Abstract

We report a numerical investigation on parametric amplification of high-bit-rate signals and related noise figure inside silicon waveguides in the presence of two-photon absorption (TPA), TPA-induced free-carrier absorption, free-carrier-induced dispersion and linear loss. Different pump parameters are considered to achieve net gain and low noise figure. We show that the net gain can only be achieved in the anomalous dispersion regime at the high-repetition-rate, if short pulses are used. An evaluation of noise properties of parametric amplification in silicon waveguides is presented. By choosing pulsed pump in suitably designed silicon waveguides, parametric amplification can be a chip-scale solution in the high-speed optical communication and optical signal processing systems.

© 2008 Optical Society of America

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

2008 (4)

X. Sang, E.-K. Tien, N.S. Yuksek, F. Qian, Q. Sang, and O. Boyraz, “Dual-Wavelength Mode-Locked Fiber Laser with an Intracavity Silicon Waveguide,” IEEE Photon. Technol. Lett. 20, 1184–1186 (2008).
[Crossref]

R. Salem, M.A. Foster, and A.C. Turner et al, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

O. Boyraz, “Nanoscale signal regeneration,” Nat. Photonics 2, 12–13 (2008).
[Crossref]

D. Dimitropoulos, D. R. Solli, R. Claps, O. Boyraz, and B. Jalali, “Noise figure of silicon Raman amplifiers,” J. Lightwave Technol. 26, 847–852 (2008).
[Crossref]

2007 (9)

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, “Nonlinear silicon-on-insulator waveguides for all-optical signal processing,” Opt. Express 15, 5976–5990 (2007).
[Crossref] [PubMed]

E. -K. Tien, N. S. Yuksek, F. Qian, and O. Boyraz, “Pulse compression and modelocking by using TPA in silicon waveguides,” Opt. Express 15, 6500–6506 (2007).
[Crossref] [PubMed]

M. Forst, J. Niehusmann, T. Plotzing, and J. Bolten et al, “High-speed all-optical switching in ion-implanted silicon-on-insulator microring resonators,” Opt. Lett. 32, 2046–2048 (2007).
[Crossref] [PubMed]

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] [PubMed]

E. Tien, F. Qian, N. S. Yuksek, and O. Boyraz, “Influence of nonlinear loss competition on pulse compression and nonlinear optics in silicon,” Appl. Phys. Lett. 91, art.201115 (2007).
[Crossref]

T. Torounidis and P. Andrekson, “Broadband single-pumped fiber-optic parametric amplifiers,” IEEE Photon. Technol.Lett. 19, 650–652 (2007).
[Crossref]

T. Torounidis, P. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70-dB gain,” IEEE Photon. Technol. Lett. 18, 1194–1196 (2007).
[Crossref]

Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90, art.211105 (2007).

2006 (8)

A. Liu, H. Rong, R. Jones, O. Cohen, D. Hak, and M. Paniccia, “Optical amplification and lasing by stimulated Raman scattering in silicon waveguides,” J. Lightwave Technol. 24, 1440–1445 (2006).
[Crossref]

Y. Liu and H. K. Tsang, “Nonlinear absorption and Raman gain in helium-ion-implanted silicon waveguides,” Opt. Lett. 31, 1714–1716 (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, 4357–4362 (2006).
[Crossref] [PubMed]

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] [PubMed]

G. Kalogerakis, K. Shimizu, M. E. Marchic, K. K.-Y. Wong, K. Uesaka, and L. G. Kazovsky, “High-repetition-rate pulsed-pump fiber OPA for amplification of communication signals,” J. Lightwave Technol. 24, 3021–3027 (2006).
[Crossref]

Y. -H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, and O. Cohen, “Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides,” Opt. Express 14, 11721–11726 (2006).
[Crossref] [PubMed]

K. K. Tsia, S. Fathpour, and B. Jalali, “Energy harvesting in silicon wavelength converters,” Opt. Express 14, 12327–12333 (2006).
[Crossref] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

2005 (7)

2004 (9)

P. Kylemark, P. O. hedekvist, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Noise characteristics of fiber optical parametric amplifiers,” J. Lightwave Technol. 22, 409–416 (2004).
[Crossref]

R. Espinola, J. Dadap, R. Osgood, Jr., S. McNab, and Y. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713–3718 (2004).
[Crossref] [PubMed]

O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express 12, 4094–4102 (2004).
[Crossref] [PubMed]

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12, 5269–5273 (2004).
[Crossref] [PubMed]

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] [PubMed]

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

A. Liu, Jones, L. Liu, and L. Liao et al, “A high speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

G. T. Reed, “The optical age of silicon,” Nature 427, 595–596(2004).
[Crossref] [PubMed]

O. Boyraz and B. Jalali. “Demonstration of 11 dB fiber-to-fiber gain in a silicon waveguides,” Electron. Express 1, 429–434(2004).
[Crossref]

2002 (1)

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

2001 (2)

1989 (1)

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[Crossref]

1987 (1)

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

1962 (1)

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev 128, 2407–2413 (1962).
[Crossref]

Agrawal, G. P.

Akasaka, Y.

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson et al, “All-optical switching on a silicon chip,” Opt. Lett. 29, 2867–2869(2005).
[Crossref] [PubMed]

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] [PubMed]

Andrekson, P.

T. Torounidis and P. Andrekson, “Broadband single-pumped fiber-optic parametric amplifiers,” IEEE Photon. Technol.Lett. 19, 650–652 (2007).
[Crossref]

T. Torounidis, P. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70-dB gain,” IEEE Photon. Technol. Lett. 18, 1194–1196 (2007).
[Crossref]

Andrekson, P. A.

P. Kylemark, P. O. hedekvist, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Noise characteristics of fiber optical parametric amplifiers,” J. Lightwave Technol. 22, 409–416 (2004).
[Crossref]

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

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson et al, “All-optical switching on a silicon chip,” Opt. Lett. 29, 2867–2869(2005).
[Crossref] [PubMed]

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] [PubMed]

Bennett, B. R.

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

Bolten, J.

Boyraz, O.

O. Boyraz, “Nanoscale signal regeneration,” Nat. Photonics 2, 12–13 (2008).
[Crossref]

X. Sang, E.-K. Tien, N.S. Yuksek, F. Qian, Q. Sang, and O. Boyraz, “Dual-Wavelength Mode-Locked Fiber Laser with an Intracavity Silicon Waveguide,” IEEE Photon. Technol. Lett. 20, 1184–1186 (2008).
[Crossref]

D. Dimitropoulos, D. R. Solli, R. Claps, O. Boyraz, and B. Jalali, “Noise figure of silicon Raman amplifiers,” J. Lightwave Technol. 26, 847–852 (2008).
[Crossref]

E. -K. Tien, N. S. Yuksek, F. Qian, and O. Boyraz, “Pulse compression and modelocking by using TPA in silicon waveguides,” Opt. Express 15, 6500–6506 (2007).
[Crossref] [PubMed]

E. Tien, F. Qian, N. S. Yuksek, and O. Boyraz, “Influence of nonlinear loss competition on pulse compression and nonlinear optics in silicon,” Appl. Phys. Lett. 91, art.201115 (2007).
[Crossref]

O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express 12, 4094–4102 (2004).
[Crossref] [PubMed]

O. Boyraz and B. Jalali. “Demonstration of 11 dB fiber-to-fiber gain in a silicon waveguides,” Electron. Express 1, 429–434(2004).
[Crossref]

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12, 5269–5273 (2004).
[Crossref] [PubMed]

Chetrit, Y.

Ciftcioglu, B.

Claps, R.

D. Dimitropoulos, D. R. Solli, R. Claps, O. Boyraz, and B. Jalali, “Noise figure of silicon Raman amplifiers,” J. Lightwave Technol. 26, 847–852 (2008).
[Crossref]

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, art.071115 (2005).
[Crossref]

Cohen, O.

Dadap, J.

Dimitropoulos, D.

D. Dimitropoulos, D. R. Solli, R. Claps, O. Boyraz, and B. Jalali, “Noise figure of silicon Raman amplifiers,” J. Lightwave Technol. 26, 847–852 (2008).
[Crossref]

D. Dimitropoulos, S. Fathpour, and B. Jalali, “Limitations of active carrier removal in silicon Raman amplifiers and lasers,” Appl. Phys. Lett. 87, art.261108 (2005).
[Crossref]

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, art.071115 (2005).
[Crossref]

Espinola, R.

Fang, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous Raman silicon laser,” Nature 433, 725–728(2005).
[Crossref] [PubMed]

Fathpour, S.

K. K. Tsia, S. Fathpour, and B. Jalali, “Energy harvesting in silicon wavelength converters,” Opt. Express 14, 12327–12333 (2006).
[Crossref] [PubMed]

D. Dimitropoulos, S. Fathpour, and B. Jalali, “Limitations of active carrier removal in silicon Raman amplifiers and lasers,” Appl. Phys. Lett. 87, art.261108 (2005).
[Crossref]

Fauchet, P. M.

Forst, M.

Foster, M. A.

Foster, M.A.

R. Salem, M.A. Foster, and A.C. Turner et al, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

Freude, W.

Fukuda, H.

Gaeta, A. L.

Hak, D.

Hansryd, J.

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

Haus, H. A.

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev 128, 2407–2413 (1962).
[Crossref]

H. A. Haus, Electromagnetic Noise and Optical Measurements (Springer-Verlag, 2000) pp. 197–237.

Haus, H.A.

hedekvist, P. O.

Hedekvist, P.-O.

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

Ho, M.-C.

Itabashi, S. -i.

Izhaky, N.

Jacome, L.

Jalali, B.

D. Dimitropoulos, D. R. Solli, R. Claps, O. Boyraz, and B. Jalali, “Noise figure of silicon Raman amplifiers,” J. Lightwave Technol. 26, 847–852 (2008).
[Crossref]

K. K. Tsia, S. Fathpour, and B. Jalali, “Energy harvesting in silicon wavelength converters,” Opt. Express 14, 12327–12333 (2006).
[Crossref] [PubMed]

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, art.071115 (2005).
[Crossref]

D. Dimitropoulos, S. Fathpour, and B. Jalali, “Limitations of active carrier removal in silicon Raman amplifiers and lasers,” Appl. Phys. Lett. 87, art.261108 (2005).
[Crossref]

O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express 12, 4094–4102 (2004).
[Crossref] [PubMed]

O. Boyraz and B. Jalali. “Demonstration of 11 dB fiber-to-fiber gain in a silicon waveguides,” Electron. Express 1, 429–434(2004).
[Crossref]

O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12, 5269–5273 (2004).
[Crossref] [PubMed]

Jhaveri, R.

D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, art.071115 (2005).
[Crossref]

Jones,

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Kalogerakis, G.

G. Kalogerakis, K. Shimizu, M. E. Marchic, K. K.-Y. Wong, K. Uesaka, and L. G. Kazovsky, “High-repetition-rate pulsed-pump fiber OPA for amplification of communication signals,” J. Lightwave Technol. 24, 3021–3027 (2006).
[Crossref]

K. K. Y. Wong, M. E. Marhic, G. Kalogerakis, and L. G. Kazovsky, “Fiber optical parametric amplifier and wavelength converter with record 360 nm gain bandwidth and 50 dB signal gain,” in Conf. Lasers and Electro-opitcs2003, Baltimore, MD, Postdeadline paper CThPDB6.

Kalogerakis, G. K.

Karlsson, M.

Kazovsky, L. G.

G. Kalogerakis, K. Shimizu, M. E. Marchic, K. K.-Y. Wong, K. Uesaka, and L. G. Kazovsky, “High-repetition-rate pulsed-pump fiber OPA for amplification of communication signals,” J. Lightwave Technol. 24, 3021–3027 (2006).
[Crossref]

M. E. Marhic, G. K. Kalogerakis, K. K. Wong, and L. G. Kazovsky, “Pump-to-signal transfer of low-frequency intensity modulation in fiber optical parametric amplifier,” J. Lightwave Technol. 23, 1049–1056 (2005).
[Crossref]

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

M.-C. Ho, M. E. Marhic, Y. Akasaka, and L. G. Kazovsky, “200-nm bandwidth fiber optical amplifier combing parametric and Raman gain,” J. Lightwave Technol. 19, 977–981 (2001).
[Crossref]

K. K. Y. Wong, M. E. Marhic, G. Kalogerakis, and L. G. Kazovsky, “Fiber optical parametric amplifier and wavelength converter with record 360 nm gain bandwidth and 50 dB signal gain,” in Conf. Lasers and Electro-opitcs2003, Baltimore, MD, Postdeadline paper CThPDB6.

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

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A. Liu, Jones, L. Liu, and L. Liao et al, “A high speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

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Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90, art.211105 (2007).

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Marchic, M. E.

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M. E. Marhic, G. K. Kalogerakis, K. K. Wong, and L. G. Kazovsky, “Pump-to-signal transfer of low-frequency intensity modulation in fiber optical parametric amplifier,” J. Lightwave Technol. 23, 1049–1056 (2005).
[Crossref]

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

M.-C. Ho, M. E. Marhic, Y. Akasaka, and L. G. Kazovsky, “200-nm bandwidth fiber optical amplifier combing parametric and Raman gain,” J. Lightwave Technol. 19, 977–981 (2001).
[Crossref]

K. K. Y. Wong, M. E. Marhic, G. Kalogerakis, and L. G. Kazovsky, “Fiber optical parametric amplifier and wavelength converter with record 360 nm gain bandwidth and 50 dB signal gain,” in Conf. Lasers and Electro-opitcs2003, Baltimore, MD, Postdeadline paper CThPDB6.

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X. Sang, E.-K. Tien, N.S. Yuksek, F. Qian, Q. Sang, and O. Boyraz, “Dual-Wavelength Mode-Locked Fiber Laser with an Intracavity Silicon Waveguide,” IEEE Photon. Technol. Lett. 20, 1184–1186 (2008).
[Crossref]

E. -K. Tien, N. S. Yuksek, F. Qian, and O. Boyraz, “Pulse compression and modelocking by using TPA in silicon waveguides,” Opt. Express 15, 6500–6506 (2007).
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R. Salem, M.A. Foster, and A.C. Turner et al, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
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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, 12949–12958 (2007).
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Sang, Q.

X. Sang, E.-K. Tien, N.S. Yuksek, F. Qian, Q. Sang, and O. Boyraz, “Dual-Wavelength Mode-Locked Fiber Laser with an Intracavity Silicon Waveguide,” IEEE Photon. Technol. Lett. 20, 1184–1186 (2008).
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X. Sang, E.-K. Tien, N.S. Yuksek, F. Qian, Q. Sang, and O. Boyraz, “Dual-Wavelength Mode-Locked Fiber Laser with an Intracavity Silicon Waveguide,” IEEE Photon. Technol. Lett. 20, 1184–1186 (2008).
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Wong, K. K. Y.

K. K. Y. Wong, M. E. Marhic, G. Kalogerakis, and L. G. Kazovsky, “Fiber optical parametric amplifier and wavelength converter with record 360 nm gain bandwidth and 50 dB signal gain,” in Conf. Lasers and Electro-opitcs2003, Baltimore, MD, Postdeadline paper CThPDB6.

Wong, K. K.-Y.

G. Kalogerakis, K. Shimizu, M. E. Marchic, K. K.-Y. Wong, K. Uesaka, and L. G. Kazovsky, “High-repetition-rate pulsed-pump fiber OPA for amplification of communication signals,” J. Lightwave Technol. 24, 3021–3027 (2006).
[Crossref]

M. E. Marhic, K. K.-Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” IEEE J. Sel. Top. Quantum Electron 10, 1133–1141(2004).
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E. -K. Tien, N. S. Yuksek, F. Qian, and O. Boyraz, “Pulse compression and modelocking by using TPA in silicon waveguides,” Opt. Express 15, 6500–6506 (2007).
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Yuksek, N.S.

X. Sang, E.-K. Tien, N.S. Yuksek, F. Qian, Q. Sang, and O. Boyraz, “Dual-Wavelength Mode-Locked Fiber Laser with an Intracavity Silicon Waveguide,” IEEE Photon. Technol. Lett. 20, 1184–1186 (2008).
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Appl. Phys. Lett. (4)

E. Tien, F. Qian, N. S. Yuksek, and O. Boyraz, “Influence of nonlinear loss competition on pulse compression and nonlinear optics in silicon,” Appl. Phys. Lett. 91, art.201115 (2007).
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D. Dimitropoulos, R. Jhaveri, R. Claps, J. C. S. Woo, and B. Jalali, “Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides,” Appl. Phys. Lett. 86, art.071115 (2005).
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Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90, art.211105 (2007).

Electron. Express (1)

O. Boyraz and B. Jalali. “Demonstration of 11 dB fiber-to-fiber gain in a silicon waveguides,” Electron. Express 1, 429–434(2004).
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IEEE J. Quantum Electron. (1)

R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. QE-23, 123–129 (1987).
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IEEE J. Sel. Top. Quantum Electron (1)

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

IEEE J. Sel. Top. Quantum Electron. (1)

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

IEEE Photon. Technol. Lett. (2)

X. Sang, E.-K. Tien, N.S. Yuksek, F. Qian, Q. Sang, and O. Boyraz, “Dual-Wavelength Mode-Locked Fiber Laser with an Intracavity Silicon Waveguide,” IEEE Photon. Technol. Lett. 20, 1184–1186 (2008).
[Crossref]

T. Torounidis, P. Andrekson, and B.-E. Olsson, “Fiber-optical parametric amplifier with 70-dB gain,” IEEE Photon. Technol. Lett. 18, 1194–1196 (2007).
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IEEE Photon. Technol.Lett. (1)

T. Torounidis and P. Andrekson, “Broadband single-pumped fiber-optic parametric amplifiers,” IEEE Photon. Technol.Lett. 19, 650–652 (2007).
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J. Lightwave Technol. (7)

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

Nat. Photonics (2)

R. Salem, M.A. Foster, and A.C. Turner et al, “Signal regeneration using low-power four-wave mixing on silicon chip,” Nat. Photonics 2, 35–38 (2008).
[Crossref]

O. Boyraz, “Nanoscale signal regeneration,” Nat. Photonics 2, 12–13 (2008).
[Crossref]

Nature (5)

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] [PubMed]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous Raman silicon laser,” Nature 433, 725–728(2005).
[Crossref] [PubMed]

G. T. Reed, “The optical age of silicon,” Nature 427, 595–596(2004).
[Crossref] [PubMed]

A. Liu, Jones, L. Liu, and L. Liao et al, “A high speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
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Opt. Express (12)

R. Espinola, J. Dadap, R. Osgood, Jr., S. McNab, and Y. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713–3718 (2004).
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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).
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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, 4357–4362 (2006).
[Crossref] [PubMed]

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
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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, 12949–12958 (2007).
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K. K. Tsia, S. Fathpour, and B. Jalali, “Energy harvesting in silicon wavelength converters,” Opt. Express 14, 12327–12333 (2006).
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Y. -H. Kuo, H. Rong, V. Sih, S. Xu, M. Paniccia, and O. Cohen, “Demonstration of wavelength conversion at 40 Gb/s data rate in silicon waveguides,” Opt. Express 14, 11721–11726 (2006).
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O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express 12, 4094–4102 (2004).
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O. Boyraz and B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12, 5269–5273 (2004).
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E. -K. Tien, N. S. Yuksek, F. Qian, and O. Boyraz, “Pulse compression and modelocking by using TPA in silicon waveguides,” Opt. Express 15, 6500–6506 (2007).
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Opt. Lett. (4)

Phys. Rev (1)

H. A. Haus and J. A. Mullen, “Quantum noise in linear amplifiers,” Phys. Rev 128, 2407–2413 (1962).
[Crossref]

Other (2)

H. A. Haus, Electromagnetic Noise and Optical Measurements (Springer-Verlag, 2000) pp. 197–237.

K. K. Y. Wong, M. E. Marhic, G. Kalogerakis, and L. G. Kazovsky, “Fiber optical parametric amplifier and wavelength converter with record 360 nm gain bandwidth and 50 dB signal gain,” in Conf. Lasers and Electro-opitcs2003, Baltimore, MD, Postdeadline paper CThPDB6.

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Figures (10)

Fig. 1.
Fig. 1.

(a). FCD contour as a function of peak pump and repetition rate at the input end. (b) FCD and FCA loss evolution along the waveguide

Fig. 2.
Fig. 2.

Schematic configuration of the OPA in silicon waveguide

Fig. 3.
Fig. 3.

Typical gain and NF spectra of OPA in the silicon waveguide

Fig. 4.
Fig. 4.

Parametric gain profiles at different dispersion values.

Fig. 5.
Fig. 5.

(a). Gain evolution at different wavelengths, (b) Maximum gain and corresponding wavelength versus peak pump power.

Fig. 6.
Fig. 6.

(a). NF evolutions at different wavelengths. (b) NF evolution at maximum gain

Fig. 7.
Fig. 7.

Gain contour at different pulse widths

Fig. 8.
Fig. 8.

(a). Parametric gain and (b). NF versus the repetition rate for different pulse widths

Fig. 9.
Fig. 9.

(a). Parametric gain and (b). NF versus the free carrier lifetime for different pulse widths

Fig. 10.
Fig. 10.

Gain and NF spectra of OPA in the silicon waveguide with a CW pump.

Equations (16)

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

d A p d z = 1 2 [ α + α p FCA ( z ) ] A p + i ( γ p + i β 2 ) A p 2 A p ,
d A s d z = 1 2 [ α + α s FCA ( z ) ] A s + 2 i ( γ s + i β 2 ) A p 2 A s + i γ s A p 2 A i * exp ( i Δ k · z ) ,
d A i * d z = 1 2 [ α + α i FCA ( z ) ] A i * 2 i ( γ i + i β 2 ) A p 2 A i * i γ i A p * 2 A s exp ( i Δ k · z ) ,
d N ( t , z ) d t = β 2 h v I 2 ( t , z ) N ( t , z ) τ
N ( t , z ) ( 1 1 e 1 R τ ) β T 0 I 2 ( t , z ) 2 h v
Δ k = k s + k i 2 k p + 2 γ P p = ( n s ω s + n i ω i 2 n p ω p ) c + 2 γ P p β 2 ( ω s ω p ) 2 + 2 γ P p = 0
Δ n FC = e 2 λ 2 8 π 2 c 2 ε 0 n ( Δ N e m ce * + Δ N h m ch * ) 8.2 × 10 22 λ 2 N
Δ D FC = 1 c d Δ n FC d λ = 5.46 × 10 30 λ N
NF silicon = T + N loss + N gain T + N gain ( T + N loss ) T 2 a 2 ,
T = exp ( 0 L ( g ( z ) l ( z ) ) d z ) ,
N gain = 0 L g ( z ) exp ( z L ( g ( x ) l ( x ) ) d x ) d z ,
N loss = 0 L l ( z ) exp ( z L ( g ( x ) l ( x ) ) d x ) d z ,
σ p ASE 2 = 4 R 2 P P S ASE Δ f
σ s P P 2 = σ p ASE 2 ( d G d P P P s ( 0 ) ) 2
N F P = σ s P P 2 G 2 2 R 2 h v P s ( 0 ) Δ f = 2 P p n s p ( G EDFA 1 ) G 2 P s ( 0 ) ( d G d P p P s ( 0 ) ) 2
NF = NF silicon + NF P

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