Abstract

This paper proposes using power transfer matrix analysis to characterize the effects of Rayleigh backscattering and Fresnel reflection on WDM-PON systems. The modeling of a WDM-PON system can be carried out simply by matrix multiplication of the corresponding matrices for all the building blocks, where all possible guided backward lights and resonant configurations along the optical network can be accounted for. The total sum of all interferences affecting the bidirectional transmission that leads to an optical crosstalk-to-signal (C/S) ratio can be modeled as back-reflections through cascaded two-port networks for the downstream and upstream signals. This approach is simple, robust, efficient, and also accurate. Its accuracy is verified for simple system architectures and then applied to study more complicated cases. The results show its versatility to analyze a wide variety of bidirectional optical transmission systems.

© 2013 Optical Society of America

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References

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  1. Y. Khan, C. X. Yu, X. J. Xin, A. Ali, A. Husain, and B. Liu, “Rayleigh backscattering minimization on single-fiber colorless WDM-PON using intensity remodulation technique,” Optoelectron. Lett.8(5), 380–383 (2012).
    [CrossRef]
  2. U. H. Hong, K. Y. Cho, Y. Takushima, and Y. C. Chung, “Maximum reach of long-reach RSOA-based WDM-PON employing remote EDFA,” in Proceedings of Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC, Los Angeles, California, 2011), Paper OMP1.
    [CrossRef]
  3. U. H. Hong, K. Y. Cho, Y. Takushima, and Y. C. Chung, “Effects of Rayleigh backscattering in long-reach RSOA-based WDM-PON,” in Proceedings of Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC, San Diego, California, 2010), Paper OThG1.
    [CrossRef]
  4. E. T. Lopez, J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Optimization of Rayleigh-limited WDM-PONs with reflective ONU by MUX positioning and optimal ONU gain,” IEEE Photon. Technol. Lett.22(2), 97–99 (2010).
    [CrossRef]
  5. C. Arellano, K. D. Langer, and J. Prat, “Reflections and multiple Rayleigh backscattering in WDM single-fiber loopback access networks,” J. Lightwave Technol.27(1), 12–18 (2009).
    [CrossRef]
  6. H. H. Lin, C. Y. Lee, S. C. Lin, S. L. Lee, and G. Keiser, “WDM-PON systems using cross-remodulation to double network capacity with reduced Rayleigh scattering effects,” in Proceedings of Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC, San Diego, California, 2008), Paper OTuH6.
    [CrossRef]
  7. C. W. Chow and C. H. Yeh, “Mitigation of Rayleigh backscattering in 10-Gb/s downstream and 2.5-Gb/s upstream DWDM 100-km long-reach PONs,” Opt. Express19(6), 4970–4976 (2011).
    [CrossRef] [PubMed]
  8. J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Rayleigh scattering reduction by means of optical frequency dithering in passive optical networks with remotely seeded ONUs,” IEEE Photon. Technol. Lett.19(1), 64–66 (2007).
    [CrossRef]
  9. J. Ko, S. Kim, J. Lee, S. Won, Y. S. Kim, and J. Jeong, “Estimation of performance degradation of bidirectional WDM transmission systems due to Rayleigh backscattering and ASE noises using numerical and analytical models,” J. Lightwave Technol.21(4), 938–946 (2003).
    [CrossRef]
  10. S. C. Lin, J. Y. Huang, S. L. Lee, G. Keiser, S. C. Ko, and T. W. Liaw, “WDM-PON with 10 Gb/s bidirectional transmission using cross-remodulation and dual-wavelength lasers,” in Proceedings of the 14th OptoElectronics and Communications Conference (OECC, Hongkong, China, 2009), Paper TuH5.
    [CrossRef]
  11. T. T. Pham, H. S. Kim, Y. Y. Won, and S. K. Han, “Colorless WDM-PON based on a Fabry-Pérot laser diode and reflective semiconductor optical amplifiers for simultaneous transmission of bidirectional gigabit baseband signals and broadcasting signal,” Opt. Express17(19), 16571–16580 (2009).
    [CrossRef] [PubMed]
  12. E. K. MacHale, G. Talli, P. D. Townsend, A. Borghesani, I. Lealman, D. G. Moodie, and D. W. Smith, “Extended-reach PON employing 10Gb/s integrated reflective EAM-SOA,” in Proceedings of 34h European Conference and Exhibition on Optical Communication (ECOC, Brussels, Belgium, 2008), Paper Th.2.F.1.
  13. Z. Xu, Y. J. Wen, W. D. Zhong, C. J. Chae, X. F. Cheng, Y. Wang, C. Lu, and J. Shankar, “High-speed WDM-PON using CW injection-locked Fabry-Pérot laser diodes,” Opt. Express15(6), 2953–2962 (2007).
    [CrossRef] [PubMed]
  14. G. Talli, C. W. Chow, and P. D. Townsend, “Modeling of modulation formats for interferometric noise mitigation,” J. Lightwave Technol.26(17), 3190–3198 (2008).
    [CrossRef]
  15. G. Talli, C. W. Chow, E. K. MacHale, and P. D. Townsend, “Rayleigh noise mitigation in long-reach hybrid DWDM-TDM PONs,” J. Opt. Netw.6(6), 765–776 (2007).
    [CrossRef]
  16. S. C. Lin, S. L. Lee, H. H. Lin, G. Keiser, and R. J. Ram, “Cross-seeding schemes for WDM-based next-generation optical access networks,” J. Lightwave Technol.29(24), 3727–3736 (2011).
    [CrossRef]
  17. S. Gao, H. Hu, and H. Anis, “Impact of backreflections on single-fiber bidirectional transmission in WDM-PONs,” J. Opt. Commun. Netw.3(10), 797–805 (2011).
    [CrossRef]
  18. W. Y. Hong, N. G. Qiang, G. Pan, and G. Kun, “Theoretical analysis on coherent noise by Rayleigh backscattering,” in Proceedings of IEEE International Forum on Information Technology and Applications (IFITA, Chengdu, China, 2009).
  19. K. Y. Cho, Y. J. Lee, H. Y. Choi, A. Murakami, A. Agata, Y. Takushima, and Y. C. Chung, “Effects of reflection in RSOA-based WDM-PON utilizing remodulation technique,” J. Lightwave Technol.27(10), 1286–1295 (2009).
    [CrossRef]
  20. J. H. Moon, K. M. Choi, S. G. Mun, and C. H. Lee, “Effects of back-reflection in WDM-PONs based on seed light injection,” IEEE Photon. Technol. Lett.19(24), 2045–2047 (2007).
    [CrossRef]
  21. M. Fujiwara, J. Kani, H. Suzuki, and K. Iwatsuki, “Impact of backreflection on upstream transmission in WDM single-fiber loopback access networks,” J. Lightwave Technol.24(2), 740–746 (2006).
    [CrossRef]
  22. B. Lannoo, G. Das, M. De Groote, D. Colle, M. Pickavet, and P. Demeester, “Techno-economic feasibility study of different WDM/TDM PON architectures, “ in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON, Munich, Germany, 2010), Paper Mo.C4.3.
    [CrossRef]
  23. H. Song, B. W. Kim, and B. Mukherjee, “Long-reach optical access networks: a survey of research challenges, demonstrations, and bandwidth assignment mechanisms,” IEEE Comm. Surveys Tutorials.12(1), 112–123 (2010).
    [CrossRef]
  24. J. Kani, “Enabling technologies for future scalable and flexible WDM-PON and WDM/TDM-PON systems,” IEEE J. Sel. Top. Quantum Electron.16(5), 1290–1297 (2010).
    [CrossRef]
  25. L. A. Coldren, S. W. Corzine, and M. L. Masanovic, Diode Lasers and Photonic Integrated Circuits 2nd Ed. (John Wiley & Sons, Inc., 2012).

2012 (1)

Y. Khan, C. X. Yu, X. J. Xin, A. Ali, A. Husain, and B. Liu, “Rayleigh backscattering minimization on single-fiber colorless WDM-PON using intensity remodulation technique,” Optoelectron. Lett.8(5), 380–383 (2012).
[CrossRef]

2011 (3)

2010 (3)

E. T. Lopez, J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Optimization of Rayleigh-limited WDM-PONs with reflective ONU by MUX positioning and optimal ONU gain,” IEEE Photon. Technol. Lett.22(2), 97–99 (2010).
[CrossRef]

H. Song, B. W. Kim, and B. Mukherjee, “Long-reach optical access networks: a survey of research challenges, demonstrations, and bandwidth assignment mechanisms,” IEEE Comm. Surveys Tutorials.12(1), 112–123 (2010).
[CrossRef]

J. Kani, “Enabling technologies for future scalable and flexible WDM-PON and WDM/TDM-PON systems,” IEEE J. Sel. Top. Quantum Electron.16(5), 1290–1297 (2010).
[CrossRef]

2009 (3)

2008 (1)

2007 (4)

Z. Xu, Y. J. Wen, W. D. Zhong, C. J. Chae, X. F. Cheng, Y. Wang, C. Lu, and J. Shankar, “High-speed WDM-PON using CW injection-locked Fabry-Pérot laser diodes,” Opt. Express15(6), 2953–2962 (2007).
[CrossRef] [PubMed]

G. Talli, C. W. Chow, E. K. MacHale, and P. D. Townsend, “Rayleigh noise mitigation in long-reach hybrid DWDM-TDM PONs,” J. Opt. Netw.6(6), 765–776 (2007).
[CrossRef]

J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Rayleigh scattering reduction by means of optical frequency dithering in passive optical networks with remotely seeded ONUs,” IEEE Photon. Technol. Lett.19(1), 64–66 (2007).
[CrossRef]

J. H. Moon, K. M. Choi, S. G. Mun, and C. H. Lee, “Effects of back-reflection in WDM-PONs based on seed light injection,” IEEE Photon. Technol. Lett.19(24), 2045–2047 (2007).
[CrossRef]

2006 (1)

2003 (1)

Agata, A.

Ali, A.

Y. Khan, C. X. Yu, X. J. Xin, A. Ali, A. Husain, and B. Liu, “Rayleigh backscattering minimization on single-fiber colorless WDM-PON using intensity remodulation technique,” Optoelectron. Lett.8(5), 380–383 (2012).
[CrossRef]

Anis, H.

Arellano, C.

E. T. Lopez, J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Optimization of Rayleigh-limited WDM-PONs with reflective ONU by MUX positioning and optimal ONU gain,” IEEE Photon. Technol. Lett.22(2), 97–99 (2010).
[CrossRef]

C. Arellano, K. D. Langer, and J. Prat, “Reflections and multiple Rayleigh backscattering in WDM single-fiber loopback access networks,” J. Lightwave Technol.27(1), 12–18 (2009).
[CrossRef]

J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Rayleigh scattering reduction by means of optical frequency dithering in passive optical networks with remotely seeded ONUs,” IEEE Photon. Technol. Lett.19(1), 64–66 (2007).
[CrossRef]

Chae, C. J.

Cheng, X. F.

Cho, K. Y.

Choi, H. Y.

Choi, K. M.

J. H. Moon, K. M. Choi, S. G. Mun, and C. H. Lee, “Effects of back-reflection in WDM-PONs based on seed light injection,” IEEE Photon. Technol. Lett.19(24), 2045–2047 (2007).
[CrossRef]

Chow, C. W.

Chung, Y. C.

Fujiwara, M.

Gao, S.

Han, S. K.

Hu, H.

Husain, A.

Y. Khan, C. X. Yu, X. J. Xin, A. Ali, A. Husain, and B. Liu, “Rayleigh backscattering minimization on single-fiber colorless WDM-PON using intensity remodulation technique,” Optoelectron. Lett.8(5), 380–383 (2012).
[CrossRef]

Iwatsuki, K.

Jeong, J.

Kani, J.

J. Kani, “Enabling technologies for future scalable and flexible WDM-PON and WDM/TDM-PON systems,” IEEE J. Sel. Top. Quantum Electron.16(5), 1290–1297 (2010).
[CrossRef]

M. Fujiwara, J. Kani, H. Suzuki, and K. Iwatsuki, “Impact of backreflection on upstream transmission in WDM single-fiber loopback access networks,” J. Lightwave Technol.24(2), 740–746 (2006).
[CrossRef]

Keiser, G.

Khan, Y.

Y. Khan, C. X. Yu, X. J. Xin, A. Ali, A. Husain, and B. Liu, “Rayleigh backscattering minimization on single-fiber colorless WDM-PON using intensity remodulation technique,” Optoelectron. Lett.8(5), 380–383 (2012).
[CrossRef]

Kim, B. W.

H. Song, B. W. Kim, and B. Mukherjee, “Long-reach optical access networks: a survey of research challenges, demonstrations, and bandwidth assignment mechanisms,” IEEE Comm. Surveys Tutorials.12(1), 112–123 (2010).
[CrossRef]

Kim, H. S.

Kim, S.

Kim, Y. S.

Ko, J.

Langer, K. D.

Lazaro, J. A.

E. T. Lopez, J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Optimization of Rayleigh-limited WDM-PONs with reflective ONU by MUX positioning and optimal ONU gain,” IEEE Photon. Technol. Lett.22(2), 97–99 (2010).
[CrossRef]

J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Rayleigh scattering reduction by means of optical frequency dithering in passive optical networks with remotely seeded ONUs,” IEEE Photon. Technol. Lett.19(1), 64–66 (2007).
[CrossRef]

Lee, C. H.

J. H. Moon, K. M. Choi, S. G. Mun, and C. H. Lee, “Effects of back-reflection in WDM-PONs based on seed light injection,” IEEE Photon. Technol. Lett.19(24), 2045–2047 (2007).
[CrossRef]

Lee, J.

Lee, S. L.

Lee, Y. J.

Lin, H. H.

Lin, S. C.

Liu, B.

Y. Khan, C. X. Yu, X. J. Xin, A. Ali, A. Husain, and B. Liu, “Rayleigh backscattering minimization on single-fiber colorless WDM-PON using intensity remodulation technique,” Optoelectron. Lett.8(5), 380–383 (2012).
[CrossRef]

Lopez, E. T.

E. T. Lopez, J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Optimization of Rayleigh-limited WDM-PONs with reflective ONU by MUX positioning and optimal ONU gain,” IEEE Photon. Technol. Lett.22(2), 97–99 (2010).
[CrossRef]

Lu, C.

MacHale, E. K.

Moon, J. H.

J. H. Moon, K. M. Choi, S. G. Mun, and C. H. Lee, “Effects of back-reflection in WDM-PONs based on seed light injection,” IEEE Photon. Technol. Lett.19(24), 2045–2047 (2007).
[CrossRef]

Mukherjee, B.

H. Song, B. W. Kim, and B. Mukherjee, “Long-reach optical access networks: a survey of research challenges, demonstrations, and bandwidth assignment mechanisms,” IEEE Comm. Surveys Tutorials.12(1), 112–123 (2010).
[CrossRef]

Mun, S. G.

J. H. Moon, K. M. Choi, S. G. Mun, and C. H. Lee, “Effects of back-reflection in WDM-PONs based on seed light injection,” IEEE Photon. Technol. Lett.19(24), 2045–2047 (2007).
[CrossRef]

Murakami, A.

Pham, T. T.

Polo, V.

E. T. Lopez, J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Optimization of Rayleigh-limited WDM-PONs with reflective ONU by MUX positioning and optimal ONU gain,” IEEE Photon. Technol. Lett.22(2), 97–99 (2010).
[CrossRef]

J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Rayleigh scattering reduction by means of optical frequency dithering in passive optical networks with remotely seeded ONUs,” IEEE Photon. Technol. Lett.19(1), 64–66 (2007).
[CrossRef]

Prat, J.

E. T. Lopez, J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Optimization of Rayleigh-limited WDM-PONs with reflective ONU by MUX positioning and optimal ONU gain,” IEEE Photon. Technol. Lett.22(2), 97–99 (2010).
[CrossRef]

C. Arellano, K. D. Langer, and J. Prat, “Reflections and multiple Rayleigh backscattering in WDM single-fiber loopback access networks,” J. Lightwave Technol.27(1), 12–18 (2009).
[CrossRef]

J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Rayleigh scattering reduction by means of optical frequency dithering in passive optical networks with remotely seeded ONUs,” IEEE Photon. Technol. Lett.19(1), 64–66 (2007).
[CrossRef]

Ram, R. J.

Shankar, J.

Song, H.

H. Song, B. W. Kim, and B. Mukherjee, “Long-reach optical access networks: a survey of research challenges, demonstrations, and bandwidth assignment mechanisms,” IEEE Comm. Surveys Tutorials.12(1), 112–123 (2010).
[CrossRef]

Suzuki, H.

Takushima, Y.

Talli, G.

Townsend, P. D.

Wang, Y.

Wen, Y. J.

Won, S.

Won, Y. Y.

Xin, X. J.

Y. Khan, C. X. Yu, X. J. Xin, A. Ali, A. Husain, and B. Liu, “Rayleigh backscattering minimization on single-fiber colorless WDM-PON using intensity remodulation technique,” Optoelectron. Lett.8(5), 380–383 (2012).
[CrossRef]

Xu, Z.

Yeh, C. H.

Yu, C. X.

Y. Khan, C. X. Yu, X. J. Xin, A. Ali, A. Husain, and B. Liu, “Rayleigh backscattering minimization on single-fiber colorless WDM-PON using intensity remodulation technique,” Optoelectron. Lett.8(5), 380–383 (2012).
[CrossRef]

Zhong, W. D.

IEEE Comm. Surveys Tutorials. (1)

H. Song, B. W. Kim, and B. Mukherjee, “Long-reach optical access networks: a survey of research challenges, demonstrations, and bandwidth assignment mechanisms,” IEEE Comm. Surveys Tutorials.12(1), 112–123 (2010).
[CrossRef]

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

J. Kani, “Enabling technologies for future scalable and flexible WDM-PON and WDM/TDM-PON systems,” IEEE J. Sel. Top. Quantum Electron.16(5), 1290–1297 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

E. T. Lopez, J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Optimization of Rayleigh-limited WDM-PONs with reflective ONU by MUX positioning and optimal ONU gain,” IEEE Photon. Technol. Lett.22(2), 97–99 (2010).
[CrossRef]

J. A. Lazaro, C. Arellano, V. Polo, and J. Prat, “Rayleigh scattering reduction by means of optical frequency dithering in passive optical networks with remotely seeded ONUs,” IEEE Photon. Technol. Lett.19(1), 64–66 (2007).
[CrossRef]

J. H. Moon, K. M. Choi, S. G. Mun, and C. H. Lee, “Effects of back-reflection in WDM-PONs based on seed light injection,” IEEE Photon. Technol. Lett.19(24), 2045–2047 (2007).
[CrossRef]

J. Lightwave Technol. (6)

J. Opt. Commun. Netw. (1)

J. Opt. Netw. (1)

Opt. Express (3)

Optoelectron. Lett. (1)

Y. Khan, C. X. Yu, X. J. Xin, A. Ali, A. Husain, and B. Liu, “Rayleigh backscattering minimization on single-fiber colorless WDM-PON using intensity remodulation technique,” Optoelectron. Lett.8(5), 380–383 (2012).
[CrossRef]

Other (8)

U. H. Hong, K. Y. Cho, Y. Takushima, and Y. C. Chung, “Maximum reach of long-reach RSOA-based WDM-PON employing remote EDFA,” in Proceedings of Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC, Los Angeles, California, 2011), Paper OMP1.
[CrossRef]

U. H. Hong, K. Y. Cho, Y. Takushima, and Y. C. Chung, “Effects of Rayleigh backscattering in long-reach RSOA-based WDM-PON,” in Proceedings of Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC, San Diego, California, 2010), Paper OThG1.
[CrossRef]

H. H. Lin, C. Y. Lee, S. C. Lin, S. L. Lee, and G. Keiser, “WDM-PON systems using cross-remodulation to double network capacity with reduced Rayleigh scattering effects,” in Proceedings of Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC, San Diego, California, 2008), Paper OTuH6.
[CrossRef]

S. C. Lin, J. Y. Huang, S. L. Lee, G. Keiser, S. C. Ko, and T. W. Liaw, “WDM-PON with 10 Gb/s bidirectional transmission using cross-remodulation and dual-wavelength lasers,” in Proceedings of the 14th OptoElectronics and Communications Conference (OECC, Hongkong, China, 2009), Paper TuH5.
[CrossRef]

E. K. MacHale, G. Talli, P. D. Townsend, A. Borghesani, I. Lealman, D. G. Moodie, and D. W. Smith, “Extended-reach PON employing 10Gb/s integrated reflective EAM-SOA,” in Proceedings of 34h European Conference and Exhibition on Optical Communication (ECOC, Brussels, Belgium, 2008), Paper Th.2.F.1.

W. Y. Hong, N. G. Qiang, G. Pan, and G. Kun, “Theoretical analysis on coherent noise by Rayleigh backscattering,” in Proceedings of IEEE International Forum on Information Technology and Applications (IFITA, Chengdu, China, 2009).

B. Lannoo, G. Das, M. De Groote, D. Colle, M. Pickavet, and P. Demeester, “Techno-economic feasibility study of different WDM/TDM PON architectures, “ in Proceedings of 12th International Conference on Transparent Optical Networks (ICTON, Munich, Germany, 2010), Paper Mo.C4.3.
[CrossRef]

L. A. Coldren, S. W. Corzine, and M. L. Masanovic, Diode Lasers and Photonic Integrated Circuits 2nd Ed. (John Wiley & Sons, Inc., 2012).

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Figures (11)

Fig. 1
Fig. 1

Mechanism of a loop-back type basic WDM-PON system with Rayleigh backscattering (RBf,d) and Fresnel reflection (Rf,d) events for single-fiber transmission.

Fig. 2
Fig. 2

Typical model of a single transfer matrix with input and output powers.

Fig. 3
Fig. 3

Building blocks of a loop-back type WDM-PON showing all RB interferences that affecting the upstream transmission.

Fig. 4
Fig. 4

T-matrix model for the upstream scenario of a WDM-PON system with the loop-back scheme.

Fig. 5
Fig. 5

Model for (a) an optical discontinuity and (b) feeder or drop fiber section in WDM-PON systems.

Fig. 6
Fig. 6

(a) Model for passive (insertion loss) or active (optical gain) components; (b) Reflective ONU is modified to obtain the transmissive ONU.

Fig. 7
Fig. 7

Upstream C/S ratio as a function of ONU gain for different values of link loss and reflections when B = 0 The curves appear overlapped and the insert figure shows the observed architecture.

Fig. 8
Fig. 8

C/S ratio as a function of ONU gain for different values of link loss and reflections situated at the ONU (ld = 1).

Fig. 9
Fig. 9

C/S ratio versus RN position for different ONU gain of a basic WDM-PON when considering (a) RB only and (b) both RB and FR. The data is calculated by T-matrix and (a) Eq. (15) and (b) effective reflection.

Fig. 10
Fig. 10

Long-reach hybrid WDM/TDM-PON system that can serve thousands of users.

Fig. 11
Fig. 11

C/S ratio versus RN-1 locations for different combinations of OA-1 and ONU gains in the loop-back scheme, and different OA-1 gains when a tunable laser is used to transmit the upstream signals.

Tables (1)

Tables Icon

Table 1 Transfer matrices for WDM-PON components.

Equations (18)

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

[ A 1 B 1 ]=[ T 11 T 12 T 21 T 22 ][ A 2 B 2 ].
[ P S P BRUL ]= T u [ P R 0 ]=[ T u11 T u12 T u21 T u22 ][ P R 0 ].
[ P S 0 ]= T u * [ P R0 0 ]=[ T u11 * T u12 * T u21 * T u22 * ][ P R0 0 ],
( C S ) u = P BRUL P R0 = T u11 * ( T u21 T u11 ).
( C S ) u T u21 .
[ P T P BR1 ]= T dn [ P Rdn 0 ]=[ T dn11 T dn12 T dn21 T dn22 ][ P Rdn 0 ],
( C S ) d =( P Rdn P Rdn0 P Rdn0 )=( T dn11 * T dn11 1 ),
T FR = 1 Γ [ 1 R R Γ 2 R 2 ];Γ=1R.
T g = 1 l f [ 1 γ f γ f l f 2 ] 1 l RN [ 1 0 0 l RN 2 ] 1 l d [ 1 γ d γ d l d 2 ] 1 G ONU [ 1 0 0 G ONU 2 ].
T g = 1 G ONU l f l RN l d [ T A T B T C T D ],
T A =1 l RN 2 γ f γ d 1 T B = G ONU 2 [ l RN 2 l d 2 γ f γ d ] T C = γ f + l f 2 l RN 2 γ d T D = G ONU 2 [ l f 2 l RN 2 l d 2 γ f γ d ] G ONU 2 l f 2 l RN 2 l d 2
T h = 1 l d [ 1 γ d γ d l d 2 ] 1 l RN [ 1 0 0 l RN 2 ] 1 l f [ 1 γ f γ f l f 2 ]= 1 l f l RN l d [ T P T Q T R T S ],
T P =1 l RN 2 γ f γ d 1 T Q = l RN 2 l d 2 γ f γ f T R = γ d + l RN 2 l d 2 γ f T S = l f 2 l RN 2 l d 2 γ f γ d l f 2 l RN 2 l d 2
T u11 M[ 1 G ONU 2 ( γ d + γ f l RN 2 l d 2 ) 2 ]M= T u11 * ,
M= 1 G ONU l f 2 l RN 2 l d 2 .
( C S ) u T u 21 =M( T C T P + T D T R ).
( C S ) u = 1 G ONU l f 2 l RN 2 l d 2 [ γ f + l f 2 l RN 2 γ d + G ONU 2 ( l f 2 l RN 4 l d 4 γ f + l f 2 l RN 2 l d 2 γ d ) ] = γ f G ONU l f 2 l RN 2 l d 2 + γ d G ONU l d 2 + G ONU γ f l RN 2 l d 2 + G ONU γ d
( C S ) u = γ t G ONU l t 2 + R G ONU l d 2 + (1R)R[ γ d + G ONU ] 1R l d 2 G ONU + γ t G ONU 1 γ t G ONU + γ f R,

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