Abstract

The first successful translation of a phase modulated optical signal over 80 THz, from the near infrared to the short-wave infrared (SWIR) band is demonstrated. A signal, phase-modulated at 10 Gbps, was received in an error-free manner in the SWIR(1.7–2.2 μm) band. A new class of highly nonlinear fiber with reduced dispersion fluctuation was utilized as the platform for this phase-preserving distant parametric conversion.

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  1. R. Jiang, C.-S. Brès, N. Alic, E. Myslivets, and S. Radic, “Translation of Gbps phase-modulated optical signal from near-infrared to visible band,” J. Lightwave Technol.26(1), 131–137 (2008).
    [CrossRef]
  2. J. Boggio, S. Moro, B. P.-P. Kuo, N. Alic, B. Stossel, and S. Radic, “Tunable parametric all-fiber short-wavelength IR transmitter,” J. Lightwave Technol.28(4), 443–447 (2010).
    [CrossRef]
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    [CrossRef]
  4. M. Ebrahim-Zadeh and I. T. Sorokina, Mid-infrared Coherent Sources and Applications (Springer, 2008).
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    [CrossRef]
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    [CrossRef]
  10. J. M. Chavez Boggio, S. Zlatanovic, F. Gholami, J. M. Aparicio, S. Moro, K. Balch, N. Alic, and S. Radic, “Short wavelength infrared frequency conversion in ultra-compact fiber device,” Opt. Express18(2), 439–445 (2010).
    [CrossRef] [PubMed]
  11. F. Gholami, S. Zlatanovic, E. Myslivets, S. Moro, B. P.-P. Kuo, C.-S. Brès, A. O. J. Wiberg, N. Alic, and S. Radic, “10Gbps parametric short-wave infrared transmitter,” in Proc. OFC/NFOEC 2011, paper OThC6, 2011.
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2012

2010

2009

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron.15(1), 103–113 (2009).
[CrossRef]

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009).
[CrossRef]

2008

2005

S. Radic and C. J. McKinstrie, “Optical amplification and signal processing in highly nonlinear optical fiber,” IEICE Trans. Electron.E88-C(5), 859–869 (2005).
[CrossRef]

2004

M. Farahmand and M. de Sterke, “Parametric amplification in presence of dispersion fluctuations,” Opt. Express12(1), 136–142 (2004).
[CrossRef] [PubMed]

M. E. Marhic, K. K.-Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004).
[CrossRef]

2003

1996

1995

M. Yu, C. J. McKinstrie, and G. P. Agrawal, “Modulational instabilities in dispersion-flattened fibers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics52(1), 1072–1080 (1995).
[CrossRef] [PubMed]

1993

A. Wada, T. Nozawa, T.-O. Tsun, and R. Yamauchi, “Suppression of stimulated Brillouin scattering by intentionally induced periodic residual –strain in single-mode optical fibers,” IEICE Trans. Commun.E76-B, 345–351 (1993).

1982

R. G. DeVoe and R. G. Brewer, “Coherence phenomena in phase-modulation laser spectroscopy,” Phys. Rev. A26(1), 705–708 (1982).
[CrossRef]

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Sel. Top. Quantum Electron.18(7), 1062–1072 (1982).
[CrossRef]

Agrawal, G. P.

M. Yu, C. J. McKinstrie, and G. P. Agrawal, “Modulational instabilities in dispersion-flattened fibers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics52(1), 1072–1080 (1995).
[CrossRef] [PubMed]

Alic, N.

Andrekson, P. A.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009).
[CrossRef]

Aparicio, J. M.

J. M. Chavez Boggio, S. Zlatanovic, F. Gholami, J. M. Aparicio, S. Moro, K. Balch, N. Alic, and S. Radic, “Short wavelength infrared frequency conversion in ultra-compact fiber device,” Opt. Express18(2), 439–445 (2010).
[CrossRef] [PubMed]

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009).
[CrossRef]

Balch, K.

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Sel. Top. Quantum Electron.18(7), 1062–1072 (1982).
[CrossRef]

Boggio, J.

Boggio, J. M. C.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Boskovic, A.

Bres, C.-S.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009).
[CrossRef]

Brès, C.-S.

Brewer, R. G.

R. G. DeVoe and R. G. Brewer, “Coherence phenomena in phase-modulation laser spectroscopy,” Phys. Rev. A26(1), 705–708 (1982).
[CrossRef]

Chavez Boggio, J. M.

Chernikov, S. V.

Choi, D.-Y.

Coen, S.

de Sterke, M.

DeVoe, R. G.

R. G. DeVoe and R. G. Brewer, “Coherence phenomena in phase-modulation laser spectroscopy,” Phys. Rev. A26(1), 705–708 (1982).
[CrossRef]

Divliansky, I. B.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Eggleton, B. J.

Farahmand, M.

Gai, X.

Gholami, F.

Gruner-Nielsen, L.

Harvey, J. D.

Hirano, M.

B. P.-P. Kuo, M. Hirano, and S. Radic, “Continuous-wave, short-wavelength infrared mixer using dispersion-stabilized highly-nonlinear fiber,” Opt. Express20(16), 18422–18431 (2012).
[CrossRef] [PubMed]

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron.15(1), 103–113 (2009).
[CrossRef]

Jiang, R.

Kazovsky, L. G.

M. E. Marhic, K. K.-Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004).
[CrossRef]

Knight, J. C.

Kuo, B. P.-P.

Lamont, M. R.

Leonhardt, R.

Levring, O. A.

Lundström, C.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009).
[CrossRef]

Luther-Davies, B.

Madden, S.

Marhic, M. E.

M. E. Marhic, K. K.-Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004).
[CrossRef]

McKinstrie, C. J.

S. Radic and C. J. McKinstrie, “Optical amplification and signal processing in highly nonlinear optical fiber,” IEICE Trans. Electron.E88-C(5), 859–869 (2005).
[CrossRef]

M. Yu, C. J. McKinstrie, and G. P. Agrawal, “Modulational instabilities in dispersion-flattened fibers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics52(1), 1072–1080 (1995).
[CrossRef] [PubMed]

Mookherjea, S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Moro, S.

J. M. Chavez Boggio, S. Zlatanovic, F. Gholami, J. M. Aparicio, S. Moro, K. Balch, N. Alic, and S. Radic, “Short wavelength infrared frequency conversion in ultra-compact fiber device,” Opt. Express18(2), 439–445 (2010).
[CrossRef] [PubMed]

S. Moro, A. Peric, N. Alic, B. Stossel, and S. Radic, “Phase noise in fiber-optic parametric amplifiers and converters and its impact on sensing and communication systems,” Opt. Express18(20), 21449–21460 (2010).
[CrossRef] [PubMed]

J. Boggio, S. Moro, B. P.-P. Kuo, N. Alic, B. Stossel, and S. Radic, “Tunable parametric all-fiber short-wavelength IR transmitter,” J. Lightwave Technol.28(4), 443–447 (2010).
[CrossRef]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009).
[CrossRef]

Myslivets, E.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009).
[CrossRef]

R. Jiang, C.-S. Brès, N. Alic, E. Myslivets, and S. Radic, “Translation of Gbps phase-modulated optical signal from near-infrared to visible band,” J. Lightwave Technol.26(1), 131–137 (2008).
[CrossRef]

Nakanishi, T.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron.15(1), 103–113 (2009).
[CrossRef]

Nozawa, T.

A. Wada, T. Nozawa, T.-O. Tsun, and R. Yamauchi, “Suppression of stimulated Brillouin scattering by intentionally induced periodic residual –strain in single-mode optical fibers,” IEICE Trans. Commun.E76-B, 345–351 (1993).

Okuno, T.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron.15(1), 103–113 (2009).
[CrossRef]

Onishi, M.

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron.15(1), 103–113 (2009).
[CrossRef]

Park, J. S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Peric, A.

Radic, S.

B. P.-P. Kuo, M. Hirano, and S. Radic, “Continuous-wave, short-wavelength infrared mixer using dispersion-stabilized highly-nonlinear fiber,” Opt. Express20(16), 18422–18431 (2012).
[CrossRef] [PubMed]

B. P.-P. Kuo and S. Radic, “Highly nonlinear fiber with dispersive characteristic invariant to fabrication fluctuations,” Opt. Express20(7), 7716–7725 (2012).
[CrossRef] [PubMed]

S. Moro, A. Peric, N. Alic, B. Stossel, and S. Radic, “Phase noise in fiber-optic parametric amplifiers and converters and its impact on sensing and communication systems,” Opt. Express18(20), 21449–21460 (2010).
[CrossRef] [PubMed]

J. M. Chavez Boggio, S. Zlatanovic, F. Gholami, J. M. Aparicio, S. Moro, K. Balch, N. Alic, and S. Radic, “Short wavelength infrared frequency conversion in ultra-compact fiber device,” Opt. Express18(2), 439–445 (2010).
[CrossRef] [PubMed]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

J. Boggio, S. Moro, B. P.-P. Kuo, N. Alic, B. Stossel, and S. Radic, “Tunable parametric all-fiber short-wavelength IR transmitter,” J. Lightwave Technol.28(4), 443–447 (2010).
[CrossRef]

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009).
[CrossRef]

R. Jiang, C.-S. Brès, N. Alic, E. Myslivets, and S. Radic, “Translation of Gbps phase-modulated optical signal from near-infrared to visible band,” J. Lightwave Technol.26(1), 131–137 (2008).
[CrossRef]

S. Radic and C. J. McKinstrie, “Optical amplification and signal processing in highly nonlinear optical fiber,” IEICE Trans. Electron.E88-C(5), 859–869 (2005).
[CrossRef]

Russell, P. St. J.

Stolen, R. H.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Sel. Top. Quantum Electron.18(7), 1062–1072 (1982).
[CrossRef]

Stossel, B.

Taylor, J. R.

Tsun, T.-O.

A. Wada, T. Nozawa, T.-O. Tsun, and R. Yamauchi, “Suppression of stimulated Brillouin scattering by intentionally induced periodic residual –strain in single-mode optical fibers,” IEICE Trans. Commun.E76-B, 345–351 (1993).

Wada, A.

A. Wada, T. Nozawa, T.-O. Tsun, and R. Yamauchi, “Suppression of stimulated Brillouin scattering by intentionally induced periodic residual –strain in single-mode optical fibers,” IEICE Trans. Commun.E76-B, 345–351 (1993).

Wadsworth, W. J.

Wiberg, A. O. J.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009).
[CrossRef]

Wong, G. K. L.

Wong, K. K.-Y.

M. E. Marhic, K. K.-Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004).
[CrossRef]

Yamauchi, R.

A. Wada, T. Nozawa, T.-O. Tsun, and R. Yamauchi, “Suppression of stimulated Brillouin scattering by intentionally induced periodic residual –strain in single-mode optical fibers,” IEICE Trans. Commun.E76-B, 345–351 (1993).

Yu, M.

M. Yu, C. J. McKinstrie, and G. P. Agrawal, “Modulational instabilities in dispersion-flattened fibers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics52(1), 1072–1080 (1995).
[CrossRef] [PubMed]

Zlatanovic, S.

J. M. Chavez Boggio, S. Zlatanovic, F. Gholami, J. M. Aparicio, S. Moro, K. Balch, N. Alic, and S. Radic, “Short wavelength infrared frequency conversion in ultra-compact fiber device,” Opt. Express18(2), 439–445 (2010).
[CrossRef] [PubMed]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Sel. Top. Quantum Electron.18(7), 1062–1072 (1982).
[CrossRef]

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-based highly nonlinear fiber and their application,” IEEE J. Sel. Top. Quantum Electron.15(1), 103–113 (2009).
[CrossRef]

M. E. Marhic, K. K.-Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron.10(5), 1133–1141 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

E. Myslivets, C. Lundström, J. M. Aparicio, S. Moro, A. O. J. Wiberg, C.-S. Bres, N. Alic, P. A. Andrekson, and S. Radic, “Spatial equalization of zero-dispersion wavelength profiles in nonlinear fibers,” IEEE Photon. Technol. Lett.21(24), 1807–1809 (2009).
[CrossRef]

IEICE Trans. Commun.

A. Wada, T. Nozawa, T.-O. Tsun, and R. Yamauchi, “Suppression of stimulated Brillouin scattering by intentionally induced periodic residual –strain in single-mode optical fibers,” IEICE Trans. Commun.E76-B, 345–351 (1993).

IEICE Trans. Electron.

S. Radic and C. J. McKinstrie, “Optical amplification and signal processing in highly nonlinear optical fiber,” IEICE Trans. Electron.E88-C(5), 859–869 (2005).
[CrossRef]

J. Lightwave Technol.

Nat. Photonics

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics4(8), 561–564 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

R. G. DeVoe and R. G. Brewer, “Coherence phenomena in phase-modulation laser spectroscopy,” Phys. Rev. A26(1), 705–708 (1982).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

M. Yu, C. J. McKinstrie, and G. P. Agrawal, “Modulational instabilities in dispersion-flattened fibers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics52(1), 1072–1080 (1995).
[CrossRef] [PubMed]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2006).

M. Ebrahim-Zadeh and I. T. Sorokina, Mid-infrared Coherent Sources and Applications (Springer, 2008).

F. Gholami, S. Zlatanovic, E. Myslivets, S. Moro, B. P.-P. Kuo, C.-S. Brès, A. O. J. Wiberg, N. Alic, and S. Radic, “10Gbps parametric short-wave infrared transmitter,” in Proc. OFC/NFOEC 2011, paper OThC6, 2011.
[CrossRef]

T. Okuno, T. Nakanishi, M. Hirano, and M. Onishi, “Practical considerations for the application of highly nonlinear fibers,” in Proc. OFC/NFOEC 2007, paper OTuJ1, 2007.
[CrossRef]

V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, Kramers–Kronig Relations in Optical Materials Research (Springer-Verlag, 2005).

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Figures (7)

Fig. 1
Fig. 1

Theoretical conversion efficiency (CE) spectra for (a) wide band, and (b) narrow-band parametric converter (λp = 1556.5nm and Δλp is the shift from this wavelength).

Fig. 2
Fig. 2

Theoretically calculated average conversion efficiencies as a function of random dispersion fluctuations. Red dotted line denotes the conversion efficiency for an ideal fiber in the absence of dispersion fluctuations.

Fig. 3
Fig. 3

Accumulated dispersion within the narrow phase-matching window in the presence of fiber dispersion fluctuation, calculated for a fiber length of 45m and a fluctuation correlation length of 1m.

Fig. 4
Fig. 4

Experimental setup schematic of the parametric SWIR converter. Acronyms: MZM: mach–zehnder modulator; SOA— semiconductor optical amplifier; EDFA—erbium-doped fiber amplifier; PC—polarization controller; WDM—wavelength multiplexer; DPSK—differential phase-shift keying; HNLH—highly nonlinear fiber; LPF—long pass filter; C—collimator; M1,M2—mirrors; PD—photo detector; BER—bit-error rate; OSA—optical spectrum analyzer; PRBS – pseudo-random bit sequence.

Fig. 5
Fig. 5

Spectra measured at the output of the HNLF reflecting the response of 20dB attenuator compared with spectrum after the LPF with pump and seed filtered out. The extent of the measurement is limited by the OSA operation range.

Fig. 6
Fig. 6

Signal integrity (BER) contour plot for (a) the O-band signal and (b) the SWIR idler.

Fig. 7
Fig. 7

Data stream waveform and eye diagrams of the 10Gbps DPSK signal (a) signal in the O-band and (b) idler in SWIR region., c) BER plots of the 10Gb/s O-band signal (red circles) and SWIR idler (blue squares).

Equations (7)

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G S =1+ ( γ P p ) 2 2 g 2 [ cosh( 2gL )1 ]
G I = ( γ P P ) 2 2 g 2 [ cosh( 2gL )1 ]= G S 1
g= (γ P p ) 2 (Δk) 2
Δk=Δβ+2γ P p
Δβ β 2 ( ω p ω s ) 2 + 1 12 β 4 ( ω p ω s ) 4
δ β 2 (z)=δ β 2 (zδz)exp(δz/ L c )+p 1exp(2δz/ L c )
D= 2πc λ 2 d 2 β d ω 2

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