Abstract

A femtosecond optical parametric oscillator (OPO) based on silicon-on-insulator (SOI) waveguide is proposed and analyzed numerically. By utilizing split-step Fourier method (SSFM), it is demonstrated that ultra-wide tunable wavelength femtosecond pulse can be realized under the phase matching condition. Due to the interaction between nonlinearity and flexible dispersion design, the output signal wavelength can be tuned from 1645 to 1805 nm and the idler wavelength can be tuned from 1350 to 1456 nm. Moreover, the peak power of the output signal pulse exceeds 10 W from 1700 to 1770 nm with the pump peak power 50 W. The proposed OPO exhibits compact configuration and can find important applications in integrated broadband optical source.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. I. D. Rukhlenko, M. Premaratne, I. L. Garanovich, A. A. Sukhorukov, and G. P. Agrawal, “Analytical study of pulse amplification in silicon Raman amplifiers,” Opt. Express 18(17), 18324–18338 (2010).
    [CrossRef] [PubMed]
  4. 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).
    [CrossRef] [PubMed]
  5. 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]
  6. 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]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2011 (2)

2010 (8)

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

W. Q. Zhang, J. E. Sharping, R. T. White, T. M. Monro, and S. Afshar V, “Design and optimization of fiber optical parametric oscillators for femtosecond pulse generation,” Opt. Express 18(16), 17294–17305 (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]

S. Zlatanovic, J. S. Park, S. Moro, J. 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. Gao, E. K. Tien, Q. Song, Y. Huang, and O. Boyraz, “Ultra-broadband one-to-two wavelength conversion using low-phase-mismatching four-wave mixing in silicon waveguides,” Opt. Express 18(11), 11898–11903 (2010).
[CrossRef] [PubMed]

S. Gao, E. K. Tien, Y. Huang, and S. He, “Experimental demonstration of bandwidth enhancement based on two-pump wavelength conversion in a silicon waveguide,” Opt. Express 18(26), 27885–27890 (2010).
[CrossRef] [PubMed]

N. Savage, “Optical parametric oscillators,” Nat. Photonics 4(2), 124–125 (2010).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, I. L. Garanovich, A. A. Sukhorukov, and G. P. Agrawal, “Analytical study of pulse amplification in silicon Raman amplifiers,” Opt. Express 18(17), 18324–18338 (2010).
[CrossRef] [PubMed]

2008 (3)

2007 (5)

2006 (6)

2005 (1)

2004 (3)

1999 (1)

M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286(5444), 1513–1517 (1999).
[CrossRef] [PubMed]

Afshar V, S.

Agrawal, G. P.

Alic, N.

S. Zlatanovic, J. S. Park, S. Moro, J. 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]

Assefa, S.

Boggio, J. C.

S. Zlatanovic, J. S. Park, S. Moro, J. 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.

Cohen, O.

Dadap, J. I.

Dimitropoulos, D.

Divliansky, I. B.

S. Zlatanovic, J. S. Park, S. Moro, J. 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.

Dunn, M. H.

M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286(5444), 1513–1517 (1999).
[CrossRef] [PubMed]

Ebrahimzadeh, M.

M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286(5444), 1513–1517 (1999).
[CrossRef] [PubMed]

Fauchet, P. M.

Foster, M. A.

Fukuda, H.

Gaeta, A. L.

Gao, S.

Garanovich, I. L.

Gondarenko, A.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Green, W. M. J.

Harvey, J. D.

He, S.

Hsieh, I.-W.

Huang, Y.

Itabashi, S.

Jalali, B.

Johnson, T. J.

Koonath, P.

Kuo, Y. H.

Leonhardt, R.

Levy, J. S.

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Lin, Q.

Lipson, M.

Liu, A.

Liu, X.

Mak, K. F.

McNab, S. J.

Michael, C. P.

Monro, T. M.

Mookherjea, S.

S. Zlatanovic, J. S. Park, S. Moro, J. 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. 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]

Murdoch, S. G.

Osgood, R. M.

Painter, O. J.

Paniccia, M.

Panoiu, N. C.

Park, J. S.

S. Zlatanovic, J. S. Park, S. Moro, J. 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.

Premaratne, M.

Radic, S.

S. Zlatanovic, J. S. Park, S. Moro, J. 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.

Rieger, G. W.

G. W. Rieger, K. S. Virk, and J. Young, “Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

Rong, H.

Rukhlenko, I. D.

Salem, R.

Savage, N.

N. Savage, “Optical parametric oscillators,” Nat. Photonics 4(2), 124–125 (2010).
[CrossRef]

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]

Sharping, J. E.

W. Q. Zhang, J. E. Sharping, R. T. White, T. M. Monro, and S. Afshar V, “Design and optimization of fiber optical parametric oscillators for femtosecond pulse generation,” Opt. Express 18(16), 17294–17305 (2010).
[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.

Song, Q.

Soref, R.

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[CrossRef]

Sukhorukov, A. A.

Takahashi, J.

Takahashi, M.

Tien, E. K.

Tsuchizawa, T.

Turner, A. C.

Turner-Foster, A. C.

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]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Virk, K. S.

G. W. Rieger, K. S. Virk, and J. Young, “Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

Vlasov, Y. A.

Watanabe, T.

White, R. T.

Xu, Y. Q.

Yamada, K.

Yin, L.

Young, J.

G. W. Rieger, K. S. Virk, and J. Young, “Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

Zhang, J.

Zhang, W. Q.

Zlatanovic, S.

S. Zlatanovic, J. S. Park, S. Moro, J. 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. (1)

G. W. Rieger, K. S. Virk, and J. Young, “Nonlinear propagation of ultrafast 1.5 μm pulses in high-index-contrast silicon-on-insulator waveguides,” Appl. Phys. Lett. 84(6), 900–902 (2004).
[CrossRef]

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

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[CrossRef]

Nat. Photonics (3)

S. Zlatanovic, J. S. Park, S. Moro, J. 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]

N. Savage, “Optical parametric oscillators,” Nat. Photonics 4(2), 124–125 (2010).
[CrossRef]

J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics 4(1), 37–40 (2010).
[CrossRef]

Nature (1)

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]

Opt. Express (17)

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006).
[CrossRef] [PubMed]

S. Gao, E. K. Tien, Q. Song, Y. Huang, and O. Boyraz, “Ultra-broadband one-to-two wavelength conversion using low-phase-mismatching four-wave mixing in silicon waveguides,” Opt. Express 18(11), 11898–11903 (2010).
[CrossRef] [PubMed]

S. Gao, E. K. Tien, Y. Huang, and S. He, “Experimental demonstration of bandwidth enhancement based on two-pump wavelength conversion in a silicon waveguide,” Opt. Express 18(26), 27885–27890 (2010).
[CrossRef] [PubMed]

Q. Lin, T. J. Johnson, R. Perahia, C. P. Michael, and O. J. Painter, “A proposal for highly tunable optical parametric oscillation in silicon micro-resonators,” Opt. Express 16(14), 10596–10610 (2008).
[CrossRef] [PubMed]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
[CrossRef] [PubMed]

I. D. Rukhlenko, M. Premaratne, I. L. Garanovich, A. A. Sukhorukov, and G. P. Agrawal, “Analytical study of pulse amplification in silicon Raman amplifiers,” Opt. Express 18(17), 18324–18338 (2010).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

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]

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]

I.-W. Hsieh, X. Chen, J. I. Dadap, N. C. Panoiu, R. M. Osgood, S. J. McNab, and Y. A. Vlasov, “Cross-phase modulation-induced spectral and temporal effects on co-propagating femtosecond pulses in silicon photonic wires,” Opt. Express 15(3), 1135–1146 (2007).
[CrossRef] [PubMed]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[CrossRef] [PubMed]

X. 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]

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12(12), 2774–2780 (2004).
[CrossRef] [PubMed]

W. Q. Zhang, J. E. Sharping, R. T. White, T. M. Monro, and S. Afshar V, “Design and optimization of fiber optical parametric oscillators for femtosecond pulse generation,” Opt. Express 18(16), 17294–17305 (2010).
[CrossRef] [PubMed]

O. Boyraz, P. Koonath, V. Raghunathan, and B. Jalali, “All optical switching and continuum generation in silicon waveguides,” Opt. Express 12(17), 4094–4102 (2004).
[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(11), 4786–4799 (2006).
[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]

Opt. Lett. (5)

Science (1)

M. H. Dunn and M. Ebrahimzadeh, “Parametric generation of tunable light from continuous-wave to femtosecond pulses,” Science 286(5444), 1513–1517 (1999).
[CrossRef] [PubMed]

Other (2)

T. E. Murphy, software available at http://www.photonics.umd.edu .

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, 2001).

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic of the SOI waveguide. (b) The fundamental quasi-TE mode field at wavelength of 1550 nm. (c) The fundamental quasi-TM mode field at wavelength of 1550 nm.

Fig. 2
Fig. 2

(a) Wavelength dependence of the effective refractive for the fundamental TE mode and TM mode using the waveguide shown in Fig. 1(a). (b) Wavelength dependence of the second order dispersion for the fundamental TE mode and TM mode using the waveguide shown in Fig. 1(a). (c) The phase matching curve of the SOI waveguide. The inset is the frequency shift detuning curve. The pump power used is Pp = 50 W.

Fig. 3
Fig. 3

Schematic of the SOI waveguide optical parametric oscillator.

Fig. 4
Fig. 4

(a) The output signal pulse of the optical parametric oscillator based on SOI waveguide. (b) The output idler pulse of the optical parametric oscillator based on SOI waveguide.

Fig. 5
Fig. 5

(a) The output signal spectra. (b) The output idler spectra. The signal wavelength is tuned on the longer wavelength side of the pump while the idler wavelength is tuned on the shorter wavelength side of the pump. T0 is the duration of the pump pulse and ν0 is the center frequency of the pump pulse.

Fig. 6
Fig. 6

(a) The peak power of the output signal pulse. (b) Comparison among the signal pulse, the initial pump pulse and output pump pulse of the optical parametric oscillator based on SOI waveguide. The signal wavelength is 1705 nm.

Fig. 7
Fig. 7

Walk-off delay of the SOI waveguide, when the wavelength is tuned from the ZDW of the waveguide 1550 nm.

Equations (11)

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Δk=2γ P p Δ k linear
Δ k linear = β 2 (Δω) 2 1 12 β 4 (Δω) 4 1 360 β 6 (Δω) 6
G s =1+ [ γ P p g sinh(gL) ] 2
g= [ γ P p Δ k linear (Δ k linear /2) 2 ] 1 2
2γ P p + β 2 (Δω) 2 + 1 12 β 4 (Δω) 4 + 1 360 β 6 (Δω) 6 =0
A p z + m=2 i m1 m! β pm m A p T m = 1 2 ( α lp + 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 * ,
A s z + m=2 i m1 m! β sm m A s T m = 1 2 ( α ls + 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 * ,
A i z + m=2 i m1 m! β im m A p T m = 1 2 ( α li + 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 * ,
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 ,

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