Abstract

Temporal optics is an emerging field in which optical signals are considered similarly to objects in spatial optics. Indeed, temporal magnifications, temporal Fourier transform, and temporal signal processing have been demonstrated by adopting optical schemes from space to time. However, temporal imaging has so far focused on the equivalent of two-dimensional spatial imaging schemes, while ignoring the depth of the input. Here we adopt the concept of three-dimensional (3D) imaging into the time domain, providing a new dimension in temporal optics. We developed the concept of temporal 3D objects and demonstrated temporal depth imaging. First, we define signals with temporal depth as signals where each point in time has a different dispersion value. Next, we demonstrate how to measure these signals with a moving time lens. Finally, we present a time lens array and use it to realize temporal depth imaging with a single measurement. Our temporal depth imaging concept will enable measurements of ultrafast nonperiodic phenomena, such as optical rogue waves and the evolution of ultrafast pulses in fiber lasers, with temporal resolution that was not possible until now.

© 2017 Optical Society of America

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References

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2017 (2)

2016 (3)

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
[Crossref]

C. Zhang, B. Li, and K. K.-Y. Wong, “Ultrafast spectroscopy based on temporal focusing and its applications,” IEEE J. Sel. Top. Quantum Electron. 22, 295–306 (2016).
[Crossref]

2015 (1)

M. Fridman, Y. Okawachi, S. Clemmen, M. Ménard, M. Lipson, and A. L. Gaeta, “Waveguide-based single-shot temporal cross-correlator,” J. Opt. 17, 035501 (2015).
[Crossref]

2014 (2)

B. C. Gross, J. L. Erkal, S. Y. Lockwood, C. Chen, and D. M. Spence, “Evaluation of 3D printing and its potential impact on biotechnology and the chemical sciences,” Anal. Chem. 86, 3240–3253 (2014).
[Crossref]

Z. Wu, L. Lei, J. Dong, J. Hou, and X. Zhang, “Reconfigurable temporal Fourier transformation and temporal imaging,” J. Lightwave Technol. 32, 3963–3968 (2014).

2013 (2)

2012 (2)

2011 (1)

2010 (1)

J. Schröder, F. Wang, A. Clarke, E. Ryckeboer, M. Pelusi, M. A. 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).
[Crossref]

2009 (3)

2008 (1)

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 (1)

D. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref]

2004 (1)

2003 (1)

T. Oggier, M. Lehmann, R. Kaufmann, M. Schweizer, M. Richter, P. Metzler, G. Lang, F. Lustenberger, and N. Blanc, “An all-solid-state optical range camera for 3D real-time imaging with sub-centimeter depth resolution (SwissRanger),” Proc. SPIE 5249, 534–545 (2003).
[Crossref]

1994 (1)

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

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

1989 (1)

1978 (1)

1972 (1)

D. Gabor, “Holography, 1948–1971,” Proc. IEEE 60, 655–668 (1972).
[Crossref]

Akhmediev, N.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Amiraranashvili, S.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Arecchi, F. T.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Azana, J.

Baronio, F.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Belic, M.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Bendahmane, A.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Berger, N. K.

Billet, C.

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
[Crossref]

Blanc, N.

T. Oggier, M. Lehmann, R. Kaufmann, M. Schweizer, M. Richter, P. Metzler, G. Lang, F. Lustenberger, and N. Blanc, “An all-solid-state optical range camera for 3D real-time imaging with sub-centimeter depth resolution (SwissRanger),” Proc. SPIE 5249, 534–545 (2003).
[Crossref]

Bortolozzo, U.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Bree, C.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Broderick, N. G. R.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Chang, W.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Chen, C.

B. C. Gross, J. L. Erkal, S. Y. Lockwood, C. Chen, and D. M. Spence, “Evaluation of 3D printing and its potential impact on biotechnology and the chemical sciences,” Anal. Chem. 86, 3240–3253 (2014).
[Crossref]

Chui, P.

Clarke, A.

J. Schröder, F. Wang, A. Clarke, E. Ryckeboer, M. Pelusi, M. A. 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).
[Crossref]

Clemmen, S.

M. Fridman, Y. Okawachi, S. Clemmen, M. Ménard, M. Lipson, and A. L. Gaeta, “Waveguide-based single-shot temporal cross-correlator,” J. Opt. 17, 035501 (2015).
[Crossref]

Coulibaly, S.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Demircan, A.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Dias, F.

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
[Crossref]

Docchio, F.

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors 9, 568–601 (2009).
[Crossref]

Dong, J.

Du, Y.

Duadi, H.

Dudley, J.

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Richardson, D. J.

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]

Richter, M.

T. Oggier, M. Lehmann, R. Kaufmann, M. Schweizer, M. Richter, P. Metzler, G. Lang, F. Lustenberger, and N. Blanc, “An all-solid-state optical range camera for 3D real-time imaging with sub-centimeter depth resolution (SwissRanger),” Proc. SPIE 5249, 534–545 (2003).
[Crossref]

Roelens, M. A.

J. Schröder, F. Wang, A. Clarke, E. Ryckeboer, M. Pelusi, M. A. 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).
[Crossref]

Ropers, C.

D. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref]

Runge, A. F. J.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Ryckeboer, E.

J. Schröder, F. Wang, A. Clarke, E. Ryckeboer, M. Pelusi, M. A. 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).
[Crossref]

Saha, K.

Salem, R.

Sansoni, G.

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors 9, 568–601 (2009).
[Crossref]

Schröder, J.

J. Schröder, F. Wang, A. Clarke, E. Ryckeboer, M. Pelusi, M. A. 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).
[Crossref]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Schweizer, M.

T. Oggier, M. Lehmann, R. Kaufmann, M. Schweizer, M. Richter, P. Metzler, G. Lang, F. Lustenberger, and N. Blanc, “An all-solid-state optical range camera for 3D real-time imaging with sub-centimeter depth resolution (SwissRanger),” Proc. SPIE 5249, 534–545 (2003).
[Crossref]

Shu, X.

Solli, D.

D. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref]

Soto-Crespo, J. M.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Spence, D. M.

B. C. Gross, J. L. Erkal, S. Y. Lockwood, C. Chen, and D. M. Spence, “Evaluation of 3D printing and its potential impact on biotechnology and the chemical sciences,” Anal. Chem. 86, 3240–3253 (2014).
[Crossref]

Steinmeyer, G.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Stern, A.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

Sylvestre, T.

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
[Crossref]

Szriftgiser, P.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Taki, M.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Tiofack, C. G.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Tlidi, M.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Toenger, S.

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
[Crossref]

Trebeschi, M.

G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors 9, 568–601 (2009).
[Crossref]

Turner-Foster, A. C.

Vouzas, P.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Wabnitz, S.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Wang, F.

J. Schröder, F. Wang, A. Clarke, E. Ryckeboer, M. Pelusi, M. A. 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).
[Crossref]

Wetzel, B.

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
[Crossref]

Wong, K. K.

Wong, K. K.-Y.

C. Zhang, B. Li, and K. K.-Y. Wong, “Ultrafast spectroscopy based on temporal focusing and its applications,” IEEE J. Sel. Top. Quantum Electron. 22, 295–306 (2016).
[Crossref]

Wu, Z.

Xiao, X.

Yaron, T.

Zhang, C.

C. Zhang, B. Li, and K. K.-Y. Wong, “Ultrafast spectroscopy based on temporal focusing and its applications,” IEEE J. Sel. Top. Quantum Electron. 22, 295–306 (2016).
[Crossref]

C. Zhang, P. Chui, and K. K. Wong, “Comparison of state-of-art phase modulators and parametric mixers in time-lens applications under different repetition rates,” Appl. Opt. 52, 8817–8826 (2013).
[Crossref]

Zhang, X.

Zhang, Y.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Zhang, Z.

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]

Zhong, W.-P.

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

Anal. Chem. (1)

B. C. Gross, J. L. Erkal, S. Y. Lockwood, C. Chen, and D. M. Spence, “Evaluation of 3D printing and its potential impact on biotechnology and the chemical sciences,” Anal. Chem. 86, 3240–3253 (2014).
[Crossref]

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[Crossref]

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

C. Zhang, B. Li, and K. K.-Y. Wong, “Ultrafast spectroscopy based on temporal focusing and its applications,” IEEE J. Sel. Top. Quantum Electron. 22, 295–306 (2016).
[Crossref]

IEEE Photon. Technol. Lett. (1)

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]

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M. Fridman, Y. Okawachi, S. Clemmen, M. Ménard, M. Lipson, and A. L. Gaeta, “Waveguide-based single-shot temporal cross-correlator,” J. Opt. 17, 035501 (2015).
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N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18, 063001 (2016).
[Crossref]

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M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
[Crossref]

Nature (2)

D. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
[Crossref]

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481, 62–65 (2012).
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J. Schröder, F. Wang, A. Clarke, E. Ryckeboer, M. Pelusi, M. A. 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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[Crossref]

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D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[Crossref]

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G. Sansoni, M. Trebeschi, and F. Docchio, “State-of-the-art and applications of 3D imaging sensors in industry, cultural heritage, medicine, and criminal investigation,” Sensors 9, 568–601 (2009).
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Figures (6)

Fig. 1.
Fig. 1.

Scheme of deviation in an image point position when shifting an object point from the object plane. The distance between the object point and lens axis is xl. The object point is shifted by Δu from the object plane u, which causes the image point to shift by Δv from the image plane v. Since we measure along the image plane, the image point is not in focus and is shifted upward by Δxi.

Fig. 2.
Fig. 2.

Schematics of a time lens array for temporal depth imaging where different points in the input signal acquire different dispersion values. (a) An input pulse travels in a dispersive fiber until (b) a point where a second pulse joins. Therefore, the signal is composed of both pulses with different dispersion values. The two pulses propagate in additional dispersive material and reach the time lens array in (c). Each time lens in the array imposes a quadratic phase shift on part of the signal. The output idler, presented in (d), propagates in the dispersive material until it reaches the image plane in (e) where three images are formed. From the separations between the two pulses in the three images, denoted as τ1, τ2, and τ3, we deduce the dispersion difference between the two pulses. Thus, by analyzing the difference between the images, we obtain the temporal depth information of the signal. (Bottom) Experimental setup of a time lens array for demonstrating depth imaging.

Fig. 3.
Fig. 3.

Schematics of a temporal imaging of double pulses with tunable pump timing. We start with an ultrafast fiber laser and split the pulse into a signal and an idler wave. The dispersion compensating fibers (DCFs), denoted as DCFp and DCFs, and the SMFi are tailored for obtaining temporal imaging with a magnification of Mt=56. Specifically, DCFp is 348 m, DCFs is 160 m, and SMFi is 23 km. We impose an extra dispersion on one of the pulses with SMFx and measure the separation between the idler pulses as a function of the pump wave timing.

Fig. 4.
Fig. 4.

Measured separation between the idler pulses as a function of the timing of the time lens when the dispersion difference between them is 80 m of an SMF. The insets show representative measured idler waves for time lens timing of 9  ps and +9  ps. The red curve denotes a linear fitted line with a slope of 8.8 ps/ps, which indicates that the dispersion difference between the two input pulses is 1.26 ps/nm. The slope of the linear fitted curve is denoted as the separation derivative.

Fig. 5.
Fig. 5.

Separation derivative as a function of the dispersion difference between the pulses. Measured peak separations as functions of pump time delay for different SMF lengths are presented in the inset. The derivatives of these curves are denoted as the separation derivatives and are presented as blue asterisks. Calculated results are presented as the red solid curve.

Fig. 6.
Fig. 6.

Output spectra of a time lens array with two lenses imaging a double-pulse signal wave. (a) Measured spectrum when the two signal pulses have the same dispersion. (b) Measured spectrum when one signal pulse has a 0.36 ps/nm more dispersion than the other. In both spectra, we identify the two images according to the time lens timing [22]. In (a), the spectral separation in the images is Δλ1=6.1  nm and Δλ2=5  nm, indicating a timing separation of 20 ps and no dispersion difference according to Eq. (7). In (b), the spectral separation is Δλ3=5.7  nm and Δλ4=3  nm, indicating a timing separation of 22 ps and 11 ps, respectively, corresponding to a dispersion difference of 0.4 ps/nm between the pulses.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

E(x,z)z=i2k2E(x,z)x2,
A(t,z)z=i2β22A(t,z)t2,
1u+Δu+1v+Δv=1f,
Δxi=xl(MsΔuuΔu),
τi=τl(MtDΔLsDLs+DΔLs),
Δτiτl=8.8  ps/ps,
Δλ=(λiλs)21DLΔτ,
Δτmin=|2πϕτp|,

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