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Anti-Stokes Raman conversion in silicon waveguides

R. Claps, V. Raghunathan, D. Dimitropoulos, and B. Jalali

Open Access Open Access

Abstract

The first observation of parametric down-conversion in silicon is reported. Conversion from 1542.3nm to 1328.8nm is achieved using a CW pump laser at 1427 nm. The conversion occurs via Coherent Anti-Stokes Raman Scattering (CARS) in which two pump photons and one Stokes photon couple through a zone-center optical phonon to an anti-Stokes photon. The maximum measured Stokes/anti-Stokes power conversion efficiency is 1×10-5. The value depends on the effective pump power, the Stimulated Raman Scattering (SRS) coefficient of bulk silicon, and waveguide dispersion. It is shown that the power conversion efficiency is a strong function of phase mismatch inside the waveguide.

©2003 Optical Society of America

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References

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  • Article Order
  • Year
  • Author
  • Publication
  1. James B. Kuo and Shih-Chia Lin, Low voltage SOI CMOS VLSI circuits and devices, John Wiley and Sons, Incorporated, 2001, ISBN 047-1417777.
  2. M. Cardona and G. Guntherodt, Light Scattering in Solids II, in Topics in Applied Physics, Vol. 50. Chapter 4, “Coherent and Hyper-Raman Techniques,” by H. Vogt. (Springer-Verlag, Berlin, 1982). ISBN 0-387-11380-0.
  3. M.C. Ho, K. Uesaka, Michel Marhic, Y. Akasaka, and L.G. Kazovsky, “200-nm-Bandwidth Fiber Optical Amplifier Combining Parametric and Raman Gain,” J. Lightwave Technol. 19, 977–981 (2001).
    [Crossref]
  4. M.E. Marhic, K.K.-Y. Wong, and L.G. Kazovsky, “Prospects for CW Fiber OPAs and OPOs,” Proceedings CLEO (Optical Society of America, Washington, D.C., 2003) CTuA1.
  5. J.K. Chee and J-M Liu, “Polarization-Dependent Parametric and Raman Processes in a Birefringent Optical Fiber,” IEEE J. Quantum Electron. 26, 541–549 (1990).
    [Crossref]
  6. Y.R. Shen and N. Bloembergen, “Theory of Stimulated Brillouin and Raman Scattering,” Phys. Rev. A 137, A1787–A1805 (1964).
  7. E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
    [Crossref]
  8. P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. A 7, 3685–3697 (1973).
  9. J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970).
    [Crossref]
  10. R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, “Observation of Raman emission in silicon waveguides at 1.54 µm,” Opt. Express 10, 1305–1313 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-22-1305
    [Crossref] [PubMed]
  11. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, “Observation of Stimulated Raman Scattering in Silicon Waveguides,” Opt. Express 11, 1731–1739 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1731
    [Crossref] [PubMed]
  12. D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters 28(20) 1954–1956 (2003).
    [Crossref] [PubMed]
  13. J.J. Wynne, “Optical Third-Order Mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. 1781295–1303 (1969).
    [Crossref]
  14. H.K. Tsang, C.S. Wong, T.K. Lang, 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 µm wavelength,” Appl. Phys. Lett. 3, 416–418 (2002).
    [Crossref]
  15. Spectra-Physics Telecom: “Model RL5 Raman Fiber Laser Specifications”.

2003 (2)

2002 (1)

2001 (1)

1990 (2)

J.K. Chee and J-M Liu, “Polarization-Dependent Parametric and Raman Processes in a Birefringent Optical Fiber,” IEEE J. Quantum Electron. 26, 541–549 (1990).
[Crossref]

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

1973 (1)

P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. A 7, 3685–3697 (1973).

1970 (1)

J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970).
[Crossref]

1969 (1)

J.J. Wynne, “Optical Third-Order Mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. 1781295–1303 (1969).
[Crossref]

1964 (1)

Y.R. Shen and N. Bloembergen, “Theory of Stimulated Brillouin and Raman Scattering,” Phys. Rev. A 137, A1787–A1805 (1964).

Akasaka, Y.

Asghari, M.

H.K. Tsang, C.S. Wong, T.K. Lang, 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 µm wavelength,” Appl. Phys. Lett. 3, 416–418 (2002).
[Crossref]

Bloembergen, N.

Y.R. Shen and N. Bloembergen, “Theory of Stimulated Brillouin and Raman Scattering,” Phys. Rev. A 137, A1787–A1805 (1964).

Cardona, M.

M. Cardona and G. Guntherodt, Light Scattering in Solids II, in Topics in Applied Physics, Vol. 50. Chapter 4, “Coherent and Hyper-Raman Techniques,” by H. Vogt. (Springer-Verlag, Berlin, 1982). ISBN 0-387-11380-0.

Chang, R.K.

J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970).
[Crossref]

Chee, J.K.

J.K. Chee and J-M Liu, “Polarization-Dependent Parametric and Raman Processes in a Birefringent Optical Fiber,” IEEE J. Quantum Electron. 26, 541–549 (1990).
[Crossref]

Claps, R.

Day, I.E.

H.K. Tsang, C.S. Wong, T.K. Lang, 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 µm wavelength,” Appl. Phys. Lett. 3, 416–418 (2002).
[Crossref]

Dianov, E.M.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

Dimitropoulos, D.

Drake, J.

H.K. Tsang, C.S. Wong, T.K. Lang, 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 µm wavelength,” Appl. Phys. Lett. 3, 416–418 (2002).
[Crossref]

Golovchenko, E.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

Guntherodt, G.

M. Cardona and G. Guntherodt, Light Scattering in Solids II, in Topics in Applied Physics, Vol. 50. Chapter 4, “Coherent and Hyper-Raman Techniques,” by H. Vogt. (Springer-Verlag, Berlin, 1982). ISBN 0-387-11380-0.

Han, Y.

Harpin, A.

H.K. Tsang, C.S. Wong, T.K. Lang, 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 µm wavelength,” Appl. Phys. Lett. 3, 416–418 (2002).
[Crossref]

Hathaway, C.E.

P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. A 7, 3685–3697 (1973).

Ho, M.C.

Houshmand, B.

D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters 28(20) 1954–1956 (2003).
[Crossref] [PubMed]

Jalali, B.

Kazovsky, L.G.

M.C. Ho, K. Uesaka, Michel Marhic, Y. Akasaka, and L.G. Kazovsky, “200-nm-Bandwidth Fiber Optical Amplifier Combining Parametric and Raman Gain,” J. Lightwave Technol. 19, 977–981 (2001).
[Crossref]

M.E. Marhic, K.K.-Y. Wong, and L.G. Kazovsky, “Prospects for CW Fiber OPAs and OPOs,” Proceedings CLEO (Optical Society of America, Washington, D.C., 2003) CTuA1.

Kuo, James B.

James B. Kuo and Shih-Chia Lin, Low voltage SOI CMOS VLSI circuits and devices, John Wiley and Sons, Incorporated, 2001, ISBN 047-1417777.

Lang, T.K.

H.K. Tsang, C.S. Wong, T.K. Lang, 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 µm wavelength,” Appl. Phys. Lett. 3, 416–418 (2002).
[Crossref]

Lin, Shih-Chia

James B. Kuo and Shih-Chia Lin, Low voltage SOI CMOS VLSI circuits and devices, John Wiley and Sons, Incorporated, 2001, ISBN 047-1417777.

Liu, J-M

J.K. Chee and J-M Liu, “Polarization-Dependent Parametric and Raman Processes in a Birefringent Optical Fiber,” IEEE J. Quantum Electron. 26, 541–549 (1990).
[Crossref]

Mamyshev, P. V.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

Marhic, M.E.

M.E. Marhic, K.K.-Y. Wong, and L.G. Kazovsky, “Prospects for CW Fiber OPAs and OPOs,” Proceedings CLEO (Optical Society of America, Washington, D.C., 2003) CTuA1.

Marhic, Michel

Pilipetskii, A. N.

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

Raghunathan, V.

Ralston, J.M.

J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970).
[Crossref]

Roberts, S.W.

H.K. Tsang, C.S. Wong, T.K. Lang, 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 µm wavelength,” Appl. Phys. Lett. 3, 416–418 (2002).
[Crossref]

Shen, Y.R.

Y.R. Shen and N. Bloembergen, “Theory of Stimulated Brillouin and Raman Scattering,” Phys. Rev. A 137, A1787–A1805 (1964).

Temple, P.A.

P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. A 7, 3685–3697 (1973).

Tsang, H.K.

H.K. Tsang, C.S. Wong, T.K. Lang, 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 µm wavelength,” Appl. Phys. Lett. 3, 416–418 (2002).
[Crossref]

Uesaka, K.

Vogt, H.

M. Cardona and G. Guntherodt, Light Scattering in Solids II, in Topics in Applied Physics, Vol. 50. Chapter 4, “Coherent and Hyper-Raman Techniques,” by H. Vogt. (Springer-Verlag, Berlin, 1982). ISBN 0-387-11380-0.

Wong, C.S.

H.K. Tsang, C.S. Wong, T.K. Lang, 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 µm wavelength,” Appl. Phys. Lett. 3, 416–418 (2002).
[Crossref]

Wong, K.K.-Y.

M.E. Marhic, K.K.-Y. Wong, and L.G. Kazovsky, “Prospects for CW Fiber OPAs and OPOs,” Proceedings CLEO (Optical Society of America, Washington, D.C., 2003) CTuA1.

Wynne, J.J.

J.J. Wynne, “Optical Third-Order Mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. 1781295–1303 (1969).
[Crossref]

IEEE J. Quantum Electron. (2)

J.K. Chee and J-M Liu, “Polarization-Dependent Parametric and Raman Processes in a Birefringent Optical Fiber,” IEEE J. Quantum Electron. 26, 541–549 (1990).
[Crossref]

E. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E.M. Dianov, “Mutual Influence of the Parametric Effects and Stimulated Raman Scattering in Optical Fibers,” IEEE J. Quantum Electron. 26, 1815–1820 (1990).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (2)

Optics Letters (1)

D. Dimitropoulos, B. Houshmand, R. Claps, and B. Jalali, “Coupled-mode theory of the Raman effect in Silicon-On-Insulator waveguides,” Optics Letters 28(20) 1954–1956 (2003).
[Crossref] [PubMed]

Phys. Rev. (1)

J.J. Wynne, “Optical Third-Order Mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. 1781295–1303 (1969).
[Crossref]

Phys. Rev. A (2)

P.A. Temple and C.E. Hathaway, “Multiphonon Raman Spectrum of Silicon,” Phys. Rev. A 7, 3685–3697 (1973).

Y.R. Shen and N. Bloembergen, “Theory of Stimulated Brillouin and Raman Scattering,” Phys. Rev. A 137, A1787–A1805 (1964).

Phys. Rev. B (1)

J.M. Ralston and R.K. Chang, “Spontaneous-Raman-scattering efficiency and stimulated scattering in silicon,” Phys. Rev. B 2, 1858–1862 (1970).
[Crossref]

Other (5)

M.E. Marhic, K.K.-Y. Wong, and L.G. Kazovsky, “Prospects for CW Fiber OPAs and OPOs,” Proceedings CLEO (Optical Society of America, Washington, D.C., 2003) CTuA1.

James B. Kuo and Shih-Chia Lin, Low voltage SOI CMOS VLSI circuits and devices, John Wiley and Sons, Incorporated, 2001, ISBN 047-1417777.

M. Cardona and G. Guntherodt, Light Scattering in Solids II, in Topics in Applied Physics, Vol. 50. Chapter 4, “Coherent and Hyper-Raman Techniques,” by H. Vogt. (Springer-Verlag, Berlin, 1982). ISBN 0-387-11380-0.

H.K. Tsang, C.S. Wong, T.K. Lang, 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 µm wavelength,” Appl. Phys. Lett. 3, 416–418 (2002).
[Crossref]

Spectra-Physics Telecom: “Model RL5 Raman Fiber Laser Specifications”.

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Figures (8)
Fig. 1
Fig. 1 Conversion efficiency, calculated from Eq. (4) using an effective pump power of 0.7 W at the input facet of the waveguide. The measured efficiency in the experiment is 1×10-5.

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Fig. 2
Fig. 2 Ratio of effective gain relative to SRS Raman gain, calculated from Eq. (6).

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Fig. 3
Fig. 3 Experimental setup used for observing CARS in silicon. F.- Pump laser filter. PBS.- Polarizing beam splitter. P(TM).- Polarizer to collect the TM0 mode from SOI waveguide. OSA.- Optical Spectrum Analyzer. ECDL.- External Cavity Diode Laser, to use as a signal, with a scan range from 1535 to 1550 nm. VOA.- Variable Optical Attenuator.

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Fig. 4
Fig. 4 Plot of the a-Stokes spectra collected for a given value of the signal (Stokes wavelength). The z-axis represents the Stokes/a-Stokes conversion efficiency, normalized to unity. Note the clear appearance of two “satellite” resonances, as mentioned in the text.

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Fig. 5.
Fig. 5. Integrated a-Stokes power signal vs. pump power, with the Stokes signal power fixed. The integration is carried out from 1323 to 1333 nm in the a-Stokes spectra (Fig. 4). The red triangles show clearly the a-Stokes amplification due to Stokes parametric down-conversion. The blue diamonds correspond to counter-propagating pump and Stokes signal in the waveguide. The crosses are the down-converted, spontaneous a-Stokes signal. The Stokes signal was set at 1542.3 nm and 300 µW of input power. The fit with Eq. (4) was performed using A = − 179 − 2.3 i . This corresponds to Δk ~ -27 cm-1.

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Fig. 6.
Fig. 6. Spectral dependence of the a-Stokes integrated power (as in Fig. 4), against Stokes wavelength, for different values of pump power. The solid lines are lorentzian fits to the data. Data fluctuation at high pump power in the region close to the Raman resonance (1542.3 nm) is most likely due to Fabry-Perot effects from the waveguide facets [11].

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Fig. 7.
Fig. 7. Stokes to a-Stokes conversion efficiency. The Stokes power was varied using the VOA shown in Fig. 3. The efficiency, defined as the slope of the plots shown, increases with pump power, as expected from Eq. (4).

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Fig. 8.
Fig. 8. Maximum amount of a-Stokes signal obtained, at 1328.8 nm. It was obtained by increasing the Stokes signal power up to ~ 5 mW effectively coupled into the waveguide.

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Equations (13)

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R ↔ 1 = 1 2 ( 0 0 1 0 0 1 1 1 0 ) ; R ↔ 2 = 1 2 ( 0 0 1 0 0 − 1 1 − 1 0 ) ; R ↔ 3 = ( 1 0 0 0 − 1 0 0 0 0 )
S ( Ω ) = S o ( Ω ) ∑ n = 1 , 2 , 3 ∣ e ̂ s · R ↔ n · e ̂ i ∣ 2 ,
Ω = ω p − ω s ; Ω 0 = 15.6 THz ,
g s ( Ω 0 ) = 8 π c 2 ω p ħ ω s 4 n 2 ( ω s ) ( N + 1 ) Δ ω S ( Ω 0 )
= − i 4 π χ R ( 3 ) ( Ω 0 ) ω 2 ( c 2 k )
= 3.7 × 10 − 8 cm W ,
R = 2 π χ NR ( 3 ) ω 2 ( c 2 k ) = 1.7 × 10 − 9 cm W .
E a S ( z ) = − i e i ( Δ k + R I p ) · z 2 · ( 2 R + i g s ( Ω ) ) I p · sinh A z 2 A · E S o .
Δ k = 2 k p TE − k S TM − k aS TM .
A = ( 2 R + i g s ( Ω ) ) I p · ( Δ k 2 ) − ( Δ k 2 ) 2 .
∣ Δ k ∣ ≫ ∣ 4 R + 2 g s ( Ω ) ∣ I p ,
∣ Δ k ∣ ≪ ∣ 4 R + 2 g s ( Ω ) ∣ I p .
∣ 4 R + 2 g s ( Ω ) ∣ I p = 2.1 cm − 1 .

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