. Alekseev and E. N. Bazarov, “Theoretical basis of the method for reducing drift of the zero level of the output signal of a fiber-optic gyroscope with the aid of a Lyot depolarizer,” Sov. J. Quantum Electron. 22, 834–839 (1992).
[CrossRef]

1984

1983

W. K. Burns, “Degree of polarization in the Lyot depolarizer,” J. Lightwave Technol. 1, 475–479 (1983).
[CrossRef]

K. Böhm, K. Petermann, and E. Weidel, “Performance of Lyot depolarizers with birefringent single-mode fibers,” J. Lightwave Technol. 1, 71–74 (1983).
[CrossRef]

1982

1978

1963

1951

1948

Alekseev, E. I.

E. I. Alekseev and E. N. Bazarov, “Theoretical basis of the method for reducing drift of the zero level of the output signal of a fiber-optic gyroscope with the aid of a Lyot depolarizer,” Sov. J. Quantum Electron. 22, 834–839 (1992).
[CrossRef]

Alonso, M. A.

M. A. Alonso and E. Wolf, “The cross-spectral density matrix of a planar, electromagnetic stochastic source as a correlation matrix,” Opt. Commun. 281, 2393–2396 (2008).
[CrossRef]

Arce-Diego, J. L.

Azzam, R. M. A.

Barakat, R.

Bazarov, E. N.

E. I. Alekseev and E. N. Bazarov, “Theoretical basis of the method for reducing drift of the zero level of the output signal of a fiber-optic gyroscope with the aid of a Lyot depolarizer,” Sov. J. Quantum Electron. 22, 834–839 (1992).
[CrossRef]

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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.

Billings, B. H.

Böhm, K.

K. Böhm, K. Petermann, and E. Weidel, “Performance of Lyot depolarizers with birefringent single-mode fibers,” J. Lightwave Technol. 1, 71–74 (1983).
[CrossRef]

Borghi, R.

Brosseau, C.

C. Brosseau, “Mueller matrix analysis of light depolarization by a linear optical medium,” Opt. Commun. 131, 229–235 (1996).
[CrossRef]

Burns, W. K.

W. K. Burns, “Degree of polarization in the Lyot depolarizer,” J. Lightwave Technol. 1, 475–479 (1983).
[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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.

Dogariu, A.

A. Dogariu and G. Popescu, “Measuring the phase of spatially coherent polychromatic fields,” Phys. Rev. Lett. 89, 243902 (2002).
[CrossRef]

Domanski, A. W.

Friberg, A. T.

P. Réfrégier, T. Setälä, and A. T. Friberg, “Temporal and spectral degrees of polarization of light,” Proc. SPIE 8171, 817102 (2011).
[CrossRef]

J. Tervo, T. Setälä, and A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space-frequency domain,” J. Opt. Soc. Am. A 21, 2205–2215 (2004).
[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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.

Gori, F.

Guattari, G.

Jones, R. C.

Korotkova, O.

Liu, D. J.

D. J. Liu and Z. X. Zhou, “Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 54, 95–101 (2009).
[CrossRef]

Loeber, A.

Luo, T.

L. Zhang, T. Luo, Y. Yue, and A. E. Willner, “High group birefringence in photonic crystal fibers with both positive and negative phase birefringences,” Pure Appl. Opt. 10, 035004 (2008).
[CrossRef]

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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.

Makowski, P. L.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.

Ortega-Quijano, N.

Petermann, K.

K. Böhm, K. Petermann, and E. Weidel, “Performance of Lyot depolarizers with birefringent single-mode fibers,” J. Lightwave Technol. 1, 71–74 (1983).
[CrossRef]

Piquero, G.

Popescu, G.

A. Dogariu and G. Popescu, “Measuring the phase of spatially coherent polychromatic fields,” Phys. Rev. Lett. 89, 243902 (2002).
[CrossRef]

Réfrégier, P.

P. Réfrégier, T. Setälä, and A. T. Friberg, “Temporal and spectral degrees of polarization of light,” Proc. SPIE 8171, 817102 (2011).
[CrossRef]

Santarsiero, M.

Setälä, T.

P. Réfrégier, T. Setälä, and A. T. Friberg, “Temporal and spectral degrees of polarization of light,” Proc. SPIE 8171, 817102 (2011).
[CrossRef]

J. Tervo, T. Setälä, and A. T. Friberg, “Theory of partially coherent electromagnetic fields in the space-frequency domain,” J. Opt. Soc. Am. A 21, 2205–2215 (2004).
[CrossRef]

Simon, R.

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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.

Szymanski, M. Z.

Tervo, J.

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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.

Tsao, C.

C. Tsao, Optical Fibre Waveguide Analysis (Oxford University, 1992).

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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.

Weidel, E.

K. Böhm, K. Petermann, and E. Weidel, “Performance of Lyot depolarizers with birefringent single-mode fibers,” J. Lightwave Technol. 1, 71–74 (1983).
[CrossRef]

Willner, A. E.

L. Zhang, T. Luo, Y. Yue, and A. E. Willner, “High group birefringence in photonic crystal fibers with both positive and negative phase birefringences,” Pure Appl. Opt. 10, 035004 (2008).
[CrossRef]

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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.

Wolf, E.

M. A. Alonso and E. Wolf, “The cross-spectral density matrix of a planar, electromagnetic stochastic source as a correlation matrix,” Opt. Commun. 281, 2393–2396 (2008).
[CrossRef]

O. Korotkova and E. Wolf, “Generalized Stokes parameters of random electromagnetic beams,” Opt. Lett. 30, 198–200 (2005).
[CrossRef]

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

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

Wolinski, T. R.

T. R. Woliński, “Polarimetric optical fibers and sensors,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2000), Vol. 40, pp. 1–75.

Yue, Y.

L. Zhang, T. Luo, Y. Yue, and A. E. Willner, “High group birefringence in photonic crystal fibers with both positive and negative phase birefringences,” Pure Appl. Opt. 10, 035004 (2008).
[CrossRef]

Zhang, L.

L. Zhang, T. Luo, Y. Yue, and A. E. Willner, “High group birefringence in photonic crystal fibers with both positive and negative phase birefringences,” Pure Appl. Opt. 10, 035004 (2008).
[CrossRef]

Zhou, Z. X.

D. J. Liu and Z. X. Zhou, “Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 54, 95–101 (2009).
[CrossRef]

Appl. Opt.

Eur. Phys. J. D

D. J. Liu and Z. X. Zhou, “Propagation of partially polarized, partially coherent beams in uniaxial crystals orthogonal to the optical axis,” Eur. Phys. J. D 54, 95–101 (2009).
[CrossRef]

J. Lightwave Technol.

W. K. Burns, “Degree of polarization in the Lyot depolarizer,” J. Lightwave Technol. 1, 475–479 (1983).
[CrossRef]

K. Böhm, K. Petermann, and E. Weidel, “Performance of Lyot depolarizers with birefringent single-mode fibers,” J. Lightwave Technol. 1, 71–74 (1983).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

C. Brosseau, “Mueller matrix analysis of light depolarization by a linear optical medium,” Opt. Commun. 131, 229–235 (1996).
[CrossRef]

M. A. Alonso and E. Wolf, “The cross-spectral density matrix of a planar, electromagnetic stochastic source as a correlation matrix,” Opt. Commun. 281, 2393–2396 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

E. Wolf, “Unified theory of coherence and polarization of random electromagnetic beams,” Phys. Lett. A 312, 263–267 (2003).
[CrossRef]

Phys. Rev. Lett.

A. Dogariu and G. Popescu, “Measuring the phase of spatially coherent polychromatic fields,” Phys. Rev. Lett. 89, 243902 (2002).
[CrossRef]

Proc. SPIE

P. L. Makowski and A. W. Domanski, “Approach for modeling influence of birefringence dispersion on polarization properties of multi-section systems,” Proc. SPIE 8697, 869703 (2012).
[CrossRef]

P. Réfrégier, T. Setälä, and A. T. Friberg, “Temporal and spectral degrees of polarization of light,” Proc. SPIE 8171, 817102 (2011).
[CrossRef]

Pure Appl. Opt.

L. Zhang, T. Luo, Y. Yue, and A. E. Willner, “High group birefringence in photonic crystal fibers with both positive and negative phase birefringences,” Pure Appl. Opt. 10, 035004 (2008).
[CrossRef]

Sov. J. Quantum Electron.

E. I. Alekseev and E. N. Bazarov, “Theoretical basis of the method for reducing drift of the zero level of the output signal of a fiber-optic gyroscope with the aid of a Lyot depolarizer,” Sov. J. Quantum Electron. 22, 834–839 (1992).
[CrossRef]

Other

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

T. R. Woliński, “Polarimetric optical fibers and sensors,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2000), Vol. 40, pp. 1–75.

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, “Sensing with photonic crystal fibres,” in IEEE International Symposium on Intelligent Signal Processing, 2007. WISP 2007 (2007), pp. 1–6.

C. Tsao, Optical Fibre Waveguide Analysis (Oxford University, 1992).

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Figures (3)

Fig. 1.
Fig. 1.

Input data: phase and group birefringence of the highly birefringent holey photonic crystal fiber plotted in the region covered by the Q1350-HP diode spectrum. The phase birefringence B(λ) is represented by a fifth-degree polynomial fitting to the samples of the original phase birefringence curve [27].

Fig. 2.
Fig. 2.

Input data: PSD samples of the superluminescent diode source along with associated phase birefringence curve of the highly birefringent photonic crystal fiber (black) and the corresponding functions after domain transformation (7b) (gray).

Fig. 3.
Fig. 3.

Results: (a) degree of polarization of superluminescent diode light after passing a dispersive Lyot depolarizer calculated by the proposed technique, Eq. (21), and its discrepancy from the result of exact numerical integration, Eq. (14), for initial number of the spectrum samples, (b) M=30, and (c) M=50. The white arrows indicate the total length L1+L2 of the depolarizer that corresponds to the half-period T0/2 of the DTFT approximation of the autocorrelation Γ11(τ0(L2)).

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

W(ρ,ρ,ω)=[Ei*(ρ,ω)Ej(ρ,ω)],(i,j=x,y),
Γ(τ)=+W(ω)exp(iωτ)dω,
Γ(τ)=[Ei*(t)Ej(t+τ)],(i,j=x,y).
J(z)=[Γxx(0)Γxy(τ(z))Γxy*(τ(z))Γyy(0)],
Γij(z)=+Wij(ω)exp[iωτ(z)(ω)]dω.
ω˜=F(ω)=B(ω)B(ω0)ω
Γij(τ0(z))=+W˜ij(ω˜)exp(iω˜τ0(z))dω˜,
W˜ij(ω˜)=|dF1(ω˜)dω˜|Wij(F1(ω˜)),
Γxy(τ(z2)(ω)±τ(z1)(ω))=+Wij(ω)exp[iω(z2cB2(ω)±z1cB1(ω))]dω.
Γij(τ0(z))|Δω˜|n=1NW˜ij(ω˜n)exp(iω˜nτ0(z)),
S=+s(ω)dω,
[Jxx+JyyJxxJyy2Re[Jxy]2Im[Jxy]]=+[Wxx(ω)+Wyy(ω)Wxx(ω)Wyy(ω)2Re[Wxy(ω)]2Im[Wxy(ω)]]dω,
s(ω)=[Ex*(ω)Ex(ω)+Ey*(ω)Ey(ω)Ex*(ω)Ex(ω)Ey*(ω)Ey(ω)2Re[Ex*(ω)Ey(ω)]2Im[Ex*(ω)Ey(ω)]],
sout(ω)=M(ω)sin(ω).
sout(ω)=M(ω)sin(ω)=M(ω)¯sin(ω),
Sout=+Meff(ω)sin(ω)dω,
M(δ)=[11cos(δ)sin(δ)sin(δ)cos(δ)],
S2out=2+Re[Wxy(ω)]cos(ωτ(z))dω2+Im[Wxy(ω)]sin(ωτ(z))dω,
S3out=2+Re[Wxy(ω)]sin(ωτ(z))dω+2+Im[Wxy(ω)]cos(ωτ(z))dω.
Γxy(τ(z))=+(Re[Wxy(ω)]+iIm[Wxy(ω)])×[cos(ωτ(z))+isin(ωτ(z))]dω.
Sout(z)=[Γxx(0)+Γyy(0)Γxx(0)Γyy(0)2Re[Γxy(τ(z))]2Im[Γxy(τ(z))]],
Sout|Δω˜|n=1NM(ω˜nτ0(z))s˜in(ω˜n),
Sout|Δω˜|n=1NMeff(ω˜n;τ0(z1),τ0(z2),,τ0(zK))s˜in(ω˜n),
Sout(τ0)|Δω˜|(n=1NMeff(ω˜n;τ0,2τ0)Ψ˜(ω˜n))s^in,

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