Abstract

We investigate the discrete temporal Talbot effect in a synthetic mesh lattice by employing two coupled fiber loops with different lengths. The lattice consists of the round-trip number and time delay of pulse trains propagating in the fiber loops. The Talbot effect occurs only as the incident pulse train in one loop has a temporal period that is 1, 2, or 4 folds of time interval corresponding to the length difference of the two loops. By varying the splitting ratio of coupler connecting the two loops, the lattice band structure can be engineered and so do the Talbot distance, which can be further tuned by imposing an initial linear phase distribution on the incident pulse train. In addition, the incident periods for Talbot effect can also be fractional fold by using time multiplexing. The study may find applications in temporal cloaking, passive amplifying, and pulse repetition rate multiplication.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref]

2018 (3)

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

F. Wang, S. Ke, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Topological interface modes in graphene multilayer arrays,” Opt. Laser Technol. 103, 272–278 (2018).
[Crossref]

S. Ke, D. Zhao, Q. Liu, S. Wu, B. Wang, and P. Lu, “Optical imaginary directional couplers,” J. Lightwave Technol. 36(12), 2510–2516 (2018).
[Crossref]

2017 (4)

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of plasmonic supermodes in graphene multilayer arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
[Crossref]

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

I. D. Vatnik, A. Tikan, G. Onishchukov, D. V. Churkin, and A. A. Sukhorukov, “Anderson localization in synthetic photonic lattices,” Sci. Rep. 7(1), 4301 (2017).
[Crossref] [PubMed]

M. Wimmer, H. M. Price, I. Carusotto, and U. Peschel, “Experimental measurement of the Berry curvature from anomalous transport,” Nat. Phys. 13(6), 545–550 (2017).
[Crossref]

2015 (1)

M. Wimmer, M. A. Miri, D. Christodoulides, and U. Peschel, “Observation of Bloch oscillations in complex PT-symmetric photonic lattices,” Sci. Rep. 5(1), 17760 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (1)

J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498(7453), 205–208 (2013).
[Crossref] [PubMed]

2012 (2)

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

2011 (1)

A. Regensburger, C. Bersch, B. Hinrichs, G. Onishchukov, A. Schreiber, C. Silberhorn, and U. Peschel, “Photon propagation in a discrete fiber network: an interplay of coherence and losses,” Phys. Rev. Lett. 107(23), 233902 (2011).
[Crossref] [PubMed]

2010 (1)

2007 (1)

D. Pudo, M. Depa, and L. R. Chen, “Single and multiwavelength all-optical clock recovery in single-mode fiber using the temporal Talbot effect,” J. Lightwave Technol. 25(10), 1729–1733 (2007).
[Crossref]

2006 (1)

J. Varona, “Rational values of the arccosine function,” Open Math. 4(2), 319–322 (2006).

2005 (1)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95(5), 053902 (2005).
[Crossref] [PubMed]

2004 (1)

J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1), 29–34 (2004).
[Crossref]

2001 (1)

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
[Crossref]

2000 (2)

1999 (2)

1996 (1)

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

1994 (1)

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994).
[Crossref]

1986 (1)

B. Ainslie and C. Day, “A review of single-mode fibers with modified dispersion characteristics,” J. Lightwave Technol. 4(8), 967–979 (1986).
[Crossref]

1981 (1)

1965 (1)

1881 (1)

L. Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
[Crossref]

1836 (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9(56), 401–407 (1836).

Agogliati, B.

Ainslie, B.

B. Ainslie and C. Day, “A review of single-mode fibers with modified dispersion characteristics,” J. Lightwave Technol. 4(8), 967–979 (1986).
[Crossref]

Alù, A.

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

Arcangeli, L.

Azaña, J.

R. Maram, J. Van Howe, M. Li, and J. Azaña, “Noiseless intensity amplification of repetitive signals by coherent addition using the temporal Talbot effect,” Nat. Commun. 5(1), 5163 (2014).
[Crossref] [PubMed]

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
[Crossref]

J. Azaña and M. A. Muriel, “Temporal Talbot effect in fiber gratings and its applications,” Appl. Opt. 38(32), 6700–6704 (1999).
[Crossref] [PubMed]

J. Azaña and M. A. Muriel, “Technique for multiplying the repetition rates of periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber gratings,” Opt. Lett. 24(23), 1672–1674 (1999).
[Crossref] [PubMed]

Belmonte, M.

Berry, M. V.

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

Bersch, C.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, B. Hinrichs, G. Onishchukov, A. Schreiber, C. Silberhorn, and U. Peschel, “Photon propagation in a discrete fiber network: an interplay of coherence and losses,” Phys. Rev. Lett. 107(23), 233902 (2011).
[Crossref] [PubMed]

Carusotto, I.

M. Wimmer, H. M. Price, I. Carusotto, and U. Peschel, “Experimental measurement of the Berry curvature from anomalous transport,” Nat. Phys. 13(6), 545–550 (2017).
[Crossref]

Chen, L. R.

D. Pudo, M. Depa, and L. R. Chen, “Single and multiwavelength all-optical clock recovery in single-mode fiber using the temporal Talbot effect,” J. Lightwave Technol. 25(10), 1729–1733 (2007).
[Crossref]

Christodoulides, D.

M. Wimmer, M. A. Miri, D. Christodoulides, and U. Peschel, “Observation of Bloch oscillations in complex PT-symmetric photonic lattices,” Sci. Rep. 5(1), 17760 (2015).
[Crossref] [PubMed]

Christodoulides, D. N.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95(5), 053902 (2005).
[Crossref] [PubMed]

Churkin, D. V.

I. D. Vatnik, A. Tikan, G. Onishchukov, D. V. Churkin, and A. A. Sukhorukov, “Anderson localization in synthetic photonic lattices,” Sci. Rep. 7(1), 4301 (2017).
[Crossref] [PubMed]

Damsgaard, H.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[Crossref]

Day, C.

B. Ainslie and C. Day, “A review of single-mode fibers with modified dispersion characteristics,” J. Lightwave Technol. 4(8), 967–979 (1986).
[Crossref]

Depa, M.

D. Pudo, M. Depa, and L. R. Chen, “Single and multiwavelength all-optical clock recovery in single-mode fiber using the temporal Talbot effect,” J. Lightwave Technol. 25(10), 1729–1733 (2007).
[Crossref]

Dong, J.

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

Dong, L.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

Edvold, B.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[Crossref]

Fan, Y.

Fatome, J.

J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1), 29–34 (2004).
[Crossref]

Grüner-Nielsen, L.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[Crossref]

Hinrichs, B.

A. Regensburger, C. Bersch, B. Hinrichs, G. Onishchukov, A. Schreiber, C. Silberhorn, and U. Peschel, “Photon propagation in a discrete fiber network: an interplay of coherence and losses,” Phys. Rev. Lett. 107(23), 233902 (2011).
[Crossref] [PubMed]

Hu, W.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

Ibsen, M.

Iwanow, R.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95(5), 053902 (2005).
[Crossref] [PubMed]

Jannson, J.

Jannson, T.

Ke, S.

S. Ke, D. Zhao, Q. Liu, S. Wu, B. Wang, and P. Lu, “Optical imaginary directional couplers,” J. Lightwave Technol. 36(12), 2510–2516 (2018).
[Crossref]

F. Wang, S. Ke, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Topological interface modes in graphene multilayer arrays,” Opt. Laser Technol. 103, 272–278 (2018).
[Crossref]

Klein, S.

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

Knudsen, S. N.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[Crossref]

Kolner, B. H.

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994).
[Crossref]

Kong, W.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

Kottos, T.

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

Kovanis, V.

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

Laporta, P.

Larsen, C. C.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[Crossref]

Leaird, D. E.

J. M. Lukens, A. J. Metcalf, D. E. Leaird, and A. M. Weiner, “Temporal cloaking for data suppression and retrieval,” Optica 1(6), 372–375 (2014).
[Crossref]

J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498(7453), 205–208 (2013).
[Crossref] [PubMed]

Li, K.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

Li, M.

R. Maram, J. Van Howe, M. Li, and J. Azaña, “Noiseless intensity amplification of repetitive signals by coherent addition using the temporal Talbot effect,” Nat. Commun. 5(1), 5163 (2014).
[Crossref] [PubMed]

Liu, Q.

Liu, S.

Liu, T.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

Long, H.

F. Wang, S. Ke, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Topological interface modes in graphene multilayer arrays,” Opt. Laser Technol. 103, 272–278 (2018).
[Crossref]

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of plasmonic supermodes in graphene multilayer arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
[Crossref]

Y. Fan, B. Wang, K. Wang, H. Long, and P. Lu, “Talbot effect in weakly coupled monolayer graphene sheet arrays,” Opt. Lett. 39(12), 3371–3373 (2014).
[Crossref] [PubMed]

Longhi, S.

Lu, P.

S. Ke, D. Zhao, Q. Liu, S. Wu, B. Wang, and P. Lu, “Optical imaginary directional couplers,” J. Lightwave Technol. 36(12), 2510–2516 (2018).
[Crossref]

F. Wang, S. Ke, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Topological interface modes in graphene multilayer arrays,” Opt. Laser Technol. 103, 272–278 (2018).
[Crossref]

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of plasmonic supermodes in graphene multilayer arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
[Crossref]

Y. Fan, B. Wang, K. Wang, H. Long, and P. Lu, “Talbot effect in weakly coupled monolayer graphene sheet arrays,” Opt. Lett. 39(12), 3371–3373 (2014).
[Crossref] [PubMed]

Lukens, J. M.

J. M. Lukens, A. J. Metcalf, D. E. Leaird, and A. M. Weiner, “Temporal cloaking for data suppression and retrieval,” Optica 1(6), 372–375 (2014).
[Crossref]

J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498(7453), 205–208 (2013).
[Crossref] [PubMed]

Magnussen, D.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[Crossref]

Maram, R.

R. Maram, J. Van Howe, M. Li, and J. Azaña, “Noiseless intensity amplification of repetitive signals by coherent addition using the temporal Talbot effect,” Nat. Commun. 5(1), 5163 (2014).
[Crossref] [PubMed]

Marano, M.

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95(5), 053902 (2005).
[Crossref] [PubMed]

Metcalf, A. J.

Millot, G.

J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1), 29–34 (2004).
[Crossref]

Min, Y.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95(5), 053902 (2005).
[Crossref] [PubMed]

Miri, M. A.

M. Wimmer, M. A. Miri, D. Christodoulides, and U. Peschel, “Observation of Bloch oscillations in complex PT-symmetric photonic lattices,” Sci. Rep. 5(1), 17760 (2015).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

Muriel, M. A.

Onishchukov, G.

I. D. Vatnik, A. Tikan, G. Onishchukov, D. V. Churkin, and A. A. Sukhorukov, “Anderson localization in synthetic photonic lattices,” Sci. Rep. 7(1), 4301 (2017).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, B. Hinrichs, G. Onishchukov, A. Schreiber, C. Silberhorn, and U. Peschel, “Photon propagation in a discrete fiber network: an interplay of coherence and losses,” Phys. Rev. Lett. 107(23), 233902 (2011).
[Crossref] [PubMed]

Peng, Y.

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

Peschel, U.

M. Wimmer, H. M. Price, I. Carusotto, and U. Peschel, “Experimental measurement of the Berry curvature from anomalous transport,” Nat. Phys. 13(6), 545–550 (2017).
[Crossref]

M. Wimmer, M. A. Miri, D. Christodoulides, and U. Peschel, “Observation of Bloch oscillations in complex PT-symmetric photonic lattices,” Sci. Rep. 5(1), 17760 (2015).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, B. Hinrichs, G. Onishchukov, A. Schreiber, C. Silberhorn, and U. Peschel, “Photon propagation in a discrete fiber network: an interplay of coherence and losses,” Phys. Rev. Lett. 107(23), 233902 (2011).
[Crossref] [PubMed]

Pitois, S.

J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1), 29–34 (2004).
[Crossref]

Price, H. M.

M. Wimmer, H. M. Price, I. Carusotto, and U. Peschel, “Experimental measurement of the Berry curvature from anomalous transport,” Nat. Phys. 13(6), 545–550 (2017).
[Crossref]

Pruneri, V.

Pudo, D.

D. Pudo, M. Depa, and L. R. Chen, “Single and multiwavelength all-optical clock recovery in single-mode fiber using the temporal Talbot effect,” J. Lightwave Technol. 25(10), 1729–1733 (2007).
[Crossref]

Qin, C.

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

F. Wang, S. Ke, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Topological interface modes in graphene multilayer arrays,” Opt. Laser Technol. 103, 272–278 (2018).
[Crossref]

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of plasmonic supermodes in graphene multilayer arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
[Crossref]

Ramezani, H.

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

Rayleigh, L.

L. Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
[Crossref]

Regensburger, A.

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, B. Hinrichs, G. Onishchukov, A. Schreiber, C. Silberhorn, and U. Peschel, “Photon propagation in a discrete fiber network: an interplay of coherence and losses,” Phys. Rev. Lett. 107(23), 233902 (2011).
[Crossref] [PubMed]

Schreiber, A.

A. Regensburger, C. Bersch, B. Hinrichs, G. Onishchukov, A. Schreiber, C. Silberhorn, and U. Peschel, “Photon propagation in a discrete fiber network: an interplay of coherence and losses,” Phys. Rev. Lett. 107(23), 233902 (2011).
[Crossref] [PubMed]

Silberhorn, C.

A. Regensburger, C. Bersch, B. Hinrichs, G. Onishchukov, A. Schreiber, C. Silberhorn, and U. Peschel, “Photon propagation in a discrete fiber network: an interplay of coherence and losses,” Phys. Rev. Lett. 107(23), 233902 (2011).
[Crossref] [PubMed]

Sohler, W.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95(5), 053902 (2005).
[Crossref] [PubMed]

Song, Y.

Sounas, D.

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

Stegeman, G. I.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95(5), 053902 (2005).
[Crossref] [PubMed]

Sukhorukov, A. A.

I. D. Vatnik, A. Tikan, G. Onishchukov, D. V. Churkin, and A. A. Sukhorukov, “Anderson localization in synthetic photonic lattices,” Sci. Rep. 7(1), 4301 (2017).
[Crossref] [PubMed]

Sun, P.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

Svelto, O.

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9(56), 401–407 (1836).

Tikan, A.

I. D. Vatnik, A. Tikan, G. Onishchukov, D. V. Churkin, and A. A. Sukhorukov, “Anderson localization in synthetic photonic lattices,” Sci. Rep. 7(1), 4301 (2017).
[Crossref] [PubMed]

Van Howe, J.

R. Maram, J. Van Howe, M. Li, and J. Azaña, “Noiseless intensity amplification of repetitive signals by coherent addition using the temporal Talbot effect,” Nat. Commun. 5(1), 5163 (2014).
[Crossref] [PubMed]

Varona, J.

J. Varona, “Rational values of the arccosine function,” Open Math. 4(2), 319–322 (2006).

Vatnik, I. D.

I. D. Vatnik, A. Tikan, G. Onishchukov, D. V. Churkin, and A. A. Sukhorukov, “Anderson localization in synthetic photonic lattices,” Sci. Rep. 7(1), 4301 (2017).
[Crossref] [PubMed]

Veng, T.

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[Crossref]

Vitebskiy, I.

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

Wang, B.

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

F. Wang, S. Ke, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Topological interface modes in graphene multilayer arrays,” Opt. Laser Technol. 103, 272–278 (2018).
[Crossref]

S. Ke, D. Zhao, Q. Liu, S. Wu, B. Wang, and P. Lu, “Optical imaginary directional couplers,” J. Lightwave Technol. 36(12), 2510–2516 (2018).
[Crossref]

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of plasmonic supermodes in graphene multilayer arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
[Crossref]

Y. Fan, B. Wang, K. Wang, H. Long, and P. Lu, “Talbot effect in weakly coupled monolayer graphene sheet arrays,” Opt. Lett. 39(12), 3371–3373 (2014).
[Crossref] [PubMed]

Wang, F.

F. Wang, S. Ke, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Topological interface modes in graphene multilayer arrays,” Opt. Laser Technol. 103, 272–278 (2018).
[Crossref]

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of plasmonic supermodes in graphene multilayer arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
[Crossref]

Wang, K.

F. Wang, S. Ke, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Topological interface modes in graphene multilayer arrays,” Opt. Laser Technol. 103, 272–278 (2018).
[Crossref]

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of plasmonic supermodes in graphene multilayer arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
[Crossref]

Y. Fan, B. Wang, K. Wang, H. Long, and P. Lu, “Talbot effect in weakly coupled monolayer graphene sheet arrays,” Opt. Lett. 39(12), 3371–3373 (2014).
[Crossref] [PubMed]

Wang, M.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

Wang, Y.

Weiner, A. M.

J. M. Lukens, A. J. Metcalf, D. E. Leaird, and A. M. Weiner, “Temporal cloaking for data suppression and retrieval,” Optica 1(6), 372–375 (2014).
[Crossref]

J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498(7453), 205–208 (2013).
[Crossref] [PubMed]

Wimmer, M.

M. Wimmer, H. M. Price, I. Carusotto, and U. Peschel, “Experimental measurement of the Berry curvature from anomalous transport,” Nat. Phys. 13(6), 545–550 (2017).
[Crossref]

M. Wimmer, M. A. Miri, D. Christodoulides, and U. Peschel, “Observation of Bloch oscillations in complex PT-symmetric photonic lattices,” Sci. Rep. 5(1), 17760 (2015).
[Crossref] [PubMed]

Winthrop, J. T.

Worthington, C. R.

Wu, S.

Xia, F.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

Yang, K.

Yun, M.

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

Zervas, M. N.

Zhang, X.

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

Y. Wang, K. Zhou, X. Zhang, K. Yang, Y. Wang, Y. Song, and S. Liu, “Discrete plasmonic Talbot effect in subwavelength metal waveguide arrays,” Opt. Lett. 35(5), 685–687 (2010).
[Crossref] [PubMed]

Zhao, D.

Zhou, F.

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

Zhou, K.

Zhu, X.

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

Appl. Opt. (1)

Carbon (1)

K. Li, F. Xia, M. Wang, P. Sun, T. Liu, W. Hu, W. Kong, M. Yun, and L. Dong, “Discrete Talbot effect in dielectric graphene plasmonic waveguide arrays,” Carbon 118, 192–199 (2017).
[Crossref]

IEEE J. Quantum Electron. (1)

B. H. Kolner, “Space-time duality and the theory of temporal imaging,” IEEE J. Quantum Electron. 30(8), 1951–1963 (1994).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

J. Azaña and M. A. Muriel, “Temporal self-imaging effects: theory and application for multiplying pulse repetition rates,” IEEE J. Sel. Top. Quantum Electron. 7(4), 728–744 (2001).
[Crossref]

F. Wang, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Rabi oscillations of plasmonic supermodes in graphene multilayer arrays,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600105 (2017).
[Crossref]

J. Lightwave Technol. (3)

S. Ke, D. Zhao, Q. Liu, S. Wu, B. Wang, and P. Lu, “Optical imaginary directional couplers,” J. Lightwave Technol. 36(12), 2510–2516 (2018).
[Crossref]

B. Ainslie and C. Day, “A review of single-mode fibers with modified dispersion characteristics,” J. Lightwave Technol. 4(8), 967–979 (1986).
[Crossref]

D. Pudo, M. Depa, and L. R. Chen, “Single and multiwavelength all-optical clock recovery in single-mode fiber using the temporal Talbot effect,” J. Lightwave Technol. 25(10), 1729–1733 (2007).
[Crossref]

J. Mod. Opt. (1)

M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43(10), 2139–2164 (1996).
[Crossref]

J. Opt. Soc. Am. (2)

Nat. Commun. (1)

R. Maram, J. Van Howe, M. Li, and J. Azaña, “Noiseless intensity amplification of repetitive signals by coherent addition using the temporal Talbot effect,” Nat. Commun. 5(1), 5163 (2014).
[Crossref] [PubMed]

Nat. Phys. (1)

M. Wimmer, H. M. Price, I. Carusotto, and U. Peschel, “Experimental measurement of the Berry curvature from anomalous transport,” Nat. Phys. 13(6), 545–550 (2017).
[Crossref]

Nature (2)

A. Regensburger, C. Bersch, M. A. Miri, G. Onishchukov, D. N. Christodoulides, and U. Peschel, “Parity-time synthetic photonic lattices,” Nature 488(7410), 167–171 (2012).
[Crossref] [PubMed]

J. M. Lukens, D. E. Leaird, and A. M. Weiner, “A temporal cloak at telecommunication data rate,” Nature 498(7453), 205–208 (2013).
[Crossref] [PubMed]

Open Math. (1)

J. Varona, “Rational values of the arccosine function,” Open Math. 4(2), 319–322 (2006).

Opt. Commun. (1)

J. Fatome, S. Pitois, and G. Millot, “Influence of third-order dispersion on the temporal Talbot effect,” Opt. Commun. 234(1), 29–34 (2004).
[Crossref]

Opt. Fiber Technol. (1)

L. Grüner-Nielsen, S. N. Knudsen, B. Edvold, T. Veng, D. Magnussen, C. C. Larsen, and H. Damsgaard, “Dispersion compensating fibers,” Opt. Fiber Technol. 6(2), 164–180 (2000).
[Crossref]

Opt. Laser Technol. (1)

F. Wang, S. Ke, C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Topological interface modes in graphene multilayer arrays,” Opt. Laser Technol. 103, 272–278 (2018).
[Crossref]

Opt. Lett. (4)

Optica (1)

Philos. Mag. (2)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9(56), 401–407 (1836).

L. Rayleigh, “On copying diffraction-gratings, and on some phenomena connected therewith,” Philos. Mag. 11(67), 196–205 (1881).
[Crossref]

Phys. Rev. Lett. (4)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95(5), 053902 (2005).
[Crossref] [PubMed]

H. Ramezani, D. N. Christodoulides, V. Kovanis, I. Vitebskiy, and T. Kottos, “PT-symmetric Talbot effects,” Phys. Rev. Lett. 109(3), 033902 (2012).
[Crossref] [PubMed]

A. Regensburger, C. Bersch, B. Hinrichs, G. Onishchukov, A. Schreiber, C. Silberhorn, and U. Peschel, “Photon propagation in a discrete fiber network: an interplay of coherence and losses,” Phys. Rev. Lett. 107(23), 233902 (2011).
[Crossref] [PubMed]

C. Qin, F. Zhou, Y. Peng, D. Sounas, X. Zhu, B. Wang, J. Dong, X. Zhang, A. Alù, and P. Lu, “Spectrum control through discrete frequency diffraction in the presence of photonic gauge potentials,” Phys. Rev. Lett. 120(13), 133901 (2018).
[Crossref] [PubMed]

Sci. Rep. (2)

I. D. Vatnik, A. Tikan, G. Onishchukov, D. V. Churkin, and A. A. Sukhorukov, “Anderson localization in synthetic photonic lattices,” Sci. Rep. 7(1), 4301 (2017).
[Crossref] [PubMed]

M. Wimmer, M. A. Miri, D. Christodoulides, and U. Peschel, “Observation of Bloch oscillations in complex PT-symmetric photonic lattices,” Sci. Rep. 5(1), 17760 (2015).
[Crossref] [PubMed]

Other (3)

M. Aigner, G. M. Ziegler, and A. Quarteroni, Proofs from the Book, 4nd ed. (Springer, 2010).

B. Li, X. Wang, J. Kang, Y. Wei, and K. K.-Y. Wong, “Extended time cloak based on inverse temporal Talbot effect,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2017), paper SF2L.2.
[Crossref]

K. Patorski, “Self-imaging and its applications,” in Progress in Optics XXVII, E. Wolf, ed. (Elsevier, 1989).

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic diagram of two coupled fiber loops. The short loop (marked in magenta) and long loop (marked in purple) are connected by a 50:50 directional coupler. OS1 and OS2 are 1 × 2 and 2 × 2 optical switches through which we can inject the initial pulse train to the long loop and couple out the pulse sequences from the loops. PD is photodiode. (b) Equivalent mesh lattice model for the two coupled fiber loops. The left path (marked in magenta) and right path (marked in purple) in the equivalent lattice correspond to short and long loops, respectively. The bottom insert is the stepwise evolution of pulse train in the long loop with the initial period being N = 4. (c) Band structure of the synthetic mesh lattice. The green crosses, red triangles and black diamonds represent the sets of Bloch modes at 2nd band for N = 2, 4, and 8, respectively.
Fig. 2
Fig. 2 (a)–(d) Pulse intensity evolutions in the long loop for N = 2, 4, 8 and 12, respectively.
Fig. 3
Fig. 3 (a) Talbot distance zT versus q. (b) (c) Talbot carpets for q = 6 and 9 as N = 2. (d) Talbot carpet for q = 6 as N = 4.
Fig. 4
Fig. 4 (a) The variation of Talbot distance zT versus the input period N as α = 0 and π/2. (b) (c) Talbot carpets with N = 6 and 10 as α = 0. (d) Talbot carpet for N = 6 as α = π/2.
Fig. 5
Fig. 5 (a) Schematic of the incident field under stepwise phase modulation. (b) Talbot distance zT versus initial momentum ϕ0. (c) Talbot carpet with N = 2 and ϕ0 = 0.71π. (d) Talbot carpet with N = 4 and ϕ0 = 0.5π.
Fig. 6
Fig. 6 (a) Schematic of the separated synthetic mesh lattices uniformly spaced in the transverse direction. The incident field with period N = 2K/L is decomposed to several identical fields with period 2K distinguished by color which evolve in the lattices in the same color independently. (b) Talbot distance zT versus K and L. (c)-(e) Talbot carpets of N = 2/3, 4/3 and 8/3, respectively.

Equations (21)

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

u n m = 1 2 ( u n + 1 m 1 + i v n + 1 m 1 ) , v n m = 1 2 ( i u n 1 m 1 + v n 1 m 1 ) ,
( u n m v n m ) = ( U 0 V 0 ) e i Q n / 2 e i θ m / 2 ,
cos θ = 1 2 ( cos Q 1 ) .
Q l = 2 π l / N ,
θ j , l = { arc cos [ ( cos Q l 1 ) / 2 ] ( j = 1 ), arc cos [ ( cos Q l 1 ) / 2 ] ( j = 2 ),
( u n m v n m ) = j = 1 2 l = 0 N 1 c j , l ( U j , l V j , l ) exp ( i Q l n / 2 ) exp ( i θ j , l m / 2 ) ,
λ j , l θ j , l / 2 = 2 μ j , l π,
z T = LCM ( λ 0 , λ 1 , λ 2 , ... , λ N 1 ) ,
cos θ = cos 2 α cos Q sin 2 α .
α = p π / q ,
z T = 2 q .
z T = { 4 q ( p is odd ) , 2 q ( p is even ) .
θ = ± Q .
θ = π .
Q l = 2 π l / N + ϕ 0 .
θ 2 , 0 = arc cos [ ( cos ϕ 0 1 ) / 2 ] .
θ 2 , 0 = a π / b ,
z T = { 4 b ( a is odd ) , 2 b ( a is even ) ,
ϕ 0 = arc cos ( 2 cos θ 0 , 2 + 1 ) .
{ θ 2 , 0 = arc cos [ ( cos ϕ 0 1 ) / 2 ] , θ 2 , 1 = arc cos [ ( cos ϕ 0 1 ) / 2 ] .
N = 2 K / L ,

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