Abstract

We demonstrate a technique for direct, real-time characterization of the complex (amplitude and phase) temporal response of ultrahigh-speed (GHz-bandwidth) optical modulators. The demonstrated technique is based on pulse interferometry combined with time-frequency mapping processes using fiber linear dispersion. A new mechanism is incorporated to overcome the temporal resolution (bandwidth) limitation of the detectable modulation response in our previously reported setup [1]. This mechanism, referred to as ‘common-path temporal image magnification’, lowers the required detection bandwidth by a factor of more than 10, enabling real-time single-shot waveform acquisition without loss of information using a conventional temporal digitizer. The design specifications of the proposed measurement setup are derived and discussed in detail. As a proof-of-concept experiment, real-time characterization of a complex electro-optic modulation temporal response with time features as fast as ~35 ps (modulation bandwidth > 40-GHz) was obtained and displayed at a video rate of 30 frames/sec.

© 2009 Optical Society of America

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References

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  1. Y. Park, T. -J. Ahn, and J. Azaña, “Direct time-response measurement of high-speed optical modulators based on stretched-pulse interferometry,” Opt. Lett. 32, 3411–3413 (2007)
    [Crossref] [PubMed]
  2. C. Dorrer, “Interferometric techniques for the characterization of temporal modulators,” IEEE Photon. Technol. Lett. 17, 2688–2690 (2005)
    [Crossref]
  3. 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]
  4. F. P. Romstad, D. Birkedal, J. Mlrk, and J. M. Hvam, “Heterodyne technique for measuring the amplitude and phase transfer functions of an optical modulator,” IEEE Photon. Technol. Lett. 14, 621–623 (2002)
    [Crossref]
  5. Y Shi, L. Yan, and A. E. Willner, “High-speed electrooptic modulator characterization using optical spectrum analysis,” J. Lightwave Technol. 21, 2358–2367 (2003)
    [Crossref]
  6. J. Azaña, “Lensless imaging of an arbitrary object,” Opt. Lett. 28, 501–503 (2003)
    [Crossref] [PubMed]
  7. Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations,” J. Lightwave Technol. 21, 3085–3103 (2003)
    [Crossref]
  8. C. V. Bennett and B. H. Kolner, “Principles of Parametric Temporal Imaging-Part I: System Configurations,” IEEE J. Quantum Electron. 36, 430–437 (2000)
    [Crossref]
  9. Y. Park, T. -J. Ahn, J. -C. Kieffer, and J. Azaña, “Optical frequency domain reflectometry based on real-time Fourier transformation,” Opt. Express 15, 4597–4616 (2007)
    [Crossref] [PubMed]
  10. J. Azaña, “Design specification of time-domain spectral shaping optical system based on dispersion and temporal modulation,” IEE Electron. Lett. 39, 1530–1532, (2003)
    [Crossref]
  11. J. Azaña and M. A. Muriel, “Temporal Talbot effect in fiber gratings and its applications,” Appl. Opt. 38, 6700–6704 (1999)
    [Crossref]
  12. J. Azaña, N. K. Berger, B. Levit, and B. Fischer, “Simplified temporal imaging systems for optical waveforms,” IEEE Photon. Technol. Lett. 17, 94–96 (2005)
    [Crossref]
  13. L. Lepetit, G. Chériaux, and M. Joffre, “Linear technique of phase measurement by femtosecond spectral inter-ferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995).
    [Crossref]
  14. R. A. Saunders, J. P. King, and I. Hardcastle, “Wideband chirp measurement techniques for high bit rate sources,” Electron. Lett. 30, 1336–1338 (1994)
    [Crossref]
  15. R. Monnard, C. R. Doerr, and C. R. Giles, “Real-time dynamic chirp measurements of optical signal,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 120–121
  16. C. Laverdière, A. Fekecs, and M. Têtu, “A new method for measuring time-resolved frequency chirp of high bit rate sources” IEEE Photon. Technol. Lett. 15, 446–448 (2003)
    [Crossref]
  17. 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]

2007 (2)

2005 (2)

J. Azaña, N. K. Berger, B. Levit, and B. Fischer, “Simplified temporal imaging systems for optical waveforms,” IEEE Photon. Technol. Lett. 17, 94–96 (2005)
[Crossref]

C. Dorrer, “Interferometric techniques for the characterization of temporal modulators,” IEEE Photon. Technol. Lett. 17, 2688–2690 (2005)
[Crossref]

2004 (1)

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]

2003 (5)

C. Laverdière, A. Fekecs, and M. Têtu, “A new method for measuring time-resolved frequency chirp of high bit rate sources” IEEE Photon. Technol. Lett. 15, 446–448 (2003)
[Crossref]

J. Azaña, “Design specification of time-domain spectral shaping optical system based on dispersion and temporal modulation,” IEE Electron. Lett. 39, 1530–1532, (2003)
[Crossref]

Y Shi, L. Yan, and A. E. Willner, “High-speed electrooptic modulator characterization using optical spectrum analysis,” J. Lightwave Technol. 21, 2358–2367 (2003)
[Crossref]

J. Azaña, “Lensless imaging of an arbitrary object,” Opt. Lett. 28, 501–503 (2003)
[Crossref] [PubMed]

Y. Han and B. Jalali, “Photonic time-stretched analog-to-digital converter: fundamental concepts and practical considerations,” J. Lightwave Technol. 21, 3085–3103 (2003)
[Crossref]

2002 (2)

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]

F. P. Romstad, D. Birkedal, J. Mlrk, and J. M. Hvam, “Heterodyne technique for measuring the amplitude and phase transfer functions of an optical modulator,” IEEE Photon. Technol. Lett. 14, 621–623 (2002)
[Crossref]

2000 (1)

C. V. Bennett and B. H. Kolner, “Principles of Parametric Temporal Imaging-Part I: System Configurations,” IEEE J. Quantum Electron. 36, 430–437 (2000)
[Crossref]

1999 (1)

1995 (1)

1994 (1)

R. A. Saunders, J. P. King, and I. Hardcastle, “Wideband chirp measurement techniques for high bit rate sources,” Electron. Lett. 30, 1336–1338 (1994)
[Crossref]

Ahn, T. -J.

Azaña, J.

Bennett, C. V.

C. V. Bennett and B. H. Kolner, “Principles of Parametric Temporal Imaging-Part I: System Configurations,” IEEE J. Quantum Electron. 36, 430–437 (2000)
[Crossref]

Berger, N. K.

J. Azaña, N. K. Berger, B. Levit, and B. Fischer, “Simplified temporal imaging systems for optical waveforms,” IEEE Photon. Technol. Lett. 17, 94–96 (2005)
[Crossref]

Birkedal, D.

F. P. Romstad, D. Birkedal, J. Mlrk, and J. M. Hvam, “Heterodyne technique for measuring the amplitude and phase transfer functions of an optical modulator,” IEEE Photon. Technol. Lett. 14, 621–623 (2002)
[Crossref]

Chériaux, G.

Doerr, C. R.

R. Monnard, C. R. Doerr, and C. R. Giles, “Real-time dynamic chirp measurements of optical signal,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 120–121

Dorrer, C.

C. Dorrer, “Interferometric techniques for the characterization of temporal modulators,” IEEE Photon. Technol. Lett. 17, 2688–2690 (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]

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]

Fekecs, A.

C. Laverdière, A. Fekecs, and M. Têtu, “A new method for measuring time-resolved frequency chirp of high bit rate sources” IEEE Photon. Technol. Lett. 15, 446–448 (2003)
[Crossref]

Fischer, B.

J. Azaña, N. K. Berger, B. Levit, and B. Fischer, “Simplified temporal imaging systems for optical waveforms,” IEEE Photon. Technol. Lett. 17, 94–96 (2005)
[Crossref]

Giles, C. R.

R. Monnard, C. R. Doerr, and C. R. Giles, “Real-time dynamic chirp measurements of optical signal,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 120–121

Han, Y.

Hardcastle, I.

R. A. Saunders, J. P. King, and I. Hardcastle, “Wideband chirp measurement techniques for high bit rate sources,” Electron. Lett. 30, 1336–1338 (1994)
[Crossref]

Hvam, J. M.

F. P. Romstad, D. Birkedal, J. Mlrk, and J. M. Hvam, “Heterodyne technique for measuring the amplitude and phase transfer functions of an optical modulator,” IEEE Photon. Technol. Lett. 14, 621–623 (2002)
[Crossref]

Jalali, B.

Joffre, M.

Kang, I.

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]

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]

Kieffer, J. -C.

King, J. P.

R. A. Saunders, J. P. King, and I. Hardcastle, “Wideband chirp measurement techniques for high bit rate sources,” Electron. Lett. 30, 1336–1338 (1994)
[Crossref]

Kolner, B. H.

C. V. Bennett and B. H. Kolner, “Principles of Parametric Temporal Imaging-Part I: System Configurations,” IEEE J. Quantum Electron. 36, 430–437 (2000)
[Crossref]

Laverdière, C.

C. Laverdière, A. Fekecs, and M. Têtu, “A new method for measuring time-resolved frequency chirp of high bit rate sources” IEEE Photon. Technol. Lett. 15, 446–448 (2003)
[Crossref]

Lepetit, L.

Levit, B.

J. Azaña, N. K. Berger, B. Levit, and B. Fischer, “Simplified temporal imaging systems for optical waveforms,” IEEE Photon. Technol. Lett. 17, 94–96 (2005)
[Crossref]

Mlrk, J.

F. P. Romstad, D. Birkedal, J. Mlrk, and J. M. Hvam, “Heterodyne technique for measuring the amplitude and phase transfer functions of an optical modulator,” IEEE Photon. Technol. Lett. 14, 621–623 (2002)
[Crossref]

Monnard, R.

R. Monnard, C. R. Doerr, and C. R. Giles, “Real-time dynamic chirp measurements of optical signal,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 120–121

Muriel, M. A.

Park, Y.

Romstad, F. P.

F. P. Romstad, D. Birkedal, J. Mlrk, and J. M. Hvam, “Heterodyne technique for measuring the amplitude and phase transfer functions of an optical modulator,” IEEE Photon. Technol. Lett. 14, 621–623 (2002)
[Crossref]

Saunders, R. A.

R. A. Saunders, J. P. King, and I. Hardcastle, “Wideband chirp measurement techniques for high bit rate sources,” Electron. Lett. 30, 1336–1338 (1994)
[Crossref]

Shi, Y

Têtu, M.

C. Laverdière, A. Fekecs, and M. Têtu, “A new method for measuring time-resolved frequency chirp of high bit rate sources” IEEE Photon. Technol. Lett. 15, 446–448 (2003)
[Crossref]

Willner, A. E.

Yan, L.

Appl. Opt. (1)

Electron. Lett. (1)

R. A. Saunders, J. P. King, and I. Hardcastle, “Wideband chirp measurement techniques for high bit rate sources,” Electron. Lett. 30, 1336–1338 (1994)
[Crossref]

IEE Electron. Lett. (1)

J. Azaña, “Design specification of time-domain spectral shaping optical system based on dispersion and temporal modulation,” IEE Electron. Lett. 39, 1530–1532, (2003)
[Crossref]

IEEE J. Quantum Electron. (1)

C. V. Bennett and B. H. Kolner, “Principles of Parametric Temporal Imaging-Part I: System Configurations,” IEEE J. Quantum Electron. 36, 430–437 (2000)
[Crossref]

IEEE Photon. Technol. Lett. (5)

C. Dorrer, “Interferometric techniques for the characterization of temporal modulators,” IEEE Photon. Technol. Lett. 17, 2688–2690 (2005)
[Crossref]

F. P. Romstad, D. Birkedal, J. Mlrk, and J. M. Hvam, “Heterodyne technique for measuring the amplitude and phase transfer functions of an optical modulator,” IEEE Photon. Technol. Lett. 14, 621–623 (2002)
[Crossref]

C. Laverdière, A. Fekecs, and M. Têtu, “A new method for measuring time-resolved frequency chirp of high bit rate sources” IEEE Photon. Technol. Lett. 15, 446–448 (2003)
[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]

J. Azaña, N. K. Berger, B. Levit, and B. Fischer, “Simplified temporal imaging systems for optical waveforms,” IEEE Photon. Technol. Lett. 17, 94–96 (2005)
[Crossref]

J. Lightwave Technol. (2)

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

Opt. Express (1)

Opt. Lett. (3)

Other (1)

R. Monnard, C. R. Doerr, and C. R. Giles, “Real-time dynamic chirp measurements of optical signal,” in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, 1998), pp. 120–121

Supplementary Material (1)

» Media 1: AVI (3898 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Concept diagram of the time-to-frequency conversion process and the temporal image magnification used for the proposed modulator direct time-response measurement in real time.

Fig. 2.
Fig. 2.

Modulation waveform in intensity (dashed red lines) and the imaged waveform via the TFM process for an insufficient amount of dispersion (a), an optimum dispersion value (b), and an excessively high dispersion (c)

Fig. 3.
Fig. 3.

Dispersion upper/lower boundaries of the first temporal stretcher ensuring a TFM accuracy higher than 99.8% as a function of the modulation time width (FWHM), assuming a fixed input optical spectrum of 3 nm

Fig. 4.
Fig. 4.

Practical experimental setup for the direct real-time E-O impulse response measurement.

Fig. 5.
Fig. 5.

Spectral-domain detection: temporal intensity and phase responses of the intensity modulator to the 28ps-FWHM electric pulse (inset)

Fig. 6.
Fig. 6.

Time-domain detection: (a) temporal intensity and phase responses for the same modulation and (b) corresponding frequency chirp.

Fig. 7.
Fig. 7.

A dynamic movie displaying the impulse response of the E-O modulator excited by a 28-ps electric pulse in terms of amplitude (top graph), phase (middle graph), and instantaneous frequency (bottom graph). The horizontal axis is a triggered time in ns. (Media 1)

Equations (13)

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a ̂ c ( t R ) = h ̂ 1 ( t R ) * a ̂ i ( t R ) h ̂ 1 ( t R ) · a ̂ i ( τ ) exp [ j τ 2 / ( 2 Φ ̈ 1 ) ] exp [ j t R τ / Φ ̈ 1 ] = h ̂ 1 ( t R ) · a ̂ s ( t R )
Φ ̈ 1 8 π Δ ω s 2
C ̂ ( ω ) exp ( j Φ ̈ 1 ω 2 2 ) · [ a ̂ s ( t ) · s ̂ ( t ) ] t = Φ ̈ 1 ω
Φ ̈ 1 ( 2 π Δ t ) > Δ t s
Δ t s · Δ t 2 π < Φ ̈ 1 8 π Δ ω s 2
C = + S ̂ ( t ) · C ̂ ( t ) / A ̂ ( t ) 2 dt [ + S ̂ ( t ) 2 dt · + C ̂ ( t ) / A ̂ ( t ) 4 dt ] 1 / 2
i ̂ ( t R ) h ̂ 1 ( t R ) · { A ̂ i ( ω ) · s ̂ ( t R ) + A ̂ i ( ω Ω ) · exp ( j 2 ω ζ ) }
= h ̂ 1 ( t R ) · i ̂ s ( t R ) ,
i ̂ out put ( t R ) i ̂ ( t R ) * h ̂ 2 ( t R ) h ̂ 2 ( t R ) · I ̂ ( ω t R / Φ ̈ 2 )
I ̂ ( ω " ) I ̂ s ( ω " ) * H ̂ 12 ( ω " )
= H ̂ 12 ( ω " ) Δ ω I ̂ s ( Ω ) · exp ( j Ω 2 4 α ) · exp ( j Ω ω " 2 α ) d Ω
H ̂ 12 ( ω " ) · i ̂ s ( τ = ω " 2 α = t R M )
M = ( Φ ̈ 1 + Φ ̈ 2 ) / Φ ̈ 1

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