Abstract

A stable optical frequency comb with 20-GHz spacing is shaped by a compact integrated silica arrayed waveguide grating (AWG) pair to produce optical waveforms with unprecedented fidelity. Complete characterization of both the intensity and phase of the crafted optical fields is accomplished with cross-correlation frequency resolved optical gating (XFROG) which has been optimized for periodic waveforms with resolvable modes. A new method is proposed to quantify, in a single number, the quality of the match in both the amplitude and phase between the measured optical waveform and the target waveform.

©2007 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  22. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11, 2206–2215 (1994).
    [Crossref]
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    [Crossref]
  24. C.-B. Huang, J. Zhi, D. E. Leaird, and A. M. Weiner, “The impact of optical comb stability on waveforms generated via spectral line-by-line pulse shaping,” Opt. Express 14, 13164–13176 (2006).
    [Crossref] [PubMed]
  25. M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. 29, 2693–2701 (1993).
    [Crossref]
  26. M. Fujiwara, J. Kani, H. Suzuki, K. Araya, and M. Teshima, “Flattened optical multicarrier generation of 12.5 GHz spaced 256 channels based on sinusoidal amplitude and phase hybrid modulation,” Electron. Lett. 37, 967–968 (2001).
    [Crossref]
  27. T. Sakamoto, T. Kawanishi, and M. Izutsu, “19×10-GHz electro-optic ultra-flat frequency comb generation only using single conventional Mach-Zehnder modulator,” in Proceedings of the Conference on Lasers and Electro- Optics (CLEO 2006) (Optical Society of America, 2006), paper CMAA5.
  28. R. P. Scott, N. K. Fontaine, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “3.5-THz wide, 175 mode optical comb source,” in Proceedings of the Optical Fiber Communications Conference (OFC 2007) (Optical Society of America, 2007), paper OWJ3.
  29. T. M. Fortier, A. Bartels, and S. A. Diddams, “Octave-spanning Ti:sapphire laser with a repetition rate > 1 GHz for optical frequency measurements and comparisons,” Opt. Lett. 31, 1011–1013 (2006).
    [Crossref] [PubMed]

2007 (1)

2006 (7)

T. M. Fortier, A. Bartels, and S. A. Diddams, “Octave-spanning Ti:sapphire laser with a repetition rate > 1 GHz for optical frequency measurements and comparisons,” Opt. Lett. 31, 1011–1013 (2006).
[Crossref] [PubMed]

Z. Jiang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform generation and characterization using spectral line-by-line control,” J. Lightwave Technol. 24, 2487–2494 (2006).
[Crossref]

P. J. Delfyett, S. Gee, C. Myoung-Taek, H. Izadpanah, L. Wangkuen, S. Ozharar, F. Quinlan, and T. Yilmaz, “Optical frequency combs from semiconductor lasers and applications in ultrawideband signal processing and communications,” J. Lightwave Technol. 24, 2701–2719 (2006).
[Crossref]

C.-B. Huang, J. Zhi, D. E. Leaird, and A. M. Weiner, “The impact of optical comb stability on waveforms generated via spectral line-by-line pulse shaping,” Opt. Express 14, 13164–13176 (2006).
[Crossref] [PubMed]

J. D. Mckinney, I. S. Lin, and A. M. Weiner, “Ultrabroadband arbitrary electromagnetic waveform synthesis,” Opt. Photon. News 17, 24–29 (2006).
[Crossref]

Z. Jiang, D. E. Leaird, and A. M. Weiner, “Optical processing based on spectral line-by-line pulse shaping on a phase-modulated CW laser,” IEEE J. Quantum Electron. 42, 657–665 (2006).
[Crossref]

D. Miyamoto, K. Mandai, T. Kurokawa, S. Takeda, T. Shioda, and H. Tsuda, “Waveform-controllable optical pulse generation using an optical pulse synthesizer,” IEEE Photon. Technol. Lett. 18, 721–723 (2006).
[Crossref]

2005 (2)

M. Knapczyk, A. Krishnan, L. G. de Peralta, A. A. Bernussi, and H. Temkin, “High-resolution pulse shaper based on arrays of digital micromirrors,” IEEE Photon. Technol. Lett. 17, 2200–2202 (2005).
[Crossref]

Z. Jiang, D. S. Seo, D. E. Leaird, and A. M. Weiner, “Spectral line-by-line pulse shaping,” Opt. Lett. 30, 1557–1559 (2005).
[Crossref] [PubMed]

2004 (1)

A. Monmayrant and B. Chatel, “New phase and amplitude high resolution pulse shaper,” Rev. Sci. Instrum. 75, 2668–2671 (2004).
[Crossref]

2001 (2)

J.-H. Chung and A. M. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” IEEE J. Sel. Top. Quantum Electron. 7, 656–666 (2001).
[Crossref]

M. Fujiwara, J. Kani, H. Suzuki, K. Araya, and M. Teshima, “Flattened optical multicarrier generation of 12.5 GHz spaced 256 channels based on sinusoidal amplitude and phase hybrid modulation,” Electron. Lett. 37, 967–968 (2001).
[Crossref]

1999 (1)

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, “Fabrication of frequency spectrum synthesiser consisting of arrayed-waveguide grating pair and thermo-optic amplitude and phase controllers,” Electron. Lett. 35, 733–734 (1999).
[Crossref]

1998 (2)

A. M. Weiner and A. M. Kan’an, “Femtosecond pulse shaping for synthesis, processing, and time-to-space conversion of ultrafast optical waveforms,” IEEE J. Sel. Top. Quantum Electron. 4, 317–331 (1998).
[Crossref]

D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15, 1615–1619 (1998).
[Crossref]

1997 (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, 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, 3277–3295 (1997).
[Crossref]

1995 (2)

A. M. Weiner, “Femtosecond optical pulse shaping and processing,” Prog. Quantum Electron. 19, 161–237 (1995).
[Crossref]

M. M. Wefers and K. A. Nelson, “Generation of high-fidelity programmable ultrafast optical waveforms,” Opt. Lett. 20, 1047–1049 (1995).
[Crossref] [PubMed]

1994 (1)

1993 (2)

M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. 29, 2693–2701 (1993).
[Crossref]

M. M. Wefers and K. A. Nelson, “Programmable phase and amplitude femtosecond pulse shaping,” Opt. Lett. 18, 2032–2034 (1993).
[Crossref] [PubMed]

1989 (1)

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

1988 (1)

1985 (1)

Araya, K.

M. Fujiwara, J. Kani, H. Suzuki, K. Araya, and M. Teshima, “Flattened optical multicarrier generation of 12.5 GHz spaced 256 channels based on sinusoidal amplitude and phase hybrid modulation,” Electron. Lett. 37, 967–968 (2001).
[Crossref]

Bartels, A.

Bernussi, A. A.

M. Knapczyk, A. Krishnan, L. G. de Peralta, A. A. Bernussi, and H. Temkin, “High-resolution pulse shaper based on arrays of digital micromirrors,” IEEE Photon. Technol. Lett. 17, 2200–2202 (2005).
[Crossref]

Cao, J.

Chatel, B.

A. Monmayrant and B. Chatel, “New phase and amplitude high resolution pulse shaper,” Rev. Sci. Instrum. 75, 2668–2671 (2004).
[Crossref]

Chung, J.-H.

J.-H. Chung and A. M. Weiner, “Ambiguity of ultrashort pulse shapes retrieved from the intensity autocorrelation and the power spectrum,” IEEE J. Sel. Top. Quantum Electron. 7, 656–666 (2001).
[Crossref]

Cohen, L.

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

de Peralta, L. G.

M. Knapczyk, A. Krishnan, L. G. de Peralta, A. A. Bernussi, and H. Temkin, “High-resolution pulse shaper based on arrays of digital micromirrors,” IEEE Photon. Technol. Lett. 17, 2200–2202 (2005).
[Crossref]

Delfyett, P. J.

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, 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, 3277–3295 (1997).
[Crossref]

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[Crossref]

Diddams, S. A.

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, 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, 3277–3295 (1997).
[Crossref]

Fontaine, N. K.

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 phase×32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32, 865–867 (2007).
[Crossref] [PubMed]

R. P. Scott, N. K. Fontaine, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “3.5-THz wide, 175 mode optical comb source,” in Proceedings of the Optical Fiber Communications Conference (OFC 2007) (Optical Society of America, 2007), paper OWJ3.

Fortier, T. M.

Fujiwara, M.

M. Fujiwara, J. Kani, H. Suzuki, K. Araya, and M. Teshima, “Flattened optical multicarrier generation of 12.5 GHz spaced 256 channels based on sinusoidal amplitude and phase hybrid modulation,” Electron. Lett. 37, 967–968 (2001).
[Crossref]

Gee, S.

Goh, T.

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, “Fabrication of frequency spectrum synthesiser consisting of arrayed-waveguide grating pair and thermo-optic amplitude and phase controllers,” Electron. Lett. 35, 733–734 (1999).
[Crossref]

Heritage, J. P.

Huang, C.-B.

Hunter, J.

Izadpanah, H.

Izutsu, M.

T. Sakamoto, T. Kawanishi, and M. Izutsu, “19×10-GHz electro-optic ultra-flat frequency comb generation only using single conventional Mach-Zehnder modulator,” in Proceedings of the Conference on Lasers and Electro- Optics (CLEO 2006) (Optical Society of America, 2006), paper CMAA5.

Jiang, Z.

Kan’an, A. M.

A. M. Weiner and A. M. Kan’an, “Femtosecond pulse shaping for synthesis, processing, and time-to-space conversion of ultrafast optical waveforms,” IEEE J. Sel. Top. Quantum Electron. 4, 317–331 (1998).
[Crossref]

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, 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, 3277–3295 (1997).
[Crossref]

Kani, J.

M. Fujiwara, J. Kani, H. Suzuki, K. Araya, and M. Teshima, “Flattened optical multicarrier generation of 12.5 GHz spaced 256 channels based on sinusoidal amplitude and phase hybrid modulation,” Electron. Lett. 37, 967–968 (2001).
[Crossref]

Karalar, A.

Kawanishi, T.

T. Sakamoto, T. Kawanishi, and M. Izutsu, “19×10-GHz electro-optic ultra-flat frequency comb generation only using single conventional Mach-Zehnder modulator,” in Proceedings of the Conference on Lasers and Electro- Optics (CLEO 2006) (Optical Society of America, 2006), paper CMAA5.

K. Mandai, T. Suzuki, H. Tsuda, T. Kurokawa, and T. Kawanishi, “Arbitrary optical short pulse generator using a high-resolution arrayed-waveguide grating,” in Proceedings of the IEEE Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 107–110.

Kirschner, E. M.

Knapczyk, M.

M. Knapczyk, A. Krishnan, L. G. de Peralta, A. A. Bernussi, and H. Temkin, “High-resolution pulse shaper based on arrays of digital micromirrors,” IEEE Photon. Technol. Lett. 17, 2200–2202 (2005).
[Crossref]

Kolner, B. H.

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 phase×32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32, 865–867 (2007).
[Crossref] [PubMed]

R. P. Scott, N. K. Fontaine, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “3.5-THz wide, 175 mode optical comb source,” in Proceedings of the Optical Fiber Communications Conference (OFC 2007) (Optical Society of America, 2007), paper OWJ3.

Kominato, T.

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, “Fabrication of frequency spectrum synthesiser consisting of arrayed-waveguide grating pair and thermo-optic amplitude and phase controllers,” Electron. Lett. 35, 733–734 (1999).
[Crossref]

Kourogi, M.

M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. 29, 2693–2701 (1993).
[Crossref]

Krishnan, A.

M. Knapczyk, A. Krishnan, L. G. de Peralta, A. A. Bernussi, and H. Temkin, “High-resolution pulse shaper based on arrays of digital micromirrors,” IEEE Photon. Technol. Lett. 17, 2200–2202 (2005).
[Crossref]

Krumbugel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, 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, 3277–3295 (1997).
[Crossref]

Kurokawa, T.

D. Miyamoto, K. Mandai, T. Kurokawa, S. Takeda, T. Shioda, and H. Tsuda, “Waveform-controllable optical pulse generation using an optical pulse synthesizer,” IEEE Photon. Technol. Lett. 18, 721–723 (2006).
[Crossref]

K. Mandai, T. Suzuki, H. Tsuda, T. Kurokawa, and T. Kawanishi, “Arbitrary optical short pulse generator using a high-resolution arrayed-waveguide grating,” in Proceedings of the IEEE Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 107–110.

Leaird, D. E.

Lin, I. S.

J. D. Mckinney, I. S. Lin, and A. M. Weiner, “Ultrabroadband arbitrary electromagnetic waveform synthesis,” Opt. Photon. News 17, 24–29 (2006).
[Crossref]

Mandai, K.

D. Miyamoto, K. Mandai, T. Kurokawa, S. Takeda, T. Shioda, and H. Tsuda, “Waveform-controllable optical pulse generation using an optical pulse synthesizer,” IEEE Photon. Technol. Lett. 18, 721–723 (2006).
[Crossref]

K. Mandai, T. Suzuki, H. Tsuda, T. Kurokawa, and T. Kawanishi, “Arbitrary optical short pulse generator using a high-resolution arrayed-waveguide grating,” in Proceedings of the IEEE Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 107–110.

Mckinney, J. D.

J. D. Mckinney, I. S. Lin, and A. M. Weiner, “Ultrabroadband arbitrary electromagnetic waveform synthesis,” Opt. Photon. News 17, 24–29 (2006).
[Crossref]

Meshulach, D.

Miyamoto, D.

D. Miyamoto, K. Mandai, T. Kurokawa, S. Takeda, T. Shioda, and H. Tsuda, “Waveform-controllable optical pulse generation using an optical pulse synthesizer,” IEEE Photon. Technol. Lett. 18, 721–723 (2006).
[Crossref]

Monmayrant, A.

A. Monmayrant and B. Chatel, “New phase and amplitude high resolution pulse shaper,” Rev. Sci. Instrum. 75, 2668–2671 (2004).
[Crossref]

Myoung-Taek, C.

Nakagawa, K.

M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. 29, 2693–2701 (1993).
[Crossref]

Nelson, K. A.

Ohtsu, M.

M. Kourogi, K. Nakagawa, and M. Ohtsu, “Wide-span optical frequency comb generator for accurate optical frequency difference measurement,” IEEE J. Quantum Electron. 29, 2693–2701 (1993).
[Crossref]

Okamoto, K.

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 phase×32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32, 865–867 (2007).
[Crossref] [PubMed]

K. Okamoto, T. Kominato, H. Yamada, and T. Goh, “Fabrication of frequency spectrum synthesiser consisting of arrayed-waveguide grating pair and thermo-optic amplitude and phase controllers,” Electron. Lett. 35, 733–734 (1999).
[Crossref]

Ozharar, S.

Quinlan, F.

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, 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, 3277–3295 (1997).
[Crossref]

Sakamoto, T.

T. Sakamoto, T. Kawanishi, and M. Izutsu, “19×10-GHz electro-optic ultra-flat frequency comb generation only using single conventional Mach-Zehnder modulator,” in Proceedings of the Conference on Lasers and Electro- Optics (CLEO 2006) (Optical Society of America, 2006), paper CMAA5.

Scott, R. P.

N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, K. Okamoto, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “32 phase×32 amplitude optical arbitrary waveform generation,” Opt. Lett. 32, 865–867 (2007).
[Crossref] [PubMed]

R. P. Scott, N. K. Fontaine, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “3.5-THz wide, 175 mode optical comb source,” in Proceedings of the Optical Fiber Communications Conference (OFC 2007) (Optical Society of America, 2007), paper OWJ3.

Seo, D. S.

Shioda, T.

D. Miyamoto, K. Mandai, T. Kurokawa, S. Takeda, T. Shioda, and H. Tsuda, “Waveform-controllable optical pulse generation using an optical pulse synthesizer,” IEEE Photon. Technol. Lett. 18, 721–723 (2006).
[Crossref]

Silberberg, Y.

Suzuki, H.

M. Fujiwara, J. Kani, H. Suzuki, K. Araya, and M. Teshima, “Flattened optical multicarrier generation of 12.5 GHz spaced 256 channels based on sinusoidal amplitude and phase hybrid modulation,” Electron. Lett. 37, 967–968 (2001).
[Crossref]

Suzuki, T.

K. Mandai, T. Suzuki, H. Tsuda, T. Kurokawa, and T. Kawanishi, “Arbitrary optical short pulse generator using a high-resolution arrayed-waveguide grating,” in Proceedings of the IEEE Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 107–110.

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, 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, 3277–3295 (1997).
[Crossref]

Takeda, S.

D. Miyamoto, K. Mandai, T. Kurokawa, S. Takeda, T. Shioda, and H. Tsuda, “Waveform-controllable optical pulse generation using an optical pulse synthesizer,” IEEE Photon. Technol. Lett. 18, 721–723 (2006).
[Crossref]

Temkin, H.

M. Knapczyk, A. Krishnan, L. G. de Peralta, A. A. Bernussi, and H. Temkin, “High-resolution pulse shaper based on arrays of digital micromirrors,” IEEE Photon. Technol. Lett. 17, 2200–2202 (2005).
[Crossref]

Teshima, M.

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Opt. Express (1)

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R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, 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, 3277–3295 (1997).
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Other (4)

K. Mandai, T. Suzuki, H. Tsuda, T. Kurokawa, and T. Kawanishi, “Arbitrary optical short pulse generator using a high-resolution arrayed-waveguide grating,” in Proceedings of the IEEE Topical Meeting on Microwave Photonics (IEEE, 2004), pp. 107–110.

R. Trebino, Frequency-resolved optical gating: the measurement of ultrashort laser pulses (Kluwer Academic, 2000).

T. Sakamoto, T. Kawanishi, and M. Izutsu, “19×10-GHz electro-optic ultra-flat frequency comb generation only using single conventional Mach-Zehnder modulator,” in Proceedings of the Conference on Lasers and Electro- Optics (CLEO 2006) (Optical Society of America, 2006), paper CMAA5.

R. P. Scott, N. K. Fontaine, J. P. Heritage, B. H. Kolner, and S. J. B. Yoo, “3.5-THz wide, 175 mode optical comb source,” in Proceedings of the Optical Fiber Communications Conference (OFC 2007) (Optical Society of America, 2007), paper OWJ3.

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Figures (8)

Fig. 1.
Fig. 1. Comparison of two different FROG traces. (a) Sample waveform used to create the traces. (b) SHG FROG trace of (a). (c) XFROG trace of (a) using a 5-ps transform-limited gate pulse. Complexity of XFROG traces can be minimized by the proper choice of the gate pulse.

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Fig. 2.
Fig. 2. Comparison of the target and measured (simulated) Gaussian pulse with cubic spectral phase. (a) Target spectral intensity (black dashes) and spectral phase (solid red line) shown with a simulated measurement of the spectral intensity (bars) and phase (circles). (b) Target temporal intensity (black dotted) and phase (red dotted) with simulated measured intensity (solid blue) and phase (solid red). (c) SHG FROG trace of target waveform. (d) SHG FROG trace of simulated measured waveform. (e) Absolute difference between (c) and (d). Calculated G′=0.124 from this example.

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Fig. 3.
Fig. 3. Experimental arrangement for the production and characterization of optical arbitrary waveforms. The 20-GHz optical frequency comb is generated via a dual-electrode Mach-Zehnder modulator (DEMZM). A silica AWG pair sets the amplitude and phase of each optical mode and XFROG is used to retrieve the amplitude and phase of the shaped waveform. The inset plot shows the retrieved spectral intensity and phase of the waveform at the output of the DEMZM.

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Fig. 4.
Fig. 4. (a) Spectral transmission of the 20-GHz pulse shaper showing one full FSR (10.23 nm). (b) Close-in view of the center portion used for this experiment. (c) The relative phase response to heater power for three typical channels.

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Fig. 5.
Fig. 5. The retrieved intensity and phase in both the spectral and temporal domains for the measured transform-limited optical waveform. (a) Target spectral intensity values are shown as black dashes and the target spectral phase is shown as a solid red line (note expanded phase axis). (b) Measured time domain data (solid lines) and target time domain data (dotted lines). Calculated G′=0.0149.

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Fig. 6.
Fig. 6. The retrieved intensity and phase in both the spectral and temporal domains for the linearly chirped optical waveform. (a) Measured spectral intensity and phase data (bars and circles, respectively) and target spectral intensity (black dashes) and spectral phase (solid line). (b) Measured time domain data (solid lines) and target time domain data (dotted lines). Calculated G′=0.0155.

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Fig. 7.
Fig. 7. The retrieved intensity and phase in both the spectral and temporal domains for two different zero-π pulses (phase shift above or below center frequency) and their corresponding XFROG traces. (a) Measured spectral data (bars and circles) and target spectral intensity (black dashes) and spectral phase (solid line). (b) Measured temporal waveform (solid lines) and target waveform (dotted lines). (a–c) Calculated G′=0.0301, (d–e) calculated G′=0.0209. XFROG traces have the same scaling as Fig. 1.

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Fig. 8.
Fig. 8. Simulation showing the limitations of using autocorrelations as a diagnostic. (a) Significant spectral phase errors are added to the zero-π pulse of Fig. 7(d). (b) Distortions appear in the temporal intensity and phase (simulation = solid lines; target waveform = dotted lines). (c) Autocorrelation of distorted (solid) zero-π pulse is compared to the autocorrelation of the target waveform (dotted). Calculated G′=0.1845

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Equations (4)

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I FROG SHG ( ω , τ ) ≜ ∣ ∫ E ( t ) E ( t − τ ) exp ( − i ω t ) d t ∣ 2 ,
G ≜ 1 N 2 ∑ i , j = 1 N ∣ I FROG ( ω i , τ j ) − α I FROG ( k ) ( ω i , τ j ) ∣ 2
= 1 N 2 ∑ i , j = 1 N ∣ I FROG Raw ( ω i , τ j ) − α I FROG ( k ) ( ω i , τ j ) ∣ 2 ( I FROG Peak ) 2
G ′ = ∬ ∣ I FROG Target ( ω , τ ) − α I FROG Meas . ( ω , τ ) ∣ 2 d ω d τ ∬ [ I FROG Target ( ω , τ ) ] 2 d ω d τ ,

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