Abstract

We report on measurements that show the strength of the spontaneous Raman scattering in strongly confining silicon waveguides to depend significantly on the propagation direction of the amplified signal wave with respect to the pump wave. Furthermore, the strength of this nonreciprocity depends on the orientation of the waveguide with respect to the crystallographic axes. We find that when changing the orientation from 〈011〉 to 〈001〉, the Raman-induced nonreciprocity increases by almost a factor of 3.

© 2010 OSA

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References

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  1. H. J. R. Dutton, Understanding Optical Communications (Upper Saddle River, NJ: Prentice Hall, 1998).
  2. B. Jalali, "Can silicon change photonics?" Phys. Stat. Solidi A 205, 213-224 (2008).
    [CrossRef]
  3. Z. Yu, and S. Fan, "Complete optical isolation created by indirect interband photonic transitions," Nat. Photonics 3, 91-94 (2009).
    [CrossRef]
  4. Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Jr., "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, 071117 (2008).
    [CrossRef]
  5. R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 15 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-11-15-1731.
    [CrossRef]
  6. H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170-174 (2008).
    [CrossRef]
  7. M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Electron. Lett. 44, 691-693 (2008).
    [CrossRef]
  8. M. Krause, H. Renner, and E. Brinkmeyer, "Raman lasers in silicon photonic wires: unidirectional ring lasing versus Fabry-Perot lasing," Electron. Lett. 45, 42-43 (2009).
    [CrossRef]
  9. M. Krause, H. Renner, and E. Brinkmeyer, "Strong enhancement of Raman-induced nonreciprocity in silicon waveguides by alignment with the crystallographic axes," Appl. Phys. Lett. 95, 261111 (2009).
    [CrossRef]
  10. M. Krause, H. Renner, and E. Brinkmeyer, "Non-Reciprocal Raman Gain in Suspended-Core and Nanowire Silica Optical Fibers," in "Conference on Lasers and Electro-Optics (CLEO)," (2010). Paper JWA39.
  11. P. Y. Yu, and M. Cardona, Fundamentals of Semiconductors (Springer-Verlag, 2005), 3rd ed.
    [CrossRef]
  12. A. W. Snyder, and J. D. Love, Optical Waveguide Theory (London: Chapman and Hall, 1983).
  13. T. Saito, K. Suto, T. Kimura, A. Watanabe, and J.-I. Nishizawa, "Backward and forward Raman scattering in highly efficient GaP Raman amplifier waveguides," J. Lumin. 87-89, 883-885 (2000).
    [CrossRef]
  14. T. Saito, K. Suto, J.-I. Nishizawa, and M. Kawasaki, "Spontaneous Raman scattering in [100], [110], and [11-2] directional GaP waveguides," J. Appl. Phys. 90, 1831-1835 (2001).
    [CrossRef]
  15. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, "Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
    [CrossRef]
  16. R. L. Espinola, J. I. Dadap, J. Richard, M. Osgood, S. J. McNab, and Y. A. Vlasov, "Raman amplification in ultrasmall silicon-on-insulator wire waveguides," Opt. Express 12, 16 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-12-16-3713.
    [CrossRef]
  17. R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, "Observation of Raman emission in silicon waveguides at 1.54μm," Opt. Express 10, 22 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-10-22-1305.
  18. J. I. Dadap, R. L. Espinola, J. R. M. Osgood, S. J. McNab, and Y. A. Vlasov, "Spontaneous Raman scattering in ultrasmall silicon waveguides," Opt. Lett. 29, 23 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=OL-29-23-2755.
    [CrossRef]

2009 (3)

Z. Yu, and S. Fan, "Complete optical isolation created by indirect interband photonic transitions," Nat. Photonics 3, 91-94 (2009).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Raman lasers in silicon photonic wires: unidirectional ring lasing versus Fabry-Perot lasing," Electron. Lett. 45, 42-43 (2009).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Strong enhancement of Raman-induced nonreciprocity in silicon waveguides by alignment with the crystallographic axes," Appl. Phys. Lett. 95, 261111 (2009).
[CrossRef]

2008 (4)

B. Jalali, "Can silicon change photonics?" Phys. Stat. Solidi A 205, 213-224 (2008).
[CrossRef]

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Jr., "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170-174 (2008).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Electron. Lett. 44, 691-693 (2008).
[CrossRef]

2006 (1)

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, "Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

2004 (2)

2003 (1)

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 15 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-11-15-1731.
[CrossRef]

2002 (1)

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, "Observation of Raman emission in silicon waveguides at 1.54μm," Opt. Express 10, 22 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-10-22-1305.

2001 (1)

T. Saito, K. Suto, J.-I. Nishizawa, and M. Kawasaki, "Spontaneous Raman scattering in [100], [110], and [11-2] directional GaP waveguides," J. Appl. Phys. 90, 1831-1835 (2001).
[CrossRef]

2000 (1)

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J.-I. Nishizawa, "Backward and forward Raman scattering in highly efficient GaP Raman amplifier waveguides," J. Lumin. 87-89, 883-885 (2000).
[CrossRef]

Ayre, M.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, "Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Baets, R.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, "Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Bienstman, P.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, "Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Bogaerts, W.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, "Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Brinkmeyer, E.

M. Krause, H. Renner, and E. Brinkmeyer, "Raman lasers in silicon photonic wires: unidirectional ring lasing versus Fabry-Perot lasing," Electron. Lett. 45, 42-43 (2009).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Strong enhancement of Raman-induced nonreciprocity in silicon waveguides by alignment with the crystallographic axes," Appl. Phys. Lett. 95, 261111 (2009).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Electron. Lett. 44, 691-693 (2008).
[CrossRef]

Claps, R.

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 15 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-11-15-1731.
[CrossRef]

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, "Observation of Raman emission in silicon waveguides at 1.54μm," Opt. Express 10, 22 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-10-22-1305.

Cohen, O.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170-174 (2008).
[CrossRef]

Dadap, J. I.

Dimitropoulos, D.

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 15 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-11-15-1731.
[CrossRef]

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, "Observation of Raman emission in silicon waveguides at 1.54μm," Opt. Express 10, 22 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-10-22-1305.

Espinola, R. L.

Fan, S.

Z. Yu, and S. Fan, "Complete optical isolation created by indirect interband photonic transitions," Nat. Photonics 3, 91-94 (2009).
[CrossRef]

Han, Y.

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 15 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-11-15-1731.
[CrossRef]

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, "Observation of Raman emission in silicon waveguides at 1.54μm," Opt. Express 10, 22 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-10-22-1305.

Hsieh, I.-W.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Jr., "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

Jalali, B.

B. Jalali, "Can silicon change photonics?" Phys. Stat. Solidi A 205, 213-224 (2008).
[CrossRef]

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 15 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-11-15-1731.
[CrossRef]

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, "Observation of Raman emission in silicon waveguides at 1.54μm," Opt. Express 10, 22 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-10-22-1305.

Kawasaki, M.

T. Saito, K. Suto, J.-I. Nishizawa, and M. Kawasaki, "Spontaneous Raman scattering in [100], [110], and [11-2] directional GaP waveguides," J. Appl. Phys. 90, 1831-1835 (2001).
[CrossRef]

Kimura, T.

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J.-I. Nishizawa, "Backward and forward Raman scattering in highly efficient GaP Raman amplifier waveguides," J. Lumin. 87-89, 883-885 (2000).
[CrossRef]

Krause, M.

M. Krause, H. Renner, and E. Brinkmeyer, "Raman lasers in silicon photonic wires: unidirectional ring lasing versus Fabry-Perot lasing," Electron. Lett. 45, 42-43 (2009).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Strong enhancement of Raman-induced nonreciprocity in silicon waveguides by alignment with the crystallographic axes," Appl. Phys. Lett. 95, 261111 (2009).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Electron. Lett. 44, 691-693 (2008).
[CrossRef]

Laere, F. V.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, "Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Lee, M.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170-174 (2008).
[CrossRef]

McNab, S. J.

Mizumoto, T.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Jr., "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

Nishizawa, J.-I.

T. Saito, K. Suto, J.-I. Nishizawa, and M. Kawasaki, "Spontaneous Raman scattering in [100], [110], and [11-2] directional GaP waveguides," J. Appl. Phys. 90, 1831-1835 (2001).
[CrossRef]

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J.-I. Nishizawa, "Backward and forward Raman scattering in highly efficient GaP Raman amplifier waveguides," J. Lumin. 87-89, 883-885 (2000).
[CrossRef]

Osgood, J. R. M.

Osgood, M.

R. L. Espinola, J. I. Dadap, J. Richard, M. Osgood, S. J. McNab, and Y. A. Vlasov, "Raman amplification in ultrasmall silicon-on-insulator wire waveguides," Opt. Express 12, 16 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-12-16-3713.
[CrossRef]

Osgood, R. M.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Jr., "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

Paniccia, M.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170-174 (2008).
[CrossRef]

Raday, O.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170-174 (2008).
[CrossRef]

Raghunathan, V.

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 15 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-11-15-1731.
[CrossRef]

Renner, H.

M. Krause, H. Renner, and E. Brinkmeyer, "Strong enhancement of Raman-induced nonreciprocity in silicon waveguides by alignment with the crystallographic axes," Appl. Phys. Lett. 95, 261111 (2009).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Raman lasers in silicon photonic wires: unidirectional ring lasing versus Fabry-Perot lasing," Electron. Lett. 45, 42-43 (2009).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Electron. Lett. 44, 691-693 (2008).
[CrossRef]

Richard, J.

R. L. Espinola, J. I. Dadap, J. Richard, M. Osgood, S. J. McNab, and Y. A. Vlasov, "Raman amplification in ultrasmall silicon-on-insulator wire waveguides," Opt. Express 12, 16 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-12-16-3713.
[CrossRef]

Rong, H.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170-174 (2008).
[CrossRef]

Saito, T.

T. Saito, K. Suto, J.-I. Nishizawa, and M. Kawasaki, "Spontaneous Raman scattering in [100], [110], and [11-2] directional GaP waveguides," J. Appl. Phys. 90, 1831-1835 (2001).
[CrossRef]

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J.-I. Nishizawa, "Backward and forward Raman scattering in highly efficient GaP Raman amplifier waveguides," J. Lumin. 87-89, 883-885 (2000).
[CrossRef]

Shoji, Y.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Jr., "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

Sih, V.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170-174 (2008).
[CrossRef]

Suto, K.

T. Saito, K. Suto, J.-I. Nishizawa, and M. Kawasaki, "Spontaneous Raman scattering in [100], [110], and [11-2] directional GaP waveguides," J. Appl. Phys. 90, 1831-1835 (2001).
[CrossRef]

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J.-I. Nishizawa, "Backward and forward Raman scattering in highly efficient GaP Raman amplifier waveguides," J. Lumin. 87-89, 883-885 (2000).
[CrossRef]

Taillaert, D.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, "Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Thourhout, D. V.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, "Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Vlasov, Y. A.

Watanabe, A.

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J.-I. Nishizawa, "Backward and forward Raman scattering in highly efficient GaP Raman amplifier waveguides," J. Lumin. 87-89, 883-885 (2000).
[CrossRef]

Xu, S.

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170-174 (2008).
[CrossRef]

Yokoi, H.

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Jr., "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

Yu, Z.

Z. Yu, and S. Fan, "Complete optical isolation created by indirect interband photonic transitions," Nat. Photonics 3, 91-94 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

Y. Shoji, T. Mizumoto, H. Yokoi, I.-W. Hsieh, and R. M. Osgood, Jr., "Magneto-optical isolator with silicon waveguides fabricated by direct bonding," Appl. Phys. Lett. 92, 071117 (2008).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Strong enhancement of Raman-induced nonreciprocity in silicon waveguides by alignment with the crystallographic axes," Appl. Phys. Lett. 95, 261111 (2009).
[CrossRef]

Electron. Lett. (2)

M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Electron. Lett. 44, 691-693 (2008).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, "Raman lasers in silicon photonic wires: unidirectional ring lasing versus Fabry-Perot lasing," Electron. Lett. 45, 42-43 (2009).
[CrossRef]

J. Appl. Phys. (1)

T. Saito, K. Suto, J.-I. Nishizawa, and M. Kawasaki, "Spontaneous Raman scattering in [100], [110], and [11-2] directional GaP waveguides," J. Appl. Phys. 90, 1831-1835 (2001).
[CrossRef]

J. Lumin. (1)

T. Saito, K. Suto, T. Kimura, A. Watanabe, and J.-I. Nishizawa, "Backward and forward Raman scattering in highly efficient GaP Raman amplifier waveguides," J. Lumin. 87-89, 883-885 (2000).
[CrossRef]

Jpn. J. Appl. Phys. (1)

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, "Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Nat. Photonics (2)

Z. Yu, and S. Fan, "Complete optical isolation created by indirect interband photonic transitions," Nat. Photonics 3, 91-94 (2009).
[CrossRef]

H. Rong, S. Xu, O. Cohen, O. Raday, M. Lee, V. Sih, and M. Paniccia, "A cascaded silicon Raman laser," Nat. Photonics 2, 170-174 (2008).
[CrossRef]

Opt. Express (3)

R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali, "Observation of stimulated Raman amplification in silicon waveguides," Opt. Express 11, 15 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-11-15-1731.
[CrossRef]

R. L. Espinola, J. I. Dadap, J. Richard, M. Osgood, S. J. McNab, and Y. A. Vlasov, "Raman amplification in ultrasmall silicon-on-insulator wire waveguides," Opt. Express 12, 16 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-12-16-3713.
[CrossRef]

R. Claps, D. Dimitropoulos, Y. Han, and B. Jalali, "Observation of Raman emission in silicon waveguides at 1.54μm," Opt. Express 10, 22 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-10-22-1305.

Opt. Lett. (1)

Phys. Stat. Solidi A (1)

B. Jalali, "Can silicon change photonics?" Phys. Stat. Solidi A 205, 213-224 (2008).
[CrossRef]

Other (4)

H. J. R. Dutton, Understanding Optical Communications (Upper Saddle River, NJ: Prentice Hall, 1998).

M. Krause, H. Renner, and E. Brinkmeyer, "Non-Reciprocal Raman Gain in Suspended-Core and Nanowire Silica Optical Fibers," in "Conference on Lasers and Electro-Optics (CLEO)," (2010). Paper JWA39.

P. Y. Yu, and M. Cardona, Fundamentals of Semiconductors (Springer-Verlag, 2005), 3rd ed.
[CrossRef]

A. W. Snyder, and J. D. Love, Optical Waveguide Theory (London: Chapman and Hall, 1983).

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Figures (5)

Fig. 1.
Fig. 1.

Measurement setup: light generated by spontaneous Raman scattering propagates in both directions of a silicon waveguide.

Fig. 2.
Fig. 2.

Silicon photonic wire with 〈001〉- and 〈011〉-oriented sections.

Fig. 3.
Fig. 3.

(a) Forward, and (b) backward spontaneous Stokes spectra for three different nominal pump powers P 0 in a 5-mm-long 〈011〉 waveguide. Solid curves: experimental data; dashed curves: fit (Lorentzian and offset).

Fig. 4.
Fig. 4.

Stars: pump power transmitted through a 5-mm-long 〈011〉 waveguide versus nominal pump-laser power P 0. Circles and crosses: corresponding forward and backward spontaneous Raman powers, respectively. Lines are zero-offset linear fits to the experimental data. The laser used did not permit setting its output power P lower than 80mW.

Fig. 5.
Fig. 5.

Measured data for 27 waveguides from the same chip (five groups of nominally identical waveguides; layout sketched above each group, not to scale). Squares: measured SpRS imbalance I = ρ · Iα . Crosses: loss-induced imbalance Iα , assuming 3.5dB/cm waveguide loss. Diamonds: sought-after Raman nonreciprocity ρ = q /q + = I/Iα .

Equations (16)

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Γ = g n p n s 4 Z 2 N p N s Si { p 2 s 2 + p · s 2 2 ( s x p x ) 2
1 2 ( cos 4 θ + 3 ) [ ( s y p y ) 2 + ( s z p z ) 2 ] 1 2 ( cos 4 θ 1 ) [ ( s y p y ) 2 + ( s z p y ) 2 ] } d A ,
d S f ( z ) d z = α S f ( z ) + q + ( z ) · P f ( z ) + q ( z ) · P b ( z ) ,
d S b ( z ) d z = α S b ( z ) + q ( z ) · P f ( z ) + q + ( z ) · P b ( z ) ,
S f ( 0 ) = 0 ,
S b ( ) = 0 .
P f ( z ) = η P L · P 0 exp ( α z ) ,
P b ( z ) = η P R · P 0 exp { α ( z ) } .
S L L = η S L · S b ( 0 ) = η S L η P L · P 0 · 0 q ( z ) · exp ( 2 α z ) d z ,
S R L = η S R · S f ( ) = η S R η P L · P 0 · exp ( α z ) 0 q + ( z ) d z ,
S R R = η S R · S f ( ) = η S R η P R · P 0 · 0 q ( z ) · exp ( 2 α z ) d z ,
S L R = η S L · S b ( 0 ) = η S L η P R · P 0 · exp ( α z ) 0 q + ( z ) d z .
I = S L L · S R R S R L · S L R = exp ( α ) · 0 q ( z ) · exp ( 2 α z ) d z 0 q ( z ) · exp ( 2 α z ) d z 0 q + ( z ) d z ,
I = I α · ρ .
I α = 1 exp ( 2 α ) 2 α · exp ( α ) = sinh α α
ρ = q q +

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