Abstract

We demonstrate the generation of a supercontinuum in a 2 cm long silicon wire by pumping the wire with mid-infrared picosecond pulses in the anomalous dispersion regime. The supercontinuum extends from 1535 nm up to 2525 nm for a coupled peak power of 12.7 W. It is shown that the supercontinuum originates primarily from the amplification of background noise. A detailed analysis of the spectral components which are generated through phase-matched processes is applied to extract the group velocity dispersion and fourth-order dispersion coefficient of the silicon wire waveguide.

© 2011 OSA

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    [CrossRef] [PubMed]

2011 (2)

2010 (4)

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. Photonics 4(8), 561–564 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Jr., Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[CrossRef]

D. Duchesne, M. Peccianti, M. R. E. Lamont, M. Ferrera, L. Razzari, F. Légaré, R. Morandotti, S. Chu, B. E. Little, and D. J. Moss, “Supercontinuum generation in a high index doped silica glass spiral waveguide,” Opt. Express 18(2), 923–930 (2010).
[CrossRef] [PubMed]

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18(23), 23598–23607 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (3)

2007 (4)

V. Raghunathan, D. Borlaug, R. R. Rice, and B. Jalali, “Demonstration of a mid-infrared silicon Raman amplifier,” Opt. Express 15(22), 14355–14362 (2007).
[CrossRef] [PubMed]

R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), 249–271 (2007).
[CrossRef]

I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, R. M. Osgood, and Jr., “Supercontinuum generation in silicon photonic wires,” Opt. Express 15(23), 15242–15249 (2007).
[CrossRef] [PubMed]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[CrossRef]

2006 (6)

N. C. Panoiu, X. G. Chen, R. M. Osgood, and Jr., “Modulation Instability in Silicon Photonic Nanowires,” Opt. Lett. 31(24), 3609–3611 (2006).
[CrossRef] [PubMed]

J. M. Dudley, G. Gently, and S. Coen, “Supercontinuum generation in photonic crystal,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express 14(9), 3853–3863 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Opt. Express 14(10), 4357–4362 (2006).
[CrossRef] [PubMed]

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).

2004 (1)

2002 (2)

W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T.-P. Martin Man, and P. St J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19(9), 2148–2155 (2002).
[CrossRef]

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[CrossRef]

2001 (2)

1995 (1)

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51(3), 2602–2607 (1995).
[CrossRef] [PubMed]

Akhmediev, N.

Alic, N.

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. Photonics 4(8), 561–564 (2010).
[CrossRef]

Ania-Castanon, J. D.

S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

Asghari, M.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[CrossRef]

Assefa, Y. A.

Baets, R.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).

Birks, T. A.

Bogaerts, W.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).

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. Photonics 4(8), 561–564 (2010).
[CrossRef]

Borlaug, D.

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
[CrossRef]

Chen, I.-W.

Chen, X.

Chen, X. G.

Choi, D. Y.

Chou, C.-Y.

Chu, S.

Chudoba, C.

Coen, S.

J. M. Dudley, G. Gently, and S. Coen, “Supercontinuum generation in photonic crystal,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Dadap, J. I.

Dadap, X.

Day, I. E.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[CrossRef]

Dekker, R.

R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), 249–271 (2007).
[CrossRef]

Dias, F.

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. Photonics 4(8), 561–564 (2010).
[CrossRef]

Drake, J.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[CrossRef]

Driessen, A.

R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), 249–271 (2007).
[CrossRef]

Driscoll, J. B.

Duchesne, D.

Dudley, J. M.

Dulkeith, E.

Dulkeith, W. M.

Dumon, P.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).

Eggleton, B. J.

Elder, A. D.

C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92(3), 367–378 (2008).
[CrossRef]

Ellingham, T. J.

S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

Ferrera, M.

Finot, C.

Forst, M.

R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), 249–271 (2007).
[CrossRef]

Foster, M. A.

Frank, J. H.

C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92(3), 367–378 (2008).
[CrossRef]

Fujimoto, J. G.

Gaeta, A. L.

Gently, G.

J. M. Dudley, G. Gently, and S. Coen, “Supercontinuum generation in photonic crystal,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[CrossRef]

Genty, G.

Ghanta, R. K.

Green,

Green, W. M.

Green, W. M. J.

Harpin, A.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[CrossRef]

Hartl, I.

Herrmann, J.

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87(20), 203901 (2001).
[CrossRef] [PubMed]

Hsieh, E.

Hsieh, I.-W.

Hult, J.

C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92(3), 367–378 (2008).
[CrossRef]

Husakou, A. V.

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87(20), 203901 (2001).
[CrossRef] [PubMed]

Jalali, B.

Jr.,

Jr., N. C.

Jr., S.

Jr., Y. A.

X. Liu, R. M. Osgood, Y. A. Jr., Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[CrossRef]

Kaminski, C. F.

C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92(3), 367–378 (2008).
[CrossRef]

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51(3), 2602–2607 (1995).
[CrossRef] [PubMed]

Kibler, B.

Knight, J. C.

Ko, T. H.

Kobtsev, S. M.

S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

Kukarin, S.

S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

Lamont, M. R.

Lamont, M. R. E.

Lantz, E.

Lau, R. K. W.

Légaré, F.

Li, X. D.

Liang, T. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[CrossRef]

Lipson, M.

Little, B. E.

Liu, X.

Luther-Davies, B.

Madden, S.

Maillotte, H.

Manolatou, C.

Martin Man, T.-P.

Ménard, M.

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. Photonics 4(8), 561–564 (2010).
[CrossRef]

Morandotti, R.

Moro, 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. Photonics 4(8), 561–564 (2010).
[CrossRef]

Moss, D. J.

Mussot, A.

Okawachi, Y.

Ortigosa-Blanch, A.

Osgood, R. M.

X. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Jr., Y. A. Assefa, Vlasov, and W. M. J. Green, “Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge,” Opt. Express 19(8), 7778–7789 (2011).
[CrossRef] [PubMed]

X. Liu, R. M. Osgood, Y. A. Jr., Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[CrossRef]

R. M. Osgood, N. C. Jr., J. I. Panoiu, X. Dadap, X. Liu, I.-W. Chen, E. Hsieh, W. M. Dulkeith, Green, and Y. A. Vlasov, “Engineering nonlinearities in nanoscale optical systems: physics and applications in dispersion-engineered silicon nanophotonic wires,” Adv. Opt. Photon. 1(1), 162–235 (2009).
[CrossRef]

X. Liu, W. M. J. Green, X. Chen, I.-W. Hsieh, J. I. Dadap, Y. A. Vlasov, R. M. Osgood, and Jr., “Conformal dielectric overlayers for engineering dispersion and effective nonlinearity of silicon nanophotonic wires,” Opt. Lett. 33(24), 2889–2891 (2008).
[CrossRef] [PubMed]

I.-W. Hsieh, X. Chen, X. Liu, J. I. Dadap, N. C. Panoiu, C.-Y. Chou, F. Xia, W. M. Green, Y. A. Vlasov, R. M. Osgood, and Jr., “Supercontinuum generation in silicon photonic wires,” Opt. Express 15(23), 15242–15249 (2007).
[CrossRef] [PubMed]

N. C. Panoiu, X. G. Chen, R. M. Osgood, and Jr., “Modulation Instability in Silicon Photonic Nanowires,” Opt. Lett. 31(24), 3609–3611 (2006).
[CrossRef] [PubMed]

Panoiu, J. I.

Panoiu, N. C.

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. Photonics 4(8), 561–564 (2010).
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A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
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Sharping, J. E.

Smirnov, S. V.

S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
[CrossRef]

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H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[CrossRef]

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S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
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Adv. Opt. Photon. (1)

Appl. Phys. B (1)

C. F. Kaminski, R. S. Watt, A. D. Elder, J. H. Frank, and J. Hult, “Supercontinuum radiation for applications in chemical sensing and microscopy,” Appl. Phys. B 92(3), 367–378 (2008).
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Appl. Phys. Lett. (2)

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90(19), 191104 (2007).
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IEEE J. Sel. Top. Quantum Electron. (1)

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 12, 1394–1401 (2006).

J. Opt. Soc. Am. B (1)

J. Phys. D Appl. Phys. (1)

R. Dekker, N. Usechak, M. Forst, and A. Driessen, “Ultrafast nonlinear all-optical processes in silicon-on-insulator waveguides,” J. Phys. D Appl. Phys. 40(14), 249–271 (2007).
[CrossRef]

Nat. Photonics (2)

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. Photonics 4(8), 561–564 (2010).
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X. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Jr., Y. A. Assefa, Vlasov, and W. M. J. Green, “Self-phase modulation and nonlinear loss in silicon nanophotonic wires near the mid-infrared two-photon absorption edge,” Opt. Express 19(8), 7778–7789 (2011).
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Opt. Fiber Technol. (1)

S. V. Smirnov, J. D. Ania-Castanon, T. J. Ellingham, S. M. Kobtsev, S. Kukarin, and S. K. Turitsyn, “Optical spectral broadening and supercontinuum generation in telecom applications,” Opt. Fiber Technol. 12(2), 122–147 (2006).
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R. Halir, Y. Okawachi, J. S. Levy, M. A. Foster, M. Lipson, A. L. Gaeta, “Octave spanning supercontinuum generation in CMOS compatible silicon nitride waveguides,” in CLEO, PDPA6 (2011).

X. Liu, B. Kuyken, G. Roelkens, R. Baets, Y. Vlasov, R. M. Osgood Jr., W. M. J. Green, “Mid-infrared broadband modulation instability and 50dB Raman assisted parametric gain in silicon photonic wires,” in CLEO, CTuS2.pdf (2011).

B. Kuyken, X. Liu, R. M. Osgood Jr., Y. Vlasov, G. Roelkens, R. Baets, and W. M. J. Green, “Frequency conversion of mid-infrared optical signals into the telecom band using nonlinear silicon nanophotonic wires,” Optical Fiber Communication Conference, OThU4 (2011).

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Figures (6)

Fig. 1
Fig. 1

Group velocity dispersion of the silicon wire waveguide as a function of the wavelength, exhibiting anomalous dispersion (β2 < 0) between 1810 nm and 2410 nm. The inset shows the fabricated wire waveguide dimensions.

Fig. 2
Fig. 2

Measured output spectrum for increasing values of coupled input peak power: 3.1 W (green), 4.3 W (blue), 7.9 W (red) and 12.7 W (black). The spectra are vertically offset by multiples of 20 dB for clarity.

Fig. 3
Fig. 3

Output spectrum on the red side of the pump, as measured by FTIR at a coupled input peak power of 12.7 W.

Fig. 4
Fig. 4

Measured output spectra obtained while seeding the supercontinuum at a wavelength of 2415 nm (green) and 2496 nm (red), using a CW mid-infrared laser. The blue curve shows the unseeded output spectrum as a reference. The coupled peak power is 12.7 W in all cases. The spectra are vertically offset by multiples of 40 dB for clarity.

Fig. 5
Fig. 5

On-chip signal gain (red dots) and wavelength conversion efficiency (black squares) at a peak power of 12.7 W as measured through seeding the supercontinuum at various wavelengths. The hatched areas label the pump’s Raman Stokes and matching anti-Stokes bands.

Fig. 6
Fig. 6

Curve fit describing the linear phase mismatch after propagation through the 2 cm long waveguide, as a function of detuning on the red side of the pump. The silicon wire dispersion coefficients extracted from this fit are β2 = −0.43 ± 0.07 ps2/m and β4 = 2.3 ± 0.4 x 10−4 ps4/m. The red squares represent the detuning wavelengths of the MI(1) and MI(2) peaks, where the corresponding nonlinear phase mismatch 2γPavg1/e term (dash-dotted lines labeled on the left) balances the linear phase mismatch at each value of input peak pump power (labeled on the right). The vertical error bars originate from a 1 dB uncertainty in the input coupling, while the horizontal error bars are associated with the 1 dB bandwidth of each modulation instability peak.

Tables (1)

Tables Icon

Table 1 Experimental Fit and Simulated Values of the β2 and β4 Dispersion Coefficients Associated with the 900-nm Wide Silicon Wire Waveguide

Equations (3)

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

β 2 Δ ω 2 + 1 12 β 4 Δ ω 4 +2 γ Re P=Δ k lin +Δ k nonlin =0
P avg1/e = 1 z 1/e 0 z 1/e P(z)dz
dP dz =αP2 γ Im P 2

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