Abstract

In this work, we investigate the properties of four-wave mixing Bragg scattering driven by orthogonally polarized pumps in a birefringent waveguide. This configuration enables a large signal conversion bandwidth, and allows strongly unidirectional frequency conversion as undesired Bragg-scattering processes are suppressed by waveguide birefringence. Moreover, we show that this form of Bragg scattering preserves the (arbitrary) signal pulse shape, even when driven by pulsed pumps.

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

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]

2018 (3)

P. Guan, F. Da Ros, M. Lillieholm, N.-K. Kjøller, H. Hu, K. M. Røge, M. Galili, T. Morioka, and L. K. Oxenløwe, “Scalable WDM phase regeneration in a single phase-sensitive amplifier through optical time lenses,” Nat. Commun. 9, 1049 (2018).
[Crossref] [PubMed]

C. Joshi, A. Farsi, S. Clemmen, S. Ramelow, and A. L. Gaeta, “Frequency multiplexing for quasi-deterministic heralded single-photon sources,” Nat. Commun. 9, 847 (2018).
[Crossref] [PubMed]

D. V. Reddy and M. G. Raymer, “High-selectivity quantum pulse gating of photonic temporal modes using all-optical ramsey interferometry,” Optica 5, 423–428 (2018).
[Crossref]

2017 (8)

Y. Zhao, D. Lombardo, J. Mathews, and I. Agha, “All-optical switching via four-wave mixing Bragg scattering in a silicon platform,” APL Photonics 2, 026102 (2017).
[Crossref]

Y.-S. Ra, C. Jacquard, A. Dufour, C. Fabre, and N. Treps, “Tomography of a mode-tunable coherent single-photon subtractor,” Phys. Rev. X 7, 031012 (2017).

K. Li, H. Sun, and A. C. Foster, “Four-wave mixing Bragg scattering in hydrogenated amorphous silicon waveguides,” Opt. Lett. 42, 1488–1491 (2017).
[Crossref] [PubMed]

F. Parmigiani, P. Horak, Y. Jung, L. Grüner-Nielsen, T. Geisler, P. Petropoulos, and D. J. Richardson, “All-optical mode and wavelength converter based on parametric processes in a three-mode fiber,” Opt. Express 25, 33602–33609 (2017).
[Crossref]

B. A. Bell, C. Xiong, D. Marpaung, C. J. McKinstrie, and B. J. Eggleton, “Uni-directional wavelength conversion in silicon using four-wave mixing driven by cross-polarized pumps,” Opt. Lett. 42, 1668–1671 (2017).
[Crossref] [PubMed]

P. Guan, K. M. Røge, M. Lillieholm, M. Galili, H. Hu, T. Morioka, and L. K. Oxenløwe, “Time lens-based optical fourier transformation for all-optical signal processing of spectrally-efficient data,” J. Light. Technol. 35, 799–806 (2017).
[Crossref]

C. J. McKinstrie, J. B. Christensen, K. Rottwitt, and M. G. Raymer, “Generation of two-temporal-mode photon states by vector four-wave mixing,” Opt. Express 25, 20877–20893 (2017).
[Crossref] [PubMed]

J. G. Koefoed, S. M. M. Friis, J. B. Christensen, and K. Rottwitt, “Spectrally pure heralded single photons by spontaneous four-wave mixing in a fiber: reducing impact of dispersion fluctuations,” Opt. Express 25, 20835–20849 (2017).
[Crossref] [PubMed]

2016 (7)

2015 (2)

B. Brecht, D. V. Reddy, C. Silberhorn, and M. Raymer, “Photon temporal modes: a complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

I. Sackey, F. D. Ros, J. K. Fischer, T. Richter, M. Jazayerifar, C. Peucheret, K. Petermann, and C. Schubert, “Kerr nonlinearity mitigation: Mid-link spectral inversion versus digital backpropagation in 5×28-GBd PDM 16-QAM signal transmission,” J. Light. Technol. 33, 1821–1827 (2015).
[Crossref]

2014 (2)

A. E. Willner, S. Khaleghi, M. R. Chitgarha, and O. F. Yilmaz, “All-optical signal processing,” J. Light. Technol. 32, 660–680 (2014).
[Crossref]

D. V. Reddy, M. G. Raymer, and C. J. McKinstrie, “Efficient sorting of quantum-optical wave packets by temporal-mode interferometry,” Opt. Lett. 39, 2924–2927 (2014).
[Crossref] [PubMed]

2013 (4)

2012 (3)

2011 (1)

Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

2010 (1)

H. McGuinness, M. Raymer, C. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

2009 (2)

2007 (3)

F. Morichetti, A. Melloni, M. Martinelli, R. G. Heideman, A. Leinse, D. H. Geuzebroek, and A. Borreman, “Box-shaped dielectric waveguides: A new concept in integrated optics?” J. Light. Technol. 25, 2579–2589 (2007).
[Crossref]

J. Zhang, Q. Lin, G. Piredda, R. Boyd, G. Agrawal, and P. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. express 15, 16604–16644 (2007).
[Crossref] [PubMed]

2005 (4)

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature. 437, 116–120 (2005).
[Crossref] [PubMed]

C. J. McKinstrie, J. D. Harvey, S. Radic, and M. G. Raymer, “Translation of quantum states by four-wave mixing in fibers,” Opt. Express 13, 9131–9142 (2005).
[Crossref] [PubMed]

I. Kiyat, A. Aydinli, and N. Dagli, “A compact silicon-on-insulator polarization splitter,” IEEE Photonics Technol. Lett. 17, 100–102 (2005).
[Crossref]

D. Amans, E. Brainis, M. Haelterman, P. Emplit, and S. Massar, “Vector modulation instability induced by vacuum fluctuations in highly birefringent fibers in the anomalous-dispersion regime,” Opt. Lett 30, 1051–1053 (2005).
[Crossref] [PubMed]

2003 (1)

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one-and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photonics Technol. Lett. 15, 957–959 (2003).
[Crossref]

2002 (1)

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[Crossref]

1994 (1)

K. Inoue, “Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,” IEEE Photonics Technol. Lett. 6, 1451–1453 (1994).
[Crossref]

1990 (1)

P. Drummond, T. Kennedy, J. Dudley, R. Leonhardt, and J. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[Crossref]

1986 (1)

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Light. Technol. 4, 1071–1089 (1986).
[Crossref]

Agha, I.

Agrawal, G.

J. Zhang, Q. Lin, G. Piredda, R. Boyd, G. Agrawal, and P. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

Agrawal, G. P.

Albrecht, B.

Alibart, O.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature. 437, 116–120 (2005).
[Crossref] [PubMed]

Alic, N.

Amans, D.

D. Amans, E. Brainis, M. Haelterman, P. Emplit, and S. Massar, “Vector modulation instability induced by vacuum fluctuations in highly birefringent fibers in the anomalous-dispersion regime,” Opt. Lett 30, 1051–1053 (2005).
[Crossref] [PubMed]

Andrekson, P.

Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Andrekson, P. A.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Li, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[Crossref]

Ates, S.

Aydinli, A.

I. Kiyat, A. Aydinli, and N. Dagli, “A compact silicon-on-insulator polarization splitter,” IEEE Photonics Technol. Lett. 17, 100–102 (2005).
[Crossref]

Baldi, P.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature. 437, 116–120 (2005).
[Crossref] [PubMed]

Begleris, I.

Bell, B. A.

Blanes, S.

S. Blanes, F. Casas, J. Oteo, and J. Ros, “The Magnus expansion and some of its applications,” Phys. Reports 470, 151–238 (2009).
[Crossref]

Blessing, D.

Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
[Crossref]

Borreman, A.

F. Morichetti, A. Melloni, M. Martinelli, R. G. Heideman, A. Leinse, D. H. Geuzebroek, and A. Borreman, “Box-shaped dielectric waveguides: A new concept in integrated optics?” J. Light. Technol. 25, 2579–2589 (2007).
[Crossref]

Boyd, R.

J. Zhang, Q. Lin, G. Piredda, R. Boyd, G. Agrawal, and P. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
[Crossref]

Brainis, E.

D. Amans, E. Brainis, M. Haelterman, P. Emplit, and S. Massar, “Vector modulation instability induced by vacuum fluctuations in highly birefringent fibers in the anomalous-dispersion regime,” Opt. Lett 30, 1051–1053 (2005).
[Crossref] [PubMed]

Brecht, B.

B. Brecht, D. V. Reddy, C. Silberhorn, and M. Raymer, “Photon temporal modes: a complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

Casas, F.

S. Blanes, F. Casas, J. Oteo, and J. Ros, “The Magnus expansion and some of its applications,” Phys. Reports 470, 151–238 (2009).
[Crossref]

Centanni, J. C.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one-and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photonics Technol. Lett. 15, 957–959 (2003).
[Crossref]

Chandrasekhar, S.

H. Hu, R. M. Jopson, A. Gnauck, M. Dinu, S. Chandrasekhar, X. Liu, C. Xie, M. Montoliu, S. Randel, and C. McKinstrie, “Fiber nonlinearity compensation of an 8-channel WDM PDM-QPSK signal using multiple phase conjugations,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2014,” (IEEE, 2014), pp. 1–3.

Chitgarha, M. R.

A. E. Willner, S. Khaleghi, M. R. Chitgarha, and O. F. Yilmaz, “All-optical signal processing,” J. Light. Technol. 32, 660–680 (2014).
[Crossref]

Chraplyvy, A. R.

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, and A. R. Chraplyvy, “All-optical regeneration in one-and two-pump parametric amplifiers using highly nonlinear optical fiber,” IEEE Photonics Technol. Lett. 15, 957–959 (2003).
[Crossref]

Christensen, J. B.

Clark, A. S.

Clemmen, S.

C. Joshi, A. Farsi, S. Clemmen, S. Ramelow, and A. L. Gaeta, “Frequency multiplexing for quasi-deterministic heralded single-photon sources,” Nat. Commun. 9, 847 (2018).
[Crossref] [PubMed]

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interference with single photons,” Phys. Rev. Lett. 117, 223601 (2016).
[Crossref] [PubMed]

Collins, M. J.

Corrielli, G.

Cristiani, M.

Da Ros, F.

P. Guan, F. Da Ros, M. Lillieholm, N.-K. Kjøller, H. Hu, K. M. Røge, M. Galili, T. Morioka, and L. K. Oxenløwe, “Scalable WDM phase regeneration in a single phase-sensitive amplifier through optical time lenses,” Nat. Commun. 9, 1049 (2018).
[Crossref] [PubMed]

Dagli, N.

I. Kiyat, A. Aydinli, and N. Dagli, “A compact silicon-on-insulator polarization splitter,” IEEE Photonics Technol. Lett. 17, 100–102 (2005).
[Crossref]

Davanço, M.

de Riedmatten, H.

Dinu, M.

H. Hu, R. M. Jopson, A. Gnauck, M. Dinu, S. Chandrasekhar, X. Liu, C. Xie, M. Montoliu, S. Randel, and C. McKinstrie, “Fiber nonlinearity compensation of an 8-channel WDM PDM-QPSK signal using multiple phase conjugations,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2014,” (IEEE, 2014), pp. 1–3.

Drummond, P.

P. Drummond, T. Kennedy, J. Dudley, R. Leonhardt, and J. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78, 137–142 (1990).
[Crossref]

Dudley, J.

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S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interference with single photons,” Phys. Rev. Lett. 117, 223601 (2016).
[Crossref] [PubMed]

Randel, S.

H. Hu, R. M. Jopson, A. Gnauck, M. Dinu, S. Chandrasekhar, X. Liu, C. Xie, M. Montoliu, S. Randel, and C. McKinstrie, “Fiber nonlinearity compensation of an 8-channel WDM PDM-QPSK signal using multiple phase conjugations,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2014,” (IEEE, 2014), pp. 1–3.

Raymer, M.

B. Brecht, D. V. Reddy, C. Silberhorn, and M. Raymer, “Photon temporal modes: a complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

H. McGuinness, M. Raymer, C. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
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Reddy, D. V.

Richardson, D.

Richardson, D. J.

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[Crossref]

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P. Guan, F. Da Ros, M. Lillieholm, N.-K. Kjøller, H. Hu, K. M. Røge, M. Galili, T. Morioka, and L. K. Oxenløwe, “Scalable WDM phase regeneration in a single phase-sensitive amplifier through optical time lenses,” Nat. Commun. 9, 1049 (2018).
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Ros, F. D.

I. Sackey, F. D. Ros, J. K. Fischer, T. Richter, M. Jazayerifar, C. Peucheret, K. Petermann, and C. Schubert, “Kerr nonlinearity mitigation: Mid-link spectral inversion versus digital backpropagation in 5×28-GBd PDM 16-QAM signal transmission,” J. Light. Technol. 33, 1821–1827 (2015).
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S. Blanes, F. Casas, J. Oteo, and J. Ros, “The Magnus expansion and some of its applications,” Phys. Reports 470, 151–238 (2009).
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Sackey, I.

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I. Sackey, F. D. Ros, J. K. Fischer, T. Richter, M. Jazayerifar, C. Peucheret, K. Petermann, and C. Schubert, “Kerr nonlinearity mitigation: Mid-link spectral inversion versus digital backpropagation in 5×28-GBd PDM 16-QAM signal transmission,” J. Light. Technol. 33, 1821–1827 (2015).
[Crossref]

Shahnia, S.

Silberhorn, C.

B. Brecht, D. V. Reddy, C. Silberhorn, and M. Raymer, “Photon temporal modes: a complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

Slattery, O.

Srinivasan, K.

Sun, H.

Tang, X.

Tanzilli, S.

S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature. 437, 116–120 (2005).
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Thurston, B.

Ting, H.-F.

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Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
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S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature. 437, 116–120 (2005).
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Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
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Tong, Z.

Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
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Y.-S. Ra, C. Jacquard, A. Dufour, C. Fabre, and N. Treps, “Tomography of a mode-tunable coherent single-photon subtractor,” Phys. Rev. X 7, 031012 (2017).

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H. Hu, R. M. Jopson, A. Gnauck, M. Dinu, S. Chandrasekhar, X. Liu, C. Xie, M. Montoliu, S. Randel, and C. McKinstrie, “Fiber nonlinearity compensation of an 8-channel WDM PDM-QPSK signal using multiple phase conjugations,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2014,” (IEEE, 2014), pp. 1–3.

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S. Tanzilli, W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, “A photonic quantum information interface,” Nature. 437, 116–120 (2005).
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Y. Zhao, D. Lombardo, J. Mathews, and I. Agha, “Low control-power wavelength conversion on a silicon chip,” Opt. Lett. 41, 3651–3654 (2016).
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Y. Zhao, D. Lombardo, J. Mathews, and I. Agha, “All-optical switching via four-wave mixing Bragg scattering in a silicon platform,” APL Photonics 2, 026102 (2017).
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J. Zhang, Q. Lin, G. Piredda, R. Boyd, G. Agrawal, and P. Fauchet, “Anisotropic nonlinear response of silicon in the near-infrared region,” Appl. Phys. Lett. 91, 071113 (2007).
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P. Guan, K. M. Røge, M. Lillieholm, M. Galili, H. Hu, T. Morioka, and L. K. Oxenløwe, “Time lens-based optical fourier transformation for all-optical signal processing of spectrally-efficient data,” J. Light. Technol. 35, 799–806 (2017).
[Crossref]

Nat. Commun. (2)

P. Guan, F. Da Ros, M. Lillieholm, N.-K. Kjøller, H. Hu, K. M. Røge, M. Galili, T. Morioka, and L. K. Oxenløwe, “Scalable WDM phase regeneration in a single phase-sensitive amplifier through optical time lenses,” Nat. Commun. 9, 1049 (2018).
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C. Joshi, A. Farsi, S. Clemmen, S. Ramelow, and A. L. Gaeta, “Frequency multiplexing for quasi-deterministic heralded single-photon sources,” Nat. Commun. 9, 847 (2018).
[Crossref] [PubMed]

Nat. Photonics (2)

Z. Tong, C. Lundström, P. Andrekson, C. McKinstrie, M. Karlsson, D. Blessing, E. Tipsuwannakul, B. Puttnam, H. Toda, and L. Grüner-Nielsen, “Towards ultrasensitive optical links enabled by low-noise phase-sensitive amplifiers,” Nat. Photonics 5, 430–436 (2011).
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J. G. Koefoed, S. M. M. Friis, J. B. Christensen, and K. Rottwitt, “Spectrally pure heralded single photons by spontaneous four-wave mixing in a fiber: reducing impact of dispersion fluctuations,” Opt. Express 25, 20835–20849 (2017).
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C. J. McKinstrie, J. B. Christensen, K. Rottwitt, and M. G. Raymer, “Generation of two-temporal-mode photon states by vector four-wave mixing,” Opt. Express 25, 20877–20893 (2017).
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Opt. Lett (1)

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K. Li, H. Sun, and A. C. Foster, “Four-wave mixing Bragg scattering in hydrogenated amorphous silicon waveguides,” Opt. Lett. 42, 1488–1491 (2017).
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Y. Zhao, D. Lombardo, J. Mathews, and I. Agha, “Low control-power wavelength conversion on a silicon chip,” Opt. Lett. 41, 3651–3654 (2016).
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Optica (1)

Phys. Reports (1)

S. Blanes, F. Casas, J. Oteo, and J. Ros, “The Magnus expansion and some of its applications,” Phys. Reports 470, 151–238 (2009).
[Crossref]

Phys. Rev. A (2)

J. B. Christensen, C. J. McKinstrie, and K. Rottwitt, “Temporally uncorrelated photon-pair generation by dual-pump four-wave mixing,” Phys. Rev. A 94, 013819 (2016).
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Phys. Rev. Lett. (2)

S. Clemmen, A. Farsi, S. Ramelow, and A. L. Gaeta, “Ramsey interference with single photons,” Phys. Rev. Lett. 117, 223601 (2016).
[Crossref] [PubMed]

H. McGuinness, M. Raymer, C. McKinstrie, and S. Radic, “Quantum frequency translation of single-photon states in a photonic crystal fiber,” Phys. Rev. Lett. 105, 093604 (2010).
[Crossref] [PubMed]

Phys. Rev. X (2)

B. Brecht, D. V. Reddy, C. Silberhorn, and M. Raymer, “Photon temporal modes: a complete framework for quantum information science,” Phys. Rev. X 5, 041017 (2015).

Y.-S. Ra, C. Jacquard, A. Dufour, C. Fabre, and N. Treps, “Tomography of a mode-tunable coherent single-photon subtractor,” Phys. Rev. X 7, 031012 (2017).

Other (1)

H. Hu, R. M. Jopson, A. Gnauck, M. Dinu, S. Chandrasekhar, X. Liu, C. Xie, M. Montoliu, S. Randel, and C. McKinstrie, “Fiber nonlinearity compensation of an 8-channel WDM PDM-QPSK signal using multiple phase conjugations,” in “Optical Fiber Communications Conference and Exhibition (OFC), 2014,” (IEEE, 2014), pp. 1–3.

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Figures (5)

Fig. 1
Fig. 1 (a) Near- and (b) distant frequency conversion by BS for fields placed symetrically around the zero-dispersion frequency ω0. The input signal s is down-shifted by δω in frequency to r by the two pumps, p and q. The separation between the average pump frequency and the average frequency of the input and converted signal is denoted Δω. The direction of the arrows indicate direction of energy flow, which may be reversed to achieve up-conversion. (c) In the near configuration, spurious Bragg scattering processes, generating the additional fields r(1) and r(2), may limit the conversion efficiency from s to r.
Fig. 2
Fig. 2 (a) Maximal conversion efficiency as a function of the dimensionless mismatch parameter Θmis = β3Δωδω2L. For small mismatches, undesired Bragg scattering modes, r(n), become significant, and thereby limit the conversion efficiency from s to r. Inset shows the phase-matching diagram interpreted as a parabola in (ω, β1)-space and the placements of the various fields. (b) and (c) show the relative power transfer versus waveguide distance between the input signal s (dashed-dotted, red) the desired output r (full, blue), the undesired bidirectional output r(1) (dashed, green), and the cascaded converted output r(2) (dashed-dotted, black), for Θmis = 9 and Θmis = 20, respectively.
Fig. 3
Fig. 3 (a) In cross-polarized BS the converted output signal is orthogonal in polarization to the input signal. (b) The direction of conversion can be controlled by setting the polarization of the input signal. (c) Undesired BS processes are suppressed by waveguide birefringence, making the cross-polarized configuration unidirectional.
Fig. 4
Fig. 4 (a) Gaussian- and (b) first-order Hermite-Gaussian signal s inputs, which multiplied by (c) the self-transfer function Gss and (d) the cross-transfer function Grs, yields, (e) the remaining signal s outputs, and (f) the converted signal r outputs, respectively. The walk-off parameter, ζ = 2, does not enable a full collision between the pumps and the signal resulting in temporally localized conversion.
Fig. 5
Fig. 5 (a) Gaussian- and (b) first-order Hermite-Gaussian signal s inputs, which multiplied by (c) the self-transfer function Gss and (d) the cross-transfer function Grs, yields, (e) the remaining signal s outputs, and (f) the converted signal r outputs, respectively. The walk-off parameter, ζ = 8, in this case enables a full collision between the pumps and the signal, resulting in shape-preserving conversion of both considered input signals.

Equations (29)

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Δ β = β ( ω s ) β ( ω r ) + β ( ω p ) β ( ω q ) + γ ( P q P p ) ,
β ( ω ) = β 0 + β 1 ω + β 3 ω 3 / 6 + 𝒪 ( ω 4 ) ,
β ( ω ) = d β / d ω = β 1 + β 3 ω 2 / 2 + 𝒪 ( ω 3 ) .
Δ β β 3 δ ω Δ ω 2 ( ω p + ω s ) ,
Ω s | 4 β 3 δ ω Δ ω L | .
Δ β spur = β ( ω s ) β ( ω s + δ ω ) β ( ω p ) + β ( ω q ) = β 3 ω p δ ω 2 ,
| β 3 ω p δ ω 2 L | 1 ,
| β 3 ω q δ ω 2 L | 1 .
β ± ( ω ) = β 0 ± + β 1 ± ω + β 2 2 ω 2 + 𝒪 ( ω 3 ) ,
β ± ( ω ) = β 1 ± + β 2 ω + 𝒪 ( ω 2 ) .
Δ β spur = 2 Δ β 0 Δ β 1 ( Δ ω + 2 δ ω ) ,
| 4 π L L B Δ β 1 ( Δ ω + 2 δ ω ) L | 1 ,
| 4 π L L B Δ β 1 ( Δ ω 2 δ ω ) L | 1 ,
( z + β ¯ t ) A p = i γ ( | A p | 2 + 2 3 | A q | 2 ) A p ,
( z + β ¯ t ) A q = i γ ( | A q | 2 + 2 3 | A p | 2 ) A q ,
A p ( z , t ) = A p 0 ( t β ¯ z ) exp ( 5 i γ 3 | A p 0 ( t β ¯ z ) | 2 z ) ,
z [ a s ( z , t ) a r ( z , t ) ] = M ( z , t ) [ a s ( z , t ) a r ( z , t ) ] ,
M ( z , t ) = i γ [ 2 | A q ( z , t ) | 2 + 2 3 | A p ( z , t ) | 2 2 3 A p * ( z , t ) A q ( z , t ) 2 3 A p ( z , t ) A q * ( z , t ) 2 | A p ( z , t ) | 2 + 2 3 | A q ( z , t ) | 2 ] ,
M ( z , t ) = 2 i γ 3 [ 4 1 1 4 ] | A ( z , t ) | 2 ,
[ a s ( z , t ) a r ( z , t ) ] = [ G z z ( z , z 0 , t ) G s r ( z , z 0 , t ) G r z ( z , z 0 , t ) G r r ( z , z 0 , t ) ] [ a s ( z 0 , t ) a r ( z 0 , t ) ] = G ( z , z 0 , t ) [ a s ( z 0 , t ) a r ( z 0 , t ) ] ,
G ( L , 0 , t ) = exp [ 4 i ξ ( t ) ] × [ cos [ ξ ( t ) ] i sin [ ξ ( t ) ] i sin [ ξ ( t ) ] cos [ ξ ( t ) ] ] ,
ξ ( t ) = 2 γ 3 z 0 = 0 z = L d z | A 0 ( t β ¯ z ) | 2 .
A 0 ( t ) = ( E π 1 / 2 τ ) 1 / 2 exp [ ( t + t 0 ) 2 / ( 2 τ 2 ) ] ,
ξ ( t ) = γ E 3 β ¯ [ erf ( t τ + ζ 2 ) erf ( t τ ζ 2 ) ] ,
Δ β j k = β ( ω j ) β ( ω k ) ± ( β ( ω p ) β ( ω q ) ) ,
z a s = 2 i γ ( | A p | 2 + | A q | 2 ) a s + 2 i γ ( A p * A q a r + A p A q * a r ( 1 ) e i Δ β r ( 1 ) s ) ,
z a r = 2 i γ ( | A p | 2 + | A q | 2 ) a r + 2 i γ ( A p * A q a r ( 2 ) e i Δ β r ( 2 ) r + A p A q * a s ) ,
z a r ( 1 ) = 2 i γ ( | A p | 2 + | A q | 2 ) a r ( 1 ) + 2 i γ ( A p * A q a s e i Δ β s r ( 1 ) + A p A q * a r ( 3 ) e i Δ β r ( 3 ) r ( 1 ) ) ,
z a r ( 2 ) = 2 i γ ( | A p | 2 + | A q | 2 ) a r ( 2 ) + 2 i γ ( A p * A q a r ( 4 ) e i Δ β r ( 4 ) r ( 2 ) + A p A q * a r e i Δ β r r ( 2 ) ) ,

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