Abstract

A two-stage polarization mode dispersion (PMD) emulator design consisting of two variable delay lines separated by a rotatable half-wave linear retarder is analyzed and shown to generate an adjustable amount of first- and second-order PMD without any higher orders. This two-stage PMD emulator configuration provides a simple easy-to-breadboard solution for second-order PMD emulators. When compared with PMD emulators based on birefringent crystals, this two-stage emulator is simpler to calibrate.

© 2004 Optical Society of America

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References

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  1. J. N. Damask, “A programmable polarization-mode dispersion emulator for systematic testing of 10 Gb/s PMD compensators,” in Optical Fiber Communication Conference, Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 28–30.
  2. I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, “Polarization mode dispersion emulator,” in Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 31–33.
  3. J. Damask, G. Simer, K. Rochford, P. Myers, “Demonstration of a programmable PMD source,” IEEE Photon. Technol. Lett. 15, 296–298 (2002).
    [CrossRef]
  4. R. A. Chipman, R. Kinnera, “A high-order polarization mode dispersion emulator,” Opt. Eng. 341, 932–937 (2002).
    [CrossRef]
  5. H. Lee, Y. C. Chung, “Statistical PMD emulator using variable DGD elements,” in Optical Fiber Communication Conference, Postconference Digest, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2002), pp. 375–376.
  6. J. H. Lee, M. S. Kim, Y. C. Chung, “Statistical PMD emulator using variable DGD elements,” IEEE Photon. Technol. Lett. 15, 54–56 (2003).
    [CrossRef]
  7. M. Wegmuller, S. Demma, C. Vinegoni, N. Gisin, “Emulator of first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14, 630–632 (2002).
    [CrossRef]
  8. E. Ibragimov, G. Shtengel, S. Suh, “Statistical correlation between first- and second-order PMD,” J. Lightwave Technol. 20, 586–590 (2002).
    [CrossRef]
  9. J. J. Drewes, R. A. Chipman, M. H. Smith, “Characterizing polarization controllers with Mueller matrix polarimetry,” in Active and Passive Optical Components for WDM Communication, A. K. Dutta, A. A. S. Awwal, N. K. Dutta, K. Okamoto, eds., Proc. SPIE4532, 462–466 (2001).
    [CrossRef]
  10. C. D. Poole, R. E. Wagner, “Phenomenological approach to the polarization mode dispersion,” Electron. Lett. 22, 1029–1039 (1986).
    [CrossRef]
  11. J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 99, 4541–4550 (1999).
  12. B. Lyot, “Recherches sur la polarisation de la lumière des planètes et de quelques substances terrestres,” Ann. Obser. Paris 8, 100–104 (1929).
  13. B. H. Billings, “A monochromatic depolarizer,” J. Opt. Soc. Am. 41, 966–975 (1951).
    [CrossRef]
  14. S. Lu, A. P. Loeber, “Depolarization of white light by a birefringent crystal,” J. Opt. Soc. Am. 65, 248–251 (1975).
    [CrossRef]
  15. A. P. Loeber, “Depolarization of white light by a birefringent crystal: the Lyot depolarizer,” J. Opt. Soc. Am. 72, 650–656 (1982).
    [CrossRef]
  16. W. K. Burns, “Degree of polarization in the Lyot depolarizer,” J. Lightwave Technol. LT-1, 475–479 (1983).
    [CrossRef]
  17. A. Djupsjobacka, “On differential group-delay statistics for polarization mode dispersion emulators,” J. Lightwave Technol. 19, 285–290 (2001).
    [CrossRef]
  18. A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
    [CrossRef]
  19. B. L. Heffner, “Automated measurements of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
    [CrossRef]

2003 (1)

J. H. Lee, M. S. Kim, Y. C. Chung, “Statistical PMD emulator using variable DGD elements,” IEEE Photon. Technol. Lett. 15, 54–56 (2003).
[CrossRef]

2002 (4)

M. Wegmuller, S. Demma, C. Vinegoni, N. Gisin, “Emulator of first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14, 630–632 (2002).
[CrossRef]

J. Damask, G. Simer, K. Rochford, P. Myers, “Demonstration of a programmable PMD source,” IEEE Photon. Technol. Lett. 15, 296–298 (2002).
[CrossRef]

R. A. Chipman, R. Kinnera, “A high-order polarization mode dispersion emulator,” Opt. Eng. 341, 932–937 (2002).
[CrossRef]

E. Ibragimov, G. Shtengel, S. Suh, “Statistical correlation between first- and second-order PMD,” J. Lightwave Technol. 20, 586–590 (2002).
[CrossRef]

2001 (1)

1999 (2)

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 99, 4541–4550 (1999).

1992 (1)

B. L. Heffner, “Automated measurements of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

1986 (1)

C. D. Poole, R. E. Wagner, “Phenomenological approach to the polarization mode dispersion,” Electron. Lett. 22, 1029–1039 (1986).
[CrossRef]

1983 (1)

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

1982 (1)

1975 (1)

1951 (1)

B. H. Billings, “A monochromatic depolarizer,” J. Opt. Soc. Am. 41, 966–975 (1951).
[CrossRef]

1929 (1)

B. Lyot, “Recherches sur la polarisation de la lumière des planètes et de quelques substances terrestres,” Ann. Obser. Paris 8, 100–104 (1929).

A. Chipman, R.

R. A. Chipman, R. Kinnera, “A high-order polarization mode dispersion emulator,” Opt. Eng. 341, 932–937 (2002).
[CrossRef]

Billings, B. H.

B. H. Billings, “A monochromatic depolarizer,” J. Opt. Soc. Am. 41, 966–975 (1951).
[CrossRef]

Burns, W. K.

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

Chipman, R. A.

J. J. Drewes, R. A. Chipman, M. H. Smith, “Characterizing polarization controllers with Mueller matrix polarimetry,” in Active and Passive Optical Components for WDM Communication, A. K. Dutta, A. A. S. Awwal, N. K. Dutta, K. Okamoto, eds., Proc. SPIE4532, 462–466 (2001).
[CrossRef]

Chung, Y. C.

J. H. Lee, M. S. Kim, Y. C. Chung, “Statistical PMD emulator using variable DGD elements,” IEEE Photon. Technol. Lett. 15, 54–56 (2003).
[CrossRef]

H. Lee, Y. C. Chung, “Statistical PMD emulator using variable DGD elements,” in Optical Fiber Communication Conference, Postconference Digest, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2002), pp. 375–376.

Damask, J.

J. Damask, G. Simer, K. Rochford, P. Myers, “Demonstration of a programmable PMD source,” IEEE Photon. Technol. Lett. 15, 296–298 (2002).
[CrossRef]

Damask, J. N.

J. N. Damask, “A programmable polarization-mode dispersion emulator for systematic testing of 10 Gb/s PMD compensators,” in Optical Fiber Communication Conference, Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 28–30.

Demma, S.

M. Wegmuller, S. Demma, C. Vinegoni, N. Gisin, “Emulator of first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14, 630–632 (2002).
[CrossRef]

Djupsjobacka, A.

Drewes, J. J.

J. J. Drewes, R. A. Chipman, M. H. Smith, “Characterizing polarization controllers with Mueller matrix polarimetry,” in Active and Passive Optical Components for WDM Communication, A. K. Dutta, A. A. S. Awwal, N. K. Dutta, K. Okamoto, eds., Proc. SPIE4532, 462–466 (2001).
[CrossRef]

Ebrahimi, P.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, “Polarization mode dispersion emulator,” in Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 31–33.

Eyal, A.

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

Gisin, N.

M. Wegmuller, S. Demma, C. Vinegoni, N. Gisin, “Emulator of first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14, 630–632 (2002).
[CrossRef]

Gordon, J. P.

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 99, 4541–4550 (1999).

Heffner, B. L.

B. L. Heffner, “Automated measurements of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

Ibragimov, E.

E. Ibragimov, G. Shtengel, S. Suh, “Statistical correlation between first- and second-order PMD,” J. Lightwave Technol. 20, 586–590 (2002).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, “Polarization mode dispersion emulator,” in Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 31–33.

Khosravani, R.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, “Polarization mode dispersion emulator,” in Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 31–33.

Kim, M. S.

J. H. Lee, M. S. Kim, Y. C. Chung, “Statistical PMD emulator using variable DGD elements,” IEEE Photon. Technol. Lett. 15, 54–56 (2003).
[CrossRef]

Kinnera, R.

R. A. Chipman, R. Kinnera, “A high-order polarization mode dispersion emulator,” Opt. Eng. 341, 932–937 (2002).
[CrossRef]

Kogelnik, H.

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 99, 4541–4550 (1999).

Lee, H.

H. Lee, Y. C. Chung, “Statistical PMD emulator using variable DGD elements,” in Optical Fiber Communication Conference, Postconference Digest, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2002), pp. 375–376.

Lee, J. H.

J. H. Lee, M. S. Kim, Y. C. Chung, “Statistical PMD emulator using variable DGD elements,” IEEE Photon. Technol. Lett. 15, 54–56 (2003).
[CrossRef]

Lima, I. T.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, “Polarization mode dispersion emulator,” in Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 31–33.

Loeber, A. P.

Lu, S.

Lyot, B.

B. Lyot, “Recherches sur la polarisation de la lumière des planètes et de quelques substances terrestres,” Ann. Obser. Paris 8, 100–104 (1929).

Marshall, W. K.

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

Menyuk, C. R.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, “Polarization mode dispersion emulator,” in Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 31–33.

Myers, P.

J. Damask, G. Simer, K. Rochford, P. Myers, “Demonstration of a programmable PMD source,” IEEE Photon. Technol. Lett. 15, 296–298 (2002).
[CrossRef]

Poole, C. D.

C. D. Poole, R. E. Wagner, “Phenomenological approach to the polarization mode dispersion,” Electron. Lett. 22, 1029–1039 (1986).
[CrossRef]

Rochford, K.

J. Damask, G. Simer, K. Rochford, P. Myers, “Demonstration of a programmable PMD source,” IEEE Photon. Technol. Lett. 15, 296–298 (2002).
[CrossRef]

Shtengel, G.

Simer, G.

J. Damask, G. Simer, K. Rochford, P. Myers, “Demonstration of a programmable PMD source,” IEEE Photon. Technol. Lett. 15, 296–298 (2002).
[CrossRef]

Smith, M. H.

J. J. Drewes, R. A. Chipman, M. H. Smith, “Characterizing polarization controllers with Mueller matrix polarimetry,” in Active and Passive Optical Components for WDM Communication, A. K. Dutta, A. A. S. Awwal, N. K. Dutta, K. Okamoto, eds., Proc. SPIE4532, 462–466 (2001).
[CrossRef]

Suh, S.

Tur, M.

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

Vinegoni, C.

M. Wegmuller, S. Demma, C. Vinegoni, N. Gisin, “Emulator of first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14, 630–632 (2002).
[CrossRef]

Wagner, R. E.

C. D. Poole, R. E. Wagner, “Phenomenological approach to the polarization mode dispersion,” Electron. Lett. 22, 1029–1039 (1986).
[CrossRef]

Wegmuller, M.

M. Wegmuller, S. Demma, C. Vinegoni, N. Gisin, “Emulator of first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14, 630–632 (2002).
[CrossRef]

Willner, A. E.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, “Polarization mode dispersion emulator,” in Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 31–33.

Yariv, A.

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

Ann. Obser. Paris (1)

B. Lyot, “Recherches sur la polarisation de la lumière des planètes et de quelques substances terrestres,” Ann. Obser. Paris 8, 100–104 (1929).

Electron. Lett. (2)

A. Eyal, W. K. Marshall, M. Tur, A. Yariv, “Representation of second-order polarization mode dispersion,” Electron. Lett. 35, 1658–1659 (1999).
[CrossRef]

C. D. Poole, R. E. Wagner, “Phenomenological approach to the polarization mode dispersion,” Electron. Lett. 22, 1029–1039 (1986).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. Damask, G. Simer, K. Rochford, P. Myers, “Demonstration of a programmable PMD source,” IEEE Photon. Technol. Lett. 15, 296–298 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

J. H. Lee, M. S. Kim, Y. C. Chung, “Statistical PMD emulator using variable DGD elements,” IEEE Photon. Technol. Lett. 15, 54–56 (2003).
[CrossRef]

M. Wegmuller, S. Demma, C. Vinegoni, N. Gisin, “Emulator of first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14, 630–632 (2002).
[CrossRef]

B. L. Heffner, “Automated measurements of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

J. Lightwave Technol. (1)

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

J. Lightwave Technol. (2)

J. Opt. Soc. Am. (1)

B. H. Billings, “A monochromatic depolarizer,” J. Opt. Soc. Am. 41, 966–975 (1951).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Eng. (1)

R. A. Chipman, R. Kinnera, “A high-order polarization mode dispersion emulator,” Opt. Eng. 341, 932–937 (2002).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

J. P. Gordon, H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. USA 99, 4541–4550 (1999).

Other (4)

J. J. Drewes, R. A. Chipman, M. H. Smith, “Characterizing polarization controllers with Mueller matrix polarimetry,” in Active and Passive Optical Components for WDM Communication, A. K. Dutta, A. A. S. Awwal, N. K. Dutta, K. Okamoto, eds., Proc. SPIE4532, 462–466 (2001).
[CrossRef]

H. Lee, Y. C. Chung, “Statistical PMD emulator using variable DGD elements,” in Optical Fiber Communication Conference, Postconference Digest, Vol. 70 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2002), pp. 375–376.

J. N. Damask, “A programmable polarization-mode dispersion emulator for systematic testing of 10 Gb/s PMD compensators,” in Optical Fiber Communication Conference, Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 28–30.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, C. R. Menyuk, “Polarization mode dispersion emulator,” in Postconference Digest, Vol. 37 of OSA Trends in Optics and Photonics (Optical Society of America, 2000), pp. 31–33.

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Figures (11)

Fig. 1
Fig. 1

Broadband light wave passing through a birefringent crystal.

Fig. 2
Fig. 2

Single-stage delay line generating first-order PMD.

Fig. 3
Fig. 3

Two-stage PMD emulator used to generate first-order and SOPMD. PBS, polarizing beam splitter.

Fig. 4
Fig. 4

DGD versus second-order DGD for τ1 = 11 ps, τ2 = 9 ps, and 0° ≤ θ ≤ 45°.

Fig. 5
Fig. 5

DGD and SOPMD for 20,000 random configurations of the two-stage PMD emulator for (0 ps ≤ τ1 ≤ 60 ps, 0 ps ≤ τ2 ≤ 60 ps, and 0° ≤ θ ≤ 45°).

Fig. 6
Fig. 6

Depolarization rate and DGD as a function of the retarder orientation θ for four different sets of {τ1, τ2}, where θ = 45° is to the left and θ = 0° is on the right.

Fig. 7
Fig. 7

As the retarder’s fast axis (θ) is varied, the principal SOPs q 1(ω) of the emulator move around circles on the Poincaré sphere.

Fig. 8
Fig. 8

Evolution of the dq 1/dω with the position of the retarder’s fast axis (θ). The magnitude of the circle is proportional to the value of the SOPMD.

Fig. 9
Fig. 9

Path of the first-order PSP when the half-wave retarder is rotated.

Fig. 10
Fig. 10

First-order PSP [q 1(0° < θ < 45°)] of the two-stage PMD emulator as the half-wave retarder is rotated: (a) τ12 = 2, (b) τ12 = 1, (b) τ12 = 1, (c) τ12 = 0.5.

Fig. 11
Fig. 11

Path of the output PSP as the retarder is rotated where different arcs represent different values of τ2.

Equations (13)

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

ddωΔτq=qdΔτdω+Δτ dqdω.
Tω=100expiωτ2cos2θsin2θsin2θ-cos2θ×100expiωτ1,
=cos2θexpiωτ1sin2θexpiωτ2sin2θ-expiωτ1+τ2cos2θ,
Tω+ω0=cos2θexpiω+ω0τ2sin2θexpiω+ω0τ1sin2θ-expiω+ω0τ1+τ2cos(2θ.
M1=Tω+ω0ωω=0 T-1ω0.
|β1-β2|=-τ12+τ22+2τ1τ2 cos4θ1/2;
DGD=τ12+τ22+2τ1τ2 cos4θ1/2.
M2=2Tω+ω0ω2ω=0 T-1ω0-M12.
|β3-β4|=iτ1τ2 sin4θ,
SOPMD=τ1τ2 sin4θ.
θ=14cot-1DGD2-τ12+τ222 SOPMD,
0DGD2-τ12+τ222π SOPMD,
-DGD2τ12+τ222π SOPMD-DGD2

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