Abstract

A novel technique is proposed for measuring the longitudinal fiber parameters of multi-core fiber (MCF). The mode field diameter (MFD)of a fiber link composed of MCF is successfully estimated with a modified optical time domain reflectometer (OTDR). The measurement accuracy of the MFD distribution is revealed by simulation as a function of the mode coupling coefficient. It is also shown that the relative-index difference and chromatic dispersion of MCF can be estimated with the present technique.

© 2014 Optical Society of America

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References

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  1. T. Morioka, “New generation optical infrastructure technologies: EXAT initiative: toward 2020 and beyond,” in Proc. OECC2009, paper FT4(2009).
    [Crossref]
  2. R. Kashyap and K. J. Blow, “Observation of catastrophic self-propelled self-focusing in optical fibres,” Electron. Lett. 24(1), 47–49 (1988).
    [Crossref]
  3. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
    [Crossref]
  4. P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express 19(17), 16680–16696 (2011).
    [Crossref] [PubMed]
  5. M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
    [Crossref]
  6. ITU-T Recommendation G.650.1.
  7. M. S. O’Sullivan and J. Ferner, “Interpretation of SM fiber OTDR signatures,” Proc. SPIE 86(661), 171–176 (1986).
    [Crossref]
  8. M. Ohashi and M. Tateda, “Novel technique for measuring longitudinal chromatic dispersion distribution in single-mode fibres,” Electron. Lett. 29(5), 426–427 (1993).
    [Crossref]
  9. K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution measurement along a single-mode optical fiber,” J. Lightwave Technol. 15(7), 1095–1101 (1997).
    [Crossref]
  10. A. Rossaro, M. Schiano, T. Tambosso, and D. D’Alessandro, “Spatially resolved chromatic dispersion measurement by a bidirectional OTDR technique,” IEEE J. Sel. Top. Quantum Electron. 7(3), 475–483 (2001).
    [Crossref]
  11. M. Ohashi, “Novel technique for measuring relative-index difference of fiber links,” IEEE Photon. Technol. Lett. 18(24), 2584–2586 (2006).
    [Crossref]
  12. M. Wuilpart, G. Ravet, P. Megret, and M. Blondel, “Distributed measurement of Raman gain spectrum in concatenations of optical fibres with OTDR,” Electron. Lett. 39(1), 88–89 (2003).
    [Crossref]
  13. K. Toge, K. Hogari, and T. Horiguchi, “Raman gain efficiency distribution measurement in single-mode optical fibers by using backscattering technique,” IEEE Photon. Technol. Lett. 17(8), 1704–1706 (2005).
    [Crossref]
  14. Y. Tsutsumi and M. Ohashi, “Indirect technique for measuring Raman gain efficiency spectrum using OTDR,” IEICEJ95-B(2), 146–154 (2012) (in Japanese).
  15. K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun., E-94-B(2), 409–416 (2011).
  16. M. Ohashi, K. Kawazu, A. Nakamura, and Y. Miyoshi, “Simple backscattered power technique for measuring crosstalk of multi-core fibers,” in Proc. OECC2012, 357–358 (2012).
    [Crossref]
  17. N. Shibata, M. Kawachi, and T. Edahiro, “Optical loss characteristics of high-GeO2 content silica fibers,” IEICE Trans. E63(12), 837–841 (1980).
  18. C. Pask, “Physical interpretation of Petermann’s strange spot size for single-mode fibres,” Electron. Lett. 20(3), 144–145 (1984).
    [Crossref]
  19. D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56(5), 703–718 (1977).
    [Crossref]
  20. M. Nakazawa, M. Yoshida, and T. Hirooka, “Nondestructive measurement of mode couplings along a multi-core fiber using a synchronous multi-channel OTDR,” Opt. Express 20(11), 12530–12540 (2012).
    [Crossref] [PubMed]
  21. E. P. Patent, 0982577–A1, “ Device for measuring crosstalk between multicore optical fibres,” (1999).

2012 (1)

2011 (2)

P. J. Winzer and G. J. Foschini, “MIMO capacities and outage probabilities in spatially multiplexed optical transport systems,” Opt. Express 19(17), 16680–16696 (2011).
[Crossref] [PubMed]

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun., E-94-B(2), 409–416 (2011).

2010 (1)

2009 (1)

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[Crossref]

2006 (1)

M. Ohashi, “Novel technique for measuring relative-index difference of fiber links,” IEEE Photon. Technol. Lett. 18(24), 2584–2586 (2006).
[Crossref]

2005 (1)

K. Toge, K. Hogari, and T. Horiguchi, “Raman gain efficiency distribution measurement in single-mode optical fibers by using backscattering technique,” IEEE Photon. Technol. Lett. 17(8), 1704–1706 (2005).
[Crossref]

2003 (1)

M. Wuilpart, G. Ravet, P. Megret, and M. Blondel, “Distributed measurement of Raman gain spectrum in concatenations of optical fibres with OTDR,” Electron. Lett. 39(1), 88–89 (2003).
[Crossref]

2001 (1)

A. Rossaro, M. Schiano, T. Tambosso, and D. D’Alessandro, “Spatially resolved chromatic dispersion measurement by a bidirectional OTDR technique,” IEEE J. Sel. Top. Quantum Electron. 7(3), 475–483 (2001).
[Crossref]

1997 (1)

K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution measurement along a single-mode optical fiber,” J. Lightwave Technol. 15(7), 1095–1101 (1997).
[Crossref]

1993 (1)

M. Ohashi and M. Tateda, “Novel technique for measuring longitudinal chromatic dispersion distribution in single-mode fibres,” Electron. Lett. 29(5), 426–427 (1993).
[Crossref]

1988 (1)

R. Kashyap and K. J. Blow, “Observation of catastrophic self-propelled self-focusing in optical fibres,” Electron. Lett. 24(1), 47–49 (1988).
[Crossref]

1986 (1)

M. S. O’Sullivan and J. Ferner, “Interpretation of SM fiber OTDR signatures,” Proc. SPIE 86(661), 171–176 (1986).
[Crossref]

1984 (1)

C. Pask, “Physical interpretation of Petermann’s strange spot size for single-mode fibres,” Electron. Lett. 20(3), 144–145 (1984).
[Crossref]

1980 (1)

N. Shibata, M. Kawachi, and T. Edahiro, “Optical loss characteristics of high-GeO2 content silica fibers,” IEICE Trans. E63(12), 837–841 (1980).

1977 (1)

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56(5), 703–718 (1977).
[Crossref]

Arakawa, Y.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun., E-94-B(2), 409–416 (2011).

Blondel, M.

M. Wuilpart, G. Ravet, P. Megret, and M. Blondel, “Distributed measurement of Raman gain spectrum in concatenations of optical fibres with OTDR,” Electron. Lett. 39(1), 88–89 (2003).
[Crossref]

Blow, K. J.

R. Kashyap and K. J. Blow, “Observation of catastrophic self-propelled self-focusing in optical fibres,” Electron. Lett. 24(1), 47–49 (1988).
[Crossref]

D’Alessandro, D.

A. Rossaro, M. Schiano, T. Tambosso, and D. D’Alessandro, “Spatially resolved chromatic dispersion measurement by a bidirectional OTDR technique,” IEEE J. Sel. Top. Quantum Electron. 7(3), 475–483 (2001).
[Crossref]

Edahiro, T.

N. Shibata, M. Kawachi, and T. Edahiro, “Optical loss characteristics of high-GeO2 content silica fibers,” IEICE Trans. E63(12), 837–841 (1980).

Essiambre, R.-J.

Ferner, J.

M. S. O’Sullivan and J. Ferner, “Interpretation of SM fiber OTDR signatures,” Proc. SPIE 86(661), 171–176 (1986).
[Crossref]

Foschini, G. J.

Goebel, B.

Guan, N.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun., E-94-B(2), 409–416 (2011).

Hirooka, T.

Hogari, K.

K. Toge, K. Hogari, and T. Horiguchi, “Raman gain efficiency distribution measurement in single-mode optical fibers by using backscattering technique,” IEEE Photon. Technol. Lett. 17(8), 1704–1706 (2005).
[Crossref]

Horiguchi, T.

K. Toge, K. Hogari, and T. Horiguchi, “Raman gain efficiency distribution measurement in single-mode optical fibers by using backscattering technique,” IEEE Photon. Technol. Lett. 17(8), 1704–1706 (2005).
[Crossref]

Kashyap, R.

R. Kashyap and K. J. Blow, “Observation of catastrophic self-propelled self-focusing in optical fibres,” Electron. Lett. 24(1), 47–49 (1988).
[Crossref]

Kawachi, M.

N. Shibata, M. Kawachi, and T. Edahiro, “Optical loss characteristics of high-GeO2 content silica fibers,” IEICE Trans. E63(12), 837–841 (1980).

Kokubun, Y.

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[Crossref]

Koshiba, M.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun., E-94-B(2), 409–416 (2011).

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[Crossref]

Kramer, G.

Marcuse, D.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56(5), 703–718 (1977).
[Crossref]

Matsuo, S.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun., E-94-B(2), 409–416 (2011).

Megret, P.

M. Wuilpart, G. Ravet, P. Megret, and M. Blondel, “Distributed measurement of Raman gain spectrum in concatenations of optical fibres with OTDR,” Electron. Lett. 39(1), 88–89 (2003).
[Crossref]

Nakajima, K.

K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution measurement along a single-mode optical fiber,” J. Lightwave Technol. 15(7), 1095–1101 (1997).
[Crossref]

Nakazawa, M.

O’Sullivan, M. S.

M. S. O’Sullivan and J. Ferner, “Interpretation of SM fiber OTDR signatures,” Proc. SPIE 86(661), 171–176 (1986).
[Crossref]

Ohashi, M.

M. Ohashi, “Novel technique for measuring relative-index difference of fiber links,” IEEE Photon. Technol. Lett. 18(24), 2584–2586 (2006).
[Crossref]

K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution measurement along a single-mode optical fiber,” J. Lightwave Technol. 15(7), 1095–1101 (1997).
[Crossref]

M. Ohashi and M. Tateda, “Novel technique for measuring longitudinal chromatic dispersion distribution in single-mode fibres,” Electron. Lett. 29(5), 426–427 (1993).
[Crossref]

Y. Tsutsumi and M. Ohashi, “Indirect technique for measuring Raman gain efficiency spectrum using OTDR,” IEICEJ95-B(2), 146–154 (2012) (in Japanese).

Pask, C.

C. Pask, “Physical interpretation of Petermann’s strange spot size for single-mode fibres,” Electron. Lett. 20(3), 144–145 (1984).
[Crossref]

Ravet, G.

M. Wuilpart, G. Ravet, P. Megret, and M. Blondel, “Distributed measurement of Raman gain spectrum in concatenations of optical fibres with OTDR,” Electron. Lett. 39(1), 88–89 (2003).
[Crossref]

Rossaro, A.

A. Rossaro, M. Schiano, T. Tambosso, and D. D’Alessandro, “Spatially resolved chromatic dispersion measurement by a bidirectional OTDR technique,” IEEE J. Sel. Top. Quantum Electron. 7(3), 475–483 (2001).
[Crossref]

Saitoh, K.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun., E-94-B(2), 409–416 (2011).

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[Crossref]

Schiano, M.

A. Rossaro, M. Schiano, T. Tambosso, and D. D’Alessandro, “Spatially resolved chromatic dispersion measurement by a bidirectional OTDR technique,” IEEE J. Sel. Top. Quantum Electron. 7(3), 475–483 (2001).
[Crossref]

Shibata, N.

N. Shibata, M. Kawachi, and T. Edahiro, “Optical loss characteristics of high-GeO2 content silica fibers,” IEICE Trans. E63(12), 837–841 (1980).

Takenaga, K.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun., E-94-B(2), 409–416 (2011).

Tambosso, T.

A. Rossaro, M. Schiano, T. Tambosso, and D. D’Alessandro, “Spatially resolved chromatic dispersion measurement by a bidirectional OTDR technique,” IEEE J. Sel. Top. Quantum Electron. 7(3), 475–483 (2001).
[Crossref]

Tanigawa, S.

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun., E-94-B(2), 409–416 (2011).

Tateda, M.

K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution measurement along a single-mode optical fiber,” J. Lightwave Technol. 15(7), 1095–1101 (1997).
[Crossref]

M. Ohashi and M. Tateda, “Novel technique for measuring longitudinal chromatic dispersion distribution in single-mode fibres,” Electron. Lett. 29(5), 426–427 (1993).
[Crossref]

Toge, K.

K. Toge, K. Hogari, and T. Horiguchi, “Raman gain efficiency distribution measurement in single-mode optical fibers by using backscattering technique,” IEEE Photon. Technol. Lett. 17(8), 1704–1706 (2005).
[Crossref]

Tsutsumi, Y.

Y. Tsutsumi and M. Ohashi, “Indirect technique for measuring Raman gain efficiency spectrum using OTDR,” IEICEJ95-B(2), 146–154 (2012) (in Japanese).

Winzer, P. J.

Wuilpart, M.

M. Wuilpart, G. Ravet, P. Megret, and M. Blondel, “Distributed measurement of Raman gain spectrum in concatenations of optical fibres with OTDR,” Electron. Lett. 39(1), 88–89 (2003).
[Crossref]

Yoshida, M.

Bell Syst. Tech. J. (1)

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56(5), 703–718 (1977).
[Crossref]

Electron. Lett. (4)

R. Kashyap and K. J. Blow, “Observation of catastrophic self-propelled self-focusing in optical fibres,” Electron. Lett. 24(1), 47–49 (1988).
[Crossref]

M. Ohashi and M. Tateda, “Novel technique for measuring longitudinal chromatic dispersion distribution in single-mode fibres,” Electron. Lett. 29(5), 426–427 (1993).
[Crossref]

M. Wuilpart, G. Ravet, P. Megret, and M. Blondel, “Distributed measurement of Raman gain spectrum in concatenations of optical fibres with OTDR,” Electron. Lett. 39(1), 88–89 (2003).
[Crossref]

C. Pask, “Physical interpretation of Petermann’s strange spot size for single-mode fibres,” Electron. Lett. 20(3), 144–145 (1984).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Rossaro, M. Schiano, T. Tambosso, and D. D’Alessandro, “Spatially resolved chromatic dispersion measurement by a bidirectional OTDR technique,” IEEE J. Sel. Top. Quantum Electron. 7(3), 475–483 (2001).
[Crossref]

IEEE Photon. Technol. Lett. (2)

M. Ohashi, “Novel technique for measuring relative-index difference of fiber links,” IEEE Photon. Technol. Lett. 18(24), 2584–2586 (2006).
[Crossref]

K. Toge, K. Hogari, and T. Horiguchi, “Raman gain efficiency distribution measurement in single-mode optical fibers by using backscattering technique,” IEEE Photon. Technol. Lett. 17(8), 1704–1706 (2005).
[Crossref]

IEICE Electron. Express (1)

M. Koshiba, K. Saitoh, and Y. Kokubun, “Heterogeneous multi-core fibers: proposal and design principle,” IEICE Electron. Express 6(2), 98–103 (2009).
[Crossref]

IEICE Trans. (1)

N. Shibata, M. Kawachi, and T. Edahiro, “Optical loss characteristics of high-GeO2 content silica fibers,” IEICE Trans. E63(12), 837–841 (1980).

IEICE Trans. Commun., (1)

K. Takenaga, Y. Arakawa, S. Tanigawa, N. Guan, S. Matsuo, K. Saitoh, and M. Koshiba, “An investigation on crosstalk in multi-core fibers by introducing random fluctuation along longitudinal direction,” IEICE Trans. Commun., E-94-B(2), 409–416 (2011).

J. Lightwave Technol. (2)

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
[Crossref]

K. Nakajima, M. Ohashi, and M. Tateda, “Chromatic dispersion distribution measurement along a single-mode optical fiber,” J. Lightwave Technol. 15(7), 1095–1101 (1997).
[Crossref]

Opt. Express (2)

Proc. SPIE (1)

M. S. O’Sullivan and J. Ferner, “Interpretation of SM fiber OTDR signatures,” Proc. SPIE 86(661), 171–176 (1986).
[Crossref]

Other (5)

T. Morioka, “New generation optical infrastructure technologies: EXAT initiative: toward 2020 and beyond,” in Proc. OECC2009, paper FT4(2009).
[Crossref]

ITU-T Recommendation G.650.1.

M. Ohashi, K. Kawazu, A. Nakamura, and Y. Miyoshi, “Simple backscattered power technique for measuring crosstalk of multi-core fibers,” in Proc. OECC2012, 357–358 (2012).
[Crossref]

Y. Tsutsumi and M. Ohashi, “Indirect technique for measuring Raman gain efficiency spectrum using OTDR,” IEICEJ95-B(2), 146–154 (2012) (in Japanese).

E. P. Patent, 0982577–A1, “ Device for measuring crosstalk between multicore optical fibres,” (1999).

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Figures (13)

Fig. 1
Fig. 1 Experimental setup for measuring MFD.
Fig. 2
Fig. 2 Relationship between fiber length and relative error Δε of the MFD as a function of mode coupling coefficient h.
Fig. 3
Fig. 3 Relationship between the mode coupling coefficient h and maximum relative error Δε of the MFD as a function of fiber length.
Fig. 4
Fig. 4 Relationship between g value and relative error Δε of the h as a function of crosstalk between center and outer cores.
Fig. 5
Fig. 5 Experimental setup for measuring crosstalk using modified OTDR.
Fig. 6
Fig. 6 Bidirectional backscattered powers of fiber link at (a) 1.31 μm and (b) 1.55 μm.
Fig. 7
Fig. 7 Backscattered powers of center and outer cores in MCF when an optical pulse was launched into the center core. (a) 1.31 μm, and (b) 1.55 μm.
Fig. 8
Fig. 8 Crosstalk between cores at λ = 1.31 and 1.55 μm.
Fig. 9
Fig. 9 Relationship between fiber length and average h at 1.55 μm.
Fig. 10
Fig. 10 Imperfection loss contribution U(z)of fiber link at 1.55 μm.
Fig. 11
Fig. 11 MFD distribution of test fiber link at λ = 1.55 μm.
Fig. 12
Fig. 12 Relative-index difference Δ (%) distribution of fiber link.
Fig. 13
Fig. 13 Chromatic dispersion distribution of fiber link at 1.55 μm.

Tables (2)

Tables Icon

Table 1 Parameters of Test MCF and Reference Fibers used in calculations

Tables Icon

Table 2 Parameters of Test MCF and Reference Fibers

Equations (23)

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

P 1 (z)= P 0 (0)[ 1+6exp(7hz) 7 ]
P 2 (z)= P 0 (0)[ 1exp(7hz) 7 ]
S 1 (z)={ 10log P 1 +10log( α s (z))+10log(B(z))2αz10loge(0z L 0 ) 10log P 1 +10log( α s (z))+10log(B(z))2αz10loge +10log[ 1+6exp[ 14h(z L 0 ) ] 7 ]( L 0 +Lz L 0 ) ,
S 2 (z)={ 10log P 2 +10log( α s (z))+10log(B(z))2α( L+ L 0 z )10loge +10log[ 1+6exp[ 14hL ] 7 ](0z L 0 ) 10log P 2 +10log( α s (z))+10log(B(z))2α( L+ L 0 z )10loge +10log[ 1+6exp[ 14h(L+ L 0 z) ] 7 ]( L 0 +Lz L 0 ) ,
U(z)=5log P 1 P 2 +10log( α s (z)B(z))2α(L+ L 0 )(10loge) ={ S 1 (z)+ S 2 (z) 2 5log[ 1+6exp[ 14hL ] 7 ](0z L 0 ) S 1 (z)+ S 2 (z) 2 5log{ [ 1+6exp[ 14h(z L 0 ) ] ][ 1+6exp[ 14h(L+ L 0 z) ] ] 49 } ( L 0 z L 0 +L) .
B(λ,z)= 3 2 log [ λ 2πnw(λ,z) ] 2 .
U n (z)=U(z)U( z 0 )=10log( α s (z) n 2 ( z 0 ) α s ( z 0 ) n 2 (z) )+20log( 2w(λ, z 0 ) 2w(λ,z) ).
2w(λ,z)=2w(λ, z 0 ) ( 2w(λ, z 0 ) 2w(λ, z 1 ) ) U(z)U( z 0 ) U( z 1 )U( z 0 ) .
S 3 (z)=10log P 3 +10log( α s1 B 1 )2 α 1 z(10loge)+10log[ 1+6exp(14hz) 7 ],
S 4 (z)=10log P 3 +10log( α s2 B 2 )2 α 2 z(10loge)+10log[ 1exp(14hz) 7 ],
XT(z)=10log[ P 4 (z) P 3 (z) ]=10log[ 1exp(14hz) 1+6exp(14hz) ].
Δ(z)= 1 k [ ( 1+kΔ( z 0 ) )× 10 U(λ,z)U(λ, z 0 )20log( 2w(λ, z 0 ) 2w(λ,z) ) 10 1 ],
D= D m +D , w
D m = λ c d 2 n d λ 2 ,
D w = λ 2 π 2 cn d dλ ( λ w 2 ),
w(λ)= g 0 + g 1 λ 1.5 .
D w = λ 2 π 2 cn w 2 ( 1 3 g 1 λ 1.5 w ).
I(z)={ U(z)+5log[ 1+6exp[ 14hL ] 7 ](0z L 0 ) U(z)+5log{ [ 1+6exp[ 14h(z l 0 ) ] ][ 1+6exp[ 14h(L+ l 0 z) ] ] 49 } ( L 0 z L 0 +L) .
Δε= 2w(λ,z)2 w * (λ,z) 2w(λ,z) =1 2 w * (λ,z) 2w(λ,z) =1 ( 2w(λ, z 0 ) 2w(λ, z 1 ) ) F(λ,z,h) U( z 1 )U( z 0 ) , F(λ,z,h)=5log [ 1+6exp(14h( z L 0 ) ][ 1+6exp(14h( L+ L 0 z ) ] 7[ 1+6exp(4hL) ] .
U n ( z 1 )=U( z 1 )U( z 0 )=10log[ { 1+kΔ( z 1 ) }{ 12Δ( z 0 ) } { 1+kΔ( z 0 ) }{ 12Δ( z 1 ) } ]+20log[ 2w(λ, z 0 ) 2w(λ, z 1 ) ]
XT(z)= S 4 (z) S 3 (z) =10log( α s2 B 2 α s1 B 1 )+2( α 1 α 2 )z(10loge)+10log[ 1exp(14hz) 1+6exp(14hz) ].
XT(z)=g(z,λ, Δ 1 , Δ 2 , w 1 , w 2 )+10log[ 1exp(14hz) 1+6exp(14hz) ] g(z,λ, Δ 1 , Δ 2 , w 1 , w 2 )=10log[ (1+k Δ 2 ) (1+k Δ 1 ) ]+10log[ n 1 2 w 1 2 n 2 2 w 2 2 ]+ R 0 k λ 4 ( Δ 1 Δ 2 )2z(10loge).
Δε= h ex h ap h ex == ln[ 1 10 XTg 10 1 10 XT 10 1+6 10 XT 10 1+6 10 XTg 10 ] ln[ 1 10 XTg 10 1+6 10 XTg 10 ] .

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