Abstract

Coupled-mode theory is used to calculate Raman gain and spontaneous efficiency in silicon waveguides with cross-sectional areas ranging from 0.16 to 16 µm2. We find a monotonic increase in the Raman gain as the waveguide cross section decreases for the range of dimensions considered. It is also found that mode coupling between the Stokes modes is insignificant, and thus polarization multiplexing is possible. The results also demonstrate that for submicrometer waveguide dimensions the Einstein relation between spontaneous efficiency and stimulated gain no longer holds.

© 2003 Optical Society of America

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  1. R. Claps, D. Dimitropoulos, and B. Jalali, Electron. Lett. 38, 1352 (2002).
    [CrossRef]
  2. R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, Opt. Express 10, 1303 (2002), http://www.opticsexpress.org.
    [CrossRef]
  3. T. Saito, K. Suto, T. Kimura, A. Watanabe, and J. Nishizawa, J. Appl. Phys. 87, 3399 (2000).
    [CrossRef]
  4. K. Suto, T. Saito, T. Kimura, J. Nishizawa, and J. Lightwave Technol. 20, 705 (2002).
    [CrossRef]
  5. P. A. Temple and C. E. Hathaway, Phys. Rev. A 7, 3685 (1973).
  6. M. Cardona, in Light Scattering in Solids II, M. Cardona and G. Guntherodt, eds. (Springer-Verlag, Berlin, 1982), pp. 19–178.
    [CrossRef]
  7. J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
    [CrossRef]
  8. J. M. Ralston and R. K. Chang, Phys. Rev. B 2, 1858 (1970).
    [CrossRef]
  9. Y. R. Shen and N. Bloembergen, Phys. Rev. A 137, 1787 (1965).
    [CrossRef]
  10. A. Yariv, Quantum Electronics (Wiley, New York, 1984).
  11. R. A. Soref, J. Schmidtchen, and K. Petermann, IEEE J. Quantum Electron. 27, 1971 (1991).
    [CrossRef]
  12. D. H. Choi and W. J. R. Hoefer, IEEE Trans. Microwave Theory Tech. 35, 1464 (1986).
    [CrossRef]
  13. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford U. Press, Oxford, England, 2000).

2002 (3)

R. Claps, D. Dimitropoulos, and B. Jalali, Electron. Lett. 38, 1352 (2002).
[CrossRef]

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, Opt. Express 10, 1303 (2002), http://www.opticsexpress.org.
[CrossRef]

K. Suto, T. Saito, T. Kimura, J. Nishizawa, and J. Lightwave Technol. 20, 705 (2002).
[CrossRef]

2000 (1)

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J. Nishizawa, J. Appl. Phys. 87, 3399 (2000).
[CrossRef]

1991 (1)

R. A. Soref, J. Schmidtchen, and K. Petermann, IEEE J. Quantum Electron. 27, 1971 (1991).
[CrossRef]

1986 (1)

D. H. Choi and W. J. R. Hoefer, IEEE Trans. Microwave Theory Tech. 35, 1464 (1986).
[CrossRef]

1975 (1)

J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
[CrossRef]

1973 (1)

P. A. Temple and C. E. Hathaway, Phys. Rev. A 7, 3685 (1973).

1970 (1)

J. M. Ralston and R. K. Chang, Phys. Rev. B 2, 1858 (1970).
[CrossRef]

1965 (1)

Y. R. Shen and N. Bloembergen, Phys. Rev. A 137, 1787 (1965).
[CrossRef]

Bloembergen, N.

Y. R. Shen and N. Bloembergen, Phys. Rev. A 137, 1787 (1965).
[CrossRef]

Cardona, M.

J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
[CrossRef]

M. Cardona, in Light Scattering in Solids II, M. Cardona and G. Guntherodt, eds. (Springer-Verlag, Berlin, 1982), pp. 19–178.
[CrossRef]

Chang, R. K.

J. M. Ralston and R. K. Chang, Phys. Rev. B 2, 1858 (1970).
[CrossRef]

Choi, D. H.

D. H. Choi and W. J. R. Hoefer, IEEE Trans. Microwave Theory Tech. 35, 1464 (1986).
[CrossRef]

Claps, R.

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, Opt. Express 10, 1303 (2002), http://www.opticsexpress.org.
[CrossRef]

R. Claps, D. Dimitropoulos, and B. Jalali, Electron. Lett. 38, 1352 (2002).
[CrossRef]

Dimitropoulos, D.

R. Claps, D. Dimitropoulos, and B. Jalali, Electron. Lett. 38, 1352 (2002).
[CrossRef]

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, Opt. Express 10, 1303 (2002), http://www.opticsexpress.org.
[CrossRef]

Han, Y.

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, Opt. Express 10, 1303 (2002), http://www.opticsexpress.org.
[CrossRef]

Hathaway, C. E.

P. A. Temple and C. E. Hathaway, Phys. Rev. A 7, 3685 (1973).

Hoefer, W. J. R.

D. H. Choi and W. J. R. Hoefer, IEEE Trans. Microwave Theory Tech. 35, 1464 (1986).
[CrossRef]

Jalali, B.

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, Opt. Express 10, 1303 (2002), http://www.opticsexpress.org.
[CrossRef]

R. Claps, D. Dimitropoulos, and B. Jalali, Electron. Lett. 38, 1352 (2002).
[CrossRef]

Kimura, T.

K. Suto, T. Saito, T. Kimura, J. Nishizawa, and J. Lightwave Technol. 20, 705 (2002).
[CrossRef]

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J. Nishizawa, J. Appl. Phys. 87, 3399 (2000).
[CrossRef]

Loudon, R.

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford U. Press, Oxford, England, 2000).

Nishizawa, J.

K. Suto, T. Saito, T. Kimura, J. Nishizawa, and J. Lightwave Technol. 20, 705 (2002).
[CrossRef]

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J. Nishizawa, J. Appl. Phys. 87, 3399 (2000).
[CrossRef]

Petermann, K.

R. A. Soref, J. Schmidtchen, and K. Petermann, IEEE J. Quantum Electron. 27, 1971 (1991).
[CrossRef]

Ralston, J. M.

J. M. Ralston and R. K. Chang, Phys. Rev. B 2, 1858 (1970).
[CrossRef]

Renucci, J. B.

J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
[CrossRef]

Saito, T.

K. Suto, T. Saito, T. Kimura, J. Nishizawa, and J. Lightwave Technol. 20, 705 (2002).
[CrossRef]

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J. Nishizawa, J. Appl. Phys. 87, 3399 (2000).
[CrossRef]

Schmidtchen, J.

R. A. Soref, J. Schmidtchen, and K. Petermann, IEEE J. Quantum Electron. 27, 1971 (1991).
[CrossRef]

Shen, Y. R.

Y. R. Shen and N. Bloembergen, Phys. Rev. A 137, 1787 (1965).
[CrossRef]

Soref, R. A.

R. A. Soref, J. Schmidtchen, and K. Petermann, IEEE J. Quantum Electron. 27, 1971 (1991).
[CrossRef]

Suto, K.

K. Suto, T. Saito, T. Kimura, J. Nishizawa, and J. Lightwave Technol. 20, 705 (2002).
[CrossRef]

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J. Nishizawa, J. Appl. Phys. 87, 3399 (2000).
[CrossRef]

Temple, P. A.

P. A. Temple and C. E. Hathaway, Phys. Rev. A 7, 3685 (1973).

Tyte, R. N.

J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
[CrossRef]

Watanabe, A.

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J. Nishizawa, J. Appl. Phys. 87, 3399 (2000).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1984).

Electron. Lett. (1)

R. Claps, D. Dimitropoulos, and B. Jalali, Electron. Lett. 38, 1352 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. A. Soref, J. Schmidtchen, and K. Petermann, IEEE J. Quantum Electron. 27, 1971 (1991).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

D. H. Choi and W. J. R. Hoefer, IEEE Trans. Microwave Theory Tech. 35, 1464 (1986).
[CrossRef]

J. Appl. Phys. (1)

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J. Nishizawa, J. Appl. Phys. 87, 3399 (2000).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (1)

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, Opt. Express 10, 1303 (2002), http://www.opticsexpress.org.
[CrossRef]

Phys. Rev. B (1)

J. B. Renucci, R. N. Tyte, and M. Cardona, Phys. Rev. B 11, 3885 (1975).
[CrossRef]

Phys. Rev. A (2)

P. A. Temple and C. E. Hathaway, Phys. Rev. A 7, 3685 (1973).

Y. R. Shen and N. Bloembergen, Phys. Rev. A 137, 1787 (1965).
[CrossRef]

Phys. Rev. B (1)

J. M. Ralston and R. K. Chang, Phys. Rev. B 2, 1858 (1970).
[CrossRef]

Other (3)

M. Cardona, in Light Scattering in Solids II, M. Cardona and G. Guntherodt, eds. (Springer-Verlag, Berlin, 1982), pp. 19–178.
[CrossRef]

A. Yariv, Quantum Electronics (Wiley, New York, 1984).

R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford U. Press, Oxford, England, 2000).

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Figures (1)

Fig. 1
Fig. 1

Rib-waveguide geometry.

Tables (1)

Tables Icon

Table 1 Coupling Coefficients and Spontaneous Efficiency for a Rib Waveguide with w/h=2/1.4 and w/H=2/2.15

Equations (13)

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

P1ωs=0χRR1·Eωp,  P2ωs=0χRR2·Eωp,  P3ωs=0χRR3·Eωp,
R1=12001001110,  R2=1200100-11-10,  R3=1000-10000.
S=S0n=1,2,3eˆs·Rn·eˆi2,  S0=k0432π2nVχR2,
χjkmn3i=1,2,3RijkRimn.
PiNLωs=0χijmn3EjωpEm-ωpEnωs.
Eωs=μ=1,2As,μyμωs,x,zexpjβμy,  As,10=aPs,  As,20=1-aPs,  Eωp=Ap,1y1ωp,x,zexpjβ1λpy,  Ap,10=Pp,
dAs,1dy=iκ11PpAs,1+iκ12PpAs,2 expiβ2-β1y,  dAs,2dy=iκ22PpAs,2+iκ21PpAs,1 exp-iβ2-β1y,
κμμ=-ji,j,m,n=1,2,34Z2gR2ξijmnμiωs*1jωp×1mωp*μnωsdxdz,
dAs,μ,λdy=iκμ,λAp,
κμ,λ=ωs0χRμωs*·Rλ·1ωpdxdz.
Sμ=1lAs,μ2Ap2=lκμ,12+κμ,22+κμ,32.
Sμ=S032π2k04ω202×λ=1,2,3μωs*·Rλ·1ωpdxdy2Aeff.
Aeff=1ωp2dxdz21ωp4dxdz.

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