Abstract

Manipulation and characterization of information using ultrafast optical signals is critical for numerous applications in telecommunications, biology, quantum information science, spectroscopy, and atomic and molecular physics. Femtosecond pulsed laser sources are available over a wide range of wavelengths and repetition rates, which enable the generation, transmission, and characterization of information at bandwidths beyond 1 THz. In this article, we review the concept of space–time duality as a system design tool for ultrafast optical processing and characterization. The combination of this design framework with recent advances in nonlinear optical devices enables the realization of highly complex signal processing systems that can generate, characterize, and manipulate arbitrary and non-repetitive optical waveforms at unprecedented processing speeds.

© 2013 Optical Society of America

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2013 (3)

2012 (8)

E. Palushani, H. C. H. Mulvad, M. Galili, H. Hu, L. K. Oxenløwe, A. T. Clausen, and P. Jeppesen, “OTDM-toWDM conversion based on time-to-frequency mapping by time-domain optical Fourier transform,” IEEE J. Sel. Top. Quantum Electron. 18, 681–688 (2012).
[CrossRef]

Y. Okawachi, R. Salem, A. R. Johnson, K. Saha, J. S. Levy, M. Lipson, and A. L. Gaeta, “Asynchronous single-shot characterization of high-repetition-rate ultrafast waveforms using a time-lens-based temporal magnifier,” Opt. Lett. 37, 4892–4894 (2012).
[CrossRef]

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481, 62–65 (2012).
[CrossRef]

L.-S. Yan, A. E. Willner, X. Wu, A.-L. Yi, A. Bogoni, Z.-Y. Chen, and H.-Y. Jiang, “All-optical signal processing for ultra-high speed optical systems and networks,” J. Lightwave Technol. 30, 3760–3770 (2012).
[CrossRef]

J. A. Weinstein and N. T. Hunt, “Ultrafast chemical physics: in search of molecular movies,” Nat. Chem. 4, 157–158 (2012).
[CrossRef]

M. Li, H.-S. Jeong, J. Azana, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20, 28273–28280 (2012).
[CrossRef]

K. Goda, A. Fard, O. Malik, G. Fu, A. Quach, and B. Jalali, “High-throughput optical coherence tomography at 800 nm,” Opt. Express 20, 19612–19617 (2012).
[CrossRef]

A. Pasquazi, Y. Y. Park, S. T. Chu, B. E. Little, F. Légaré, R. Morandotti, J. Azana, and D. J. Moss, “Time-lens measurement of subpicosecond optical pulses in CMOS-compatible high-index glass waveguides,” IEEE J. Sel. Top. Quantum Electron. 18, 629–636 (2012).
[CrossRef]

2011 (11)

N. K. Fontaine, R. P. Scott, and S. J. B. Yoo, “Dynamic optical arbitrary waveform generation and detection in InP photonic integrated circuits for Tb/s optical communications,” Opt. Commun. 284, 3693–3705 (2011).
[CrossRef]

V. Torres-Company, J. L. Sáez, and P. Andres, “Space-time analogies in optics,” Prog. Opt. 56, 1–80 (2011).
[CrossRef]

M. A. Foster, R. Salem, and A. L. Gaeta, “Ultrahigh-speed optical processing using space-time duality,” Opt. Photon. News 22(5), 29–35 (2011).
[CrossRef]

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26  Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5, 364–371 (2011).
[CrossRef]

K. Dolgaleva, A. Malacarne, P. Tannouri, L. A. Fernandes, J. R. Grenier, J. S. Aitchison, J. Azaña, R. Morandotti, P. R. Herman, and P. V. S. Marques, “Integrated optical temporal Fourier transformer based on a chirped Bragg grating waveguide,” Opt. Lett. 36, 4416–4418 (2011).
[CrossRef]

E. D. Diebold, N. K. Hon, Z. Tan, J. Chou, T. Sienicki, C. Wang, and B. Jalali, “Giant tunable optical dispersion using chromo-modal excitation of a multimode waveguide,” Opt. Express 19, 23809–23817 (2011).
[CrossRef]

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, “A spacetime cloak, or a history editor,” J. Opt. 13, 024003 (2011).
[CrossRef]

K. G. Petrillo and M. A. Foster, “Scalable ultrahigh-speed optical transmultiplexer using a time lens,” Opt. Express 19, 14051–14059 (2011).
[CrossRef]

H. C. H. Mulvad, E. Palushani, H. Hu, H. Ji, M. Lillieholm, M. Galili, A. T. Clausen, M. Pu, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed optical serial-to-parallel data conversion by time-domain optical Fourier transformation in a silicon nanowire,” Opt. Express 19, B825–B835 (2011).
[CrossRef]

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, H. Nakano, T. Sogawa, A. Takada, and M. Koga, “Generation of 120 fs laser pulses at 1 GHz repetition rate derived from continuous wave laser diode,” Opt. Express 19, 22402–22409 (2011).
[CrossRef]

H. Hu, H. C. H. Mulvad, C. Peucheret, M. Galili, A. Clausen, P. Jeppesen, and L. K. Oxenløwe, “10 GHz pulse source for 640 Gbit/s OTDM based on phase modulator and self-phase modulation,” Opt. Express 19, B343–B349 (2011).
[CrossRef]

2010 (6)

J. Schröder, F. Wang, A. Clarke, E. Ryckeboer, M. Pelusi, M. A. F. Roelens, and B. J. Eggleton, “Aberration-free ultra-fast optical oscilloscope using a four-wave mixing based time-lens,” Opt. Commun. 283, 2611–2614 (2010).
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A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18, 1904–1908 (2010).
[CrossRef]

D. H. Broaddus, M. A. Foster, O. Kuzucu, A. C. Turner-Foster, K. W. Koch, M. Lipson, and A. L. Gaeta, “Temporal-imaging system with simple external-clock triggering,” Opt. Express 18, 14262–14269 (2010).
[CrossRef]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azana, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, 1–5 (2010).
[CrossRef]

S. Thomas, A. Malacarne, F. Fresi, L. Potì, and J. Azaña, “Fiber-based programmable picosecond optical pulse shaper,” J. Lightwave Technol. 28, 1832–1843 (2010).
[CrossRef]

Y. Shen, G. L. Carr, J. B. Murphy, T. Y. Tsang, X. Wang, and X. Yang, “Electro-optic time lensing with an intense single-cycle terahertz pulse,” Phys. Rev. A 81, 053835 (2010).
[CrossRef]

2009 (9)

E. Palushani, L. K. Oxenlowe, M. Galili, H. Mulvad, A. T. Clausen, and P. Jeppesen, “Flat-top pulse generation by the optical Fourier transform technique for ultrahigh speed signal processing,” IEEE J. Quantum Electron. 45, 1317–1324 (2009).
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K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
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M. Li, D. Janner, J. P. Yao, and V. Pruneri, “Arbitrary-order all-fiber temporal differentiator based on a fiber Bragg grating: design and experimental demonstration,” Opt. Express 17, 19798–19807 (2009).
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K. E. Sheetz and J. Squier, “Ultrafast optics: imaging and manipulating biological systems,” J. Appl. Phys. 105, 051101 (2009).
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O. Kuzucu, Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Spectral phase conjugation via temporal imaging,” Opt. Express 17, 20605–20614 (2009).
[CrossRef]

R. Salem, M. A. Foster, A. C. Turner-Foster, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “High-speed optical sampling using a silicon-chip temporal magnifier,” Opt. Express 17, 4324–4329 (2009).
[CrossRef]

M. A. Foster, R. Salem, Y. Okawachi, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Ultrafast waveform compression using a time-domain telescope,” Nat. Photonics 3, 581–585 (2009).
[CrossRef]

Y. Okawachi, R. Salem, M. A. Foster, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “High-resolution spectroscopy using a frequency magnifier,” Opt. Express 17, 5691–5697 (2009).
[CrossRef]

Y. Dai and C. Xu, “Generation of high repetition rate femtosecond pulses from a CW laser by a time-lens loop,” Opt. Express 17, 6584–6590 (2009).
[CrossRef]

2008 (7)

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azana, “Photonic temporal integrator for all-optical computing,” Opt. Express 16, 18202–18214 (2008).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength–time transformation for real-time spectroscopy,” Nat. Photonics 2, 48–51 (2008).
[CrossRef]

D. F. Geraghty, R. Salem, M. A. Foster, and A. L. Gaeta, “A simplified optical correlator and its application to packet-header recognition,” IEEE Photon. Technol. Lett. 20, 487–489 (2008).
[CrossRef]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33, 1047–1049 (2008).
[CrossRef]

M. A. Foster, R. Salem, D. F. Geraghty, A. C. Turner-Foster, M. Lipson, and A. L. Gaeta, “Silicon-chip-based ultrafast optical oscilloscope,” Nature 456, 81–84 (2008).
[CrossRef]

T. Hirooka and M. Nakazawa, “All-optical 40 GHz time-domain Fourier transformation using XPM With a dark parabolic pulse,” IEEE Photon. Technol. Lett. 20, 1869–1871 (2008).
[CrossRef]

T. T. Ng, F. Parmigiani, M. Ibsen, Z. Zhang, P. Petropoulos, and D. J. Richardson, “Compensation of linear distortions by using XPM with parabolic pulses as a time lens,” IEEE Photon. Technol. Lett. 20, 1097–1099 (2008).
[CrossRef]

2007 (3)

2006 (7)

2005 (3)

A. Bogoni, L. Poti, R. Proietti, G. Meloni, F. Ponzini, and P. Ghelfi, “Regenerative and reconfigurable all-optical logic gates for ultra-fast applications,” Electron. Lett. 41, 435–436 (2005).
[CrossRef]

I. S. Lin, J. D. McKinney, and A. M. Weiner, “Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication,” IEEE Microw. Wirel. Compon. Lett. 15, 226–228 (2005).
[CrossRef]

M. Hanna, P.-A. Lacourt, S. Poinsot, and J. Dudley, “Optical pulse generation using soliton-assisted time-lens compression,” Opt. Express 13, 1743–1748 (2005).
[CrossRef]

2004 (2)

M. Nakazawa, T. Hirooka, F. Futami, and S. Watanabe, “Ideal distortion-free transmission using optical Fourier transformation and Fourier transform-limited optical pulses,” IEEE Photon. Technol. Lett. 16, 1059–1061 (2004).
[CrossRef]

J. van Howe, J. Hansryd, and C. Xu, “Multiwavelength pulse generator using time-lens compression,” Opt. Lett. 29, 1470–1472 (2004).
[CrossRef]

2003 (6)

2001 (3)

T. Yamamoto and M. Nakazawa, “Third- and fourth-order active dispersion compensation with a phase modulator in a terabit-per-second optical time-division multiplexed transmission,” Opt. Lett. 26, 647–649 (2001).
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C. V. Bennett and B. H. Kolner, “Aberrations in temporal imaging,” IEEE J. Quantum Electron. 37, 20–32 (2001).
[CrossRef]

D. M. Marom, D. Panasenko, S. Pang-Chen, Y. T. Mazurenko, and Y. Fainman, “Real-time spatial-temporal signal processing with optical nonlinearities,” IEEE J. Sel. Top. Quantum Electron. 7, 683–693 (2001).
[CrossRef]

2000 (5)

N. K. Berger, B. Levit, S. Atkins, and B. Fischer, “Time-lens-based spectral analysis of optical pulses by electrooptic phase modulation,” Electron. Lett. 36, 1644–1646 (2000).
[CrossRef]

L. K. Mouradian, F. Louradour, V. Messager, A. Barthelemy, and C. Froehly, “Spectro-temporal imaging of femtosecond events,” IEEE J. Quantum Electron. 36, 795–801 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging. I. System configurations,” IEEE J. Quantum Electron. 36, 430–437 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging. II. System performance,” IEEE J. Quantum Electron. 36, 649–655 (2000).
[CrossRef]

J. Azana and 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).
[CrossRef]

1999 (4)

P. V. Kelkar, F. Coppinger, A. S. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett. 35, 1661–1662 (1999).
[CrossRef]

M. D. Pelusi, Y. Matsui, and A. Suzuki, “Electrooptic phase modulation of stretched 250  fs pulses for suppression of third-order fiber dispersion in transmission,” IEEE Photon. Technol. Lett. 11, 1461–1463 (1999).
[CrossRef]

M. Romagnoli, P. Franco, R. Corsini, A. Schiffini, and M. Midrio, “Time-domain Fourier optics for polarization-mode dispersion,” Opt. Lett. 24, 1197–1199 (1999).
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C. V. Bennett and B. H. Kolner, “Upconversion time microscope demonstrating 103× magnification of femtosecond waveforms,” Opt. Lett. 24, 783–785 (1999).
[CrossRef]

1998 (1)

Z. Jiang and X.-C. Zhang, “Electro-optic measurement of THz field pulses with a chirped optical beam,” Appl. Phys. Lett. 72, 1945–1947 (1998).
[CrossRef]

1997 (1)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
[CrossRef]

1994 (4)

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30, 1951–1963 (1994).
[CrossRef]

A. A. Godil, B. A. Auld, and D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827–837 (1994).
[CrossRef]

C. V. Bennett, R. P. Scott, and B. H. Kolner, “Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope,” Appl. Phys. Lett. 65, 2513–2515 (1994).
[CrossRef]

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)

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical systems,” Electron. Lett. 29, 268–269 (1993).
[CrossRef]

1990 (1)

I. P. Christov, “Theory of a time telescope,” Opt. Quantum Electron. 22, 473–479 (1990).
[CrossRef]

1989 (1)

1988 (3)

B. H. Kolner, “Active pulse compression using an integrated electro-optic phase modulator,” Appl. Phys. Lett. 52, 1122–1124 (1988).
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A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
[CrossRef]

T. Kobayashi, H. Yao, K. Amano, Y. Fukushima, A. Morimoto, and T. Sueta, “Optical pulse compression using high-frequency electrooptic phase modulation,” IEEE J. Quantum Electron. 24, 382–387 (1988).
[CrossRef]

1984 (1)

1983 (1)

1978 (1)

J. K. Wigmore and D. R. Grischkowsky, “Temporal compression of light,” IEEE J. Quantum Electron. QE-14, 310–315 (1978).
[CrossRef]

1975 (1)

J. E. Bjorkholm, E. H. Turner, and D. B. Pearson, “Conversion of cw light beam into a train of subnanosecond pulses using frequency modulation and the dispersion of a near resonant atomic vapor,” Appl. Phys. Lett. 26, 564–566 (1975).
[CrossRef]

1971 (1)

W. J. Caputi, “Stretch: a time transformation technique,” IEEE Trans. Aerosp. Electronic Syst. AES-7, 269–278 (1971).
[CrossRef]

1969 (3)

S. A. Akhmanov, A. P. Sukhorukov, and A. S. Chirkin, “Nonstationary phenomena and space-time analogy in nonlinear optics,” Sov. Phys. JETP 28, 748–757 (1969).

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

M. A. Duguay and J. W. Hansen, “Compression of pulses from a modelocked He-Ne laser,” Appl. Phys. Lett. 14, 14–16 (1969).
[CrossRef]

1968 (2)

J. A. Giordmaine, M. A. Duguay, and J. W. Hansen, “Compression of optical pulses,” IEEE J. Quantum Electron. QE-4, 252–255 (1968).
[CrossRef]

P. Tournois, J.-L. Verner, and G. Bienvenu, “Sur l’analogie optique de certains montages electroniques: formation d’images temporelles de signaux electriques,” C. R. Acad. Sci. 267, 375–378 (1968).

1964 (2)

P. Tournois, “Analogie optique de la compression d’impulsion,” C. R. Acad. Sci. 258, 3839–3842 (1964).

A. V. Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[CrossRef]

Ahn, T. J.

Ahn, T.-J.

Aitchison, J. S.

Akhmanov, S. A.

S. A. Akhmanov, A. P. Sukhorukov, and A. S. Chirkin, “Nonstationary phenomena and space-time analogy in nonlinear optics,” Sov. Phys. JETP 28, 748–757 (1969).

Amano, K.

T. Kobayashi, H. Yao, K. Amano, Y. Fukushima, A. Morimoto, and T. Sueta, “Optical pulse compression using high-frequency electrooptic phase modulation,” IEEE J. Quantum Electron. 24, 382–387 (1988).
[CrossRef]

Andres, P.

V. Torres-Company, J. L. Sáez, and P. Andres, “Space-time analogies in optics,” Prog. Opt. 56, 1–80 (2011).
[CrossRef]

Atkins, S.

N. K. Berger, B. Levit, S. Atkins, and B. Fischer, “Time-lens-based spectral analysis of optical pulses by electrooptic phase modulation,” Electron. Lett. 36, 1644–1646 (2000).
[CrossRef]

Auld, B. A.

A. A. Godil, B. A. Auld, and D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827–837 (1994).
[CrossRef]

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical systems,” Electron. Lett. 29, 268–269 (1993).
[CrossRef]

Ayotte, N.

Azana, J.

M. Li, H.-S. Jeong, J. Azana, and T.-J. Ahn, “25-terahertz-bandwidth all-optical temporal differentiator,” Opt. Express 20, 28273–28280 (2012).
[CrossRef]

A. Pasquazi, Y. Y. Park, S. T. Chu, B. E. Little, F. Légaré, R. Morandotti, J. Azana, and D. J. Moss, “Time-lens measurement of subpicosecond optical pulses in CMOS-compatible high-index glass waveguides,” IEEE J. Sel. Top. Quantum Electron. 18, 629–636 (2012).
[CrossRef]

M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azana, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun. 1, 1–5 (2010).
[CrossRef]

R. Slavík, Y. Park, N. Ayotte, S. Doucet, T.-J. Ahn, S. LaRochelle, and J. Azana, “Photonic temporal integrator for all-optical computing,” Opt. Express 16, 18202–18214 (2008).
[CrossRef]

Y. Park, T. J. Ahn, J. C. Kieffer, and J. Azana, “Optical frequency domain reflectometry based on real-time Fourier transformation,” Opt. Express 15, 4597–4616 (2007).

R. Slavík, Y. Park, M. Kulishov, R. Morandotti, and J. Azana, “Ultrafast all-optical differentiators,” Opt. Express 14, 10699–10707 (2006).
[CrossRef]

J. Azana and 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).
[CrossRef]

Azaña, J.

Banaszek, K.

A. B. U’ren, E. Mukamel, K. Banaszek, and I. A. Walmsley, “Managing photons for quantum information processing,” Phil. Trans. R. Soc. A 361, 1493–1506 (2003).
[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]

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical systems,” Electron. Lett. 29, 268–269 (1993).
[CrossRef]

Barthelemy, A.

L. K. Mouradian, F. Louradour, V. Messager, A. Barthelemy, and C. Froehly, “Spectro-temporal imaging of femtosecond events,” IEEE J. Quantum Electron. 36, 795–801 (2000).
[CrossRef]

Becker, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26  Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5, 364–371 (2011).
[CrossRef]

Ben Ezra, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26  Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5, 364–371 (2011).
[CrossRef]

Bennett, C. V.

V. J. Hernandez, C. V. Bennett, B. D. Moran, A. D. Drobshoff, D. Chang, C. Langrock, M. M. Fejer, and M. Ibsen, “104 MHz rate single-shot recording with subpicosecond resolution using temporal imaging,” Opt. Express 21, 196–203 (2013).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Aberrations in temporal imaging,” IEEE J. Quantum Electron. 37, 20–32 (2001).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging. I. System configurations,” IEEE J. Quantum Electron. 36, 430–437 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Principles of parametric temporal imaging. II. System performance,” IEEE J. Quantum Electron. 36, 649–655 (2000).
[CrossRef]

C. V. Bennett and B. H. Kolner, “Upconversion time microscope demonstrating 103× magnification of femtosecond waveforms,” Opt. Lett. 24, 783–785 (1999).
[CrossRef]

C. V. Bennett, R. P. Scott, and B. H. Kolner, “Temporal magnification and reversal of 100 Gb/s optical data with an up-conversion time microscope,” Appl. Phys. Lett. 65, 2513–2515 (1994).
[CrossRef]

C. V. Bennett, B. D. Moran, C. Langrock, M. M. Fejer, and M. Ibsen, “640  GHz real-time recording using temporal imaging,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CTuA6.

Berger, N. K.

N. K. Berger, B. Levit, S. Atkins, and B. Fischer, “Time-lens-based spectral analysis of optical pulses by electrooptic phase modulation,” Electron. Lett. 36, 1644–1646 (2000).
[CrossRef]

Bergman, K.

R. Salem, N. Ophir, X. Zhu, and K. Bergman, “Rapid eye diagram generation of a 640 Gb/s OTDM signal using a time lens,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2013), paper CM4G.1.

Bhushan, A. S.

P. V. Kelkar, F. Coppinger, A. S. Bhushan, and B. Jalali, “Time-domain optical sensing,” Electron. Lett. 35, 1661–1662 (1999).
[CrossRef]

Bienvenu, G.

P. Tournois, J.-L. Verner, and G. Bienvenu, “Sur l’analogie optique de certains montages electroniques: formation d’images temporelles de signaux electriques,” C. R. Acad. Sci. 267, 375–378 (1968).

Bjorkholm, J. E.

J. E. Bjorkholm, E. H. Turner, and D. B. Pearson, “Conversion of cw light beam into a train of subnanosecond pulses using frequency modulation and the dispersion of a near resonant atomic vapor,” Appl. Phys. Lett. 26, 564–566 (1975).
[CrossRef]

Bloom, D. M.

A. A. Godil, B. A. Auld, and D. M. Bloom, “Picosecond time-lenses,” IEEE J. Quantum Electron. 30, 827–837 (1994).
[CrossRef]

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]

M. T. Kauffman, A. A. Godil, B. A. Auld, W. C. Banyai, and D. M. Bloom, “Applications of time lens optical systems,” Electron. Lett. 29, 268–269 (1993).
[CrossRef]

Boardman, A.

M. W. McCall, A. Favaro, P. Kinsler, and A. Boardman, “A spacetime cloak, or a history editor,” J. Opt. 13, 024003 (2011).
[CrossRef]

Bogoni, A.

L.-S. Yan, A. E. Willner, X. Wu, A.-L. Yi, A. Bogoni, Z.-Y. Chen, and H.-Y. Jiang, “All-optical signal processing for ultra-high speed optical systems and networks,” J. Lightwave Technol. 30, 3760–3770 (2012).
[CrossRef]

A. Bogoni, L. Poti, R. Proietti, G. Meloni, F. Ponzini, and P. Ghelfi, “Regenerative and reconfigurable all-optical logic gates for ultra-fast applications,” Electron. Lett. 41, 435–436 (2005).
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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Optical time lens based on four-wave mixing on a silicon chip,” Opt. Lett. 33, 1047–1049 (2008).
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T. Yamamoto and M. Nakazawa, “Third- and fourth-order active dispersion compensation with a phase modulator in a terabit-per-second optical time-division multiplexed transmission,” Opt. Lett. 26, 647–649 (2001).
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Opt. Photon. News (1)

M. A. Foster, R. Salem, and A. L. Gaeta, “Ultrahigh-speed optical processing using space-time duality,” Opt. Photon. News 22(5), 29–35 (2011).
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A. B. U’ren, E. Mukamel, K. Banaszek, and I. A. Walmsley, “Managing photons for quantum information processing,” Phil. Trans. R. Soc. A 361, 1493–1506 (2003).
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Y. Shen, G. L. Carr, J. B. Murphy, T. Y. Tsang, X. Wang, and X. Yang, “Electro-optic time lensing with an intense single-cycle terahertz pulse,” Phys. Rev. A 81, 053835 (2010).
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Other (8)

A. Weiner, Ultrafast Optics (Wiley, 2011).

K. G. Petrillo, J. R. Stroud, and M. A. Foster, “An all-optical sample-and-hold architecture incorporating amplitude jitter suppression,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper CM2B.7.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005).

B. H. Kolner, “Electro-optic time lenses for shaping and imaging optical waveforms,” in Broadband Optical Modulators: Science, Technology, and Applications, A. Chen and E. Murphy, eds. (CRC Press, 2011), Chap. 19.

R. Salem, N. Ophir, X. Zhu, and K. Bergman, “Rapid eye diagram generation of a 640 Gb/s OTDM signal using a time lens,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2013), paper CM4G.1.

C. V. Bennett, B. D. Moran, C. Langrock, M. M. Fejer, and M. Ibsen, “640  GHz real-time recording using temporal imaging,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CTuA6.

L. F. Mollenauer and C. Xu, “Time-lens timing-jitter compensator in ultra-long haul DWDM dispersion managed soliton transmissions,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2002), paper CPDBl.

D. H. Broaddus, M. A. Foster, O. Kuzucu, K. W. Koch, and A. L. Gaeta, “Ultrafast, single-shot phase and amplitude measurement via a temporal imaging approach,” in Conference on Lasers and Electro-Optics 2010, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMK6.

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Figures (27)

Figure 1
Figure 1

(a) Diffraction of a highly confined beam and its collimation by a conventional lens. (b) Temporal equivalent of the beam collimation showing a short pulse undergoing dispersion and passing through a time lens, which shrinks the signal bandwidth and creates a long transform-limited pulse.

Figure 2
Figure 2

(a) Far-field diffraction of a uniformly illuminated slit and its far-field diffraction pattern showing the 1D Fourier transformation. (b) Equivalent of the far-field diffraction in the time domain caused by dispersion. The output waveform in time has the same shape as that of the input spectrum.

Figure 3
Figure 3

(a) Spatial 4 - f system using two lenses. (b) Temporal equivalent of the 4 - f system utilizing time lenses. (c) Reduced temporal 4 - f system using the concept of far-field dispersion and opposite signs of dispersion to eliminate the time-lens components.

Figure 4
Figure 4

(a) Experimental setup demonstrating the concept of temporal 4 - f correlator. The phase mask is applied using an electro-optic phase modulator. (b) Measured output on a cross-correlator for an input pattern matched to the target pattern. A distinct peak at the center can be seen. (c) Measured output for an unmatched input pattern. Copyright 2008 IEEE. Reprinted, with permission, from Geraghty et al., IEEE Photon. Technol. Lett. 20, 487–489 (2008) [47].

Figure 5
Figure 5

(a) Experimental setup demonstrating a programmable waveform generator based on a temporal 4 - f system. The phase mask is applied using an electro-optic phase modulator, and the dispersion is implemented using a chirped fiber Bragg grating. (b) Output of the waveform generator shown for two consecutive waveforms demonstrating a program update rate of 625 MHz. Copyright 2010 IEEE. Reprinted, with permission, from Thomas et al., J. Lightwave Technol. 28, 1832–1843 (2010) [49].

Figure 6
Figure 6

(a) Gaussian beam focusing using a thin lens. (b) Pulse compression using a time lens. A long narrow-band pulse that fits within the time-lens aperture ( Δ T ) can be compressed using a time lens and a dispersive path that matches the focal GDD of the time lens. The shortest pulse that can be achieved in this configuration is defined as the temporal resolution δ τ of the time lens.

Figure 7
Figure 7

Time-lens system based on FWM. A short pulse is linearly chirped before mixing with the signal via the FWM process.

Figure 8
Figure 8

Conceptual diagram showing the temporal 2 - f system, which functions as a Fourier processor analogous to its dual system in the spatial domain.

Figure 9
Figure 9

(a) Conceptual diagram of the 2 - f system, which functions as a Fourier processor converting the waveform from the time domain to the frequency domain [70]. (b) Comparison between the measurement of a complex waveform performed using the 2 - f system on an optical spectrum analyzer and the cross-correlation measurement. (c) Comparison between single-shot measurements performed for three different waveforms using the 2 - f system on a single-shot spectrometer and the corresponding multi-shot measurements by a cross-correlator.

Figure 10
Figure 10

(a) Experimental setup used for demonstrating OTDM-to-WDM conversion. (b) Output from the FWM device showing the format conversion from 640 Gb / s OTDM to WDM. (c) Output WDM spectrum and the BER values for different channels across the spectrum. (d) Eye diagrams of the references DPSK and two output channels corresponding to the center and the edge of the time-lens window. Reproduced with permission. Copyright 2011, Optical Society of America [81].

Figure 11
Figure 11

(a) Spectrogram depiction of the ideal time-lens FWM interaction for full OTDM demultiplexing. (b) The temporally overlapping regions of the pump pulses yield an undesirable non-degenerate FWM process that causes crosstalk from the edge channels onto the center channels. (c) Spectrum of the generated WDM idlers for all channels present (red curve) and with the center channels blocked (black dashed curve) showing the transfer of power from the edge channels to the center channels through the non-degenerate FWM process. (d) Eye diagram of a channel suffering from non-degenerate FWM crosstalk. (e) Received power necessary for a BER of 10 6 and 10 9 versus WDM channel. Reproduced with permission. Copyright 2013, Optical Society of America [84].

Figure 12
Figure 12

Short pulse generation using an electro-optic time lens. The system can be seen as a 2 - f Fourier processor in which the first dispersive path is removed due to the fact that it does not affect the long input pulse.

Figure 13
Figure 13

(a) Experimental setup demonstrating pulse compression using a phase-modulator-based time lens in a re-circulating loop configuration. (b) Optical spectrum of the pulse generated after nine round-trips in the loop. (c) Autocorrelation of the output pulse showing a FWHM width of 697 fs corresponding to a 516 fs pulsewidth. Reproduced with permission. Copyright 2007, Optical Society of America [90].

Figure 14
Figure 14

Temporal Fourier processor based on a 2 - f configuration used for compensating for the effects of dispersion and timing jitter on a pulse.

Figure 15
Figure 15

Concept of temporal magnification and its spatial analog. Two dispersive paths are placed before and after a time-lens system in order to achieve temporal magnification (or compression).

Figure 16
Figure 16

(a) Experimental setup showing a temporal magnification system based on a sum-frequency-generation time lens using a PPLN waveguide. (b) Magnified output for a 776 fs impulse input with inset FROG measurement. (c) Resolution comparison of a three-pulse packet ( < 1 ps FWHM each) before and after temporal imaging, as captured on a 20 GHz real-time scope (interpolated). Adapted with permission. Copyright 2013, Optical Society of America [78].

Figure 17
Figure 17

Temporal magnification with large magnification factors. The system is equivalent to a time-to-frequency conversion stage in a 2 - f Fourier processor, followed by a large dispersive path for frequency-to-time conversion.

Figure 18
Figure 18

(a) Experimental setup used for temporal magnification with large magnification factors. (b) Input cross-correlation and magnified output trace for an ultrafast waveform magnified by 520 times. (c) Single-shot traces of a random bit sequences at 80 Gb / s , stretched by 65 times and measured on a real-time oscilloscope. (d) Eye diagram of an 80 Gb / s data signal that is stretched by 65 times and measured on a 10 Gb / s digital communication analyzer. Adapted with permission. Copyright 2009, Optical Society of America [98].

Figure 19
Figure 19

Temporal telescope based on a 4 - f system. The system functions similar to its spatial counterpart. Two time lenses with two different focal GDDs are used. The ratio between the GDDs gives the temporal compression (spectral magnification) factor of the system.

Figure 20
Figure 20

Experimental results showing the compression of optical waveforms in a temporal 4 - f system [103]. Two digital packets and an analog waveform were compressed by 27 times. Red traces show the input measured on a 10 GHz oscilloscope, and blue traces show the cross-correlation measurement of the output waveform.

Figure 21
Figure 21

(a) Experimental setup used for demonstrating spectral magnification in a 4 - f system. The setup includes a gas cell to imprint narrow absorption features onto a broadband ASE spectrum. (b) Input and output spectra showing a spectral magnification factor of 105. Adapted with permission. Copyright 2009, Optical Society of America [104].

Figure 22
Figure 22

Correspondence between temporal and spectral magnification systems, which is realized by interchanging the time lens and GDD components.

Figure 23
Figure 23

(a) Spectral phase conjugation (SPC) system used for compensating all orders of dispersion and some nonlinear effects. The SPC system is placed at the mid-point of a transmission link. (b) SPC system based on a conjugating time lens and a non-conjugating time lens in a 4 - f configuration. The system has a magnification factor of M = 1 , which provides the time reversal.

Figure 24
Figure 24

Time-lens systems used for SPC in [107]. The first time lens is a standard FWM lens that conjugates the signal. The second time lens uses the output from the first time lens as one of its pump sources in order to create a non-conjugating time lens. The system is wavelength preserving.

Figure 25
Figure 25

(a) Spectral phase conjugation experimental setup based on a 4 - f configuration. (b) Cross-correlation measurement of the pulse at four points throughout a transmission system with GVD or TOD. Adapted with permission. Copyright 2009, Optical Society of America [107].

Figure 26
Figure 26

(a) Comparison between a conventional time lens and a split time lens. The temporal profile of the phase and its derivative are shown. (b) Conceptual diagram of a 4 - f system with split time lenses designed to produce a temporal gap at the Fourier plane of the system for the purpose of temporal cloaking [108].

Figure 27
Figure 27

(a) Block diagram of the temporal cloaking experimental setup [108]. The time-wavelength plots show the changes in the signal as it travels through the system. A temporal gap in the beam is created at the Fourier plane of the system. (b) The time-wavelength distribution measured after the first time lens, at the Fourier plane, and before the second time lens. (c) Detected output when the cloaking system in on (solid red) and when the cloaking system is off (dashed blue), showing the events have been masked by the cloaking system.

Equations (38)

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A z = i 2 k 2 A x 2 ,
A z = i β 2 2 2 A τ 2 ,
ϕ ( k x ) = k x 2 z 2 k ,
ϕ ( Ω ) = β 2 Ω 2 z 2 = D 2 Ω 2 2 ,
h ( x ) = h S exp ( i π λ z x 2 ) ,
ϕ ( x ) = k x 2 2 f .
h T ( τ ) = h T exp ( i τ 2 2 D 2 ) ,
ϕ ( τ ) = τ 2 2 D f ,
u out ( τ ) = h T exp ( i τ 2 2 D 2 ) U ˜ in ( Ω = τ D 2 ) ,
w 2 = λ f π w 1 .
δ τ = 4 ln ( 2 ) | D f | Δ T .
N = Δ T δ τ = Δ T 2 4 ln ( 2 ) | D f | .
φ ( t ) = ± ( π V m V π ) cos ( ω m t ) ± ( π V m V π ) ( 1 ω m 2 t 2 2 ) ,
| D f | = V π π V m ω m 2 .
δ τ = ( 4 ln ( 2 ) π ) V π V m ω m ,
N = ( π 4 ln ( 2 ) ) V m V π .
ϕ XPM ( t ) = 2 γ L P ( t ) .
ϕ XPM ( t ) = 2 γ L P 0 ( 1 t 2 T 0 2 ) ,
N = 4 γ P 0 L ln ( 2 ) .
u i ( τ ) = η u p 2 ( τ ) u s * ( τ ) ,
ϕ p ( τ ) = τ 2 2 D p .
D f = D p 2 .
Δ T = 1 2 | D p | Δ Ω p .
δ τ = 2 2 ln ( 2 ) 1 Δ Ω p .
N = Δ T δ τ = | D p | Δ Ω p 2 4 ln ( 2 ) .
L TOD = τ 1 / e 3 | β 3 , p | ,
| D p | Δ Ω p 3 < | β 2 , p β 3 , p | .
ϕ total = ϕ N L + ϕ L = 2 γ P L Δ k L L ,
ϕ total β 2 , FWM Δ ω 2 L ,
1 2 β 3 , FWM Δ ω 2 L Δ Ω p < 1 ,
U ˜ out ( Ω ) = H Ω u in ( τ = D f Ω ) ,
u out ( τ ) = H τ U ˜ in ( Ω = τ D f ) ,
1 D in + 1 D out = 1 D f .
u out ( τ ) = M 1 2 exp ( i τ 2 2 M D f ) u in ( τ M ) ,
M = D out D in .
U ˜ FP ( Ω ) = H Ω u in ( τ = D in Ω ) .
u out ( τ ) = h T H Ω exp ( i τ 2 2 D out ) u in ( D in D out τ ) .
u i , 2 ( τ ) = η u CW u p , 2 * ( τ ) u i , 1 ( τ ) .

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