Abstract

Two parallel combinative long-period fiber gratings (LPFGs) can convert the fundamental core mode LP01 in a single-mode fiber (SMF) into one desired higher order core mode LP0m in a few-mode fiber (FMF), in the process of which one specific cladding mode acts as a medium coupled from one fiber to another. Different LP0m modes can be obtained by controlling the grating period of LPFG in FMF to meet the phase matching condition. In this article we focus on the design and analyses of LP02 and LP03 mode add / drop multiplexers (MADMs). This device has some advantages of facile and good scalability, and particularly, of eliminating coupling interferences for the ahead multiplexed modes by the posterior MADMs or couplers. Furthermore, the conversion rate of mode power theoretically can approach as much as98%and the 3dB bandwidth can reach 10nm or more.

© 2014 Optical Society of America

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References

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  1. Y. Kokubun, M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
    [CrossRef]
  2. N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. A. Li, X. Chen, A. A. Amin, W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013 (4)

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

N. Riesen, J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photon. Technol. Lett. 25(24), 2501–2504 (2013).
[CrossRef]

Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[CrossRef]

M. Z. Alam, J. Albert, “Selective excitation of radially and azimuthally polarized optical fiber cladding modes,” J. Lightwave Technol. 31(19), 3167–3175 (2013).
[CrossRef]

2012 (4)

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

N. Riesen, J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Quantum Electron. 48(7), 941–945 (2012).
[CrossRef]

J. D. Love, N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett. 37(19), 3990–3992 (2012).
[CrossRef] [PubMed]

A. Li, X. Chen, A. A. Amin, W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[CrossRef]

2011 (2)

2009 (1)

Y. Kokubun, M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[CrossRef]

2007 (2)

2005 (1)

F. Abrishamian, S. Sato, M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg gratings and its application to acoustically induced superstructure modulation,” Opt. Rev. 12(6), 467–471 (2005).
[CrossRef]

2004 (1)

2001 (1)

1997 (2)

Abrishamian, F.

F. Abrishamian, S. Sato, M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg gratings and its application to acoustically induced superstructure modulation,” Opt. Rev. 12(6), 467–471 (2005).
[CrossRef]

Ahmed, N.

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Al Amin, A.

Alam, M. Z.

Albert, J.

Amin, A. A.

A. Li, X. Chen, A. A. Amin, W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[CrossRef]

Astruc, M.

Bigo, S.

Birnbaum, K. M.

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Boutin, A.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Brindel, P.

Cerou, F.

Chan, F. Y. M.

Charlet, G.

Chen, X.

A. Li, X. Chen, A. A. Amin, W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[CrossRef]

A. Li, A. Al Amin, X. Chen, W. Shieh, “Transmission of 107-Gb/s mode and polarization multiplexed CO-OFDM signal over a two-mode fiber,” Opt. Express 19(9), 8808–8814 (2011).
[CrossRef] [PubMed]

Chiang, K. S.

Doliner, S.

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Erdogan, T.

Erkmen, B. I.

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Fu, S.

Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[CrossRef]

Han, W. T.

Huang, H.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Imai, M.

F. Abrishamian, S. Sato, M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg gratings and its application to acoustically induced superstructure modulation,” Opt. Rev. 12(6), 467–471 (2005).
[CrossRef]

Jung, Y. M.

Kim, B. H.

Kim, M. J.

Koebele, C.

Kokubun, Y.

Y. Kokubun, M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[CrossRef]

Koshiba, M.

Y. Kokubun, M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[CrossRef]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Lee, B. H.

Lee, K. S.

Li, A.

A. Li, X. Chen, A. A. Amin, W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[CrossRef]

A. Li, A. Al Amin, X. Chen, W. Shieh, “Transmission of 107-Gb/s mode and polarization multiplexed CO-OFDM signal over a two-mode fiber,” Opt. Express 19(9), 8808–8814 (2011).
[CrossRef] [PubMed]

Liu, D.

Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[CrossRef]

Liu, H.

Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[CrossRef]

Liu, Y.

Love, J. D.

N. Riesen, J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photon. Technol. Lett. 25(24), 2501–2504 (2013).
[CrossRef]

N. Riesen, J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Quantum Electron. 48(7), 941–945 (2012).
[CrossRef]

J. D. Love, N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett. 37(19), 3990–3992 (2012).
[CrossRef] [PubMed]

Mardoyan, H.

Ng, M. N.

Provost, L.

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Ran, Z. L.

Rao, Y. J.

Ren, Y.

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Ren, Y. X.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Riesen, N.

N. Riesen, J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photon. Technol. Lett. 25(24), 2501–2504 (2013).
[CrossRef]

J. D. Love, N. Riesen, “Mode-selective couplers for few-mode optical fiber networks,” Opt. Lett. 37(19), 3990–3992 (2012).
[CrossRef] [PubMed]

N. Riesen, J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Quantum Electron. 48(7), 941–945 (2012).
[CrossRef]

Salsi, M.

Sato, S.

F. Abrishamian, S. Sato, M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg gratings and its application to acoustically induced superstructure modulation,” Opt. Rev. 12(6), 467–471 (2005).
[CrossRef]

Shieh, W.

A. Li, X. Chen, A. A. Amin, W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[CrossRef]

A. Li, A. Al Amin, X. Chen, W. Shieh, “Transmission of 107-Gb/s mode and polarization multiplexed CO-OFDM signal over a two-mode fiber,” Opt. Express 19(9), 8808–8814 (2011).
[CrossRef] [PubMed]

Shum, P.

Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[CrossRef]

Sillard, P.

Sperti, D.

Tang, M.

Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[CrossRef]

Tran, P.

Tur, M.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Verluise, F.

Willner, A. E.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Xie, Y.

Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[CrossRef]

Yan, Y.

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Yang, J.

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Yue, Y.

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Zhang, H.

Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[CrossRef]

Zhang, L.

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

Zhu, T.

IEEE J. Quantum Electron. (1)

N. Riesen, J. D. Love, “Weakly-guiding mode-selective fiber couplers,” IEEE J. Quantum Electron. 48(7), 941–945 (2012).
[CrossRef]

IEEE Photon. J. (1)

Y. Yue, Y. Yan, N. Ahmed, N. Ahmed, J. Yang, L. Zhang, Y. Ren, H. Huang, K. M. Birnbaum, B. I. Erkmen, S. Doliner, M. Tur, A. E. Willner, “Mode properties and propagation effects of optical orbital angular momentum (OAM) modes in a ring fiber,” IEEE Photon. J. 4, 535–543 (2012).

IEEE Photon. Technol. Lett. (2)

A. Li, X. Chen, A. A. Amin, W. Shieh, “Fused fiber mode couplers for few-mode transmission,” IEEE Photon. Technol. Lett. 24(21), 1953–1956 (2012).
[CrossRef]

N. Riesen, J. D. Love, “Ultra-broadband tapered mode-selective couplers for few-mode optical fiber networks,” IEEE Photon. Technol. Lett. 25(24), 2501–2504 (2013).
[CrossRef]

IEICE Electron. Express (1)

Y. Kokubun, M. Koshiba, “Novel multi-core fibers for mode division multiplexing: proposal and design principle,” IEICE Electron. Express 6(8), 522–528 (2009).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. (1)

Y. Xie, S. Fu, H. Liu, H. Zhang, M. Tang, P. Shum, D. Liu, “Design and numerical optimization of a mode multiplexer based on few-mode fiber couplers,” J. Opt. 15(12), 125404 (2013).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Express (4)

Opt. Lett. (1)

Opt. Rev. (1)

F. Abrishamian, S. Sato, M. Imai, “A new method of solving multimode coupled equations for analysis of uniform and non-uniform fiber Bragg gratings and its application to acoustically induced superstructure modulation,” Opt. Rev. 12(6), 467–471 (2005).
[CrossRef]

Science (1)

N. Bozinovic, Y. Yue, Y. X. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[CrossRef] [PubMed]

Other (2)

K. Okamoto, Fundamentals of Optical Waveguides (Elsevier Academic Press, 2006), Chap. 3.

C. Tsao, Optical Fibre Waveguide Analysis (Oxford University, 1992), Part 3.

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Figures (7)

Fig. 1
Fig. 1

Diagram of MADM and mode conversion from the fundamental mode LP01 to cladding mode HE16 and then to HOMs LP02 and LP03, with their transverse electric field distributions shown from left to right and up to down.

Fig. 2
Fig. 2

Coupling coefficients for LP02 and LP03 to all cladding modes HE1m.

Fig. 3
Fig. 3

Cross section of parallel SMF and FMF, and coordinate transformation in two fibers.

Fig. 4
Fig. 4

Effective indexes of the cladding mode HE16 in SMF and FMF with fiber parameters listed in Table 1.

Fig. 5
Fig. 5

Radial electric field distributions of cladding mode HE16 with n 3 = 1.445 in FMF (solid line) and SMF (dotted line).

Fig. 6
Fig. 6

(a) Exchange relationship of mode power with coupling crosstalk from SMF to FMF. (b) Coupling efficiency of respective LPFG in SMF and FMF. (c) Total conversion ratio of MADMs for multiplexing LP02 and LP03 .

Fig. 7
Fig. 7

Connection diagram of multiplexing modes LP01, LP02 and LP03.

Tables (4)

Tables Icon

Table 1 Parameters of Two Fibers in MADM

Tables Icon

Table 2 Coupling coefficients and Coupling Lengths for Four Types of Polarization Coupling

Tables Icon

Table 3 Parameters of Device Components of MADMs

Tables Icon

Table 4 Effective Indexes of the Core Modes LP0m and Cladding Modes HE1m

Equations (4)

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

κ v u = 1 2 ω ε 0 n 1 2 δ ( z ) 0 2 π d ϕ 0 a 1 E v E u r d r ,
C 16 16 F S = 1 2 ω ε 0 [ ( n 1 2 n 3 2 ) 0 2 π d ϕ 0 a 1 E s u ( r , ϕ ) E c o ( r , ϕ ) r d r + ( n 2 2 n 3 2 ) 0 2 π d ϕ a 1 a 2 E s u ( r , ϕ ) E c l ( r , ϕ ) r d r ] ,
r = r 2 + d 2 + 2 r d cos ϕ ϕ = sin 1 ( r r sin ϕ ) ,
d A 1 dz = 1 2 j B 1 κ 1601 S exp[ j( β 01 S β 16 S 2π Λ S )z ] d B 1 dz +j β 16 S B 1 =j C 1616 FS B 2 +j C 5616 FS B 3 +j C 6516 FS B 4 + 1 2 j A 1 κ 0116 S exp[ j( β 01 S β 16 S 2π Λ S )z ], d B 3 dz +j β 56 F B 3 =j C 1656 SF B 1 d B 4 dz +j β 65 F B 4 =j C 1665 SF B 1 d B 2 dz +j β 16 F B 2 =j C 1616 SF B 1 + 1 2 j A i κ 0i16 F exp[ j( β 0i F β 16 F 2π Λ i F )z ] d A i dz = 1 2 j B 2 κ 160i F exp[ j( β 0i F β 16 F 2π Λ i F )z ]

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