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

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    [Crossref]
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    [Crossref]

2005 (4)

A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23(1), 115–130 (2005).
[Crossref]

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]

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]

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

2004 (3)

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]

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 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

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]

2003 (1)

2001 (3)

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 http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328.
[Crossref] [PubMed]

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

K. Kikuchi and K. Taira, “Theory of sonogram characterization of optical pulses,” IEEE J. Quantum Electron. 37(4), 533–537 (2001).
[Crossref]

2000 (3)

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),137–44 (2000).
[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]

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]

1999 (2)

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]

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

1998 (1)

1997 (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]

1993 (2)

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]

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).

1991 (1)

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]

1989 (1)

L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE 77(7), 941–981 (1989).
[Crossref]

1985 (2)

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]

R. A. Linke, “Modulation induced transient chirping in single frequency lasers,” IEEE J. Quantum Electron. QE–21(6), 593–597 (1985).
[Crossref]

1984 (1)

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]

Abe, J.

Agrawal, A.

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 × 42.7 Gb/s) transmission over 40 × 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.

Akasaka, Y.

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, “DWDM 40G 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.

Anderson, W.

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.

Azary, Z.

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).

Bakhshi, B.

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.

Baltuska, A.

Banerjee, S.

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 × 42.7 Gb/s) transmission over 40 × 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.

Bennike, J.

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, “DWDM 40G 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.

Bergano, N. S.

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.

Bigo, S.

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 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

Cai, J.-X.

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.

Cai, Y.

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.

Carroll, J. E.

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]

Chandrasekhar, S.

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 × 42.7 Gb/s) transmission over 40 × 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.

Charlet, G.

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 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

Chien, C.-C.

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

Chilla, J. L. A.

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]

Cohen, L.

L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE 77(7), 941–981 (1989).
[Crossref]

Corbett, P. C.

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.

Davidson, C. R.

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.

DeLong, K. W.

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]

Dey, S.

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, “DWDM 40G 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.

Dischler, R.

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 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

Doerr, C.

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 × 42.7 Gb/s) transmission over 40 × 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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Doerr, C. R.

Domagala, G.

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.

Dorrer, C.

Emori, Y.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Fittinghoff, D. N.

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]

Fjelde, T.

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, “DWDM 40G 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.

Flannery, B. P.

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

Foursa, D. G.

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.

Gallmann, L.

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]

Gapontsev, D.

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, “DWDM 40G 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.

Gill, D. M.

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 × 42.7 Gb/s) transmission over 40 × 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.

Gnauck, A. H.

A. H. Gnauck and P. J. Winzer, “Optical phase-shift-keyed transmission,” J. Lightwave Technol. 23(1), 115–130 (2005).
[Crossref]

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

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 × 42.7 Gb/s) transmission over 40 × 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.

Goto, T.

Grosz, D.

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 × 42.7 Gb/s) transmission over 40 × 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.

Grüner-Nielsen, L.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Gupta, V.

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.

Harmon, R. A.

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]

Harris, D.

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, “DWDM 40G 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.

Ho, K.-P.

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

Hodgkinson, T. G.

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]

Hunsche, S.

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 × 42.7 Gb/s) transmission over 40 × 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.

Idler, W.

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 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

Ishida, K.

Ivshin, V.

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, “DWDM 40G 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.

Jiang, S.

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.

Kane, D. J.

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

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]

Kane, J. D.

Kang, I.

Kasahara, K.

Katoh, K.

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]

Keller, U.

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]

Kikuchi, K.

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]

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

K. Kikuchi and K. Taira, “Theory of sonogram characterization of optical pulses,” IEEE J. Quantum Electron. 37(4), 533–537 (2001).
[Crossref]

Kim, J.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Kinjo, K.

Klekamp, A.

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 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

Kobayashi, T.

Koumans, R. G. M. P.

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),137–44 (2000).
[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]

Krumbügel, M. A.

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]

Kung, A.

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 × 42.7 Gb/s) transmission over 40 × 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.

Leuthold, J.

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]

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 × 42.7 Gb/s) transmission over 40 × 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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Li, H.

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.

Lingle, R.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Linke, R. A.

R. A. Linke, “Modulation induced transient chirping in single frequency lasers,” IEEE J. Quantum Electron. QE–21(6), 593–597 (1985).
[Crossref]

Liu, F.

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, “DWDM 40G 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.

Liu, L.

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.

Liu, X.

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]

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 × 42.7 Gb/s) transmission over 40 × 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.

Lucero, A. J.

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.

Ly-Gagnon, D.-S.

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]

Lyubomirsky, I.

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

Mamyshev, P.

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, “DWDM 40G 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.

Mardoyan, H.

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 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

Marhelyuk, A.

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 × 42.7 Gb/s) transmission over 40 × 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.

Martinez, O. E.

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]

Matuschek, N.

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]

Maymar, D.

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 × 42.7 Gb/s) transmission over 40 × 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.

Mazurczyk, M.

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.

Mikkelsen, B.

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, “DWDM 40G 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.

Mizuochi, T.

Mohs, G.

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.

Motoshima, K.

Movassaghi, M.

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 × 42.7 Gb/s) transmission over 40 × 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.

Namiki, S.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Nelson, L. E.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Nishizawa, N.

Nissov, M.

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.

Oguri, A.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Ohki, Y.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Patterson, W. W.

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.

Pederson, M. O.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Pierre, L.

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 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

Pilipetskii, A. N.

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.

Press, W. H.

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

Pshenichnikov, M. S.

Qian, S.

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

Rasmussen, C.

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, “DWDM 40G 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.

Raybon, G.

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 × 42.7 Gb/s) transmission over 40 × 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.

Reeves-Hall, P.

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, “DWDM 40G 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.

Reid, D. T.

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]

Richman, B. A.

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]

Ryf, R.

Serbe, P.

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, “DWDM 40G 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.

Smith, D. W.

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]

Steinmeyer, G.

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]

Stulz, L.

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 × 42.7 Gb/s) transmission over 40 × 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.

Stulz, S.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Sutter, D.

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]

Sweetser, J. N.

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]

Taira, K.

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

K. Kikuchi and K. Taira, “Theory of sonogram characterization of optical pulses,” IEEE J. Quantum Electron. 37(4), 533–537 (2001).
[Crossref]

Taylor, M. G.

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]

Teukolsky, S. A.

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

Tran, P.

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 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

Trebino, R.

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]

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]

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

Tsukiji, N.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

Vaa, M.

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.

van de Wagt, P.

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, “DWDM 40G 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.

Vetterling, W. T.

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

Walker, N. G.

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]

Wei, X.

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]

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 × 42.7 Gb/s) transmission over 40 × 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.

Wiersma, D. A.

Wildnauer, K. R.

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).

Winzer, P. J.

Xu, C.

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]

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 × 42.7 Gb/s) transmission over 40 × 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.

Yariv, A.

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]

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),137–44 (2000).
[Crossref]

Zhu, B.

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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 100 km of fiber using CSRZ-DPSK format,” in Optical Fiber Commun. Conf. (Optical Society of America, Washington, DC., 2003). Postdeadline paper PD19.

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]

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)

R. A. Linke, “Modulation induced transient chirping in single frequency lasers,” IEEE J. Quantum Electron. QE–21(6), 593–597 (1985).
[Crossref]

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]

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),137–44 (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 1.55μm 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)

Proc. IEEE (1)

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[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]

Other (11)

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).

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 × 42.7 Gb/s) transmission over 40 × 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 × 42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32 × 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, “DWDM 40G 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.

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 × 42.7 Gbit/s over transpacific distance with large Q-factor margin,” in European Conf. on Optical Commun. (2004). Postdeadline paper Th4.4.5.

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

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

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

“Spectrogram,” Wikipedia Encyclopedia. URL http://en.wikipedia.org/wiki/Spectrogram.

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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 )

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