Abstract

The impact of dispersion profiles of silicon waveguides on femtosecond optical parametric amplification (OPA) is theoretically investigated. It is found that flat quasi-phase-matching, smooth temporal profiles and separable spectra for 200 fs pulses can be obtained by tailoring the cross-section of silicon rib waveguide. We achieve on-chip parametric gain as high as 26.8 dB and idler conversion gain of 25.6 dB for a low pump peak power over a flat bandwidth of 400 nm in a 10-mm-long dispersion engineered silicon waveguide. Our on-chip OPA can find important potential applications in highly integrated optical circuits for all-optical ultrafast signal processing.

© 2011 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2010 (5)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[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(3), 1904–1908 (2010).
[CrossRef] [PubMed]

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (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]

J. Y. Lee, L. Yin, G. P. Agrawal, and P. M. Fauchet, “Ultrafast optical switching based on nonlinear polarization rotation in silicon waveguides,” Opt. Express 18(11), 11514–11523 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (3)

2007 (5)

2006 (6)

2005 (6)

2002 (2)

T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett. 81(7), 1323–1325 (2002).
[CrossRef]

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

Agrawal, G. P.

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]

Asghari, M.

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

T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett. 81(7), 1323–1325 (2002).
[CrossRef]

Baets, R.

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]

Boyraz, O.

Chen, X.

Claps, R.

D. Dimitripoulos, 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(7), 071115–071117 (2005).
[CrossRef]

V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Parametric Raman wavelength conversion in scaled silicon waveguides,” J. Lightwave Technol. 23(6), 2094–2102 (2005).
[CrossRef]

Cohen, O.

Dadap, J. I.

Day, I. E.

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

T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett. 81(7), 1323–1325 (2002).
[CrossRef]

Dimitripoulos, D.

D. Dimitripoulos, 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(7), 071115–071117 (2005).
[CrossRef]

Dimitropoulos, D.

Divliansky, I. B.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Drake, J.

T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett. 81(7), 1323–1325 (2002).
[CrossRef]

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

Dumon, P.

Espinola, R. L.

Fang, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Fauchet, P. M.

Foster, M. A.

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[CrossRef]

Fukuda, H.

Gaeta, A. L.

Green, W. M. J.

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]

Hak, D.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Harpin, A.

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

Hsieh, I.-W.

Itabashi, S.

Jalali, B.

V. Raghunathan, R. Claps, D. Dimitropoulos, and B. Jalali, “Parametric Raman wavelength conversion in scaled silicon waveguides,” J. Lightwave Technol. 23(6), 2094–2102 (2005).
[CrossRef]

D. Dimitripoulos, 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(7), 071115–071117 (2005).
[CrossRef]

Jhaveri, R.

D. Dimitripoulos, 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(7), 071115–071117 (2005).
[CrossRef]

Johnson, T. J.

Jones, R.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Kawanishi, T.

Knights, A. P.

T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett. 81(7), 1323–1325 (2002).
[CrossRef]

Koos, C.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[CrossRef]

Kuo, Y.-H.

Lee, J. Y.

Leuthold, J.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4(8), 535–544 (2010).
[CrossRef]

Liang, T. K.

T. K. Liang, L. Nunes, T. Sakamoto, K. Sasagawa, T. Kawanishi, M. Tsuchiya, G. Priem, D. Van Thourhout, P. Dumon, R. Baets, and H. Tsang, “Ultrafast all-optical switching by cross-absorption modulation in silicon wire waveguides,” Opt. Express 13(19), 7298–7303 (2005).
[CrossRef] [PubMed]

T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett. 81(7), 1323–1325 (2002).
[CrossRef]

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

Lin, Q.

Lipson, M.

Liu, A.

H. Rong, Y.-H. Kuo, A. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14(3), 1182–1188 (2006).
[CrossRef] [PubMed]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005).
[CrossRef] [PubMed]

Liu, X.

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]

N. C. Panoiu, X. Liu, and R. M. Osgood., “Self-steepening of ultrashort pulses in silicon photonic nanowires,” Opt. Lett. 34(7), 947–949 (2009).
[CrossRef] [PubMed]

Liu, Y.

Y. Liu and H. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90(21), 211105 (2007).
[CrossRef]

Manolatou, C.

Mathlouthi, W.

McNab, S.

McNab, S. J.

Michael, C. P.

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]

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]

Nunes, L.

Osgood, R. M.

Painter, O. J.

Paniccia, M.

Panoiu, N. C.

Park, J. S.

S. Zlatanovic, J. S. Park, S. Moro, J. M. C. Boggio, I. B. Divliansky, N. Alic, S. Mookherjea, and S. Radic, “Mid-infrared wavelength conversion in silicon waveguides using ultracompact telecom-band-derived pump source,” Nat. Photonics 4(8), 561–564 (2010).
[CrossRef]

Perahia, R.

Priem, G.

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]

Raghunathan, V.

Roberts, S. W.

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

Rong, H.

Sakamoto, T.

Salem, R.

Sang, X.

Sasagawa, K.

Schmidt, B. S.

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(7096), 960–963 (2006).
[CrossRef] [PubMed]

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

Sharping, J. E.

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]

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(7096), 960–963 (2006).
[CrossRef] [PubMed]

Shoji, T.

Sih, V.

Takahashi, J.

Takahashi, M.

Tsang, H.

Tsang, H. K.

T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett. 81(7), 1323–1325 (2002).
[CrossRef]

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

Tsuchiya, M.

Tsuchizawa, T.

Turner, A. C.

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(7096), 960–963 (2006).
[CrossRef] [PubMed]

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

Turner-Foster, A. C.

Van Thourhout, D.

Vlasov, Y.

Vlasov, Y. A.

Watanabe, T.

Wong, C. S.

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

Woo, J. C. S.

D. Dimitripoulos, 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(7), 071115–071117 (2005).
[CrossRef]

Xu, S.

Yamada, K.

Yin, L.

Zhang, J.

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]

Appl. Phys. Lett. (4)

T. K. Liang, H. K. Tsang, I. E. Day, J. Drake, A. P. Knights, and M. Asghari, “Silicon waveguide two-photon absorption detector at 1.5 μm wavelength for auto-correlation measurements,” Appl. Phys. Lett. 81(7), 1323–1325 (2002).
[CrossRef]

D. Dimitripoulos, 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(7), 071115–071117 (2005).
[CrossRef]

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Other (2)

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of rib silicon waveguide.

Fig. 2
Fig. 2

Plots of computed effective index of refraction (a), and (b) first-order (c) second-order (d) third order dispersion as a function of wavelength for different waveguide widths.

Fig. 3
Fig. 3

Calculated phase mismatch for the three waveguides when the pump peak power are (a) 2 W and (b) 5W, respectively.

Fig. 4
Fig. 4

Output temporal profiles from the waveguides with width of (a) 550 nm, (b) 600 nm and (c) 650 nm, respectively.

Fig. 5
Fig. 5

Output spectra of the waveguides with widths of (a) 550 nm, (b) 600 nm and (c) 650 nm.

Fig. 6
Fig. 6

Output spectra for different pump peak power.

Fig. 7
Fig. 7

On-chip parametric gain as a function of (a) signal center wavelength and (b) pump peak power.

Tables (1)

Tables Icon

Table 1 The characteristic lengths for the three waveguides when the pump peak power is 5 W.

Equations (9)

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A p z + i β 2p 2 2 A p T 2 β 3p 6 3 A p T 3 = 1 2 ( α p + α fcp ) A p +i γ pe ( 1+ i ω p t ) | A p | 2 A p +i 2π λ p δ nfcp A P +2i γ p A s A i A p * exp( iΔβz ),
A s z + d s A s T + i β 2s 2 2 A s T 2 β 3s 6 3 A s T 3 = 1 2 ( α s + α fcs ) A s +i γ se i ω s t | A s | 2 A s +i 2π λ s δ nfcs A s +2i γ se | A p | 2 A s +i γ s A p 2 A i * exp( iΔβz ),
A i z + d i A i T + i β 2i 2 2 A i T 2 β 3i 6 3 A i T 3 = 1 2 ( α i + α fci ) A i +i γ ie i ω i t | A i | 2 A i +i 2π λ i δ nfci A i +2i γ ie | A p | 2 A i +i γ i A p 2 A s * exp( iΔβz ),
γ je = γ j +i β TPA 2 A eff ,
σ j =1.45× 10 21 ( λ j / λ ref ) 2 m 2 , ζ j =1.35× 10 27 ( λ j / λ ref ) 2 m 3 ,
N c (z,t) t = π β TPA 2h ω p A eff 2 | A p (z,t) | 4 N c (z,t) τ c ,
Δκ=Δβ+2 γ p P p ,
L D = T 0 2 / β 2p , L D ' = T 0 3 / β 3p , L W = T 0 / | d | , L NL =1/ γ p P p ,
δ ω max = 0.86 φ max T 0 ,

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