Abstract

An all-pass microring resonator is utilized in silicon waveguides to adjust the relative phase relationship among the involved waves in the degenerated four-wave mixing (FWM). By using the microring resonator as a phase shifter, the phase matching can be ameliorated, and the conversion efficiency can be enhanced effectively. The influences of key factors including the coupling strength of the ring resonator, and the nonlinear loss introduced by two-photon absorption and free carrier absorption, on the improvement of conversion efficiency are discussed. By properly selecting the parameters, the spectra of conversion efficiency are flattened in the wavelength range of 10 nm. Since the ring resonator has a periodic response spectrum and tunable resonant wavelength, the FWM with a microring phase shifter provides an efficient approach to wavelength conversion in silicon waveguides.

© 2013 Optical Society of America

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2012 (7)

P. Dong, C. Xie, L. Chen, N. Fontaine, and Y. Chen, “Experimental demonstration of microring quadrature phase-shift keying modulators,” Opt. Lett. 37, 1178–1180 (2012).
[CrossRef]

K. Padmaraju, N. Ophir, Q. Xu, B. Schmidt, J. Shakya, S. Manipatruni, M. Lipson, and K. Bergman, “Error-free transmission of microring-modulated BPSK,” Opt. Express 20, 8681–8688 (2012).
[CrossRef]

J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, “Width-modulation of Si photonic wires for quasi-phase-matching of four-wave-mixing: experimental and theoretical demonstration,” Opt. Express 20, 9227–9242 (2012).
[CrossRef]

H. Zhu, B. Luo, W. Pan, L. Yan, S. Xiang, and K. Wen, “Gain enhancement of fiber optical parametric amplifier via introducing phase-shifted fiber Bragg grating for phase matching,” J. Opt. Soc. Am. B 29, 1497–1502 (2012).
[CrossRef]

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

P. Orlandi, C. Ferrari, M. J. Strain, A. Canciamilla, F. Morichetti, M. Sorel, P. Bassi, and A. Melloni, “Reconfigurable silicon filter with continuous bandwidth tunability,” Opt. Lett. 37, 3669–3671 (2012).
[CrossRef]

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photon. Rev. 6, 145–177 (2012).
[CrossRef]

2011 (8)

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, 1416–1418 (2011).
[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, 1078–1091 (2011).
[CrossRef]

F. D. Leonardis and V. M. N. Passaro, “Efficient wavelength conversion in optimized SOI waveguides via pulsed four-wave mixing,” J. Lightwave Technol. 29, 3523–3535 (2011).
[CrossRef]

Z. Li, S. Gao, Q. Liu, and S. He, “Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators,” Opt. Commun. 284, 2215–2221 (2011).
[CrossRef]

F. Li, M. Pelusi, D.-X. Xu, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical wavelength conversion for 10 Gb/s DPSK signals in a silicon ring resonator,” Opt. Express 19, 22410–22416 (2011).
[CrossRef]

H. Hu, H. Ji, M. Galili, M. Pu, C. Peucheret, H. C. H. Mulvad, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed wavelength conversion in a silicon photonic chip,” Opt. Express 19, 19886–19894 (2011).
[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, 73–75 (2011).
[CrossRef]

M. Pu, H. Hu, M. Galili, H. Ji, L. K. Oxenløwe, K. Yvind, P. Jeppsen, and J. M. Hvam, “15 THz tunable wavelength conversion of picosecond pulses in silicon waveguide,” IEEE Photon. Technol. Lett. 23, 1409–1411 (2011).
[CrossRef]

2010 (3)

2009 (1)

2008 (3)

2007 (3)

2006 (1)

2004 (2)

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

2002 (1)

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

2001 (1)

Afeyan, B.

Agrawal, G. P.

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

Andrekson, P.

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

Asghari, M.

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

Bassi, P.

Beausoleil, R. G.

Bergman, K.

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, 73–75 (2011).
[CrossRef]

Boyd, R. W.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

Boyraz, O.

Boyraz, Ö.

Cai, H.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photon. Rev. 6, 145–177 (2012).
[CrossRef]

Canciamilla, A.

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, 73–75 (2011).
[CrossRef]

Charbonneau-Lefort, M.

Chen, H.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photon. Rev. 6, 145–177 (2012).
[CrossRef]

Chen, L.

Chen, X.

Chen, Y.

Cunningham, J. E.

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

Dadap, J. I.

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, 1078–1091 (2011).
[CrossRef]

Dong, P.

Driscoll, J. B.

Dulkeith, E.

Eggleton, B. J.

Fauchet, P. M.

Fejer, M. M.

Feng, D.

Feng, N.-N.

Feng, S.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photon. Rev. 6, 145–177 (2012).
[CrossRef]

Ferrari, C.

Fontaine, N.

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, 73–75 (2011).
[CrossRef]

Foster, M.

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, 73–75 (2011).
[CrossRef]

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, 1904–1908 (2010).
[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, 12949–12958 (2007).
[CrossRef]

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

Gaeta, A.

Gaeta, A. L.

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, 73–75 (2011).
[CrossRef]

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, 1904–1908 (2010).
[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, 12949–12958 (2007).
[CrossRef]

Galili, M.

H. Hu, H. Ji, M. Galili, M. Pu, C. Peucheret, H. C. H. Mulvad, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed wavelength conversion in a silicon photonic chip,” Opt. Express 19, 19886–19894 (2011).
[CrossRef]

M. Pu, H. Hu, M. Galili, H. Ji, L. K. Oxenløwe, K. Yvind, P. Jeppsen, and J. M. Hvam, “15 THz tunable wavelength conversion of picosecond pulses in silicon waveguide,” IEEE Photon. Technol. Lett. 23, 1409–1411 (2011).
[CrossRef]

Gao, S.

Z. Li, S. Gao, Q. Liu, and S. He, “Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators,” Opt. Commun. 284, 2215–2221 (2011).
[CrossRef]

Green, W. M.

Grote, R. R.

Hansryd, J.

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

He, S.

Z. Li, S. Gao, Q. Liu, and S. He, “Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators,” Opt. Commun. 284, 2215–2221 (2011).
[CrossRef]

Hedekvist, P.-O.

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

Heebner, J. E.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

Hsieh, I.-W.

Hu, H.

H. Hu, H. Ji, M. Galili, M. Pu, C. Peucheret, H. C. H. Mulvad, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed wavelength conversion in a silicon photonic chip,” Opt. Express 19, 19886–19894 (2011).
[CrossRef]

M. Pu, H. Hu, M. Galili, H. Ji, L. K. Oxenløwe, K. Yvind, P. Jeppsen, and J. M. Hvam, “15 THz tunable wavelength conversion of picosecond pulses in silicon waveguide,” IEEE Photon. Technol. Lett. 23, 1409–1411 (2011).
[CrossRef]

Hvam, J. M.

M. Pu, H. Hu, M. Galili, H. Ji, L. K. Oxenløwe, K. Yvind, P. Jeppsen, and J. M. Hvam, “15 THz tunable wavelength conversion of picosecond pulses in silicon waveguide,” IEEE Photon. Technol. Lett. 23, 1409–1411 (2011).
[CrossRef]

H. Hu, H. Ji, M. Galili, M. Pu, C. Peucheret, H. C. H. Mulvad, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed wavelength conversion in a silicon photonic chip,” Opt. Express 19, 19886–19894 (2011).
[CrossRef]

Islam, M. N.

Jackson, D. J.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

Janz, S.

Jeppesen, P.

Jeppsen, P.

M. Pu, H. Hu, M. Galili, H. Ji, L. K. Oxenløwe, K. Yvind, P. Jeppsen, and J. M. Hvam, “15 THz tunable wavelength conversion of picosecond pulses in silicon waveguide,” IEEE Photon. Technol. Lett. 23, 1409–1411 (2011).
[CrossRef]

Ji, H.

M. Pu, H. Hu, M. Galili, H. Ji, L. K. Oxenløwe, K. Yvind, P. Jeppsen, and J. M. Hvam, “15 THz tunable wavelength conversion of picosecond pulses in silicon waveguide,” IEEE Photon. Technol. Lett. 23, 1409–1411 (2011).
[CrossRef]

H. Hu, H. Ji, M. Galili, M. Pu, C. Peucheret, H. C. H. Mulvad, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed wavelength conversion in a silicon photonic chip,” Opt. Express 19, 19886–19894 (2011).
[CrossRef]

Kim, J.

Koos, C.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

Krishnamoorthy, A. V.

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

P. Dong, R. Shafiiha, S. Liao, H. Liang, N.-N. Feng, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Wavelength-tunable silicon microring modulator,” Opt. Express 18, 10941–10946 (2010).
[CrossRef]

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, 1078–1091 (2011).
[CrossRef]

Lei, T.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photon. Rev. 6, 145–177 (2012).
[CrossRef]

Leonardis, F. D.

Leuthold, J.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

Li, F.

Li, G.

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

P. Dong, R. Shafiiha, S. Liao, H. Liang, N.-N. Feng, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Wavelength-tunable silicon microring modulator,” Opt. Express 18, 10941–10946 (2010).
[CrossRef]

Li, J.

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

Li, Y.

Li, Z.

Z. Li, S. Gao, Q. Liu, and S. He, “Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators,” Opt. Commun. 284, 2215–2221 (2011).
[CrossRef]

Liang, H.

Liao, S.

Lim, J. H.

Lin, Q.

Lipson, M.

Liu, Q.

Z. Li, S. Gao, Q. Liu, and S. He, “Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators,” Opt. Commun. 284, 2215–2221 (2011).
[CrossRef]

Liu, X.

Liu, X. P.

Luo, B.

Luo, X.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photon. Rev. 6, 145–177 (2012).
[CrossRef]

Luo, Y.

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

Ma, R.

Manipatruni, S.

Melloni, A.

Morichetti, F.

Moss, D. J.

Mulvad, H. C. H.

Ophir, N.

Orlandi, P.

Osgood, M. R.

Osgood, R. M.

Oxenløwe, L. K.

H. Hu, H. Ji, M. Galili, M. Pu, C. Peucheret, H. C. H. Mulvad, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed wavelength conversion in a silicon photonic chip,” Opt. Express 19, 19886–19894 (2011).
[CrossRef]

M. Pu, H. Hu, M. Galili, H. Ji, L. K. Oxenløwe, K. Yvind, P. Jeppsen, and J. M. Hvam, “15 THz tunable wavelength conversion of picosecond pulses in silicon waveguide,” IEEE Photon. Technol. Lett. 23, 1409–1411 (2011).
[CrossRef]

Padmaraju, K.

K. Padmaraju, N. Ophir, Q. Xu, B. Schmidt, J. Shakya, S. Manipatruni, M. Lipson, and K. Bergman, “Error-free transmission of microring-modulated BPSK,” Opt. Express 20, 8681–8688 (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, 73–75 (2011).
[CrossRef]

Painter, O. J.

Pan, W.

Panepucci, R. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

Panoiu, N. C.

Park, N.

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

Passaro, V. M. N.

Pelusi, M.

Peucheret, C.

Poon, A. W.

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photon. Rev. 6, 145–177 (2012).
[CrossRef]

Pu, M.

M. Pu, H. Hu, M. Galili, H. Ji, L. K. Oxenløwe, K. Yvind, P. Jeppsen, and J. M. Hvam, “15 THz tunable wavelength conversion of picosecond pulses in silicon waveguide,” IEEE Photon. Technol. Lett. 23, 1409–1411 (2011).
[CrossRef]

H. Hu, H. Ji, M. Galili, M. Pu, C. Peucheret, H. C. H. Mulvad, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed wavelength conversion in a silicon photonic chip,” Opt. Express 19, 19886–19894 (2011).
[CrossRef]

Salem, R.

Sang, X.

Schmidt, B.

Schweinsberg, A.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

Shafiiha, R.

Shakya, J.

Shubin, I.

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

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, 1078–1091 (2011).
[CrossRef]

Song, M.

Sorel, M.

Strain, M. J.

Thacker, H.

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

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, 1078–1091 (2011).
[CrossRef]

Turner, A.

Turner, A. C.

Turner-Foster, A. C.

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, 1078–1091 (2011).
[CrossRef]

Vlasov, Y. A.

Wen, K.

Westlund, M.

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

Willner, A. E.

Wong, V.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

Xiang, S.

Xie, C.

Xu, D.-X.

Xu, Q.

Yan, L.

Yang, J. Y.

Yao, J.

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

Yvind, K.

M. Pu, H. Hu, M. Galili, H. Ji, L. K. Oxenløwe, K. Yvind, P. Jeppsen, and J. M. Hvam, “15 THz tunable wavelength conversion of picosecond pulses in silicon waveguide,” IEEE Photon. Technol. Lett. 23, 1409–1411 (2011).
[CrossRef]

H. Hu, H. Ji, M. Galili, M. Pu, C. Peucheret, H. C. H. Mulvad, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed wavelength conversion in a silicon photonic chip,” Opt. Express 19, 19886–19894 (2011).
[CrossRef]

Zhang, B.

Zhang, J.

Zhang, L.

Zheng, X.

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

P. Dong, R. Shafiiha, S. Liao, H. Liang, N.-N. Feng, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Wavelength-tunable silicon microring modulator,” Opt. Express 18, 10941–10946 (2010).
[CrossRef]

Zhu, H.

Adv. Opt. Photon. (1)

IEEE J. Quantum Electron. (1)

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

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

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

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, 1078–1091 (2011).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

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, 73–75 (2011).
[CrossRef]

M. Pu, H. Hu, M. Galili, H. Ji, L. K. Oxenløwe, K. Yvind, P. Jeppsen, and J. M. Hvam, “15 THz tunable wavelength conversion of picosecond pulses in silicon waveguide,” IEEE Photon. Technol. Lett. 23, 1409–1411 (2011).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

Laser Photon. Rev. (1)

S. Feng, T. Lei, H. Chen, H. Cai, X. Luo, and A. W. Poon, “Silicon photonics: from a microresonator perspective,” Laser Photon. Rev. 6, 145–177 (2012).
[CrossRef]

Nat. Photonics (1)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

Nature (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[CrossRef]

Opt. Commun. (1)

Z. Li, S. Gao, Q. Liu, and S. He, “Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators,” Opt. Commun. 284, 2215–2221 (2011).
[CrossRef]

Opt. Express (12)

F. Li, M. Pelusi, D.-X. Xu, R. Ma, S. Janz, B. J. Eggleton, and D. J. Moss, “All-optical wavelength conversion for 10 Gb/s DPSK signals in a silicon ring resonator,” Opt. Express 19, 22410–22416 (2011).
[CrossRef]

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, 1904–1908 (2010).
[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, 12949–12958 (2007).
[CrossRef]

H. Hu, H. Ji, M. Galili, M. Pu, C. Peucheret, H. C. H. Mulvad, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Ultra-high-speed wavelength conversion in a silicon photonic chip,” Opt. Express 19, 19886–19894 (2011).
[CrossRef]

K. Padmaraju, N. Ophir, Q. Xu, B. Schmidt, J. Shakya, S. Manipatruni, M. Lipson, and K. Bergman, “Error-free transmission of microring-modulated BPSK,” Opt. Express 20, 8681–8688 (2012).
[CrossRef]

L. Zhang, J. Y. Yang, M. Song, Y. Li, B. Zhang, R. G. Beausoleil, and A. E. Willner, “Microring-based modulation and demodulation of DPSK signal,” Opt. Express 15, 11564–11569 (2007).
[CrossRef]

P. Dong, R. Shafiiha, S. Liao, H. Liang, N.-N. Feng, D. Feng, G. Li, X. Zheng, A. V. Krishnamoorthy, and M. Asghari, “Wavelength-tunable silicon microring modulator,” Opt. Express 18, 10941–10946 (2010).
[CrossRef]

J. B. Driscoll, N. Ophir, R. R. Grote, J. I. Dadap, N. C. Panoiu, K. Bergman, and R. M. Osgood, “Width-modulation of Si photonic wires for quasi-phase-matching of four-wave-mixing: experimental and theoretical demonstration,” Opt. Express 20, 9227–9242 (2012).
[CrossRef]

A. Turner, M. Foster, A. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16, 4881–4887 (2008).
[CrossRef]

Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express 14, 4786–4799 (2006).
[CrossRef]

X. Sang and O. Boyraz, “Gain and noise characteristics of high-bit-rate silicon parametric amplifiers,” Opt. Express 16, 13122–13132 (2008).
[CrossRef]

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

Opt. Lett. (3)

Opt. Quantum Electron. (1)

I. Shubin, G. Li, X. Zheng, Y. Luo, H. Thacker, J. Yao, N. Park, A. V. Krishnamoorthy, and J. E. Cunningham, “Integration, processing and performance of low power thermally tunable CMOS-SOI WDM resonators,” Opt. Quantum Electron. 44, 589–604 (2012).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) Schematic illustration of the microring for introducing additional phase shift in FWM. φR is responsible for the thermo-optical effects. (b) Intensity transmission factor and (c) phase response for the microring resonator with τ=0.95 and varying values of the transmission coefficient. The normalized detuning is defined as the roundtrip phase shift modular divided by 2π.

Fig. 2.
Fig. 2.

Evolution of (a) idler power, (b) signal power, and (c) sinθ as functions of the propagation length when the idler is generated at 1700 nm.

Fig. 3.
Fig. 3.

Evolution of (a) idler power, (b) signal power, and (c) sinθ as functions of the propagation length when the idler is generated at 1581 nm.

Fig. 4.
Fig. 4.

Effects of the transmission coefficient and TPA on the improvement of the maximum conversion efficiency at different idler wavelengths with (a) λp=1571nm and (b) λp=1531nm.

Fig. 5.
Fig. 5.

Effects of the free carrier lifetime and pulsewidth on the improvement of the maximum conversion efficiency with λp=1571nm, λi=1700nm, and R=10GHz.

Fig. 6.
Fig. 6.

(a) Shift of the relative phase difference and optical intensity as functions of the idler wavelength. (b) Spectra of the conversion efficiency as a function of the idler wavelength with and without the microring resonator.

Tables (1)

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Table 1. Comparisons with Experimental Measurements Proposed in Literature

Equations (10)

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

dApdz=12[α+αpFCA(z)]Ap+i(γp+iβTPA2)(|Ap|2+2|As|2+2|Ai|2)Ap+2iγpAp*AsAiexp(iΔβ·z),
dAsdz=12[α+αsFCA(z)]As+i(γs+iβTPA2)(2|Ap|2+|As|2+2|Ai|2)As+iγsAp2Ai*exp(iΔβ·z),
dAi*dz=12[α+αiFCA(z)]Ai*i(γiiβTPA2)(2|Ap|2+2|As|2+|Ai|2)Ai*iγiAp*2Asexp(iΔβ·z),
dPpdz=(α+αpFCA+βTPAIp)4γ(Pp2PsPi)1/2sinθ,
dPsdz=(α+αsFCA+2βTPAIp)+2γ(Pp2PsPi)1/2sinθ,
dPidz=(α+αiFCA+2βTPAIp)+2γ(Pp2PsPi)1/2sinθ,
dθdz=Δβ+γ(2PpPsPi)+γ[(Pp2Pi/Ps)1/2+(Pp2Ps/Pi)1/24(PsPi)1/2]cosθ.
N(t,z)(11exp(1/Rτ0))βTPAT0I2(t,z)2hν,
T=|E2E1|2=τ22rτcosϕ+r212rτcosϕ+r2τ2,
Φ=arg(E2E1)=π+ϕ+arctan(rsinϕτrcosϕ)+arctan(rτsinϕ1rτcosϕ),

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