Abstract

We experimentally demonstrate quasi-phase-matched (QPM) four-wave-mixing (FWM) in silicon (Si) nanowire waveguides with sinusoidally modulated width. We perform discrete wavelength conversion over 250 nm, and observe 12 dB conversion efficiency (CE) enhancement for targeted wavelengths more than 100 nm away from the edge of the 3-dB conversion bandwidth. The QPM process in Si nanowires is rigorously modeled, with results explaining experimental observations. The model is further used to investigate the dependence of the CE on key device parameters, and to introduce devices that facilitate wavelength conversion between the C-band and mid-IR. Devices based on a superposition of sinusoidal gratings are investigated theoretically, and are shown to provide CE enhancement over the entire C-band. Width-modulation is further shown to be compatible with zero-dispersion-wavelength pumping for broadband wavelength conversion. The results indicate that QPM via width-modulation is an effective technique for extending the spectral domain of efficient FWM in Si waveguides.

© 2012 OSA

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2012 (1)

N. Ophir, R. K. W. Lau, M. Menard, R. Salem, K. Padmaraju, Y. Okawachi, M. Lipson, A. L. Gaeta, and K. Bergman, “First demonstration of a 10-Gb/s RZ end-to-end four-wave mixing-based link at 1884 nm using silicon nanowaveguides,” IEEE Photon. Technol. Lett. 24(4), 276–278 (2012).
[CrossRef]

2011 (12)

R. K. W. Lau, M. Ménard, Y. Okawachi, M. A. Foster, A. C. Turner-Foster, R. Salem, M. Lipson, and A. L. Gaeta, “Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides,” Opt. Lett. 36(7), 1263–1265 (2011).
[CrossRef] [PubMed]

B. Kuyken, X. Liu, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “50 dB parametric on-chip gain in silicon photonic wires,” Opt. Lett. 36(22), 4401–4403 (2011).
[CrossRef] [PubMed]

X. P. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Assefa, Y. A. 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]

B. Kuyken, X. P. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. J. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[CrossRef] [PubMed]

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

H. Ji, M. H. Pu, H. Hu, M. Galili, L. K. Oxenlowe, K. Yvind, J. M. Hvam, and P. Jeppesen, “Optical waveform sampling and error-free demultiplexing of 1.28 Tb/s serial data in a nanoengineered silicon waveguide,” J. Lightwave Technol. 29(4), 426–431 (2011).
[CrossRef]

J. B. Driscoll, R. R. Grote, X. P. Liu, J. I. Dadap, N. C. Panoiu, and R. M. Osgood., “Directionally anisotropic Si nanowires: on-chip nonlinear grating devices in uniform waveguides,” Opt. Lett. 36(8), 1416–1418 (2011).
[CrossRef] [PubMed]

N. Vermeulen, J. E. Sipe, Y. Lefevre, C. Debaes, and H. Thienpont, “Wavelength conversion based on Raman- and non-resonant four-wave mixing in silicon nanowire rings without dispersion engineering,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1078–1091 (2011).
[CrossRef]

Y. Huang, E.-K. Tien, S. Gao, S. K. Kalyoncu, Q. Song, F. Qian, and O. Boyraz, “Quasi phase matching in SOI and SOS based parametric wavelength converters,” Proc. SPIE 8120, 81200F, 81200F-7 (2011).
[CrossRef]

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

R. R. Grote, J. B. Driscoll, C. G. Biris, N. C. Panoiu, and R. M. Osgood., “Weakly modulated silicon-dioxide-cladding gratings for silicon waveguide Fabry-Pérot cavities,” Opt. Express 19(27), 26406–26415 (2011).
[CrossRef] [PubMed]

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

2010 (11)

N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Sel. Top. Quantum Electron. 16(1), 257–266 (2010).
[CrossRef]

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18(4), 3582–3591 (2010).
[CrossRef] [PubMed]

G. R. N. Satyan and A. Yariv, “Chirp multiplication by four wave mixing for wideband swept-frequency sources for high resolution imaging,” J. Lightwave Technol. 28(14), 2077–2083 (2010).
[CrossRef]

F. Li, M. Pelusi, D. X. Xu, A. Densmore, R. Ma, S. Janz, and D. J. Moss, “Error-free all-optical demultiplexing at 160Gb/s via FWM in a silicon nanowire,” Opt. Express 18(4), 3905–3910 (2010).
[CrossRef] [PubMed]

A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express 18(17), 18047–18055 (2010).
[CrossRef] [PubMed]

W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood., “All-optical format conversion of NRZ-OOK to RZ-OOK in a silicon nanowire utilizing either XPM or FWM and resulting in a receiver sensitivity gain of ~2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010).
[CrossRef]

E. K. Tien, Y. W. Huang, S. M. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express 18(21), 21981–21989 (2010).
[CrossRef] [PubMed]

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010).
[CrossRef] [PubMed]

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (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. Photonics 4(8), 561–564 (2010).
[CrossRef]

2009 (5)

2008 (2)

2007 (2)

2006 (4)

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]

X. G. Chen, N. C. Panoiu, and R. M. Osgood., “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42(2), 160–170 (2006).
[CrossRef]

N. C. Panoiu, X. Chen, and R. M. Osgood., “Modulation instability in silicon photonic nanowires,” Opt. Lett. 31(24), 3609–3611 (2006).
[CrossRef] [PubMed]

R. A. Soref, S. J. Emelett, and A. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[CrossRef]

2005 (2)

2003 (1)

2001 (1)

1995 (1)

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase-matched four-wave-mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett. 7(11), 1378–1380 (1995).
[CrossRef]

1987 (1)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

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]

S. Zlatanovic, J. S. Park, F. Gholami, J. M. C. Boggio, S. Moro, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides pumped by silica-fiber-based source,” IEEE J. Sel. Top. Quantum Electron. (accepted).

Almeida, V. R.

Assefa, S.

Astar, W.

W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood., “All-optical format conversion of NRZ-OOK to RZ-OOK in a silicon nanowire utilizing either XPM or FWM and resulting in a receiver sensitivity gain of ~2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010).
[CrossRef]

Baets, R.

Bennett, B. R.

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

Bergman, K.

N. Ophir, R. K. W. Lau, M. Menard, R. Salem, K. Padmaraju, Y. Okawachi, M. Lipson, A. L. Gaeta, and K. Bergman, “First demonstration of a 10-Gb/s RZ end-to-end four-wave mixing-based link at 1884 nm using silicon nanowaveguides,” IEEE Photon. Technol. Lett. 24(4), 276–278 (2012).
[CrossRef]

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express 18(17), 18047–18055 (2010).
[CrossRef] [PubMed]

Bianco, F.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Biberman, A.

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express 18(17), 18047–18055 (2010).
[CrossRef] [PubMed]

Biris, C. G.

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]

S. Zlatanovic, J. S. Park, F. Gholami, J. M. C. Boggio, S. Moro, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides pumped by silica-fiber-based source,” IEEE J. Sel. Top. Quantum Electron. (accepted).

Borga, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Boyraz, O.

Buchwald, A. R.

R. A. Soref, S. J. Emelett, and A. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[CrossRef]

Carter, G. M.

W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood., “All-optical format conversion of NRZ-OOK to RZ-OOK in a silicon nanowire utilizing either XPM or FWM and resulting in a receiver sensitivity gain of ~2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010).
[CrossRef]

Cazzanelli, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Chan, J.

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

Chen, R. Y.

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Chen, X.

Chen, X. G.

Chen, X. P.

Chou, C. Y.

Dadap, J.

Dadap, J. I.

X. P. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Assefa, Y. A. 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]

J. B. Driscoll, R. R. Grote, X. P. Liu, J. I. Dadap, N. C. Panoiu, and R. M. Osgood., “Directionally anisotropic Si nanowires: on-chip nonlinear grating devices in uniform waveguides,” Opt. Lett. 36(8), 1416–1418 (2011).
[CrossRef] [PubMed]

W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood., “All-optical format conversion of NRZ-OOK to RZ-OOK in a silicon nanowire utilizing either XPM or FWM and resulting in a receiver sensitivity gain of ~2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010).
[CrossRef]

R. M. Osgood, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. Hsieh, E. Dulkeith, W. M. J. 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]

J. B. Driscoll, X. P. Liu, S. Yasseri, I. Hsieh, J. I. Dadap, and R. M. Osgood., “Large longitudinal electric fields (Ez) in silicon nanowire waveguides,” Opt. Express 17(4), 2797–2804 (2009).
[CrossRef] [PubMed]

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
[CrossRef] [PubMed]

Dai, Y. T.

Debaes, C.

N. Vermeulen, J. E. Sipe, Y. Lefevre, C. Debaes, and H. Thienpont, “Wavelength conversion based on Raman- and non-resonant four-wave mixing in silicon nanowire rings without dispersion engineering,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1078–1091 (2011).
[CrossRef]

Degoli, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Densmore, A.

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]

Driscoll, J. B.

Dulkeith, E.

Emelett, S. J.

R. A. Soref, S. J. Emelett, and A. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[CrossRef]

Espinola, R.

Fainman, Y.

Foster, A. C.

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

Foster, M. A.

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

R. K. W. Lau, M. Ménard, Y. Okawachi, M. A. Foster, A. C. Turner-Foster, R. Salem, M. Lipson, and A. L. Gaeta, “Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides,” Opt. Lett. 36(7), 1263–1265 (2011).
[CrossRef] [PubMed]

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010).
[CrossRef] [PubMed]

A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express 18(17), 18047–18055 (2010).
[CrossRef] [PubMed]

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18(4), 3582–3591 (2010).
[CrossRef] [PubMed]

Y. T. Dai, X. P. Chen, Y. Okawachi, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and C. Xu, “1 micros tunable delay using parametric mixing and optical phase conjugation in Si waveguides,” Opt. Express 17(9), 7004–7010 (2009).
[CrossRef] [PubMed]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2008).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[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]

Fukuda, H.

Futami, F.

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase-matched four-wave-mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett. 7(11), 1378–1380 (1995).
[CrossRef]

Gaeta, A. L.

N. Ophir, R. K. W. Lau, M. Menard, R. Salem, K. Padmaraju, Y. Okawachi, M. Lipson, A. L. Gaeta, and K. Bergman, “First demonstration of a 10-Gb/s RZ end-to-end four-wave mixing-based link at 1884 nm using silicon nanowaveguides,” IEEE Photon. Technol. Lett. 24(4), 276–278 (2012).
[CrossRef]

R. K. W. Lau, M. Ménard, Y. Okawachi, M. A. Foster, A. C. Turner-Foster, R. Salem, M. Lipson, and A. L. Gaeta, “Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides,” Opt. Lett. 36(7), 1263–1265 (2011).
[CrossRef] [PubMed]

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express 18(17), 18047–18055 (2010).
[CrossRef] [PubMed]

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010).
[CrossRef] [PubMed]

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18(4), 3582–3591 (2010).
[CrossRef] [PubMed]

Y. T. Dai, X. P. Chen, Y. Okawachi, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and C. Xu, “1 micros tunable delay using parametric mixing and optical phase conjugation in Si waveguides,” Opt. Express 17(9), 7004–7010 (2009).
[CrossRef] [PubMed]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2008).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[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]

Galili, M.

Gao, S.

Y. Huang, E.-K. Tien, S. Gao, S. K. Kalyoncu, Q. Song, F. Qian, and O. Boyraz, “Quasi phase matching in SOI and SOS based parametric wavelength converters,” Proc. SPIE 8120, 81200F, 81200F-7 (2011).
[CrossRef]

Gao, S. M.

Geraghty, D. F.

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2008).
[CrossRef]

Gholami, F.

S. Zlatanovic, J. S. Park, F. Gholami, J. M. C. Boggio, S. Moro, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides pumped by silica-fiber-based source,” IEEE J. Sel. Top. Quantum Electron. (accepted).

Ghulinyan, M.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Green, W. M. J.

B. Kuyken, X. Liu, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “50 dB parametric on-chip gain in silicon photonic wires,” Opt. Lett. 36(22), 4401–4403 (2011).
[CrossRef] [PubMed]

B. Kuyken, X. P. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. J. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[CrossRef] [PubMed]

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

W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood., “All-optical format conversion of NRZ-OOK to RZ-OOK in a silicon nanowire utilizing either XPM or FWM and resulting in a receiver sensitivity gain of ~2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010).
[CrossRef]

R. M. Osgood, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. Hsieh, E. Dulkeith, W. M. J. 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]

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
[CrossRef] [PubMed]

Grote, R. R.

Hon, N. K.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

Hsieh, I.

Hsieh, I. W.

Hu, H.

Huang, Y.

Y. Huang, E.-K. Tien, S. Gao, S. K. Kalyoncu, Q. Song, F. Qian, and O. Boyraz, “Quasi phase matching in SOI and SOS based parametric wavelength converters,” Proc. SPIE 8120, 81200F, 81200F-7 (2011).
[CrossRef]

Huang, Y. W.

Hvam, J. M.

Ikeda, K.

Islam, M. N.

Itabashi, S.

Jalali, B.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

Janz, S.

Jeppesen, P.

Ji, H.

Jiang, G. M.

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Jiang, X. Q.

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Kalyoncu, S. K.

Y. Huang, E.-K. Tien, S. Gao, S. K. Kalyoncu, Q. Song, F. Qian, and O. Boyraz, “Quasi phase matching in SOI and SOS based parametric wavelength converters,” Proc. SPIE 8120, 81200F, 81200F-7 (2011).
[CrossRef]

E. K. Tien, Y. W. Huang, S. M. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express 18(21), 21981–21989 (2010).
[CrossRef] [PubMed]

Kaneko, S.

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase-matched four-wave-mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett. 7(11), 1378–1380 (1995).
[CrossRef]

Kikuchi, K.

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase-matched four-wave-mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett. 7(11), 1378–1380 (1995).
[CrossRef]

Kim, J.

Kuyken, B.

Lau, R. K. W.

N. Ophir, R. K. W. Lau, M. Menard, R. Salem, K. Padmaraju, Y. Okawachi, M. Lipson, A. L. Gaeta, and K. Bergman, “First demonstration of a 10-Gb/s RZ end-to-end four-wave mixing-based link at 1884 nm using silicon nanowaveguides,” IEEE Photon. Technol. Lett. 24(4), 276–278 (2012).
[CrossRef]

R. K. W. Lau, M. Ménard, Y. Okawachi, M. A. Foster, A. C. Turner-Foster, R. Salem, M. Lipson, and A. L. Gaeta, “Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides,” Opt. Lett. 36(7), 1263–1265 (2011).
[CrossRef] [PubMed]

Lee, B. G.

Lefevre, Y.

N. Vermeulen, J. E. Sipe, Y. Lefevre, C. Debaes, and H. Thienpont, “Wavelength conversion based on Raman- and non-resonant four-wave mixing in silicon nanowire rings without dispersion engineering,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1078–1091 (2011).
[CrossRef]

Levy, J. S.

Li, F.

Lim, J. H.

Lipson, M.

N. Ophir, R. K. W. Lau, M. Menard, R. Salem, K. Padmaraju, Y. Okawachi, M. Lipson, A. L. Gaeta, and K. Bergman, “First demonstration of a 10-Gb/s RZ end-to-end four-wave mixing-based link at 1884 nm using silicon nanowaveguides,” IEEE Photon. Technol. Lett. 24(4), 276–278 (2012).
[CrossRef]

R. K. W. Lau, M. Ménard, Y. Okawachi, M. A. Foster, A. C. Turner-Foster, R. Salem, M. Lipson, and A. L. Gaeta, “Continuous-wave mid-infrared frequency conversion in silicon nanowaveguides,” Opt. Lett. 36(7), 1263–1265 (2011).
[CrossRef] [PubMed]

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express 18(17), 18047–18055 (2010).
[CrossRef] [PubMed]

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010).
[CrossRef] [PubMed]

A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18(4), 3582–3591 (2010).
[CrossRef] [PubMed]

Y. T. Dai, X. P. Chen, Y. Okawachi, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and C. Xu, “1 micros tunable delay using parametric mixing and optical phase conjugation in Si waveguides,” Opt. Express 17(9), 7004–7010 (2009).
[CrossRef] [PubMed]

R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2008).
[CrossRef]

M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[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]

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
[CrossRef] [PubMed]

Liu, X.

Liu, X. P.

J. B. Driscoll, R. R. Grote, X. P. Liu, J. I. Dadap, N. C. Panoiu, and R. M. Osgood., “Directionally anisotropic Si nanowires: on-chip nonlinear grating devices in uniform waveguides,” Opt. Lett. 36(8), 1416–1418 (2011).
[CrossRef] [PubMed]

X. P. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Assefa, Y. A. 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]

B. Kuyken, X. P. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. J. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[CrossRef] [PubMed]

W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood., “All-optical format conversion of NRZ-OOK to RZ-OOK in a silicon nanowire utilizing either XPM or FWM and resulting in a receiver sensitivity gain of ~2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010).
[CrossRef]

J. B. Driscoll, X. P. Liu, S. Yasseri, I. Hsieh, J. I. Dadap, and R. M. Osgood., “Large longitudinal electric fields (Ez) in silicon nanowire waveguides,” Opt. Express 17(4), 2797–2804 (2009).
[CrossRef] [PubMed]

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
[CrossRef] [PubMed]

Lorattanasane, C.

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase-matched four-wave-mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett. 7(11), 1378–1380 (1995).
[CrossRef]

Luppi, E.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Ma, R.

Manolatou, C.

McMillan, J. F.

N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Sel. Top. Quantum Electron. 16(1), 257–266 (2010).
[CrossRef]

McNab, S.

McNab, S. J.

Menard, M.

N. Ophir, R. K. W. Lau, M. Menard, R. Salem, K. Padmaraju, Y. Okawachi, M. Lipson, A. L. Gaeta, and K. Bergman, “First demonstration of a 10-Gb/s RZ end-to-end four-wave mixing-based link at 1884 nm using silicon nanowaveguides,” IEEE Photon. Technol. Lett. 24(4), 276–278 (2012).
[CrossRef]

Ménard, M.

Modotto, D.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[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. Photonics 4(8), 561–564 (2010).
[CrossRef]

S. Zlatanovic, J. S. Park, F. Gholami, J. M. C. Boggio, S. Moro, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides pumped by silica-fiber-based source,” IEEE J. Sel. Top. Quantum Electron. (accepted).

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]

S. Zlatanovic, J. S. Park, F. Gholami, J. M. C. Boggio, S. Moro, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides pumped by silica-fiber-based source,” IEEE J. Sel. Top. Quantum Electron. (accepted).

Moss, D. J.

Okawachi, Y.

Ophir, N.

N. Ophir, R. K. W. Lau, M. Menard, R. Salem, K. Padmaraju, Y. Okawachi, M. Lipson, A. L. Gaeta, and K. Bergman, “First demonstration of a 10-Gb/s RZ end-to-end four-wave mixing-based link at 1884 nm using silicon nanowaveguides,” IEEE Photon. Technol. Lett. 24(4), 276–278 (2012).
[CrossRef]

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

Osgood, R. M.

X. P. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Assefa, Y. A. 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]

B. Kuyken, X. Liu, G. Roelkens, R. Baets, R. M. Osgood, and W. M. J. Green, “50 dB parametric on-chip gain in silicon photonic wires,” Opt. Lett. 36(22), 4401–4403 (2011).
[CrossRef] [PubMed]

B. Kuyken, X. P. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. J. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
[CrossRef] [PubMed]

J. B. Driscoll, R. R. Grote, X. P. Liu, J. I. Dadap, N. C. Panoiu, and R. M. Osgood., “Directionally anisotropic Si nanowires: on-chip nonlinear grating devices in uniform waveguides,” Opt. Lett. 36(8), 1416–1418 (2011).
[CrossRef] [PubMed]

R. R. Grote, J. B. Driscoll, C. G. Biris, N. C. Panoiu, and R. M. Osgood., “Weakly modulated silicon-dioxide-cladding gratings for silicon waveguide Fabry-Pérot cavities,” Opt. Express 19(27), 26406–26415 (2011).
[CrossRef] [PubMed]

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

W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood., “All-optical format conversion of NRZ-OOK to RZ-OOK in a silicon nanowire utilizing either XPM or FWM and resulting in a receiver sensitivity gain of ~2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010).
[CrossRef]

J. B. Driscoll, X. P. Liu, S. Yasseri, I. Hsieh, J. I. Dadap, and R. M. Osgood., “Large longitudinal electric fields (Ez) in silicon nanowire waveguides,” Opt. Express 17(4), 2797–2804 (2009).
[CrossRef] [PubMed]

R. M. Osgood, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. Hsieh, E. Dulkeith, W. M. J. 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]

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
[CrossRef] [PubMed]

X. G. Chen, N. C. Panoiu, and R. M. Osgood., “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42(2), 160–170 (2006).
[CrossRef]

N. C. Panoiu, X. Chen, and R. M. Osgood., “Modulation instability in silicon photonic nanowires,” Opt. Lett. 31(24), 3609–3611 (2006).
[CrossRef] [PubMed]

R. Espinola, J. Dadap, R. M. Osgood, S. McNab, and Y. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13(11), 4341–4349 (2005).
[CrossRef] [PubMed]

Ossicini, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Oxenlowe, L. K.

Padmaraju, K.

N. Ophir, R. K. W. Lau, M. Menard, R. Salem, K. Padmaraju, Y. Okawachi, M. Lipson, A. L. Gaeta, and K. Bergman, “First demonstration of a 10-Gb/s RZ end-to-end four-wave mixing-based link at 1884 nm using silicon nanowaveguides,” IEEE Photon. Technol. Lett. 24(4), 276–278 (2012).
[CrossRef]

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

Panepucci, R. R.

Panoiu, N. C.

R. R. Grote, J. B. Driscoll, C. G. Biris, N. C. Panoiu, and R. M. Osgood., “Weakly modulated silicon-dioxide-cladding gratings for silicon waveguide Fabry-Pérot cavities,” Opt. Express 19(27), 26406–26415 (2011).
[CrossRef] [PubMed]

J. B. Driscoll, R. R. Grote, X. P. Liu, J. I. Dadap, N. C. Panoiu, and R. M. Osgood., “Directionally anisotropic Si nanowires: on-chip nonlinear grating devices in uniform waveguides,” Opt. Lett. 36(8), 1416–1418 (2011).
[CrossRef] [PubMed]

N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Sel. Top. Quantum Electron. 16(1), 257–266 (2010).
[CrossRef]

R. M. Osgood, N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. Hsieh, E. Dulkeith, W. M. J. 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]

J. I. Dadap, N. C. Panoiu, X. G. Chen, I. W. Hsieh, X. P. Liu, C. Y. Chou, E. Dulkeith, S. J. McNab, F. N. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood., “Nonlinear-optical phase modification in dispersion-engineered Si photonic wires,” Opt. Express 16(2), 1280–1299 (2008).
[CrossRef] [PubMed]

X. G. Chen, N. C. Panoiu, and R. M. Osgood., “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42(2), 160–170 (2006).
[CrossRef]

N. C. Panoiu, X. Chen, and R. M. Osgood., “Modulation instability in silicon photonic nanowires,” Opt. Lett. 31(24), 3609–3611 (2006).
[CrossRef] [PubMed]

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).
[CrossRef]

S. Zlatanovic, J. S. Park, F. Gholami, J. M. C. Boggio, S. Moro, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides pumped by silica-fiber-based source,” IEEE J. Sel. Top. Quantum Electron. (accepted).

Pavesi, L.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Pelusi, M.

Pierobon, R.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Poitras, C. B.

Pruessner, M. W.

Pu, M. H.

Pucker, G.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Qian, F.

Y. Huang, E.-K. Tien, S. Gao, S. K. Kalyoncu, Q. Song, F. Qian, and O. Boyraz, “Quasi phase matching in SOI and SOS based parametric wavelength converters,” Proc. SPIE 8120, 81200F, 81200F-7 (2011).
[CrossRef]

E. K. Tien, Y. W. Huang, S. M. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express 18(21), 21981–21989 (2010).
[CrossRef] [PubMed]

Rabinovich, W. S.

Radic, 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]

S. Zlatanovic, J. S. Park, F. Gholami, J. M. C. Boggio, S. Moro, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides pumped by silica-fiber-based source,” IEEE J. Sel. Top. Quantum Electron. (accepted).

Roelkens, G.

Salem, R.

Satyan, G. R. N.

Schmidt, B. S.

Sekaric, L.

Sharping, J. E.

Shoji, T.

Sipe, J. E.

N. Vermeulen, J. E. Sipe, Y. Lefevre, C. Debaes, and H. Thienpont, “Wavelength conversion based on Raman- and non-resonant four-wave mixing in silicon nanowire rings without dispersion engineering,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1078–1091 (2011).
[CrossRef]

Solli, D. R.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

Song, Q.

Y. Huang, E.-K. Tien, S. Gao, S. K. Kalyoncu, Q. Song, F. Qian, and O. Boyraz, “Quasi phase matching in SOI and SOS based parametric wavelength converters,” Proc. SPIE 8120, 81200F, 81200F-7 (2011).
[CrossRef]

E. K. Tien, Y. W. Huang, S. M. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express 18(21), 21981–21989 (2010).
[CrossRef] [PubMed]

Soref, R.

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010).
[CrossRef]

Soref, R. A.

R. A. Soref, S. J. Emelett, and A. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[CrossRef]

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

Stievater, T. H.

Takahashi, J.

Takahashi, M.

Tan, D. T. H.

Thienpont, H.

N. Vermeulen, J. E. Sipe, Y. Lefevre, C. Debaes, and H. Thienpont, “Wavelength conversion based on Raman- and non-resonant four-wave mixing in silicon nanowire rings without dispersion engineering,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1078–1091 (2011).
[CrossRef]

Tien, E. K.

Tien, E.-K.

Y. Huang, E.-K. Tien, S. Gao, S. K. Kalyoncu, Q. Song, F. Qian, and O. Boyraz, “Quasi phase matching in SOI and SOS based parametric wavelength converters,” Proc. SPIE 8120, 81200F, 81200F-7 (2011).
[CrossRef]

Tsia, K. K.

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

Tsuchizawa, T.

Turner, A. C.

Turner-Foster, A. C.

Véniard, V.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Vermeulen, N.

N. Vermeulen, J. E. Sipe, Y. Lefevre, C. Debaes, and H. Thienpont, “Wavelength conversion based on Raman- and non-resonant four-wave mixing in silicon nanowire rings without dispersion engineering,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1078–1091 (2011).
[CrossRef]

Vlasov, Y.

Vlasov, Y. A.

Wabnitz, S.

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Wang, M. H.

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Watanabe, T.

Wong, C. W.

N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Sel. Top. Quantum Electron. 16(1), 257–266 (2010).
[CrossRef]

Xia, F. N.

Xu, C.

Xu, D. X.

Yamada, K.

Yang, J. Y.

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Yariv, A.

Yasseri, S.

Yvind, K.

Zhou, Q. A.

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

Zlatanovic, 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]

S. Zlatanovic, J. S. Park, F. Gholami, J. M. C. Boggio, S. Moro, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides pumped by silica-fiber-based source,” IEEE J. Sel. Top. Quantum Electron. (accepted).

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (1)

N. K. Hon, K. K. Tsia, D. R. Solli, and B. Jalali, “Periodically poled silicon,” Appl. Phys. Lett. 94(9), 091116 (2009).
[CrossRef]

IEEE J. Quantum Electron. (2)

X. G. Chen, N. C. Panoiu, and R. M. Osgood., “Theory of Raman-mediated pulsed amplification in silicon-wire waveguides,” IEEE J. Quantum Electron. 42(2), 160–170 (2006).
[CrossRef]

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (4)

N. C. Panoiu, J. F. McMillan, and C. W. Wong, “Theoretical analysis of pulse dynamics in silicon photonic crystal wire waveguides,” IEEE J. Sel. Top. Quantum Electron. 16(1), 257–266 (2010).
[CrossRef]

N. Vermeulen, J. E. Sipe, Y. Lefevre, C. Debaes, and H. Thienpont, “Wavelength conversion based on Raman- and non-resonant four-wave mixing in silicon nanowire rings without dispersion engineering,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1078–1091 (2011).
[CrossRef]

W. Astar, J. B. Driscoll, X. P. Liu, J. I. Dadap, W. M. J. Green, Y. A. Vlasov, G. M. Carter, and R. M. Osgood., “All-optical format conversion of NRZ-OOK to RZ-OOK in a silicon nanowire utilizing either XPM or FWM and resulting in a receiver sensitivity gain of ~2.5 dB,” IEEE J. Sel. Top. Quantum Electron. 16(1), 234–249 (2010).
[CrossRef]

S. Zlatanovic, J. S. Park, F. Gholami, J. M. C. Boggio, S. Moro, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides pumped by silica-fiber-based source,” IEEE J. Sel. Top. Quantum Electron. (accepted).

IEEE Photon. Technol. Lett. (4)

N. Ophir, R. K. W. Lau, M. Menard, R. Salem, K. Padmaraju, Y. Okawachi, M. Lipson, A. L. Gaeta, and K. Bergman, “First demonstration of a 10-Gb/s RZ end-to-end four-wave mixing-based link at 1884 nm using silicon nanowaveguides,” IEEE Photon. Technol. Lett. 24(4), 276–278 (2012).
[CrossRef]

N. Ophir, J. Chan, K. Padmaraju, A. Biberman, A. C. Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Continuous wavelength conversion of 40-Gb/s data over 100 nm using a dispersion-engineered silicon waveguide,” IEEE Photon. Technol. Lett. 23(2), 73–75 (2011).
[CrossRef]

K. Kikuchi, C. Lorattanasane, F. Futami, and S. Kaneko, “Observation of quasi-phase-matched four-wave-mixing assisted by periodic power variation in a long-distance optical amplifier chain,” IEEE Photon. Technol. Lett. 7(11), 1378–1380 (1995).
[CrossRef]

G. M. Jiang, R. Y. Chen, Q. A. Zhou, J. Y. Yang, M. H. Wang, and X. Q. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–8 (2011).

J. Lightwave Technol. (3)

J. Opt. A, Pure Appl. Opt. (1)

R. A. Soref, S. J. Emelett, and A. R. Buchwald, “Silicon waveguided components for the long-wave infrared region,” J. Opt. A, Pure Appl. Opt. 8(10), 840–848 (2006).
[CrossRef]

Nat. Mater. (1)

M. Cazzanelli, F. Bianco, E. Borga, G. Pucker, M. Ghulinyan, E. Degoli, E. Luppi, V. Véniard, S. Ossicini, D. Modotto, S. Wabnitz, R. Pierobon, and L. Pavesi, “Second-harmonic generation in silicon waveguides strained by silicon nitride,” Nat. Mater. 11(2), 148–154 (2011).
[CrossRef] [PubMed]

Nat. Photonics (4)

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4(8), 495–497 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (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. Photonics 4(8), 561–564 (2010).
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R. Salem, M. A. Foster, A. C. Turner, D. F. Geraghty, M. Lipson, and A. L. Gaeta, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2(1), 35–38 (2008).
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Opt. Express (15)

A. Biberman, B. G. Lee, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and K. Bergman, “Wavelength multicasting in silicon photonic nanowires,” Opt. Express 18(17), 18047–18055 (2010).
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H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
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M. A. Foster, A. C. Turner, R. Salem, M. Lipson, and A. L. Gaeta, “Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides,” Opt. Express 15(20), 12949–12958 (2007).
[CrossRef] [PubMed]

R. Espinola, J. Dadap, R. M. Osgood, S. McNab, and Y. Vlasov, “C-band wavelength conversion in silicon photonic wire waveguides,” Opt. Express 13(11), 4341–4349 (2005).
[CrossRef] [PubMed]

F. Li, M. Pelusi, D. X. Xu, A. Densmore, R. Ma, S. Janz, and D. J. Moss, “Error-free all-optical demultiplexing at 160Gb/s via FWM in a silicon nanowire,” Opt. Express 18(4), 3905–3910 (2010).
[CrossRef] [PubMed]

Y. T. Dai, X. P. Chen, Y. Okawachi, A. C. Turner-Foster, M. A. Foster, M. Lipson, A. L. Gaeta, and C. Xu, “1 micros tunable delay using parametric mixing and optical phase conjugation in Si waveguides,” Opt. Express 17(9), 7004–7010 (2009).
[CrossRef] [PubMed]

A. C. Turner-Foster, M. A. Foster, R. Salem, A. L. Gaeta, and M. Lipson, “Frequency conversion over two-thirds of an octave in silicon nanowaveguides,” Opt. Express 18(3), 1904–1908 (2010).
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X. P. Liu, J. B. Driscoll, J. I. Dadap, R. M. Osgood, S. Assefa, Y. A. 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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B. Kuyken, X. P. Liu, R. M. Osgood, R. Baets, G. Roelkens, and W. M. J. Green, “Mid-infrared to telecom-band supercontinuum generation in highly nonlinear silicon-on-insulator wire waveguides,” Opt. Express 19(21), 20172–20181 (2011).
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E. K. Tien, Y. W. Huang, S. M. Gao, Q. Song, F. Qian, S. K. Kalyoncu, and O. Boyraz, “Discrete parametric band conversion in silicon for mid-infrared applications,” Opt. Express 18(21), 21981–21989 (2010).
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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).
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A. C. Turner-Foster, M. A. Foster, J. S. Levy, C. B. Poitras, R. Salem, A. L. Gaeta, and M. Lipson, “Ultrashort free-carrier lifetime in low-loss silicon nanowaveguides,” Opt. Express 18(4), 3582–3591 (2010).
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R. R. Grote, J. B. Driscoll, C. G. Biris, N. C. Panoiu, and R. M. Osgood., “Weakly modulated silicon-dioxide-cladding gratings for silicon waveguide Fabry-Pérot cavities,” Opt. Express 19(27), 26406–26415 (2011).
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Opt. Lett. (7)

Proc. SPIE (1)

Y. Huang, E.-K. Tien, S. Gao, S. K. Kalyoncu, Q. Song, F. Qian, and O. Boyraz, “Quasi phase matching in SOI and SOS based parametric wavelength converters,” Proc. SPIE 8120, 81200F, 81200F-7 (2011).
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B. E. A. Saleh and M. C. Teich, Fundamentals of photonics, 2nd ed., Wiley Series in Pure and Applied Optics (Wiley Interscience, 2007).

B. Kuyken, X. Liu, and 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,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThU2014.

B. Kuyken, X. Liu, R. M. Osgood, Jr., R. Baets, G. Roelkens, and W. M. J. Green, “Widely tunable silicon mid-infrared optical parametric oscillator,” in Group IV Photonics, United Kingdom (2011).

J. B. Driscoll, R. R. Grote, J. I. Dadap, N. C. Panoiu, and J. R. M. Osgood, Jr., “Quasi-phase-matching four-wave-mixing via width-modulated silicon nanowire waveguides,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper FThN4. (2011).

J. B. Driscoll, X. Liu, R. Grote, J. I. Dadap, N. C. Panoiu, and R. M. Osgood, Jr., “Enhancing FWM conversion efficiency in a silicon waveguide by exploiting phase-matching via a pump-induced nonlinear grating,” in Integrated Photonics Research, Silicon and Nanophotonics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper IMB2013.

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Figures (11)

Fig. 1
Fig. 1

Illustration of QPM FWM in a w-modulated SiNWG. Input pump and signal waves interact via FWM to generate an idler. The conversion efficiency of this FWM process is enhanced for specific wavelengths due to the periodic modulation of waveguide parameters.

Fig. 2
Fig. 2

(a) SEM image of the narrowest region. (b) SEM image of the widest region. (c) SEM image of SiNWG sidewall. (d) SEM of the tip of the inverse-taper. (e) Sketch of a w-modulated SiNWG.

Fig. 3
Fig. 3

FWM experimental set-up: PC = polarization controller, WDM = wavelength division multiplexer, LP = linear polarizer, LTF = lensed tapered fiber, PRX = power meter, OSA = optical spectrum analyzer.

Fig. 4
Fig. 4

FWM spectra for λp = 1543 nm and varying λs, in the case of (a) a 250 nm × 600 nm uniform waveguide and (b) a w-modulated waveguide with wDC = 600 nm, Δw = 30 nm, Λ = 1 mm, h = 250 nm. The background noise level is raised for C-band wavelengths since a different laser was used to access this spectral region, as illustrated in Fig. 3. The generated idlers also interact with the pump via cascaded FWM to produce higher order idlers, which can be observed as artifacts on the red side of the pump.

Fig. 5
Fig. 5

(a) Experimentally determined FWM CE spectrum demonstrating a CE enhancement near λ = 1668 nm for the w-modulated device () compared to the straight device (). (b) Measured CE enhancement as a function of signal wavelength, indicating a ~12 dB enhancement for λs = 1668 nm. (b) is found by taking the difference (in dB) between the two curves in (a).

Fig. 6
Fig. 6

Variation of two important waveguide parameters, β2 and γ, along the length of a w-modulated waveguide for wDC = 600 nm, Δw = 30 nm, and Λ = 1 mm.

Fig. 7
Fig. 7

(a) Wavelength dependence of Dλ of the waveguide used in the calculations, for w = 600 nm. The inset shows a diagram of the cross-section used to approximate the sidewall etched profile observed in Fig. 2(d). (b) Calculated CE spectrum for the straight (black line), and w-modulated waveguide case (red line), indicating a ~12 dB CE enhancement for the w-modulated device. Results match well with the measured CE spectrum shown in Fig. 5(a). The inset shows how the peak CE of the enhanced sideband varies with pump power.

Fig. 8
Fig. 8

Calculated CE spectrum for (a) Δw = 30 nm, and Λ varying between 0 and 5 mm (offset 10 dB for clarity), (b) Λ = 1 mm, and varying Δw between 0 and 60 nm (offset 10 dB for clarity). (c) A more detailed plot of the enhanced sideband for the Δw = 20 nm Λ = 1 mm case, demonstrating spectral splitting.

Fig. 9
Fig. 9

(a) FWM CE spectrum for a uniform 250 nm × 500 nm SiNWG (black line), and a w-modulated SiNWG with wDC = 500 nm, Δw = 15 nm, and Λ = 280 µm (red line). A CE enhancement is observed between the C-band and mid-IR, for the w-modulated device. Insets show the Ex component of the fundamental QTE mode, for a wavelength of 1550 nm and 2000 nm, demonstrating that the mode is confined at both wavelengths. (b) Enhanced sideband on both the blue- and red-side of the pump, for different Δw, showing the ability to tune the sideband bandwidth. Spectra are offset by 10 dB for clarity.

Fig. 10
Fig. 10

The FWM CE spectrum resulting from both a uniform 250 nm × 500 nm SiNWG (black line), and a w-modulated device with w(z) formed by a superposition of sinusoidal w-modulations. A CE enhancement is observed across the entire C-band. The inset shows the waveguide width, w(z), formed by using Eq. (10), with cn (n = 1, 2, … 10) = 10 nm, wDC = 500 nm, and Λn as listed in Table 1.

Fig. 11
Fig. 11

The CE spectrum for a 300 nm × 1000 nm SiNWG with 30 nm slab height and Δwslab = 100 nm, wDC,slab = 600 nm, and Λ = 3000 μm. An enhanced CE sideband is present due to QPM, and facilitates FWM over more than 1000 nm, between 1625 nm and 2695 nm. The peak CE of the sideband is −25 dB, only 8 dB below the CE near the pump wavelength. The inset shows a schematic illustrating a slab-modulated SiNWG.

Tables (1)

Tables Icon

Table 1 Grating periodicities and weights used to for the grating profile plotted in Fig. 10. The table also shows the idler and signal wavelengths targeted by each periodicity.

Equations (16)

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2 ω p = ω s + ω i
Δβ=2γ P p Δ β lin =2γ P p (2 β p β s β i )
Λ=2πm/Δβ.
w(z)=Δwsin( 2πz Λ )+ w DC ,
CE= P i,out P s,out ,
d A j dz = d a j dz e i β j z +i β 0,j A j ,
d a p dz = c κ p (z) 2n v gp (z) ( α p in + α p FC (z) ) a p +i ω κ p (z) n v g p (z) δ n p FC (z) a p +i 3 ω p 4 ε 0 A 0 (z) v gp (z) ( Γ pppp (z) v gp (z) | a p | 2 ) a p ,
d a s,i dz = c κ s,i (z) 2n v g(s,i) (z) ( α s,i in + α s,i FC (z) ) a s,i +i ω κ s,i (z) n v g(s,i) (z) δ n s,i FC (z) a s,i +i 3 ω s,i 4 ε 0 A 0 (z) v g(s,i) (z) ( 2 Γ (s,i)pp(s,i) (z) v g,p (z) | a p | 2 ) a s,i +i 3 ω i,s 4 ε 0 A 0 (z) v g(i,s) (z) Γ (s,i)p(i,s)p (z) v g,p (z) a p 2 a i,s * e i( Δ β lin (z) ) ,
β n = n β ω n .
δ n FC = e 2 2 ε 0 n ω 2 ( N m ce * + N 0.8 m ch * ),
α FC = e 3 N ε 0 cn ω 2 ( 1 μ e m ce *2 + 1 μ h m ch *2 ),
N= 6 τ c Γ p '' 8 ε 0 A 0 2 v gp 2 | A p | 4 ,
Γ klmn = A 0 A 0 e k *( r ; ω k ) χ (3) ( r ) e l ( r ; ω l ) e m * ( r ; ω m ) e n ( r ; ω n )dA ζ k ζ l ζ m ζ n ,
ζ= A n 2 ( r ;ω) | e( r ;ω) | 2 dA
D λ = 2πc λ 2 β 2 ,
w(z)=[ 1 N n=1 N c n sin( 2πz Λ n ) ]+ w DC .

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