Abstract

The dependence of Brillouin linewidth and peak frequency on lightwave state of polarization (SOP) due to fiber inhomogeneity in single mode fiber (SMF) is investigated by using Brillouin optical time domain analysis (BOTDA) system. Theoretical analysis shows fiber inhomogeneity leads to fiber birefringence and sound velocity variation, both of which can cause the broadening and asymmetry of the Brillouin gain spectrum (BGS) and thus contribute to the variation of Brillouin linewidth and peak frequency with lightwave SOP. Due to fiber inhomogeneity both in lateral profile and longitudinal direction, the measured BGS is the superposition of several spectrum components with different peak frequencies within the interaction length. When pump or probe SOP changes, both the peak Brillouin gain and the overlapping area of the optical and acoustic mode profile that determine the peak efficiency of each spectrum component vary within the interaction length, which further changes the linewidth and peak frequency of the superimposed BGS. The SOP dependence of Brillouin linewidth and peak frequency was experimentally demonstrated and quantified by measuring the spectrum asymmetric factor and fitting obtained effective peak frequency respectively via BOTDA system on standard step-index SMF-28 fiber. Experimental results show that on this fiber the Brillouin spectrum asymmetric factor and effective peak frequency vary in the range of 2% and 0.06MHz respectively over distance with orthogonal probe input SOPs. Experimental results also show that in distributed fiber Brillouin sensing, polarization scrambler (PS) can be used to reduce the SOP dependence of Brillouin linewidth and peak frequency caused by fiber inhomogeneity in lateral profile, however it maintains the effects caused by fiber inhomogeneity in longitudinal direction. In the case of non-ideal polarization scrambling using practical PS, the fluctuation of effective Brillouin peak frequency caused by fiber inhomogeneity provides another limit of sensing frequency resolution of distributed fiber Brillouin sensor.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press 2007), Chap. 9.
  2. X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13(7), 1340–1348 (1995).
    [CrossRef]
  3. T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
    [CrossRef]
  4. M. Niklès, L. Thévenaz, and P. A. Robert, “Simple distributed fiber sensor based on Brillouin gain spectrum analysis,” Opt. Lett. 21(10), 758–760 (1996).
    [CrossRef] [PubMed]
  5. M. N. Alahbabi, Y. T. Cho, and T. P. Newson, “150-km-range distributed temperature sensor based on coherent detection of spontaneous Brillouin backscatter and in-line Raman amplification,” J. Opt. Soc. Am. B 22(6), 1321–1324 (2005).
    [CrossRef]
  6. B. Y. Zel’dovich and A. N. Pilipetskii, “Influence of sound diffraction on stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 16(4), 546–548 (1986).
    [CrossRef]
  7. B. Ya. Zel’dovich and A. N. Pilipetskii, “Role of a “soundguide” and “antisoundguide” in stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 18(6), 818–822 (1988).
    [CrossRef]
  8. N. Shibata, R. G. Waarts, and R. P. Braun, “Brillouin-gain spectra for single-mode fibers having pure-silica, GeO2-doped, and P2 05-doped cores,” Opt. Lett. 12(4), 269–271 (1987).
    [CrossRef] [PubMed]
  9. A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 2(1), 1–59 (2010).
    [CrossRef]
  10. M. Li and D. A. Nolan, “Optical transmission fiber design evolution,” J. Lightwave Technol. 26(9), 1079–1092 (2008).
    [CrossRef]
  11. A. Kobyakov, S. Kumar, D. Q. Chowdhury, A. B. Ruffin, M. Sauer, S. R. Bickham, and R. Mishra, “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 13(14), 5338–5346 (2005).
    [CrossRef] [PubMed]
  12. M. J. Li, X. Chen, J. Wang, S. Gray, A. Liu, J. A. Demeritt, A. B. Ruffin, A. M. Crowley, D. T. Walton, and L. A. Zenteno, “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15(13), 8290–8299 (2007).
    [CrossRef] [PubMed]
  13. A. H. McCurdy, “Modeling of stimulated Brillouin scattering in optical fibers with arbitrary radial index profile,” J. Lightwave Technol. 23(11), 3509–3516 (2005).
    [CrossRef]
  14. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” J. Lightwave Technol. 22(2), 631–639 (2004).
    [CrossRef]
  15. B. Ward and J. Spring, “Finite element analysis of Brillouin gain in SBS-suppressing optical fibers with non-uniform acoustic velocity profiles,” Opt. Express 17(18), 15685–15699 (2009).
    [CrossRef] [PubMed]
  16. M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
    [CrossRef]
  17. A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16(26), 21692–21707 (2008).
    [CrossRef] [PubMed]
  18. T. Gogolla and K. Krebber, “Distributed beat length measurement in single-mode optical fibers using Stimulated Brillouin-Scattering and Frequency-Domain Analysis,” J. Lightwave Technol. 18(3), 320–328 (2000).
    [CrossRef]
  19. J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
    [CrossRef] [PubMed]
  20. M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
    [CrossRef]
  21. F. Heismann, “Compact electro-optic polarization scramblers for optically amplified lightwave systems,” J. Lightwave Technol. 14(8), 1801–1814 (1996).
    [CrossRef]
  22. D. Waddy, L. Chen, and X. Bao, “State of polarization bias in aerial fibers,” Electron. Lett. 38(19), 1086–1087 (2002).
    [CrossRef]
  23. E. Lichtman, “Limitations imposed by polarization-dependent gain and loss on all-optical ultralong communication systems,” J. Lightwave Technol. 13(5), 906–913 (1995).
    [CrossRef]
  24. F. Bruyere and O. Audouin, “Penalties in long-haul optical amplifier systems due to polarization dependent loss and gain,” IEEE Photon. Technol. Lett. 6(5), 654–656 (1994).
    [CrossRef]
  25. N. S. Bergano and C. R. Davidson, “Polarizdtion-scrambling-induced timing jitter in optical-amplifier systems,” Conf. Opt. Fiber Commun. 8, 122–123 (1995).
  26. Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22(18), 1364–1366 (2010).
    [CrossRef]

2010 (2)

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22(18), 1364–1366 (2010).
[CrossRef]

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 2(1), 1–59 (2010).
[CrossRef]

2009 (1)

2008 (2)

2007 (1)

2005 (3)

2004 (1)

2002 (1)

D. Waddy, L. Chen, and X. Bao, “State of polarization bias in aerial fibers,” Electron. Lett. 38(19), 1086–1087 (2002).
[CrossRef]

2000 (2)

1996 (2)

F. Heismann, “Compact electro-optic polarization scramblers for optically amplified lightwave systems,” J. Lightwave Technol. 14(8), 1801–1814 (1996).
[CrossRef]

M. Niklès, L. Thévenaz, and P. A. Robert, “Simple distributed fiber sensor based on Brillouin gain spectrum analysis,” Opt. Lett. 21(10), 758–760 (1996).
[CrossRef] [PubMed]

1995 (3)

E. Lichtman, “Limitations imposed by polarization-dependent gain and loss on all-optical ultralong communication systems,” J. Lightwave Technol. 13(5), 906–913 (1995).
[CrossRef]

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13(7), 1340–1348 (1995).
[CrossRef]

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[CrossRef]

1994 (3)

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[CrossRef]

F. Bruyere and O. Audouin, “Penalties in long-haul optical amplifier systems due to polarization dependent loss and gain,” IEEE Photon. Technol. Lett. 6(5), 654–656 (1994).
[CrossRef]

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[CrossRef]

1988 (1)

B. Ya. Zel’dovich and A. N. Pilipetskii, “Role of a “soundguide” and “antisoundguide” in stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 18(6), 818–822 (1988).
[CrossRef]

1987 (1)

1986 (1)

B. Y. Zel’dovich and A. N. Pilipetskii, “Influence of sound diffraction on stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 16(4), 546–548 (1986).
[CrossRef]

Alahbabi, M. N.

Audouin, O.

F. Bruyere and O. Audouin, “Penalties in long-haul optical amplifier systems due to polarization dependent loss and gain,” IEEE Photon. Technol. Lett. 6(5), 654–656 (1994).
[CrossRef]

Bao, X.

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22(18), 1364–1366 (2010).
[CrossRef]

D. Waddy, L. Chen, and X. Bao, “State of polarization bias in aerial fibers,” Electron. Lett. 38(19), 1086–1087 (2002).
[CrossRef]

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13(7), 1340–1348 (1995).
[CrossRef]

Bickham, S. R.

Boot, A. J.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[CrossRef]

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[CrossRef]

Braun, R. P.

Bruyere, F.

F. Bruyere and O. Audouin, “Penalties in long-haul optical amplifier systems due to polarization dependent loss and gain,” IEEE Photon. Technol. Lett. 6(5), 654–656 (1994).
[CrossRef]

Chen, L.

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22(18), 1364–1366 (2010).
[CrossRef]

D. Waddy, L. Chen, and X. Bao, “State of polarization bias in aerial fibers,” Electron. Lett. 38(19), 1086–1087 (2002).
[CrossRef]

Chen, X.

Cho, Y. T.

Chowdhury, D.

Chowdhury, D. Q.

Chujo, W.

Crowley, A. M.

Demeritt, J. A.

Dhliwayo, J.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13(7), 1340–1348 (1995).
[CrossRef]

Dong, Y.

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22(18), 1364–1366 (2010).
[CrossRef]

Eyal, A.

Gogolla, T.

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

Gray, S.

Heismann, F.

F. Heismann, “Compact electro-optic polarization scramblers for optically amplified lightwave systems,” J. Lightwave Technol. 14(8), 1801–1814 (1996).
[CrossRef]

Heron, N.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13(7), 1340–1348 (1995).
[CrossRef]

Horiguchi, T.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[CrossRef]

Jackson, D. A.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13(7), 1340–1348 (1995).
[CrossRef]

Kobyakov, A.

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

Koyamada, Y.

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” J. Lightwave Technol. 22(2), 631–639 (2004).
[CrossRef]

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[CrossRef]

Krebber, K.

Kumar, S.

Kurashima, T.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[CrossRef]

Li, M.

Li, M. J.

Lichtman, E.

E. Lichtman, “Limitations imposed by polarization-dependent gain and loss on all-optical ultralong communication systems,” J. Lightwave Technol. 13(5), 906–913 (1995).
[CrossRef]

Liu, A.

McCurdy, A. H.

Mishra, R.

Nakamura, S.

Newson, T. P.

Niklès, M.

Nolan, D. A.

Pilipetskii, A. N.

B. Ya. Zel’dovich and A. N. Pilipetskii, “Role of a “soundguide” and “antisoundguide” in stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 18(6), 818–822 (1988).
[CrossRef]

B. Y. Zel’dovich and A. N. Pilipetskii, “Influence of sound diffraction on stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 16(4), 546–548 (1986).
[CrossRef]

Robert, P. A.

Ruffin, A. B.

Sato, S.

Sauer, M.

Shibata, N.

Shimizu, K.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[CrossRef]

Sotobayashi, H.

Spring, J.

Tateda, M.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[CrossRef]

Thévenaz, L.

Tur, M.

van Deventer, M. O.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[CrossRef]

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[CrossRef]

Waarts, R. G.

Waddy, D.

D. Waddy, L. Chen, and X. Bao, “State of polarization bias in aerial fibers,” Electron. Lett. 38(19), 1086–1087 (2002).
[CrossRef]

Walton, D. T.

Wang, J.

Ward, B.

Webb, D. J.

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13(7), 1340–1348 (1995).
[CrossRef]

Zadok, A.

Zel’dovich, B. Y.

B. Y. Zel’dovich and A. N. Pilipetskii, “Influence of sound diffraction on stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 16(4), 546–548 (1986).
[CrossRef]

Zel’dovich, B. Ya.

B. Ya. Zel’dovich and A. N. Pilipetskii, “Role of a “soundguide” and “antisoundguide” in stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 18(6), 818–822 (1988).
[CrossRef]

Zenteno, L. A.

Zilka, E.

Adv. Opt. Photon. (1)

Electron. Lett. (1)

D. Waddy, L. Chen, and X. Bao, “State of polarization bias in aerial fibers,” Electron. Lett. 38(19), 1086–1087 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

F. Bruyere and O. Audouin, “Penalties in long-haul optical amplifier systems due to polarization dependent loss and gain,” IEEE Photon. Technol. Lett. 6(5), 654–656 (1994).
[CrossRef]

Y. Dong, L. Chen, and X. Bao, “High-spatial-resolution time-domain simultaneous strain and temperature sensor using Brillouin scattering and birefringence in a polarization-maintaining fiber,” IEEE Photon. Technol. Lett. 22(18), 1364–1366 (2010).
[CrossRef]

J. Lightwave Technol. (10)

A. H. McCurdy, “Modeling of stimulated Brillouin scattering in optical fibers with arbitrary radial index profile,” J. Lightwave Technol. 23(11), 3509–3516 (2005).
[CrossRef]

M. Li and D. A. Nolan, “Optical transmission fiber design evolution,” J. Lightwave Technol. 26(9), 1079–1092 (2008).
[CrossRef]

E. Lichtman, “Limitations imposed by polarization-dependent gain and loss on all-optical ultralong communication systems,” J. Lightwave Technol. 13(5), 906–913 (1995).
[CrossRef]

T. Gogolla and K. Krebber, “Distributed beat length measurement in single-mode optical fibers using Stimulated Brillouin-Scattering and Frequency-Domain Analysis,” J. Lightwave Technol. 18(3), 320–328 (2000).
[CrossRef]

Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” J. Lightwave Technol. 22(2), 631–639 (2004).
[CrossRef]

X. Bao, J. Dhliwayo, N. Heron, D. J. Webb, and D. A. Jackson, “Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering,” J. Lightwave Technol. 13(7), 1340–1348 (1995).
[CrossRef]

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[CrossRef]

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[CrossRef]

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12(4), 585–590 (1994).
[CrossRef]

F. Heismann, “Compact electro-optic polarization scramblers for optically amplified lightwave systems,” J. Lightwave Technol. 14(8), 1801–1814 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (4)

Opt. Lett. (2)

Proc. Natl. Acad. Sci. U.S.A. (1)

J. P. Gordon and H. Kogelnik, “PMD fundamentals: polarization mode dispersion in optical fibers,” Proc. Natl. Acad. Sci. U.S.A. 97(9), 4541–4550 (2000).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (2)

B. Y. Zel’dovich and A. N. Pilipetskii, “Influence of sound diffraction on stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 16(4), 546–548 (1986).
[CrossRef]

B. Ya. Zel’dovich and A. N. Pilipetskii, “Role of a “soundguide” and “antisoundguide” in stimulated Brillouin scattering in a single-mode waveguide,” Sov. J. Quantum Electron. 18(6), 818–822 (1988).
[CrossRef]

Other (2)

N. S. Bergano and C. R. Davidson, “Polarizdtion-scrambling-induced timing jitter in optical-amplifier systems,” Conf. Opt. Fiber Commun. 8, 122–123 (1995).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press 2007), Chap. 9.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Illustration of the superimposed Brillouin spectrums with different AF values: (a) AF=1 (b) AF<1 (c) AF>1

Fig. 2
Fig. 2

Experimental setup

Fig. 3
Fig. 3

40 times’ repeat measurements of (a) AF and (b) ν B eff , and the averaged curves for the same probe input SOP

Fig. 4
Fig. 4

(a) AF curves for two orthogonal probe input SOPs measured in three days (b) | δAF | varies over distance (c) A F PS curves for the scrambled probe input SOP measured in three days (d) | δA F PS | varies over distance

Fig. 5
Fig. 5

(a) ν B eff curves for two orthogonal probe input SOPs measured in three days (b) | δ ν B eff | varies over distance (c) ν B( PS ) eff curves for the scrambled probe input SOP measured in three days (d) | δ ν B( PS ) eff | varies over distance

Fig. 6
Fig. 6

PDF of ν B eff (a) SOP1 (b) SOP2 (c) scrambled

Fig. 7
Fig. 7

| δ ν B( PS ) eff | max varies with scrambling frequency of PS3

Tables (2)

Tables Icon

Table 1 Measurement Uncertainties of AF and ν B eff

Tables Icon

Table 2 Statistical Parameters of ν B eff PDF of SOP1, SOP2 and Scrambled Case

Equations (19)

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

ν Bm = 2 n o eff V am eff λ p
δ ν Bm ν Bm = δ n o eff n o eff + δ V am eff V am eff
2 f( r,θ )+ k 2 ( ( n o mat ( r,θ ) ) 2 ( n o eff ) 2 )f( r,θ )=0
| E p (r,θ,z,t) = A px f px ( r,θ,z )exp[ i( 0 z k px ( u )du ω p t ) ]| x ^ p (z) + A py f py ( r,θ,z )exp[ i( 0 z k py ( u )du ω p t ) ]| y ^ p (z)
| E r (r,θ,z,t) = A rx f rx ( r,θ,z )exp[ i( L z k rx ( u )du ω r t ) ]| x ^ r (z) + A ry f ry ( r,θ,z )exp[ i( L z k ry ( u )du ω r t ) ]| y ^ r (z)
E r (r,θ,z,t) | E p (r,θ,z,t) = A px A rx * f px ( r,θ,z ) f rx * ( r,θ,z )exp[ i( 0 z [ k px ( u ) k rx ( u ) ]du ( ω p ω r )t+ 0 L k rx ( u )du ) ] x ^ r (z) | x ^ p (z) + A py A ry * f py ( r,θ,z ) f ry * ( r,θ,z )exp[ i( 0 z [ k py ( u ) k ry ( u ) ]du ( ω p ω r )t+ 0 L k ry ( u )du ) ] y ^ r (z) | y ^ p (z) + A px A ry * f px ( r,θ,z ) f ry * ( r,θ,z )exp[ i( 0 z [ k px ( u ) k ry ( u ) ]du ( ω p ω r )t+ 0 L k ry ( u )du ) ] y ^ r (z) | x ^ p (z) + A py A rx * f py ( r,θ,z ) f rx * ( r,θ,z )exp[ i( 0 z [ k py ( u ) k rx ( u ) ]du ( ω p ω r )t+ 0 L k rx ( u )du ) ] x ^ r (z) | y ^ p (z)
ν Bm( 1 ) ( z )= V am eff 2πc ( n o( px ) eff ( z ) ω p + n o( rx ) eff ( z ) ω r ) 2 V am eff λ p n o( px ) eff ( z ), n o( rx ) eff ( z ) = 2 V am eff λ p n o( 1 ) eff ( z )
ν Bm( 2 ) ( z )= V am eff 2πc ( n o( py ) eff ( z ) ω p + n o( ry ) eff ( z ) ω r ) 2 V am eff λ p n o( py ) eff ( z ), n o( ry ) eff ( z ) = 2 V am eff λ p n o( 2 ) eff ( z )
ν Bm( 3 ) ( z )= V am eff 2πc ( n o( px ) eff ( z ) ω p + n o( ry ) eff ( z ) ω r ) 2 V am eff λ p n o( px ) eff ( z ), n o( ry ) eff ( z ) = 2 V am eff λ p n o( 3 ) eff ( z )
ν Bm( 4 ) ( z )= V am eff 2πc ( n o( py ) eff ( z ) ω p + n o( rx ) eff ( z ) ω r ) 2 V am eff λ p n o( py ) eff ( z ), n o( rx ) eff ( z ) = 2 V am eff λ p n o( 4 ) eff ( z )
2 ξ m ( r,θ )+ q 2 ( ρ( r,θ ) ( V am eff ) 2 G( r,θ ) 1 ) ξ m ( r,θ )=0
S A ( ν,SOP )= ν Bmin ν Bmax γ B1 ( ν B ,SOP ) S( ν, ν B )d ν B
γ B m = g B m A m ao
A m ao = [ f 2 ξ m f 2 ] 2 ξ m 2
f( r,θ,z,SOP )= κ x (SOP) f x ( r,θ,z )+ κ y (SOP) f y ( r,θ,z )
AF= Δ ν Br Δ ν Bl
ν B eff (z,SOP) | W = 2 λ p z z+W [ j=1 4 ( α j (τ,SOP) n o( j ) eff (τ) ) ( η( τ,SOP ) V a1 eff ( τ ) ) ] dτ
ν B( PS ) eff (z) | W = 2 λ p z z+W [ j=1 4 ( α j (τ,SOP) SOP n o( j ) eff (τ) ) ( η( τ,SOP ) SOP V a1 eff ( τ ) ) ] dτ
= 2 λ p n ¯ o eff (z) V ¯ a1 eff (z)

Metrics