Abstract

Time-resolved optical filtering (TROF) measures the spectrogram or sonogram by a fast photodiode followed a tunable narrowband optical filter. For periodic signal and to match the spectrogram, numerical TROF algorithm is used to find the original complex electric field or equivalently both the amplitude and phase. For phase-modulated optical signals, the TROF algorithm is initiated using the craters and ridges of the spectrogram.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, "2.5 Tb=s (64 x 42.7 Gb=s) transmission over 40 x 100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans," in Optical Fiber Commun. Conf. (Optical Society of America, Washington, D.C., 2002). Postdeadline paper FC2.
  2. B. Zhu, L. E. Nelson, S. Stulz, A. H. Gnauck, C. Doerr, J. Leuthold, L. Grüner-Nielsen, M. O. Pederson, J. Kim, R. Lingle, Y. Emori, Y. Ohki, N. Tsukiji, A. Oguri, and S. Namiki, "6.4-Tb/s (160 x 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 x 100 km of fiber using CSRZ-DPSK format," in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.
  3. C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van de Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, "DWDM40G transmission over trans-Pacific distance (10,000 km) using CSRZ-DPSK, enhanced FEC and all-Raman amplified 100 km Ultra-WaveTM fiber spans," in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD18.
  4. J.-X. Cai, D. G. Foursa, L. Liu, C. R. Davidson, Y. Cai, W. W. Patterson, A. J. Lucero, B. Bakhshi, G. Mohs, P. C. Corbett, V. Gupta, W. Anderson, M. Vaa, G. Domagala, M. Mazurczyk, H. Li, S. Jiang, M. Nissov, A. N. Pilipetskii, and N. S. Bergano, "RZ-DPSK field trial over 13,100 km of installed non slope-matched submarine fibers," in Optical Fiber Commun. Conf. (Optical Society of America, Washington, D.C., 2004). Postdeadline paper PDP34.
  5. G. Charlet, R. Dischler, A. Klekamp, P. Tran, H. Mardoyan, L. Pierre, W. Idler, and S. Bigo, "WDM bit-to-bit alternate-polarisation RZ-DPSK transmission at 40 x 42.7 Gbit/s over transpacific distance with large Q-factor margin," in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.
  6. C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10(2), 281-293 (2004).
    [CrossRef]
  7. A. H. Gnauck and P. J. Winzer, "Optical phase-shift-keyed transmission," J. Lightwave Technol. 23(1), 115-130 (2005).
    [CrossRef]
  8. K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, New York, 2005).
  9. T. Mizuochi, K. Ishida, T. Kobayashi, J. Abe, K. Kinjo, K. Motoshima, and K. Kasahara, "A comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise," J. Lightwave Technol. 21(9), 1933-1943 (2003).
    [CrossRef]
  10. N. G. Walker and J. E. Carroll, "Simultaneous phase and amplitude measurements on optical signals using a multiport junction," Electron. Lett. 20(23), 981-983 (1984).
    [CrossRef]
  11. T. G. Hodgkinson, R. A. Harmon, and D. W. Smith, "Demodulation of optical DPSK using in-phase and quadrature detection," Electron. Lett. 21(21), 867-868 (1985).
    [CrossRef]
  12. C. Dorrer, C. R. Doerr, I. Kang, R. Ryf, J. Leuthold, and P. J. Winzer, "Measurement of eye diagrams and constellation diagrams of optical sources using linear optics and waveguide technology," J. Lightwave Technol. 23(1), 178-186 (2005).
    [CrossRef]
  13. M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photonics Technol. Lett. 16(2), 674-676 (2004).
    [CrossRef]
  14. D.-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, "Unrepeatered optical transmission of 20 Gbit/s quadrature phase-shift keying signals over 210 km using homodyne phase-diversity receiver and digital signal processing," Electron. Lett. 41(4), 59-60 (2005).
    [CrossRef]
  15. R. Trebino and J. D. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating," J. Opt. Soc. Am. A 10(5), 1101-1111 (1993).
    [CrossRef]
  16. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68(9), 3277-3295 (1997).
    [CrossRef]
  17. D. J. Kane, "Recent progress toward real-time measurement of ultrashort laser pulses," IEEE J. Quantum Electron. 35(4), 421-431 (1999).
    [CrossRef]
  18. L. Cohen, "Time-frequency distributions-a review," Proc. IEEE 77(7), 941-981 (1989).
    [CrossRef]
  19. S. Qian, Introduction to Time-Frequency and Wavelet Transforms (Prentice Hall, Upper Saddle River, NJ, 2001).
  20. A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, "Amplitude and phase characterization of 4.5-fs pulses by frequency-resolved optical gating," Opt. Lett. 23(18), 1474-1476 (1998).
    [CrossRef]
  21. N. Nishizawa and T. Goto, "Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlation frequency resolved optical gating," Opt. Express 8(6), 328-334 (2001). URL <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328</a>.
    [CrossRef] [PubMed]
  22. L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, "Techniques for the characterization of sub-10-fs optical pulses: a comparison," Appl. Phys. B 70(S1), S67-S75 (2000).
    [CrossRef]
  23. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic, Boston, 2002).
    [CrossRef]
  24. J. L. A. Chilla and O. E. Martinez, "Analysis of a method of phase measurement of ultrashort pulses in the frequency domain," IEEE J. Quantum Electron. 27(5), 1228-1235 (1991).
    [CrossRef]
  25. K. Taira and K. Kikuchi, "Optical sampling system at 1.55 µm for the measurement of pulse waveform and phase employing sonogram characterization," IEEE Photonics Technol. Lett. 13(5), 505-507 (2001).
    [CrossRef]
  26. D. T. Reid, "Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram," IEEE J. Quantum Electron. 35(11), 1584-1589 (1999).
    [CrossRef]
  27. R. G. M. P. Koumans and A. Yariv, "Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses," IEEE J. Quantum Electron. 36(2), 137-144 (2000).
    [CrossRef]
  28. R. G. M. P. Koumans and A. Yariv, "Pulse characterization at 1.5 µm using time-resolved optical gating based on dispersive propagation," IEEE Photonics Technol. Lett. 12(6), 666-668 (2000).
    [CrossRef]
  29. "Spectrogram," Wikipedia Encyclopedia. URL <a href="http://en.wikipedia.org/wiki/Spectrogram">http://en.wikipedia.org/wiki/Spectrogram</a>.
  30. R. A. Linke, "Modulation induced transient chirping in single frequency lasers," IEEE J. Quantum Electron. QE-21(6), 593-597 (1985).
    [CrossRef]
  31. Agilent App. Note 1550-7, Making Time-Resolved Chirp Measurements Using the Optical Spectrum Analyzer and Digital Communications Analyzer, (2002).
  32. I. Lyubomirsky and C.-C. Chien, "DPSK demodulator based on optical discriminator filter," IEEE Photonics Technol. Lett. 17(2), 492-494 (2005).
    [CrossRef]
  33. K. R. Wildnauer and Z. Azary, "A double-pass monochromator for wavelength selection in an optical spectrum analyzer," Hewlett-Packard J. 44(6), 68-74 (1993).
  34. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge Univ., Cambridge, UK, 1992). Ch. 10.
  35. K. Kikuchi and K. Taira, "Theory of sonogram characterization of optical pulses," IEEE J. Quantum Electron. 37(4), 533-537 (2001).
    [CrossRef]

Appl. Phys. B (1)

L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, "Techniques for the characterization of sub-10-fs optical pulses: a comparison," Appl. Phys. B 70(S1), S67-S75 (2000).
[CrossRef]

Electron. Lett. (3)

N. G. Walker and J. E. Carroll, "Simultaneous phase and amplitude measurements on optical signals using a multiport junction," Electron. Lett. 20(23), 981-983 (1984).
[CrossRef]

T. G. Hodgkinson, R. A. Harmon, and D. W. Smith, "Demodulation of optical DPSK using in-phase and quadrature detection," Electron. Lett. 21(21), 867-868 (1985).
[CrossRef]

D.-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, "Unrepeatered optical transmission of 20 Gbit/s quadrature phase-shift keying signals over 210 km using homodyne phase-diversity receiver and digital signal processing," Electron. Lett. 41(4), 59-60 (2005).
[CrossRef]

European Conf. on Optical Commun. (1)

G. Charlet, R. Dischler, A. Klekamp, P. Tran, H. Mardoyan, L. Pierre, W. Idler, and S. Bigo, "WDM bit-to-bit alternate-polarisation RZ-DPSK transmission at 40 x 42.7 Gbit/s over transpacific distance with large Q-factor margin," in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

Hewlett-Packard J. (1)

K. R. Wildnauer and Z. Azary, "A double-pass monochromator for wavelength selection in an optical spectrum analyzer," Hewlett-Packard J. 44(6), 68-74 (1993).

IEEE J. Quantum Electron. (6)

K. Kikuchi and K. Taira, "Theory of sonogram characterization of optical pulses," IEEE J. Quantum Electron. 37(4), 533-537 (2001).
[CrossRef]

J. L. A. Chilla and O. E. Martinez, "Analysis of a method of phase measurement of ultrashort pulses in the frequency domain," IEEE J. Quantum Electron. 27(5), 1228-1235 (1991).
[CrossRef]

R. A. Linke, "Modulation induced transient chirping in single frequency lasers," IEEE J. Quantum Electron. QE-21(6), 593-597 (1985).
[CrossRef]

D. T. Reid, "Algorithm for complete and rapid retrieval of ultrashort pulse amplitude and phase from a sonogram," IEEE J. Quantum Electron. 35(11), 1584-1589 (1999).
[CrossRef]

R. G. M. P. Koumans and A. Yariv, "Time-resolved optical gating based on dispersive propagation: a new method to characterize optical pulses," IEEE J. Quantum Electron. 36(2), 137-144 (2000).
[CrossRef]

D. J. Kane, "Recent progress toward real-time measurement of ultrashort laser pulses," IEEE J. Quantum Electron. 35(4), 421-431 (1999).
[CrossRef]

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

C. Xu, X. Liu, and X. Wei, "Differential phase-shift keying for high spectral efficiency optical transmissions," IEEE J. Sel. Top. Quantum Electron. 10(2), 281-293 (2004).
[CrossRef]

IEEE Photonics Technol. Lett. (4)

M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photonics Technol. Lett. 16(2), 674-676 (2004).
[CrossRef]

R. G. M. P. Koumans and A. Yariv, "Pulse characterization at 1.5 µm using time-resolved optical gating based on dispersive propagation," IEEE Photonics Technol. Lett. 12(6), 666-668 (2000).
[CrossRef]

K. Taira and K. Kikuchi, "Optical sampling system at 1.55 µm for the measurement of pulse waveform and phase employing sonogram characterization," IEEE Photonics Technol. Lett. 13(5), 505-507 (2001).
[CrossRef]

I. Lyubomirsky and C.-C. Chien, "DPSK demodulator based on optical discriminator filter," IEEE Photonics Technol. Lett. 17(2), 492-494 (2005).
[CrossRef]

J. Lightwave Technol. (3)

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

Opt. Express (1)

Opt. Lett. (1)

Optical Fiber Commun. Conf. (4)

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, "2.5 Tb=s (64 x 42.7 Gb=s) transmission over 40 x 100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans," in Optical Fiber Commun. Conf. (Optical Society of America, Washington, D.C., 2002). Postdeadline paper FC2.

B. Zhu, L. E. Nelson, S. Stulz, A. H. Gnauck, C. Doerr, J. Leuthold, L. Grüner-Nielsen, M. O. Pederson, J. Kim, R. Lingle, Y. Emori, Y. Ohki, N. Tsukiji, A. Oguri, and S. Namiki, "6.4-Tb/s (160 x 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 x 100 km of fiber using CSRZ-DPSK format," in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

C. Rasmussen, T. Fjelde, J. Bennike, F. Liu, S. Dey, B. Mikkelsen, P. Mamyshev, P. Serbe, P. van de Wagt, Y. Akasaka, D. Harris, D. Gapontsev, V. Ivshin, and P. Reeves-Hall, "DWDM40G transmission over trans-Pacific distance (10,000 km) using CSRZ-DPSK, enhanced FEC and all-Raman amplified 100 km Ultra-WaveTM fiber spans," in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD18.

J.-X. Cai, D. G. Foursa, L. Liu, C. R. Davidson, Y. Cai, W. W. Patterson, A. J. Lucero, B. Bakhshi, G. Mohs, P. C. Corbett, V. Gupta, W. Anderson, M. Vaa, G. Domagala, M. Mazurczyk, H. Li, S. Jiang, M. Nissov, A. N. Pilipetskii, and N. S. Bergano, "RZ-DPSK field trial over 13,100 km of installed non slope-matched submarine fibers," in Optical Fiber Commun. Conf. (Optical Society of America, Washington, D.C., 2004). Postdeadline paper PDP34.

Proc. IEEE (1)

L. Cohen, "Time-frequency distributions-a review," Proc. IEEE 77(7), 941-981 (1989).
[CrossRef]

Rev. Sci. Instrum. (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68(9), 3277-3295 (1997).
[CrossRef]

Wikipedia Encyclopedia (1)

"Spectrogram," Wikipedia Encyclopedia. URL <a href="http://en.wikipedia.org/wiki/Spectrogram">http://en.wikipedia.org/wiki/Spectrogram</a>.

Other (5)

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic, Boston, 2002).
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge Univ., Cambridge, UK, 1992). Ch. 10.

Agilent App. Note 1550-7, Making Time-Resolved Chirp Measurements Using the Optical Spectrum Analyzer and Digital Communications Analyzer, (2002).

S. Qian, Introduction to Time-Frequency and Wavelet Transforms (Prentice Hall, Upper Saddle River, NJ, 2001).

K.-P. Ho, Phase-Modulated Optical Communication Systems (Springer, New York, 2005).

Cited By

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

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

The TROF trace for 7-bit NRZ- and RZ-DPSK signals. (a) NRZ-DPSK signal. (b) NRZ-DPSK signal with chromatic dispersion. (c) RZ-DPSK signal. (d) RZ-DPSK signal with SPM. (Blue lines: real part; Green lines: imaginary part)

Fig. 2.
Fig. 2.

Experimental setup to measure TROF trace

Fig. 3.
Fig. 3.

Measured TROF traces for NRZ-DPSK signal after 0-, 20-, 40-, and 60-km of single-mode fiber. The arrows are the beginning of data acquisition.

Fig. 4.
Fig. 4.

The normalized complex electric field calculated numerically from the TROF traces of Fig. 3. (a) Real part, (b) imaginary part.

Equations (18)

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

I FROG ω τ = E ( t ) G ( t τ ) e jωt d t 2 ,
I TROF t ν = E ( ω ) H ( ω ν ) e jωt d ω 2 ,
E ( t ) = k c k exp ( 2 πjkt T ) ,
I TROF t ν = k c k H ( 2 πk T ν ) exp ( 2 πjkt T ) 2 ,
= l m [ I means t m ν l I TROF t m ν l ] 2 ,
E k = 2 l m [ I means t m ν l I TROF t m ν l ] I TROF ( t m , v l ) E k .
I TROF ( t m , v l ) E k = 2 N E ( t m , v l ) k l H ( 2 π k 1 T v l ) exp [ 2 πj k 1 ( m k ) N ] ,
E t m ν l = k c k 1 H ( 2 π k T v l ) exp ( 2 πj km N ) .
I TROF ( t , ν ) = k m c k c k m * H ( 2 π k T v ) H * [ 2 π ( k m ) T ν ] exp ( 2 πj mt T ) .
h m ( τ ) = 1 2 π H ( ω ) H * ( ω 2 πm T ) e jωτ ,
r m ( τ ) = k c k c k m * e 2 πjkτ T
i m ( ν ) = h m ( τ ) r m ( τ ) e jντ ,
i m ( v ) = 1 T 0 T I TROF ( t , v ) exp ( 2 πjmt T ) d t .
r m ( τ ) = 1 2 π h m ( τ ) i m ( ν ) e jντ .
E ( t ) = k c k exp ( 2 πjkt T )
= 1 2 πT c 0 * 0 T k r k ( τ ) exp [ 2 πjk ( t + τ ) T ]
= 1 2 πT c 1 * 0 T k r k 1 ( τ ) exp { 2 πj [ ( k 1 ) t + ] T }
h m ( τ ) exp ( π 2 m 2 ω 0 2 T 2 + πjmτ T τ 2 ω 0 2 4 )

Metrics