Abstract

A practical scheme to perform the fast Fourier transform in the optical domain is introduced. Optical real-time FFT signal processing is performed at speeds far beyond the limits of electronic digital processing, and with negligible energy consumption. To illustrate the power of the method we demonstrate an optical 400 Gbit/s OFDM receiver. It performs an optical real-time FFT on the consolidated OFDM data stream, thereby demultiplexing the signal into lower bit rate subcarrier tributaries, which can then be processed electronically.

© 2010 OSA

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References

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  1. M. E. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett. 12(1), 63–65 (1987).
    [CrossRef] [PubMed]
  2. K. B. Howell, Principles of Fourier Analysis (CRC Press, 2001).
  3. J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19(90), 297–301 (1965).
    [CrossRef]
  4. A. E. Siegman, “Fiber Fourier optics,” Opt. Lett. 26(16), 1215–1217 (2001).
    [CrossRef]
  5. A. E. Siegman, “Fiber Fourier optics: previous publication,” Opt. Lett. 27(6), 381 (2002).
    [CrossRef]
  6. S. Kodama, T. Ito, N. Watanabe, S. Kondo, H. Takeuchi, H. Ito, and T. Ishibashi, “2.3 picoseconds optical gate monolithically integrating photodiode and electroabsorption modulator,” Electron. Lett. 37(19), 1185–1186 (2001).
    [CrossRef]
  7. H. Sanjoh, E. Yamada, and Y. Yoshikuni, “Optical orthogonal frequency division multiplexing using frequency/time domain filtering for high spectral efficiency up to 1 bit/s/Hz,” in Proceedings of Optical Fiber Communication Conference and Exhibit, (Optical Society of America, 2002), paper ThD1.
  8. C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley-Interscience, 1999).
  9. B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, and B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
    [CrossRef]
  10. N. Takato, K. Jinguji, M. Yasu, H. Toba, and M. Kawachi, “Silica-based single-mode waveguides on silicon and their application to guided-wave optical interferometers,” J. Lightwave Technol. 6(6), 1003–1010 (1988).
    [CrossRef]
  11. S. Suzuki, Y. Inoue, and T. Kominato, “High-density integrated 1×16 optical FDM multi/demultiplexer,” in Proceedings of Lasers and Electro-Optics Society Annual Meeting (IEEE, 1994), pp. 263–264.
  12. N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm," IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990).
    [CrossRef]
  13. K. Takiguchi, M. Oguma, T. Shibata, and H. Takahashi, “Demultiplexer for optical orthogonal frequency-division multiplexing using an optical fast-Fourier-transform circuit,” Opt. Lett. 34(12), 1828–1830 (2009).
    [CrossRef] [PubMed]
  14. A. J. Lowery, L. B. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol. 25(1), 131–138 (2007).
    [CrossRef]
  15. A. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14(6), 2079–2084 (2006).
    [CrossRef] [PubMed]
  16. W. Shieh and I. Djordjevic, OFDM for Optical Communications (Academic Press, 2010).
  17. J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009).
    [CrossRef]
  18. R. P. Giddings, X. Q. Jin, and J. M. Tang, “First experimental demonstration of 6Gb/s real-time optical OFDM transceivers incorporating channel estimation and variable power loading,” Opt. Express 17(22), 19727–19738 (2009).
    [CrossRef] [PubMed]
  19. Q. Yang, S. Chen, Y. Ma, and W. Shieh, “Real-time reception of multi-gigabit coherent optical OFDM signals,” Opt. Express 17(10), 7985–7992 (2009).
    [CrossRef] [PubMed]
  20. Y. Benlachtar, P. M. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. C. Hoe, M. Püschel, M. Glick, and R. I. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17(20), 17658–17668 (2009).
    [CrossRef] [PubMed]
  21. H. C. Hansen Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010).
    [CrossRef] [PubMed]
  22. E. Yamada, A. Sano, H. Masuda, T. Kobayashi, E. Yoshida, Y. Miyamoto, Y. Hibino, K. Ishihara, Y. Takatori, K. Okada, K. Hagimoto, T. Yamada, and H. Yamazaki, “Novel no-guard-interval PDM CO-OFDM transmission in 4.1 Tb/s (50 × 88.8-Gb/s) DWDM link over 800 km SMF including 50-Ghz spaced ROADM nodes,” in Proceedings of Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference (Optical Society of America, 2008), paper PDP8.
  23. S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” in Proceedings of European Conference on Optical Communication (IEEE, 2009), paper PD2.6.
  24. A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. 17(2), 504–506 (2005).
    [CrossRef]
  25. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009).
    [CrossRef] [PubMed]
  26. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
    [CrossRef] [PubMed]
  27. T. Kobayashi, A. Sano, E. Yamada, Y. Miyamoto, H. Takara, and A. Takada, “Electro-optically multiplexed 110 Gbit/s optical OFDM signal transmission over 80 km SMF without dispersion compensation,” Electron. Lett. 44(3), 225–226 (2008).
    [CrossRef]
  28. D. Hillerkuss, A. Marculescu, J. Li, M. Teschke, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Novel optical fast Fourier transform scheme enabling real-time OFDM processing at 392 Gbit/s and beyond,” in Proceedings of Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper OWW3.

2010

2009

2008

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
[CrossRef] [PubMed]

T. Kobayashi, A. Sano, E. Yamada, Y. Miyamoto, H. Takara, and A. Takada, “Electro-optically multiplexed 110 Gbit/s optical OFDM signal transmission over 80 km SMF without dispersion compensation,” Electron. Lett. 44(3), 225–226 (2008).
[CrossRef]

2007

2006

2005

A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. 17(2), 504–506 (2005).
[CrossRef]

2002

2001

S. Kodama, T. Ito, N. Watanabe, S. Kondo, H. Takeuchi, H. Ito, and T. Ishibashi, “2.3 picoseconds optical gate monolithically integrating photodiode and electroabsorption modulator,” Electron. Lett. 37(19), 1185–1186 (2001).
[CrossRef]

A. E. Siegman, “Fiber Fourier optics,” Opt. Lett. 26(16), 1215–1217 (2001).
[CrossRef]

1990

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm," IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990).
[CrossRef]

1988

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, and B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

N. Takato, K. Jinguji, M. Yasu, H. Toba, and M. Kawachi, “Silica-based single-mode waveguides on silicon and their application to guided-wave optical interferometers,” J. Lightwave Technol. 6(6), 1003–1010 (1988).
[CrossRef]

1987

1965

J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19(90), 297–301 (1965).
[CrossRef]

Armstrong, J.

Bao, H.

Benlachtar, Y.

Bouziane, R.

Cartolano, A.

Chen, S.

Clausen, A. T.

Cooley, J. W.

J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19(90), 297–301 (1965).
[CrossRef]

Du, L. B.

Ellis, A. D.

A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. 17(2), 504–506 (2005).
[CrossRef]

Galili, M.

Giddings, R. P.

Glick, M.

Gunning, F. C. G.

A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. 17(2), 504–506 (2005).
[CrossRef]

Hansen Mulvad, H. C.

Henry, C. H.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, and B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Hoe, J. C.

Hu, H.

Ishibashi, T.

S. Kodama, T. Ito, N. Watanabe, S. Kondo, H. Takeuchi, H. Ito, and T. Ishibashi, “2.3 picoseconds optical gate monolithically integrating photodiode and electroabsorption modulator,” Electron. Lett. 37(19), 1185–1186 (2001).
[CrossRef]

Ito, H.

S. Kodama, T. Ito, N. Watanabe, S. Kondo, H. Takeuchi, H. Ito, and T. Ishibashi, “2.3 picoseconds optical gate monolithically integrating photodiode and electroabsorption modulator,” Electron. Lett. 37(19), 1185–1186 (2001).
[CrossRef]

Ito, T.

S. Kodama, T. Ito, N. Watanabe, S. Kondo, H. Takeuchi, H. Ito, and T. Ishibashi, “2.3 picoseconds optical gate monolithically integrating photodiode and electroabsorption modulator,” Electron. Lett. 37(19), 1185–1186 (2001).
[CrossRef]

Jensen, J. B.

Jeppesen, P.

Jin, X. Q.

Jinguji, K.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm," IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990).
[CrossRef]

N. Takato, K. Jinguji, M. Yasu, H. Toba, and M. Kawachi, “Silica-based single-mode waveguides on silicon and their application to guided-wave optical interferometers,” J. Lightwave Technol. 6(6), 1003–1010 (1988).
[CrossRef]

Johnson, B. H.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, and B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Kawachi, M.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm," IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990).
[CrossRef]

N. Takato, K. Jinguji, M. Yasu, H. Toba, and M. Kawachi, “Silica-based single-mode waveguides on silicon and their application to guided-wave optical interferometers,” J. Lightwave Technol. 6(6), 1003–1010 (1988).
[CrossRef]

Kazarinov, R. F.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, and B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Killey, R. I.

Kobayashi, T.

T. Kobayashi, A. Sano, E. Yamada, Y. Miyamoto, H. Takara, and A. Takada, “Electro-optically multiplexed 110 Gbit/s optical OFDM signal transmission over 80 km SMF without dispersion compensation,” Electron. Lett. 44(3), 225–226 (2008).
[CrossRef]

Kodama, S.

S. Kodama, T. Ito, N. Watanabe, S. Kondo, H. Takeuchi, H. Ito, and T. Ishibashi, “2.3 picoseconds optical gate monolithically integrating photodiode and electroabsorption modulator,” Electron. Lett. 37(19), 1185–1186 (2001).
[CrossRef]

Kominato, T.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm," IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990).
[CrossRef]

Kondo, S.

S. Kodama, T. Ito, N. Watanabe, S. Kondo, H. Takeuchi, H. Ito, and T. Ishibashi, “2.3 picoseconds optical gate monolithically integrating photodiode and electroabsorption modulator,” Electron. Lett. 37(19), 1185–1186 (2001).
[CrossRef]

Koutsoyannis, R.

Lowery, A.

Lowery, A. J.

Ma, Y.

Marhic, M. E.

Milder, P.

Miyamoto, Y.

T. Kobayashi, A. Sano, E. Yamada, Y. Miyamoto, H. Takara, and A. Takada, “Electro-optically multiplexed 110 Gbit/s optical OFDM signal transmission over 80 km SMF without dispersion compensation,” Electron. Lett. 44(3), 225–226 (2008).
[CrossRef]

Oguma, M.

Olsson, N. A.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, and B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Orlowsky, K. J.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, and B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Oxenløwe, L. K.

Peucheret, C.

Püschel, M.

Rangaraj, D.

Sano, A.

T. Kobayashi, A. Sano, E. Yamada, Y. Miyamoto, H. Takara, and A. Takada, “Electro-optically multiplexed 110 Gbit/s optical OFDM signal transmission over 80 km SMF without dispersion compensation,” Electron. Lett. 44(3), 225–226 (2008).
[CrossRef]

Shibata, T.

Shieh, W.

Siegman, A. E.

Sugita, A.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm," IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990).
[CrossRef]

Takada, A.

T. Kobayashi, A. Sano, E. Yamada, Y. Miyamoto, H. Takara, and A. Takada, “Electro-optically multiplexed 110 Gbit/s optical OFDM signal transmission over 80 km SMF without dispersion compensation,” Electron. Lett. 44(3), 225–226 (2008).
[CrossRef]

Takahashi, H.

Takara, H.

T. Kobayashi, A. Sano, E. Yamada, Y. Miyamoto, H. Takara, and A. Takada, “Electro-optically multiplexed 110 Gbit/s optical OFDM signal transmission over 80 km SMF without dispersion compensation,” Electron. Lett. 44(3), 225–226 (2008).
[CrossRef]

Takato, N.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm," IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990).
[CrossRef]

N. Takato, K. Jinguji, M. Yasu, H. Toba, and M. Kawachi, “Silica-based single-mode waveguides on silicon and their application to guided-wave optical interferometers,” J. Lightwave Technol. 6(6), 1003–1010 (1988).
[CrossRef]

Takeuchi, H.

S. Kodama, T. Ito, N. Watanabe, S. Kondo, H. Takeuchi, H. Ito, and T. Ishibashi, “2.3 picoseconds optical gate monolithically integrating photodiode and electroabsorption modulator,” Electron. Lett. 37(19), 1185–1186 (2001).
[CrossRef]

Takiguchi, K.

Tang, J. M.

Tang, Y.

Toba, H.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm," IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990).
[CrossRef]

N. Takato, K. Jinguji, M. Yasu, H. Toba, and M. Kawachi, “Silica-based single-mode waveguides on silicon and their application to guided-wave optical interferometers,” J. Lightwave Technol. 6(6), 1003–1010 (1988).
[CrossRef]

Tukey, J. W.

J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19(90), 297–301 (1965).
[CrossRef]

Verbeek, B. H.

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, and B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

Watanabe, N.

S. Kodama, T. Ito, N. Watanabe, S. Kondo, H. Takeuchi, H. Ito, and T. Ishibashi, “2.3 picoseconds optical gate monolithically integrating photodiode and electroabsorption modulator,” Electron. Lett. 37(19), 1185–1186 (2001).
[CrossRef]

Watts, P. M.

Yamada, E.

T. Kobayashi, A. Sano, E. Yamada, Y. Miyamoto, H. Takara, and A. Takada, “Electro-optically multiplexed 110 Gbit/s optical OFDM signal transmission over 80 km SMF without dispersion compensation,” Electron. Lett. 44(3), 225–226 (2008).
[CrossRef]

Yang, Q.

Yasu, M.

N. Takato, K. Jinguji, M. Yasu, H. Toba, and M. Kawachi, “Silica-based single-mode waveguides on silicon and their application to guided-wave optical interferometers,” J. Lightwave Technol. 6(6), 1003–1010 (1988).
[CrossRef]

Electron. Lett.

S. Kodama, T. Ito, N. Watanabe, S. Kondo, H. Takeuchi, H. Ito, and T. Ishibashi, “2.3 picoseconds optical gate monolithically integrating photodiode and electroabsorption modulator,” Electron. Lett. 37(19), 1185–1186 (2001).
[CrossRef]

T. Kobayashi, A. Sano, E. Yamada, Y. Miyamoto, H. Takara, and A. Takada, “Electro-optically multiplexed 110 Gbit/s optical OFDM signal transmission over 80 km SMF without dispersion compensation,” Electron. Lett. 44(3), 225–226 (2008).
[CrossRef]

IEEE J. Sel. Areas Comm.

N. Takato, T. Kominato, A. Sugita, K. Jinguji, H. Toba, and M. Kawachi, “Silica-based integrated optic Mach-Zehnder multi/demultiplexer family with channel spacing of 0.01-250 nm," IEEE J. Sel. Areas Comm. 8(6), 1120–1127 (1990).
[CrossRef]

IEEE Photon. Technol. Lett.

A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. 17(2), 504–506 (2005).
[CrossRef]

J. Lightwave Technol.

A. J. Lowery, L. B. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol. 25(1), 131–138 (2007).
[CrossRef]

J. Armstrong, “OFDM for optical communications,” J. Lightwave Technol. 27(3), 189–204 (2009).
[CrossRef]

B. H. Verbeek, C. H. Henry, N. A. Olsson, K. J. Orlowsky, R. F. Kazarinov, and B. H. Johnson, “Integrated four-channel Mach-Zehnder multi/demultiplexer fabricated with phosphorous doped SiO2 waveguides on Si,” J. Lightwave Technol. 6(6), 1011–1015 (1988).
[CrossRef]

N. Takato, K. Jinguji, M. Yasu, H. Toba, and M. Kawachi, “Silica-based single-mode waveguides on silicon and their application to guided-wave optical interferometers,” J. Lightwave Technol. 6(6), 1003–1010 (1988).
[CrossRef]

Math. Comput.

J. W. Cooley and J. W. Tukey, “An algorithm for the machine calculation of complex Fourier series,” Math. Comput. 19(90), 297–301 (1965).
[CrossRef]

Opt. Express

R. P. Giddings, X. Q. Jin, and J. M. Tang, “First experimental demonstration of 6Gb/s real-time optical OFDM transceivers incorporating channel estimation and variable power loading,” Opt. Express 17(22), 19727–19738 (2009).
[CrossRef] [PubMed]

Q. Yang, S. Chen, Y. Ma, and W. Shieh, “Real-time reception of multi-gigabit coherent optical OFDM signals,” Opt. Express 17(10), 7985–7992 (2009).
[CrossRef] [PubMed]

Y. Benlachtar, P. M. Watts, R. Bouziane, P. Milder, D. Rangaraj, A. Cartolano, R. Koutsoyannis, J. C. Hoe, M. Püschel, M. Glick, and R. I. Killey, “Generation of optical OFDM signals using 21.4 GS/s real time digital signal processing,” Opt. Express 17(20), 17658–17668 (2009).
[CrossRef] [PubMed]

H. C. Hansen Mulvad, M. Galili, L. K. Oxenløwe, H. Hu, A. T. Clausen, J. B. Jensen, C. Peucheret, and P. Jeppesen, “Demonstration of 5.1 Tbit/s data capacity on a single-wavelength channel,” Opt. Express 18(2), 1438–1443 (2010).
[CrossRef] [PubMed]

A. Lowery and J. Armstrong, “Orthogonal-frequency-division multiplexing for dispersion compensation of long-haul optical systems,” Opt. Express 14(6), 2079–2084 (2006).
[CrossRef] [PubMed]

Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009).
[CrossRef] [PubMed]

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
[CrossRef] [PubMed]

Opt. Lett.

Other

K. B. Howell, Principles of Fourier Analysis (CRC Press, 2001).

S. Suzuki, Y. Inoue, and T. Kominato, “High-density integrated 1×16 optical FDM multi/demultiplexer,” in Proceedings of Lasers and Electro-Optics Society Annual Meeting (IEEE, 1994), pp. 263–264.

H. Sanjoh, E. Yamada, and Y. Yoshikuni, “Optical orthogonal frequency division multiplexing using frequency/time domain filtering for high spectral efficiency up to 1 bit/s/Hz,” in Proceedings of Optical Fiber Communication Conference and Exhibit, (Optical Society of America, 2002), paper ThD1.

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley-Interscience, 1999).

W. Shieh and I. Djordjevic, OFDM for Optical Communications (Academic Press, 2010).

E. Yamada, A. Sano, H. Masuda, T. Kobayashi, E. Yoshida, Y. Miyamoto, Y. Hibino, K. Ishihara, Y. Takatori, K. Okada, K. Hagimoto, T. Yamada, and H. Yamazaki, “Novel no-guard-interval PDM CO-OFDM transmission in 4.1 Tb/s (50 × 88.8-Gb/s) DWDM link over 800 km SMF including 50-Ghz spaced ROADM nodes,” in Proceedings of Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference (Optical Society of America, 2008), paper PDP8.

S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” in Proceedings of European Conference on Optical Communication (IEEE, 2009), paper PD2.6.

D. Hillerkuss, A. Marculescu, J. Li, M. Teschke, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Novel optical fast Fourier transform scheme enabling real-time OFDM processing at 392 Gbit/s and beyond,” in Proceedings of Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference (Optical Society of America, 2010), paper OWW3.

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Fig. 1
Fig. 1

Four point example of the traditional fast Fourier transform and its optical equivalent. (a) Exemplary signal in time sampled at N = 4 points; (b) the structure consists of a serial-to-parallel (S/P) conversion that generates parallel samples of the signal, a sampling stage to generate the time samples xn and a conventional FFT stage that calculates the fast Fourier transform of the sampled signal; (c) the optical equivalent of the circuit uses passive splitters and optical time delays for serial-to-parallel conversion; optical gates perform the sampling of the optical waveform; afterwards the optical FFT is computed using optical 2 × 2 couplers and phase shifts as described in [1]. Right-hand sides of (b) and (c) show typical output signals for input signal (a).

Fig. 2
Fig. 2

Exemplary four-point optical FFT for symbol period T; (a) traditional implementation as in Fig. 1; (b) leading to a structure consisting of two DIs with the same differential delay; the additional T/4 delay is moved out of the second DI (c), which leads to two identical DIs that can be replaced by a single DI followed by signal splitters; (d) low-complexity scheme with combined S/P conversion and FFT.

Fig. 3
Fig. 3

(a) Direct FFT implementation versus (b) simplified all-optical FFT circuit for N = 8 showing the arrangement of delays and phase shifts as derived in Appendix A. The order of the outputs is different from that of the conventional FFT scheme. The sub-circuits for the FFT of order 2 and 4 are also marked, respectively.

Fig. 4
Fig. 4

Optical FFT circuit based on Fig. 3 for the extraction of Fourier component Xn . By tuning the phases φ 1, φ 2 and φ 3, any required Fourier component may be extracted without physically changing the setup.

Fig. 5
Fig. 5

Exemplary illustration of the intensity transfer functions of each stage (blue, red, and green) in the cascade of Fig. 3 and the total transfer function of the FFT circuit (black) for outputs X 0 (left side) and X 4 (right side).

Fig. 6
Fig. 6

Inter-symbol interference and frequency crosstalk occurring when replacing (parts of) the DI filters by 1st-order Gaussian filters with appropriate passbands in order to extract frequency component X 4. The left column shows the setup schematic, the middle column shows the real part of the impulse response and the right column shows the logarithmic intensity transfer functions of the involved DI stages (blue, red, and green), the optical filter (purple) and their cascade (black). In case of the approximations, the transfer function is not nulled for all outputs except X 4, leading to frequency crosstalk (red arrows). Also with decreasing filter bandwidth, the impulse response exceeds the DFT summation interval T (marked red), leading to crosstalk/interference from neighboring time slots.

Fig. 7
Fig. 7

Optical spectra of (a) an OFDM signal with 4 subchannels and (b) a DWDM signal with 4 channels. Due to the overlap, the OFDM subchannels cannot be extracted by simple optical filtering and the whole of the spectrum has to be processed simultaneously.

Fig. 8
Fig. 8

Two examples for the implementation of an all-optical OFDM transmitter-receiver pair. (a) The output of a pulse source (e.g. a mode-locked laser) is split onto N copies and each copy of the pulse train is encoded individually with an arbitrary subcarrier modulation format before being combined in the optical IFFT circuit. (b) The output of a pulse or frequency comb source is split into its spectral components, each of which satisfies Eq. (7). Those spectral components are separately encoded with an arbitrary subcarrier modulation format and combined to form the OFDM signal. At the receiver, the subchannels are separated using the optical FFT circuit. The receiver is identical to the one above. Green insets show exemplary waveforms before WDM filtering at the transmitter with OTDM-like pulses after the optical IFFT. Blue insets show exemplary eye diagrams at various locations within the receiver.

Fig. 9
Fig. 9

Function of an OFDM guard interval using the setup of Fig. 8(b) and an 8-FFT. On the left-hand side, the exemplary eye diagram of a single modulated subchannel is shown, as is, on the right side, the received signal before optical gating. If the symbol duration equals the integration interval T, the signal transitions, described by the 10-90% rise/fall time T rise (red), cause inter- and intra-subchannel crosstalk and the received eye is almost fully closed within the observation window of length TS = T/N. With increasing length of the guard interval τ GI, interference vanishes during T. Further increasing the guard interval increases the duration in which the orthogonality condition is fulfilled and thus increases the duration of the open “eye.”

Fig. 10
Fig. 10

Mitigating dispersion by means of a cyclic prefix (CP). (a) An OFDM signal with data and cyclic prefix. (b) Frequency dependent delay of subcarriers after transmission due to dispersion. The amount of dispersion that can be tolerated is limited by the length of the cyclic prefix (CP) as all subcarrier symbols must stay within the FFT window. (c) By means of optical filtering, an OFDM subband has been extracted, as discussed in Fig. 6. This way, only the extracted symbols must stay within the FFT window, and thus a larger amount of dispersion can be tolerated.

Fig. 11
Fig. 11

Achievable quality of the received signal for various FFT filter schemes performed on an 8-channel OFDM signal with 20 GBd on a 25 GHz subcarrier spacings. . The solid red plot shows the signal quality if the FFT is performed with a Gaussian filter as a function of the Gaussian filter bandwidth. The blue and green curves show the signal qualities if one and two DI cascades are used. The black curve shows how a perfect FFT can be performed if the FFT is performed with DIs only.

Fig. 12
Fig. 12

Setup of OFDM transmission system with (a) transmitter and (b) receiver. Two cascaded Mach-Zehnder modulators generate an optical frequency comb, which is split by a disinterleaver into 4 odd and 5 even channels. Spectrally adjacent subcarriers are modulated alternately using DBPSK or DQPSK modulation. All subcarriers are combined in a coupler and transmitted. The received OFDM signal is processed using the low-complexity OFFT circuit of Section 2.3 with 2 DIs and one standard optical filter. The resulting signals are sampled by electro-absorption modulators (EAM) and detected using DBPSK and DQPSK receivers. Bit error rates were measured with a BERT.The receiver comprises the all-optical FFT scheme followed by a preamplified receiver with differential direct detection. The optical FFT circuit consists of a cascade of two DIs, followed by passive splitters and a bank of bandpass filters. We thus adopt the low-complexity FFT circuit of Section 2.3, partially compensating for the associated performance loss by the increased guard interval. The final element of the OFFT are the EAM sampling gates.

Fig. 13
Fig. 13

BER performance of different subcarriers. No penalty is observed compared to back-to-back performance for DBPSK carriers (−3, −1, 1, 3) and no significant penalty for the central DQPSK carriers (−2, 0, 2). A 5 dB penalty or error floor occurs for the two outer DQPSK subcarriers (−4, 4), which are launched with 11 dB less power in the optical comb.

Equations (16)

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X m = n = 0 N 1 exp [ j   2 π m n N ] x n       ,         m = 0 , .. , N 1
X m = { E m + exp [ j 2 π N m ] O m if  m < N 2 E m N / 2 exp [ j 2 π N ( m N 2 ) ] O m N / 2 if  m N 2
h 4 ( t ) = 1 8 [ n = 0 3 δ ( t 2 n + 1 8 T ) k = 0 3 δ ( t 2 n 8 T ) ]
H 4 ( ω ) = 1 8 [ 1 + exp ( j   [ ω T 2 ] ) ] [ 1 + exp ( j   [ ω T 4 ] ) ] [ 1 + exp ( j   [ ω T 8 + π ] ) ]
h Gauss ( t ) = 1 2 π δ exp ( t 2 2 δ 2 ) exp ( j   ω F t )   with   δ = ln 2 ω B T
Δ ω = 2 π T
1 N n = 0 N 1 exp [ j   p Δ ω n T N ] exp [ j   q Δ ω n T N ] = { 1 if  p = q 0 else
B 2 = z = 0 L β 2 d z = τ G I Δ ω
Q = I ¯ 0 I ¯ 1 σ 0 + σ 1
X m ( t ) = 1 N n = 0 N 1 exp ( j   2 π n m N ) δ ( t n T N ) x ( t )
X ^ m ( ω ) = 1 N n = 0 N 1 exp ( j   2 π n m N ) exp ( j   ω n T N ) H m ( ω ) x ^ ( ω )
H m ( ω ) = 1 N n = 0 N 2 1 { exp ( j   2 π [ 2 n ] m N ) exp ( j   ω [ 2 n ] T N ) + exp ( j   2 π [ 2 n + 1 ] m N ) exp ( j   ω [ 2 n + 1 ] T N ) }
H m ( ω ) = 2 N n = 0 N 2 1 exp ( j   2 n N [ 2 π m + ω T ] ) FFT of order  N /2 1 2 [ 1 + exp ( j   [ ω T N + 2 π m N ] ) ] H p m , 1 ( ω )
T p = T N = T 2 p
φ p m = 2 π m N π
H p m ( ω ) = 1 2 ( 1 j j 1 ) output coupler ( 1 0 0 exp [ j   ( ω T p + φ m ) ] ) 1 2 ( 1 j j 1 ) input coupler ( 1 0 0 0 ) upper input isolation

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