Abstract

Linear self-referencing techniques for the characterization of the electric field of short optical pulses are presented. The theoretical and practical advantages of these techniques are developed. Experimental implementations are described, and their performance is compared to the performance of their nonlinear counterparts. Linear techniques demonstrate unprecedented sensitivity and are a perfect fit in many domains where the precise, accurate measurement of the electric field of an optical pulse is required.

© 2008 Optical Society of America

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2007 (5)

J. D. Schwartz, J. Azaña, and D. V. Plant, “A fully electronic system for the time magnification of ultra-wideband signals,” IEEE Trans. Microwave Theory Tech. 55, 327-334 (2007).
[CrossRef]

D. Reid and J. Harvey, “Linear spectrograms using electrooptic modulators,” IEEE Photon. Technol. Lett. 19, 535-537 (2007).
[CrossRef]

H. Miao, M. Weiner, C. Langrock, R. V. Roussev, and M. M. Fejer, “Polarization-insensitive ultralow-power second-harmonic generation frequency-resolved optical gating,” Opt. Lett. 32, 874-876 (2007).
[CrossRef] [PubMed]

J. M. Dailey and T. L. Koch, “Impact of carrier heating on SOA transmission dynamics for wavelength conversion,” IEEE Photon. Technol. Lett. 19, 1078-1080 (2007).
[CrossRef]

I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett. 32, 2538-2540 (2007).
[CrossRef] [PubMed]

2006 (6)

Y. Ozeki, S. Takasaka, and M. Sakano, “Electrooptic spectral shearing interferometry using a Mach-Zehnder modulator with a bias voltage sweeper,” IEEE Photon. Technol. Lett. 18, 911-913 (2006).
[CrossRef]

J. Bromage, C. Dorrer, I. A. Begishev, N. G. Usechak, and J. D. Zuegel, “Highly sensitive, single-shot characterization for pulse widths from 0.4to85 ps using electro-optic shearing interferometry,” Opt. Lett. 31, 3523-3525 (2006).
[CrossRef] [PubMed]

C. Dorrer, “Measurement of nonlinear temporal phase shifts using spectral Foucault technique,” Electron. Lett. 42, 649-650 (2006).
[CrossRef]

C. Dorrer, “Single-shot measurement of the electric field of optical waveforms by use of time-magnification and heterodyning,” Opt. Lett. 31, 540-542 (2006).
[CrossRef] [PubMed]

C. Dorrer, “Monitoring of optical signals from constellation diagrams measured with linear optical sampling,” J. Lightwave Technol. 24, 313-321 (2006).
[CrossRef]

C. Dorrer, “High-speed measurements for optical telecommunication systems,” IEEE J. Sel. Top. Quantum Electron. 12, 843-858 (2006).
[CrossRef]

2005 (6)

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, “Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications,” IEEE Photon. Technol. Lett. 17, 1914-1916 (2005).
[CrossRef]

C. Dorrer and I. A. Walmsley, “Concepts for the temporal characterization of short optical pulses,” EURASIP J. Appl. Signal Process. 2005, 1541-1553 (2005).
[CrossRef]

C. Dorrer, “Complete characterization of periodic optical sources by use of sampled test-plus-reference interferometry,” Opt. Lett. 30, 2022-2024 (2005).
[CrossRef] [PubMed]

Y. Ozeki, Y. Takushima, H. Yoshimi, K. Kikuchi, H. Yamauchi, and H. Taga, “Complete characterization of picosecond optical pulses in long-haul dispersion-managed transmission systems,” IEEE Photon. Technol. Lett. 17, 648-650 (2005).
[CrossRef]

C. Dorrer, “Characterization of nonlinear phase shifts by use of the temporal transport-of-intensity equation,” Opt. Lett. 30, 3237-3239 (2005).
[CrossRef] [PubMed]

I. Kang and C. Dorrer, “Highly sensitive differential tomographic technique for real-time ultrashort pulse characterization,” Opt. Lett. 30, 1545-1547 (2005).
[CrossRef] [PubMed]

2004 (5)

C. Dorrer and I. Kang, “Real-time implementation of linear spectrograms for the characterization of high bit-rate optical pulse trains,” IEEE Photon. Technol. Lett. 16, 858-860 (2004).
[CrossRef]

P. Kockaert, J. Azaña, R. L. Chen, and S. LaRochelle, “Full characterization of uniform ultrahigh-speed trains of optical pulses fiber Bragg gratings and linear detectors,” IEEE Photon. Technol. Lett. 16, 1540-1542 (2004).
[CrossRef]

P. Kockaert, M. Haelterman, P. Emplit, and C. Froehly, “Complete characterization of (ultra)short optical pulses using fast linear detectors,” IEEE J. Sel. Top. Quantum Electron. 10, 206-212 (2004).
[CrossRef]

P. J. Winzer, C. Dorrer, R.-J. Essiambre, and I. Kang, “Chirped returned-to-zero modulation by imbalanced pulse carver driving signals,” IEEE Photon. Technol. Lett. 16, 1379-1381 (2004).
[CrossRef]

C. Dorrer, “Chromatic dispersion characterization by direct instantaneous frequency measurement,” Opt. Lett. 29, 204-206 (2004).
[CrossRef] [PubMed]

2003 (5)

2002 (2)

L. P. Barry, S. Del burgo, B. Thomsen, R. T. Watts, D. A. Reid, and J. Harvey, “Optimization of optical data transmitters for 40-Gb/s lightwave systems using frequency resolved optical gating,” IEEE Photon. Technol. Lett. 14, 971-973 (2002).
[CrossRef]

C. Dorrer and I. Kang, “Simultaneous temporal characterization of telecommunication optical pulses and modulators by use of spectrograms,” Opt. Lett. 27, 1315-1317 (2002).
[CrossRef]

2000 (2)

M. Kwakernaak, R. Schreieck, A. Neiger, H. Jäckel, E. Gini, and W. Vogt, “Spectral phase measurement of mode-locked diode laser pulses by beating sidebands generated by electrooptical mixing,” IEEE Photon. Technol. Lett. 12, 1677-1679 (2000).
[CrossRef]

P. Kockaert, M. Peeters, S. Coen, Ph. Emplit, M. Haelterman, and O. Deparis, “Simple amplitude and phase measuring technique for ultrahigh-repetition-rate lasers,” IEEE Photon. Technol. Lett. 12, 187-189 (2000).
[CrossRef]

1998 (2)

1996 (3)

1995 (1)

1994 (2)

V. Wong and I. A. Walmsley, “Analysis of ultrashort pulse-shape measurement using linear interferometers,” Opt. Lett. 19, 287-289 (1994).
[CrossRef] [PubMed]

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270-272 (1994).
[CrossRef]

1993 (1)

1991 (1)

V. A. Zubov and T. I. Kuznetsova, “Solution of the phase problem for time-dependent optical signals by an interference system,” Sov. J. Quantum Electron. 21, 1285-1286 (1991).
[CrossRef]

1986 (1)

A. S. L. Gomes, A. S. Gouveia-Neto, and J. R. Taylor, “Direct measurement of chirped optical pulses with picosecond resolution,” Electron. Lett. 22, 41-42 (1986).
[CrossRef]

1985 (1)

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

1979 (1)

1977 (1)

J. P. Gex, C. Sauteret, P. Vallat, H. Tourbez, and M. Schelev, “Direct streak measurement of frequency sweeping and self focusing in single picosecond pulse,” Opt. Commun. 23, 430-434 (1977).
[CrossRef]

1974 (2)

D. J. Bradley and G. H. C. New, “Ultrashort pulse measurements,” Proc. IEEE 62, 313-345 (1974).
[CrossRef]

L. Mandel, “Interpretation of instantaneous frequencies,” Am. J. Phys. 42, 840-846 (1974).
[CrossRef]

1970 (1)

A. E. Siegman and D. J. Kuizenga, “Proposed method for measuring picosecond pulsewidths and pulse shapes in cw mode-locked lasers,” IEEE J. Quantum Electron. QE-6, 212-215 (1970).
[CrossRef]

1899 (1)

H. Abraham and J. Lemoine, “Disparition instantanée du phénomène de Kerr,” C. R. Acad. Sci. Hebd Seances Acad. Sci. D 129, 206-208 (1899).

Abraham, H.

H. Abraham and J. Lemoine, “Disparition instantanée du phénomène de Kerr,” C. R. Acad. Sci. Hebd Seances Acad. Sci. D 129, 206-208 (1899).

Agostinelli, J.

Alieva, T.

T. Alieva, M. M. Bastiaans, and L. Stankovic, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112-123 (2003).
[CrossRef]

Andersen, J. K.

R. M. Fortenberry, W. V. Sorin, H. Lin, S. A. Newton, J. K. Andersen, and M. N. Islam, “Low-power ultrashort optical pulse characterization using linear dispersion,” in Optical Fiber Communication Conference Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, 1997), pp. 290-291, paper ThL3.
[CrossRef]

Azaña, J.

J. D. Schwartz, J. Azaña, and D. V. Plant, “A fully electronic system for the time magnification of ultra-wideband signals,” IEEE Trans. Microwave Theory Tech. 55, 327-334 (2007).
[CrossRef]

P. Kockaert, J. Azaña, R. L. Chen, and S. LaRochelle, “Full characterization of uniform ultrahigh-speed trains of optical pulses fiber Bragg gratings and linear detectors,” IEEE Photon. Technol. Lett. 16, 1540-1542 (2004).
[CrossRef]

Banyai, W. C.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270-272 (1994).
[CrossRef]

Barry, L. P.

L. P. Barry, S. Del burgo, B. Thomsen, R. T. Watts, D. A. Reid, and J. Harvey, “Optimization of optical data transmitters for 40-Gb/s lightwave systems using frequency resolved optical gating,” IEEE Photon. Technol. Lett. 14, 971-973 (2002).
[CrossRef]

Bastiaans, M. M.

T. Alieva, M. M. Bastiaans, and L. Stankovic, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112-123 (2003).
[CrossRef]

Beck, M.

Begishev, I. A.

Berntson, A.

M. A. F. Roelens, P. Petropoulos, D. J. Richardson, M. Forzati, A. Djupsjöbacka, and A. Berntson, “Linear frequency resolved optical gating as a line monitoring tool,” in Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Technical Digest (Optical Society of America, 2006), paper OWN2.
[CrossRef] [PubMed]

Bloom, D. M.

M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270-272 (1994).
[CrossRef]

Boittin, R.

Bolle, C.

D. M. Marom, C. Dorrer, L. Kang, C. R. Doerr, M. Cappuzzo, L. Gomez, E. Chen, A. Wong-Foy, E. Laskowski, F. Klemens, C. Bolle, R. Cirelli, E. Ferry, T. Sorsch, J. Miner, E. Bower, M. E. Simon, F. Pardo, and D. Lopez, “Compact spectral pulse shaping using hybrid planar lightwave circuit and free-space optics with MEMS piston micromirrors and spectrogram feedback control,” in the 17th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2004) (IEEE, 2004), Vol. 2, paper WP1, pp. 585-586.

Bower, E.

D. M. Marom, C. Dorrer, L. Kang, C. R. Doerr, M. Cappuzzo, L. Gomez, E. Chen, A. Wong-Foy, E. Laskowski, F. Klemens, C. Bolle, R. Cirelli, E. Ferry, T. Sorsch, J. Miner, E. Bower, M. E. Simon, F. Pardo, and D. Lopez, “Compact spectral pulse shaping using hybrid planar lightwave circuit and free-space optics with MEMS piston micromirrors and spectrogram feedback control,” in the 17th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2004) (IEEE, 2004), Vol. 2, paper WP1, pp. 585-586.

Bowie, J. L.

Bradley, D. J.

D. J. Bradley and G. H. C. New, “Ultrashort pulse measurements,” Proc. IEEE 62, 313-345 (1974).
[CrossRef]

Bromage, J.

Cappuzzo, M.

D. M. Marom, C. Dorrer, L. Kang, C. R. Doerr, M. Cappuzzo, L. Gomez, E. Chen, A. Wong-Foy, E. Laskowski, F. Klemens, C. Bolle, R. Cirelli, E. Ferry, T. Sorsch, J. Miner, E. Bower, M. E. Simon, F. Pardo, and D. Lopez, “Compact spectral pulse shaping using hybrid planar lightwave circuit and free-space optics with MEMS piston micromirrors and spectrogram feedback control,” in the 17th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2004) (IEEE, 2004), Vol. 2, paper WP1, pp. 585-586.

Chen, E.

D. M. Marom, C. Dorrer, L. Kang, C. R. Doerr, M. Cappuzzo, L. Gomez, E. Chen, A. Wong-Foy, E. Laskowski, F. Klemens, C. Bolle, R. Cirelli, E. Ferry, T. Sorsch, J. Miner, E. Bower, M. E. Simon, F. Pardo, and D. Lopez, “Compact spectral pulse shaping using hybrid planar lightwave circuit and free-space optics with MEMS piston micromirrors and spectrogram feedback control,” in the 17th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2004) (IEEE, 2004), Vol. 2, paper WP1, pp. 585-586.

Chen, R. L.

P. Kockaert, J. Azaña, R. L. Chen, and S. LaRochelle, “Full characterization of uniform ultrahigh-speed trains of optical pulses fiber Bragg gratings and linear detectors,” IEEE Photon. Technol. Lett. 16, 1540-1542 (2004).
[CrossRef]

Chériaux, G.

Cirelli, R.

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I. Kang and C. Dorrer, “Method of optical pulse characterization using sinusoidal optical phase modulations,” Opt. Lett. 32, 2538-2540 (2007).
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M. T. Kauffman, W. C. Banyai, A. A. Godil, and D. M. Bloom, “Time-to-frequency converter for measuring picosecond optical pulses,” Appl. Phys. Lett. 64, 270-272 (1994).
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[CrossRef]

Pardo, F.

D. M. Marom, C. Dorrer, L. Kang, C. R. Doerr, M. Cappuzzo, L. Gomez, E. Chen, A. Wong-Foy, E. Laskowski, F. Klemens, C. Bolle, R. Cirelli, E. Ferry, T. Sorsch, J. Miner, E. Bower, M. E. Simon, F. Pardo, and D. Lopez, “Compact spectral pulse shaping using hybrid planar lightwave circuit and free-space optics with MEMS piston micromirrors and spectrogram feedback control,” in the 17th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2004) (IEEE, 2004), Vol. 2, paper WP1, pp. 585-586.

Peeters, M.

P. Kockaert, M. Peeters, S. Coen, Ph. Emplit, M. Haelterman, and O. Deparis, “Simple amplitude and phase measuring technique for ultrahigh-repetition-rate lasers,” IEEE Photon. Technol. Lett. 12, 187-189 (2000).
[CrossRef]

Petropoulos, P.

K. T. Vu, A. Malinowski, M. A. F. Roelens, M. Ibsen, P. Petropoulos, and D. J. Richardson, “Full characterisation of low power picosecond pulses from a gain-switched diode laser using electro-optic modulation based FROG,” presented at CLEO/QELS 2007, Baltimore, Maryland, 6-11 May 2007, paper CFF4.

M. A. F. Roelens, P. Petropoulos, D. J. Richardson, M. Forzati, A. Djupsjöbacka, and A. Berntson, “Linear frequency resolved optical gating as a line monitoring tool,” in Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Technical Digest (Optical Society of America, 2006), paper OWN2.
[CrossRef] [PubMed]

Plant, D. V.

J. D. Schwartz, J. Azaña, and D. V. Plant, “A fully electronic system for the time magnification of ultra-wideband signals,” IEEE Trans. Microwave Theory Tech. 55, 327-334 (2007).
[CrossRef]

Prein, S.

S. Prein, S. Diddams, and J.-C. Diels, “Complete characterization of femtosecond pulses using an all-electronic detector,” Opt. Commun. 123, 567-573 (1996).
[CrossRef]

Quochi, F.

Raybon, G.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear optical sampling,” IEEE Photon. Technol. Lett. 15, 1746-1748 (2003).
[CrossRef]

Raymer, M. G.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear optical sampling,” IEEE Photon. Technol. Lett. 15, 1746-1748 (2003).
[CrossRef]

M. Beck, M. G. Raymer, I. A. Walmsley, and V. Wong, “Chronocyclic tomography for measuring the amplitude and phase structure of optical pulses,” Opt. Lett. 18, 2041-2043 (1993).
[CrossRef] [PubMed]

Reid, D.

D. Reid and J. Harvey, “Linear spectrograms using electrooptic modulators,” IEEE Photon. Technol. Lett. 19, 535-537 (2007).
[CrossRef]

Reid, D. A.

L. P. Barry, S. Del burgo, B. Thomsen, R. T. Watts, D. A. Reid, and J. Harvey, “Optimization of optical data transmitters for 40-Gb/s lightwave systems using frequency resolved optical gating,” IEEE Photon. Technol. Lett. 14, 971-973 (2002).
[CrossRef]

Richardson, D. J.

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, “Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications,” IEEE Photon. Technol. Lett. 17, 1914-1916 (2005).
[CrossRef]

M. A. F. Roelens, P. Petropoulos, D. J. Richardson, M. Forzati, A. Djupsjöbacka, and A. Berntson, “Linear frequency resolved optical gating as a line monitoring tool,” in Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Technical Digest (Optical Society of America, 2006), paper OWN2.
[CrossRef] [PubMed]

K. T. Vu, A. Malinowski, M. A. F. Roelens, M. Ibsen, P. Petropoulos, and D. J. Richardson, “Full characterisation of low power picosecond pulses from a gain-switched diode laser using electro-optic modulation based FROG,” presented at CLEO/QELS 2007, Baltimore, Maryland, 6-11 May 2007, paper CFF4.

Roelens, M. A. F.

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, “Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications,” IEEE Photon. Technol. Lett. 17, 1914-1916 (2005).
[CrossRef]

M. A. F. Roelens, P. Petropoulos, D. J. Richardson, M. Forzati, A. Djupsjöbacka, and A. Berntson, “Linear frequency resolved optical gating as a line monitoring tool,” in Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Technical Digest (Optical Society of America, 2006), paper OWN2.
[CrossRef] [PubMed]

K. T. Vu, A. Malinowski, M. A. F. Roelens, M. Ibsen, P. Petropoulos, and D. J. Richardson, “Full characterisation of low power picosecond pulses from a gain-switched diode laser using electro-optic modulation based FROG,” presented at CLEO/QELS 2007, Baltimore, Maryland, 6-11 May 2007, paper CFF4.

Roussev, R. V.

Sakano, M.

Y. Ozeki, S. Takasaka, and M. Sakano, “Electrooptic spectral shearing interferometry using a Mach-Zehnder modulator with a bias voltage sweeper,” IEEE Photon. Technol. Lett. 18, 911-913 (2006).
[CrossRef]

Sauteret, C.

J. P. Gex, C. Sauteret, P. Vallat, H. Tourbez, and M. Schelev, “Direct streak measurement of frequency sweeping and self focusing in single picosecond pulse,” Opt. Commun. 23, 430-434 (1977).
[CrossRef]

Schelev, M.

J. P. Gex, C. Sauteret, P. Vallat, H. Tourbez, and M. Schelev, “Direct streak measurement of frequency sweeping and self focusing in single picosecond pulse,” Opt. Commun. 23, 430-434 (1977).
[CrossRef]

Schreieck, R.

M. Kwakernaak, R. Schreieck, A. Neiger, H. Jäckel, E. Gini, and W. Vogt, “Spectral phase measurement of mode-locked diode laser pulses by beating sidebands generated by electrooptical mixing,” IEEE Photon. Technol. Lett. 12, 1677-1679 (2000).
[CrossRef]

Schwartz, J. D.

J. D. Schwartz, J. Azaña, and D. V. Plant, “A fully electronic system for the time magnification of ultra-wideband signals,” IEEE Trans. Microwave Theory Tech. 55, 327-334 (2007).
[CrossRef]

Siegman, A. E.

A. E. Siegman and D. J. Kuizenga, “Proposed method for measuring picosecond pulsewidths and pulse shapes in cw mode-locked lasers,” IEEE J. Quantum Electron. QE-6, 212-215 (1970).
[CrossRef]

Simon, M. E.

D. M. Marom, C. Dorrer, L. Kang, C. R. Doerr, M. Cappuzzo, L. Gomez, E. Chen, A. Wong-Foy, E. Laskowski, F. Klemens, C. Bolle, R. Cirelli, E. Ferry, T. Sorsch, J. Miner, E. Bower, M. E. Simon, F. Pardo, and D. Lopez, “Compact spectral pulse shaping using hybrid planar lightwave circuit and free-space optics with MEMS piston micromirrors and spectrogram feedback control,” in the 17th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2004) (IEEE, 2004), Vol. 2, paper WP1, pp. 585-586.

Sorin, W. V.

R. M. Fortenberry, W. V. Sorin, H. Lin, S. A. Newton, J. K. Andersen, and M. N. Islam, “Low-power ultrashort optical pulse characterization using linear dispersion,” in Optical Fiber Communication Conference Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, 1997), pp. 290-291, paper ThL3.
[CrossRef]

R. M. Fortenberry and W. V. Sorin, “Apparatus for characterizing short optical pulses,” U.S. Patent No. 5,684,586 (13 June 1996).

Sorsch, T.

D. M. Marom, C. Dorrer, L. Kang, C. R. Doerr, M. Cappuzzo, L. Gomez, E. Chen, A. Wong-Foy, E. Laskowski, F. Klemens, C. Bolle, R. Cirelli, E. Ferry, T. Sorsch, J. Miner, E. Bower, M. E. Simon, F. Pardo, and D. Lopez, “Compact spectral pulse shaping using hybrid planar lightwave circuit and free-space optics with MEMS piston micromirrors and spectrogram feedback control,” in the 17th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2004) (IEEE, 2004), Vol. 2, paper WP1, pp. 585-586.

Stankovic, L.

T. Alieva, M. M. Bastiaans, and L. Stankovic, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112-123 (2003).
[CrossRef]

Stone, T.

Stuart, H. R.

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear optical sampling,” IEEE Photon. Technol. Lett. 15, 1746-1748 (2003).
[CrossRef]

Sweetser, J. N.

Taga, H.

Y. Ozeki, Y. Takushima, H. Yoshimi, K. Kikuchi, H. Yamauchi, and H. Taga, “Complete characterization of picosecond optical pulses in long-haul dispersion-managed transmission systems,” IEEE Photon. Technol. Lett. 17, 648-650 (2005).
[CrossRef]

Takasaka, S.

Y. Ozeki, S. Takasaka, and M. Sakano, “Electrooptic spectral shearing interferometry using a Mach-Zehnder modulator with a bias voltage sweeper,” IEEE Photon. Technol. Lett. 18, 911-913 (2006).
[CrossRef]

Takushima, Y.

Y. Ozeki, Y. Takushima, H. Yoshimi, K. Kikuchi, H. Yamauchi, and H. Taga, “Complete characterization of picosecond optical pulses in long-haul dispersion-managed transmission systems,” IEEE Photon. Technol. Lett. 17, 648-650 (2005).
[CrossRef]

Taylor, J. R.

A. S. L. Gomes, A. S. Gouveia-Neto, and J. R. Taylor, “Direct measurement of chirped optical pulses with picosecond resolution,” Electron. Lett. 22, 41-42 (1986).
[CrossRef]

Thomsen, B.

L. P. Barry, S. Del burgo, B. Thomsen, R. T. Watts, D. A. Reid, and J. Harvey, “Optimization of optical data transmitters for 40-Gb/s lightwave systems using frequency resolved optical gating,” IEEE Photon. Technol. Lett. 14, 971-973 (2002).
[CrossRef]

Thomsen, B. C.

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, “Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications,” IEEE Photon. Technol. Lett. 17, 1914-1916 (2005).
[CrossRef]

Tomaru, T.

Tourbez, H.

J. P. Gex, C. Sauteret, P. Vallat, H. Tourbez, and M. Schelev, “Direct streak measurement of frequency sweeping and self focusing in single picosecond pulse,” Opt. Commun. 23, 430-434 (1977).
[CrossRef]

Trebino, R.

Usechak, N. G.

Vallat, P.

J. P. Gex, C. Sauteret, P. Vallat, H. Tourbez, and M. Schelev, “Direct streak measurement of frequency sweeping and self focusing in single picosecond pulse,” Opt. Commun. 23, 430-434 (1977).
[CrossRef]

Vampouille, M.

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E.Wolf, ed. (North-Holland, 1983), Chap. II, pp. 63-153.

Vogt, W.

M. Kwakernaak, R. Schreieck, A. Neiger, H. Jäckel, E. Gini, and W. Vogt, “Spectral phase measurement of mode-locked diode laser pulses by beating sidebands generated by electrooptical mixing,” IEEE Photon. Technol. Lett. 12, 1677-1679 (2000).
[CrossRef]

Vu, K. T.

K. T. Vu, A. Malinowski, M. A. F. Roelens, M. Ibsen, P. Petropoulos, and D. J. Richardson, “Full characterisation of low power picosecond pulses from a gain-switched diode laser using electro-optic modulation based FROG,” presented at CLEO/QELS 2007, Baltimore, Maryland, 6-11 May 2007, paper CFF4.

Walmsley, I. A.

Watts, R. T.

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, “Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications,” IEEE Photon. Technol. Lett. 17, 1914-1916 (2005).
[CrossRef]

L. P. Barry, S. Del burgo, B. Thomsen, R. T. Watts, D. A. Reid, and J. Harvey, “Optimization of optical data transmitters for 40-Gb/s lightwave systems using frequency resolved optical gating,” IEEE Photon. Technol. Lett. 14, 971-973 (2002).
[CrossRef]

Wei, X.

X. Wei, J. Leuthold, C. Dorrer, D. M. Gill, and X. Liu, “Chirp reduction of π/2 alternate-phase pulses by optical filtering,” in Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference (OFC/NFOEC) Technical Digest (Optical Society of America, 2005), paper JWA42.
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Weiner, M.

Winzer, P. J.

P. J. Winzer, C. Dorrer, R.-J. Essiambre, and I. Kang, “Chirped returned-to-zero modulation by imbalanced pulse carver driving signals,” IEEE Photon. Technol. Lett. 16, 1379-1381 (2004).
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Wong, V.

Wong-Foy, A.

D. M. Marom, C. Dorrer, L. Kang, C. R. Doerr, M. Cappuzzo, L. Gomez, E. Chen, A. Wong-Foy, E. Laskowski, F. Klemens, C. Bolle, R. Cirelli, E. Ferry, T. Sorsch, J. Miner, E. Bower, M. E. Simon, F. Pardo, and D. Lopez, “Compact spectral pulse shaping using hybrid planar lightwave circuit and free-space optics with MEMS piston micromirrors and spectrogram feedback control,” in the 17th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2004) (IEEE, 2004), Vol. 2, paper WP1, pp. 585-586.

Yamauchi, H.

Y. Ozeki, Y. Takushima, H. Yoshimi, K. Kikuchi, H. Yamauchi, and H. Taga, “Complete characterization of picosecond optical pulses in long-haul dispersion-managed transmission systems,” IEEE Photon. Technol. Lett. 17, 648-650 (2005).
[CrossRef]

Yoshimi, H.

Y. Ozeki, Y. Takushima, H. Yoshimi, K. Kikuchi, H. Yamauchi, and H. Taga, “Complete characterization of picosecond optical pulses in long-haul dispersion-managed transmission systems,” IEEE Photon. Technol. Lett. 17, 648-650 (2005).
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V. A. Zubov and T. I. Kuznetsova, “Solution of the phase problem for time-dependent optical signals by an interference system,” Sov. J. Quantum Electron. 21, 1285-1286 (1991).
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C. Dorrer, “Measurement of nonlinear temporal phase shifts using spectral Foucault technique,” Electron. Lett. 42, 649-650 (2006).
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C. Dorrer and I. A. Walmsley, “Concepts for the temporal characterization of short optical pulses,” EURASIP J. Appl. Signal Process. 2005, 1541-1553 (2005).
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C. Dorrer, “High-speed measurements for optical telecommunication systems,” IEEE J. Sel. Top. Quantum Electron. 12, 843-858 (2006).
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IEEE Photon. Technol. Lett. (12)

Y. Ozeki, S. Takasaka, and M. Sakano, “Electrooptic spectral shearing interferometry using a Mach-Zehnder modulator with a bias voltage sweeper,” IEEE Photon. Technol. Lett. 18, 911-913 (2006).
[CrossRef]

P. Kockaert, M. Peeters, S. Coen, Ph. Emplit, M. Haelterman, and O. Deparis, “Simple amplitude and phase measuring technique for ultrahigh-repetition-rate lasers,” IEEE Photon. Technol. Lett. 12, 187-189 (2000).
[CrossRef]

P. Kockaert, J. Azaña, R. L. Chen, and S. LaRochelle, “Full characterization of uniform ultrahigh-speed trains of optical pulses fiber Bragg gratings and linear detectors,” IEEE Photon. Technol. Lett. 16, 1540-1542 (2004).
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L. P. Barry, S. Del burgo, B. Thomsen, R. T. Watts, D. A. Reid, and J. Harvey, “Optimization of optical data transmitters for 40-Gb/s lightwave systems using frequency resolved optical gating,” IEEE Photon. Technol. Lett. 14, 971-973 (2002).
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D. Reid and J. Harvey, “Linear spectrograms using electrooptic modulators,” IEEE Photon. Technol. Lett. 19, 535-537 (2007).
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J. M. Dailey and T. L. Koch, “Impact of carrier heating on SOA transmission dynamics for wavelength conversion,” IEEE Photon. Technol. Lett. 19, 1078-1080 (2007).
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P. J. Winzer, C. Dorrer, R.-J. Essiambre, and I. Kang, “Chirped returned-to-zero modulation by imbalanced pulse carver driving signals,” IEEE Photon. Technol. Lett. 16, 1379-1381 (2004).
[CrossRef]

B. C. Thomsen, M. A. F. Roelens, R. T. Watts, and D. J. Richardson, “Comparison between nonlinear and linear spectrographic techniques for the complete characterization of high bit-rate pulses used in optical communications,” IEEE Photon. Technol. Lett. 17, 1914-1916 (2005).
[CrossRef]

C. Dorrer, D. C. Kilper, H. R. Stuart, G. Raybon, and M. G. Raymer, “Linear optical sampling,” IEEE Photon. Technol. Lett. 15, 1746-1748 (2003).
[CrossRef]

Y. Ozeki, Y. Takushima, H. Yoshimi, K. Kikuchi, H. Yamauchi, and H. Taga, “Complete characterization of picosecond optical pulses in long-haul dispersion-managed transmission systems,” IEEE Photon. Technol. Lett. 17, 648-650 (2005).
[CrossRef]

C. Dorrer and I. Kang, “Real-time implementation of linear spectrograms for the characterization of high bit-rate optical pulse trains,” IEEE Photon. Technol. Lett. 16, 858-860 (2004).
[CrossRef]

M. Kwakernaak, R. Schreieck, A. Neiger, H. Jäckel, E. Gini, and W. Vogt, “Spectral phase measurement of mode-locked diode laser pulses by beating sidebands generated by electrooptical mixing,” IEEE Photon. Technol. Lett. 12, 1677-1679 (2000).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. D. Schwartz, J. Azaña, and D. V. Plant, “A fully electronic system for the time magnification of ultra-wideband signals,” IEEE Trans. Microwave Theory Tech. 55, 327-334 (2007).
[CrossRef]

IEEE Trans. Signal Process. (1)

T. Alieva, M. M. Bastiaans, and L. Stankovic, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112-123 (2003).
[CrossRef]

J. Lightwave Technol. (2)

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

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J. P. Gex, C. Sauteret, P. Vallat, H. Tourbez, and M. Schelev, “Direct streak measurement of frequency sweeping and self focusing in single picosecond pulse,” Opt. Commun. 23, 430-434 (1977).
[CrossRef]

S. Prein, S. Diddams, and J.-C. Diels, “Complete characterization of femtosecond pulses using an all-electronic detector,” Opt. Commun. 123, 567-573 (1996).
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V. Wong and I. A. Walmsley, “Analysis of ultrashort pulse-shape measurement using linear interferometers,” Opt. Lett. 19, 287-289 (1994).
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I. Kang, C. Dorrer, and F. Quochi, “Implementation of electro-optic spectral shearing interferometry for ultrashort pulse characterization,” Opt. Lett. 28, 2264-2266 (2003).
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C. Dorrer and I. Kang, “Simultaneous temporal characterization of telecommunication optical pulses and modulators by use of spectrograms,” Opt. Lett. 27, 1315-1317 (2002).
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C. Dorrer and I. Kang, “Highly sensitive direct characterization of femtosecond pulses by electro-optic spectral shearing interferometry,” Opt. Lett. 28, 477-479 (2003).
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C. Dorrer and I. Kang, “Complete temporal characterization of short optical pulses by simplified chronocyclic tomography,” Opt. Lett. 28, 1481-1483 (2003).
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D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884-886 (1996).
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C. Dorrer, “Single-shot measurement of the electric field of optical waveforms by use of time-magnification and heterodyning,” Opt. Lett. 31, 540-542 (2006).
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M. Beck, M. G. Raymer, I. A. Walmsley, and V. Wong, “Chronocyclic tomography for measuring the amplitude and phase structure of optical pulses,” Opt. Lett. 18, 2041-2043 (1993).
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Other (9)

C. Froehly, B. Colombeau, and M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E.Wolf, ed. (North-Holland, 1983), Chap. II, pp. 63-153.

C. Dorrer, “Investigation of the spectrogram technique for the characterization of picosecond optical pulses,” in Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference (OFC/NFOEC) Technical Digest (Optical Society of America, 2005), paper OTuB3.
[PubMed]

D. M. Marom, C. Dorrer, L. Kang, C. R. Doerr, M. Cappuzzo, L. Gomez, E. Chen, A. Wong-Foy, E. Laskowski, F. Klemens, C. Bolle, R. Cirelli, E. Ferry, T. Sorsch, J. Miner, E. Bower, M. E. Simon, F. Pardo, and D. Lopez, “Compact spectral pulse shaping using hybrid planar lightwave circuit and free-space optics with MEMS piston micromirrors and spectrogram feedback control,” in the 17th Annual Meeting of the IEEE Lasers & Electro-Optics Society (LEOS 2004) (IEEE, 2004), Vol. 2, paper WP1, pp. 585-586.

I. Kang and C. Dorrer, “Measurements of gain and phase dynamics of a semiconductor optical amplifier using spectrograms,” in Optical Fiber Conference 2004 (OFC 2004) (IEEE, 2004), Vol. 1, Paper MF43.

X. Wei, J. Leuthold, C. Dorrer, D. M. Gill, and X. Liu, “Chirp reduction of π/2 alternate-phase pulses by optical filtering,” in Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference (OFC/NFOEC) Technical Digest (Optical Society of America, 2005), paper JWA42.
[PubMed]

K. T. Vu, A. Malinowski, M. A. F. Roelens, M. Ibsen, P. Petropoulos, and D. J. Richardson, “Full characterisation of low power picosecond pulses from a gain-switched diode laser using electro-optic modulation based FROG,” presented at CLEO/QELS 2007, Baltimore, Maryland, 6-11 May 2007, paper CFF4.

M. A. F. Roelens, P. Petropoulos, D. J. Richardson, M. Forzati, A. Djupsjöbacka, and A. Berntson, “Linear frequency resolved optical gating as a line monitoring tool,” in Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, Technical Digest (Optical Society of America, 2006), paper OWN2.
[CrossRef] [PubMed]

R. M. Fortenberry and W. V. Sorin, “Apparatus for characterizing short optical pulses,” U.S. Patent No. 5,684,586 (13 June 1996).

R. M. Fortenberry, W. V. Sorin, H. Lin, S. A. Newton, J. K. Andersen, and M. N. Islam, “Low-power ultrashort optical pulse characterization using linear dispersion,” in Optical Fiber Communication Conference Vol. 6 of 1997 OSA Technical Digest Series (Optical Society of America, 1997), pp. 290-291, paper ThL3.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Schematic of a linear spectrogram setup based on an electro-absorption modulator (EAM). The delay between the gate and the pulse under test is scanned using a voltage-controlled phase shifter acting on the sinusoidal electric drive. The optical spectrum is measured with an optical spectrum analyzer (OSA). In the real-time implementation of this technique, the optical spectrum is measured using a fast-scanning Fabry–Perot etalon followed by a photodiode.

Fig. 2
Fig. 2

(a) Temporal intensity (solid curve) and phase (dashed curve) of a 2.4 ps pulse characterized with the EAM-based spectrogram technique. (b) Transmission (solid curve) and phase (dashed curve) of the EAM driven by a 10 GHz sinusoidal electric drive. (c) Spectral phase induced by linear propagation in 55 m of SSMF (solid curve) and the difference with second-order fit corresponding to the known dispersion of SSMF (dashed curve). (d) Temporal phase induced by nonlinear propagation of the 2.4 ps pulse in a highly nonlinear fiber (solid circles) compared to the temporal intensity of the pulse (solid curve). (e) Spectral intensity and phase of the 2.4 ps pulse measured at an average power of 5 dBm (solid curve and dashed curve, respectively) and 45 dBm (square markers and round markers, respectively). (f) Temporal intensity of the pulse on a logarithmic scale before (dashed curve) and after (solid curve) compression. The duration of the main pulse is reduced from 2.4 ps to 900 fs , but the low-intensity postpulses are not compressed.

Fig. 3
Fig. 3

(a) Spectral intensity (solid curve) and phase (dashed curve) of a 2.4 ps pulse after propagation in a pulse shaper inducing a π phase on a set of spectral components. (b) Temporal intensity (solid curve) and phase (dashed curve) of the pulse represented in (a).

Fig. 4
Fig. 4

Schematic of an implementation of simplified chronocyclic tomography based on a temporal modulator. The spectrum of the pulse is measured after quadratic temporal-phase modulation. Using a phase shifter, the pulse is synchronized with either the maximum or minimum of the phase modulation, which provides temporal-phase modulations of opposite signs. For enhanced accuracy, lock-in detection of the difference between the two optical spectra can be implemented by alternating the synchronization of the temporal-phase modulations and detecting the differential signal with a Fabry–Perot etalon and a photodiode.

Fig. 5
Fig. 5

Spectral intensity (short dashed curve) and spectral phase of a pulse before and after propagation into 330 m of SSMF (dashed line with open squares and dashed curve with open circles, respectively) measured with simplified chronocyclic tomography. The corresponding differential spectra are plotted respectively by a solid line with solid squares and a solid curve with solid circles.

Fig. 6
Fig. 6

Schematic of an implementation of electro-optic spectral-shearing interferometry for the characterization of an 82 MHz source. Two replicas of the pulse under test are generated by an interferometer and modulated by linear temporal phases of opposite slope in a phase modulator. The 10 GHz modulator drive is synchronized to the 82 MHz train of pulses under test by photodetection and a phase-lock loop. The optical spectrum of the two sheared pulses is measured with an optical spectrum analyzer.

Fig. 7
Fig. 7

Spectral intensity (solid curve) and phase (dashed curve) of a pulse characterized with EOSI. The spectral phase of the initial 200 fs pulse (dashed line without markers) gets various amounts of parabolic phase after propagation into 1.2 m (dashed curve with open circles), 6.2 m (dashed curve with solid circles), 11.2 m (dashed curve with open squares), and 16.2 m (dashed curve with solid squares) of SSMF. Propagation in 16.2 m of the fiber stretches the pulse to 5.6 ps .

Fig. 8
Fig. 8

Schematic of an implementation of electro-optic spectral-shearing interferometry for the single-shot characterization of an optical pulse. The pulse under test is split into two replicas. Each replica propagates in a phase modulator driven by a pulse generator synchronized to the pulse under test, and the replicas experience shears of opposite signs. The replicas are then recombined and their optical spectrum is measured with an optical spectrum analyzer.

Fig. 9
Fig. 9

(a) Measured second-order dispersion of an optical pulse after chirping by a compressor plotted as a function of the dispersion calculated from the parameters of the compressor. The circles correspond to the average of the measured dispersion over 100 shots, and the range of the 100 measured dispersions is represented as a small segment around the average. The solid line represents the expected dependence between measured and calculated dispersion. The two insets show the comparison between the measured (markers) and calculated (solid line) second-order intensity autocorrelations for the unchirped 400 fs pulse (c) and the pulse chirped to 50 ps (b).

Fig. 10
Fig. 10

Measured temporal intensity (solid curve) and phase (dashed curve) of a pair of chirped pulses generated by an interferometer. The delay between the two pulses is 25 ps . The inset represents the temporal intensity of the pulse and the 10 GHz sinusoidal drive driving the phase modulator.

Equations (17)

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E ̃ ( ω ) = T ̃ ( ω ) E ̃ ( ω ) .
E ̃ ( ω ) = F [ E ̃ ( ω ) ] ,
E ̃ ( ω ) = E ̃ ( ω ) F E ̃ [ E ̃ ( ω ) ] .
E ( t ) = R ( t ) E ( t ) .
E ̃ ( ω ) = T ̃ 1 ( ω ) T ̃ 2 ( ω ) T ̃ N ( ω ) E ̃ ( ω ) .
s = E ̃ ( ω ) 2 d ω = T ̃ 1 : N ( ω ) 2 S ( ω ) d ω .
S ( ω , t ) = E ( t ) R ( t τ ) exp ( i ω t ) d t 2 .
S ψ ψ ψ = 0 = ω [ S φ ω ] .
S = S 1 + S 2 2
S 2 S 1 2 ψ = ω [ S φ ω ] .
S ( ω ) = E ̃ ( ω ) + E ̃ ( ω + Ω ) exp ( i ω τ ) 2 .
S τ ( ω ) = S ( ω ) + 2 φ 0 Re [ i E ̃ * ( ω ) E ̃ ( ω Ω ) exp ( i Ω τ ) ] + 2 φ 0 Re [ i E ̃ * ( ω ) E ̃ ( ω + Ω ) exp ( i Ω τ ) ] .
E ̃ z Ω L E ̃ ω i β d ( ω ) L E ̃ = 0 ,
E ̃ Ω ( L , ω ) = E ̃ ( ω + Ω ) exp [ i Ω ω ω + Ω β d ( ω ) d ω ] .
E ̃ Ω ( L , ω ) = E ̃ ( ω Ω ) exp [ i Ω ω Ω ω β d ( ω ) d ω ] .
φ Ω ( ω ) φ Ω ( ω ) = φ ( ω + Ω ) φ ( ω Ω ) + 1 Ω [ ω ω + Ω β d ( ω ) d ω ω Ω ω β d ( ω ) d ω ] .
ε ( ω ) = 1 2 [ 1 2 β 2 ( ω + Ω ) 2 1 2 β 2 ( ω Ω ) 2 + 1 6 β 3 ( ω + Ω ) 3 1 6 β 3 ( ω Ω ) 3 ] .

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