Abstract

In the complete reconstruction of ultrashort optical pulses based on temporal interferometry, the chromatic dispersion and the optical time delay are two key factors, which determine the measurement accuracy. Due to the higher order dispersion, the wavelength-to-time mapping becomes nonlinear, leading to a nonuniformly spaced interference pattern and a decreased fringe visibility in the time domain, even though the input pulse is transform limited. On the other hand, an estimation of the time delay difference with a minor deviation from the true value will result in an artificial linear chirp in the reconstructed phase of the pulse under test. In this paper, a rigorous mathematical analysis on the nonlinear frequency-to-time mapping is performed, with which the phenomena of a nonuniformly spaced interference pattern and a decreased fringe visibility are explained. A frequency-to-time mapping function including higher order dispersion is developed. With a general mapping function, using a transform-limited pulse as the reference signal, we propose a method for real-time tracking of the system parameters, including the chromatic dispersion corresponding to all the optical devices incorporated in the system and the time delay introduced by the interferometer. Finally, a complete reconstruction of a 237 fs optical pulse is demonstrated experimentally with an average angular error of 0.18 rad ranging from 190.65 to 193.85 THz.

© 2009 IEEE

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2009 (1)

N. Savage, "Ultrashort pulse characterization," Nat. Photon. 3, 230-232 (2009).

2008 (2)

T.-J. Ahn, Y. Park, J. Azaña, "Improved optical pulse characterization based on feedback-controlled Hilbert transformation temporal interferometry," IEEE Photon. Technol. Lett. 20, 475-477 (2008).

K. Goda, D. R. Solli, B. Jalali, "Real-time optical reflectometry enabled by amplified dispersive Fourier transformation," Appl. Phys. Lett. 93, 0311061-0311063 (2008).

2006 (1)

C. Dorrer, "High-speed measurements for optical telecommunication systems," IEEE J. Sel. Topics Quantum Electron. 12, 843-858 (2006).

2005 (2)

M. Westlund, P. A. Andrekson, H. Sunnerud, J. Hansryd, J. Li, "High performance optical-fiber-nonlinearity-based optical waveform monitoring," J. Lightw. Technol. 23, 2012-2022 (2005).

N. K. Berger, B. Levit, V. Smulakovsky, B. Fischer, "Complete characterization of optical pulses by real-time spectral interferometry," Appl. Opt. 44, 7862-7855 (2005).

2004 (1)

2003 (1)

2001 (1)

F. Hakimi, H. Hakimi, "Measurement of optical fiber dispersion and dispersion slope using a pair of short optical pulses and Fourier transform property of dispersive medium," Opt. Eng. 40, 1053-1056 (2001).

2000 (2)

J. Azaña, M. A. Muriel, "Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings," IEEE J. Quantum Electron. 36, 517-526 (2000).

R. G. M. P. Koumans, A. Yariv, "Pulse characterization at 1.5 $\mu{\hbox {m}}$ using time-resolved optical gating based on dispersive propagation," IEEE Photon. Technol. Lett. 12, 666-668 (2000).

1999 (1)

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, U. Keller, "Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).

1998 (2)

1997 (1)

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

1996 (1)

1995 (2)

1983 (1)

1982 (2)

M. Takeda, H. Ina, S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982).

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, "Phase shift technique for the megsurement of chromatic dispersion in optical fibers using LED's," IEEE J. Quantum Electron. QE-18, 1509-1515 (1982).

1979 (1)

Appl. Opt. (2)

Appl. Phys. Lett. (1)

K. Goda, D. R. Solli, B. Jalali, "Real-time optical reflectometry enabled by amplified dispersive Fourier transformation," Appl. Phys. Lett. 93, 0311061-0311063 (2008).

IEEE J. Quantum Electron. (2)

J. Azaña, M. A. Muriel, "Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings," IEEE J. Quantum Electron. 36, 517-526 (2000).

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, "Phase shift technique for the megsurement of chromatic dispersion in optical fibers using LED's," IEEE J. Quantum Electron. QE-18, 1509-1515 (1982).

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

C. Dorrer, "High-speed measurements for optical telecommunication systems," IEEE J. Sel. Topics Quantum Electron. 12, 843-858 (2006).

IEEE Photon. Technol. Lett. (2)

T.-J. Ahn, Y. Park, J. Azaña, "Improved optical pulse characterization based on feedback-controlled Hilbert transformation temporal interferometry," IEEE Photon. Technol. Lett. 20, 475-477 (2008).

R. G. M. P. Koumans, A. Yariv, "Pulse characterization at 1.5 $\mu{\hbox {m}}$ using time-resolved optical gating based on dispersive propagation," IEEE Photon. Technol. Lett. 12, 666-668 (2000).

J. Lightw. Technol. (1)

M. Westlund, P. A. Andrekson, H. Sunnerud, J. Hansryd, J. Li, "High performance optical-fiber-nonlinearity-based optical waveform monitoring," J. Lightw. Technol. 23, 2012-2022 (2005).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (3)

Nat. Photon. (1)

N. Savage, "Ultrashort pulse characterization," Nat. Photon. 3, 230-232 (2009).

Opt. Eng. (1)

F. Hakimi, H. Hakimi, "Measurement of optical fiber dispersion and dispersion slope using a pair of short optical pulses and Fourier transform property of dispersive medium," Opt. Eng. 40, 1053-1056 (2001).

Opt. Lett. (5)

Rev. Sci. Instrum. (1)

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

Science (1)

G. Steinmeyer, D. H. Sutter, L. Gallmann, N. Matuschek, U. Keller, "Frontiers in ultrashort pulse generation: Pushing the limits in linear and nonlinear optics," Science 286, 1507-1512 (1999).

Other (4)

R. M. Fortenberry, W. V. Sorin, H. Lin, S. A. Newton, J. K. Andersen, M. N. Islam, "Low-power ultrashort optical pulse characterization using linear dispersion," Proc. Opt. Fiber Commun. Conf. pp. 290-291.

R. M. Fortenberry, W. V. Sorin, Apparatus for characterizing short optical pulses U.S. Patent 5,684,586 (1997).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 2007).

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