Abstract

Computational studies are used to show that the crystalline structure of Si causes the waveguide Kerr effective nonlinearity, γ, to vary by 10% for in-plane variation of the orientation of a silicon nanowire waveguide (SiNWG) fabricated on a standard silicon-on-insulator wafer. Our analysis shows that this angular dependence of γ can be employed to form a nonlinear Kerr grating in dimensionally uniform SiNWGs based on either ring resonators or cascaded waveguide bends. The magnitude of the nonlinear index variation in these gratings is found to be sufficient for phase matching in four-wave mixing and other optical parametric processes.

© 2011 Optical Society of America

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  1. R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., IEEE Photon. Technol. Lett. 14, 65 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
  3. R. M. Osgood, Jr., N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. Hsieh, E. Dulkeith, W. M. Green, and Y. A. Vlasov, Adv. Opt. Photon. 1, 162 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. D. G. Rabus, Integrated Ring Resonators, Vol. 127 of Springer Series in Optical Sciences (Springer, 2007).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010

N. Vermeulen, J. E. Sipe, and H. Thienpont, IEEE Photon. Technol. Lett. 22, 1796 (2010).
[CrossRef]

N. C. Panoiu, J. F. McMillan, and C. W. Wong, IEEE J. Sel. Top. Quantum Electron. 16, 257 (2010).
[CrossRef]

J. O’Dowd, W. H. Guo, M. Lynch, E. Flood, A. L. Bradley, and J. F. Donegan, Electron. Lett. 46, 854 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Jr., Y. A. Vlasov, and W. M. J. Green, Nat. Photon. 4, 557 (2010).
[CrossRef]

M. P. Chethiya, M. Dissanayake, I. D. Rukhlenko, and G. P. Agrawal, Opt. Express 18, 21427 (2010).
[CrossRef]

2009

2008

Q. F. Xu, D. Fattal, and R. G. Beausoleil, Opt. Express 16, 4309 (2008).
[CrossRef] [PubMed]

M. Krause, H. Renner, and E. Brinkmeyer, Electron. Lett. 44, 691 (2008).
[CrossRef]

2007

2006

X. G. Chen, N. C. Panoiu, and R. M. Osgood, Jr., IEEE J. Quantum Electron. 42, 160 (2006).
[CrossRef]

2004

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, Appl. Phys. Lett. 85, 3346 (2004).
[CrossRef]

Y. A. Vlasov and S. J. McNab, Opt. Express 12, 1622 (2004).
[CrossRef] [PubMed]

2003

M. Dinu, F. Quochi, and H. Garcia, Appl. Phys. Lett. 82, 2954 (2003).
[CrossRef]

2002

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

2001

1996

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Agrawal, G. P.

M. P. Chethiya, M. Dissanayake, I. D. Rukhlenko, and G. P. Agrawal, Opt. Express 18, 21427 (2010).
[CrossRef]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, Appl. Phys. Lett. 91, 071113 (2007).
[CrossRef]

Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007).
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Elsevier, 2007).

Ahmad, R. U.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Baehr-Jones, T.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, Appl. Phys. Lett. 85, 3346 (2004).
[CrossRef]

Beausoleil, R. G.

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Boyd, R. W.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, Appl. Phys. Lett. 91, 071113 (2007).
[CrossRef]

Boyraz, O.

Bradley, A. L.

J. O’Dowd, W. H. Guo, M. Lynch, E. Flood, A. L. Bradley, and J. F. Donegan, Electron. Lett. 46, 854 (2010).
[CrossRef]

Brinkmeyer, E.

M. Krause, H. Renner, and E. Brinkmeyer, Electron. Lett. 44, 691 (2008).
[CrossRef]

Camarda, G. S.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Chen, X.

Chen, X. G.

X. G. Chen, N. C. Panoiu, and R. M. Osgood, Jr., IEEE J. Quantum Electron. 42, 160 (2006).
[CrossRef]

Chethiya, M. P.

Dadap, J. I.

Debaes, C.

N. Vermeulen, J. E. Sipe, C. Debaes, and H. Thienpont, in 2010 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2010), pp. 92–93.
[CrossRef]

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, Appl. Phys. Lett. 82, 2954 (2003).
[CrossRef]

Dissanayake, M.

Donegan, J. F.

J. O’Dowd, W. H. Guo, M. Lynch, E. Flood, A. L. Bradley, and J. F. Donegan, Electron. Lett. 46, 854 (2010).
[CrossRef]

Driscoll, J. B.

Dulkeith, E.

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Espinola, R. L.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Fattal, D.

Fauchet, P. M.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, Appl. Phys. Lett. 91, 071113 (2007).
[CrossRef]

Flood, E.

J. O’Dowd, W. H. Guo, M. Lynch, E. Flood, A. L. Bradley, and J. F. Donegan, Electron. Lett. 46, 854 (2010).
[CrossRef]

Foster, M. A.

Gaeta, A. L.

Garcia, H.

M. Dinu, F. Quochi, and H. Garcia, Appl. Phys. Lett. 82, 2954 (2003).
[CrossRef]

Green, W. M.

Green, W. M. J.

X. Liu, R. M. Osgood, Jr., Y. A. Vlasov, and W. M. J. Green, Nat. Photon. 4, 557 (2010).
[CrossRef]

Guo, W. H.

J. O’Dowd, W. H. Guo, M. Lynch, E. Flood, A. L. Bradley, and J. F. Donegan, Electron. Lett. 46, 854 (2010).
[CrossRef]

Hochberg, M.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, Appl. Phys. Lett. 85, 3346 (2004).
[CrossRef]

Hsieh, I.

Hsieh, I. W.

Islam, M. N.

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Kim, J.

Krause, M.

M. Krause, H. Renner, and E. Brinkmeyer, Electron. Lett. 44, 691 (2008).
[CrossRef]

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Lim, J. H.

Lin, Q.

Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007).
[CrossRef] [PubMed]

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, Appl. Phys. Lett. 91, 071113 (2007).
[CrossRef]

Lipson, M.

Liu, X.

Liu, X. P.

Lynch, M.

J. O’Dowd, W. H. Guo, M. Lynch, E. Flood, A. L. Bradley, and J. F. Donegan, Electron. Lett. 46, 854 (2010).
[CrossRef]

McMillan, J. F.

N. C. Panoiu, J. F. McMillan, and C. W. Wong, IEEE J. Sel. Top. Quantum Electron. 16, 257 (2010).
[CrossRef]

McNab, S. J.

O’Dowd, J.

J. O’Dowd, W. H. Guo, M. Lynch, E. Flood, A. L. Bradley, and J. F. Donegan, Electron. Lett. 46, 854 (2010).
[CrossRef]

Osgood, R. M.

X. Liu, R. M. Osgood, Jr., Y. A. Vlasov, and W. M. J. Green, Nat. Photon. 4, 557 (2010).
[CrossRef]

R. M. Osgood, Jr., N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. Hsieh, E. Dulkeith, W. M. Green, and Y. A. Vlasov, Adv. Opt. Photon. 1, 162 (2009).
[CrossRef]

J. B. Driscoll, X. P. Liu, S. Yasseri, I. Hsieh, J. I. Dadap, and R. M. Osgood, Jr., Opt. Express 17, 2797 (2009).
[CrossRef] [PubMed]

X. G. Chen, N. C. Panoiu, and R. M. Osgood, Jr., IEEE J. Quantum Electron. 42, 160 (2006).
[CrossRef]

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Painter, O. J.

Panoiu, N. C.

N. C. Panoiu, J. F. McMillan, and C. W. Wong, IEEE J. Sel. Top. Quantum Electron. 16, 257 (2010).
[CrossRef]

R. M. Osgood, Jr., N. C. Panoiu, J. I. Dadap, X. Liu, X. Chen, I. W. Hsieh, E. Dulkeith, W. M. Green, and Y. A. Vlasov, Adv. Opt. Photon. 1, 162 (2009).
[CrossRef]

X. G. Chen, N. C. Panoiu, and R. M. Osgood, Jr., IEEE J. Quantum Electron. 42, 160 (2006).
[CrossRef]

Piredda, G.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, Appl. Phys. Lett. 91, 071113 (2007).
[CrossRef]

Pizzuto, F.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Quochi, F.

M. Dinu, F. Quochi, and H. Garcia, Appl. Phys. Lett. 82, 2954 (2003).
[CrossRef]

Rabus, D. G.

D. G. Rabus, Integrated Ring Resonators, Vol. 127 of Springer Series in Optical Sciences (Springer, 2007).

Rao, H.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

Renner, H.

M. Krause, H. Renner, and E. Brinkmeyer, Electron. Lett. 44, 691 (2008).
[CrossRef]

Rukhlenko, I. D.

Salem, R.

Scherer, A.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, Appl. Phys. Lett. 85, 3346 (2004).
[CrossRef]

Sipe, J. E.

N. Vermeulen, J. E. Sipe, and H. Thienpont, IEEE Photon. Technol. Lett. 22, 1796 (2010).
[CrossRef]

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

N. Vermeulen, J. E. Sipe, C. Debaes, and H. Thienpont, in 2010 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2010), pp. 92–93.
[CrossRef]

Thienpont, H.

N. Vermeulen, J. E. Sipe, and H. Thienpont, IEEE Photon. Technol. Lett. 22, 1796 (2010).
[CrossRef]

N. Vermeulen, J. E. Sipe, C. Debaes, and H. Thienpont, in 2010 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2010), pp. 92–93.
[CrossRef]

Turner, A. C.

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

Vermeulen, N.

N. Vermeulen, J. E. Sipe, and H. Thienpont, IEEE Photon. Technol. Lett. 22, 1796 (2010).
[CrossRef]

N. Vermeulen, J. E. Sipe, C. Debaes, and H. Thienpont, in 2010 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2010), pp. 92–93.
[CrossRef]

Vlasov, Y. A.

Walker, C.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, Appl. Phys. Lett. 85, 3346 (2004).
[CrossRef]

Wong, C. W.

N. C. Panoiu, J. F. McMillan, and C. W. Wong, IEEE J. Sel. Top. Quantum Electron. 16, 257 (2010).
[CrossRef]

Xu, Q. F.

Yasseri, S.

Zhang, J.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, Appl. Phys. Lett. 91, 071113 (2007).
[CrossRef]

Adv. Opt. Photon.

Appl. Phys. Lett.

J. Zhang, Q. Lin, G. Piredda, R. W. Boyd, G. P. Agrawal, and P. M. Fauchet, Appl. Phys. Lett. 91, 071113 (2007).
[CrossRef]

M. Dinu, F. Quochi, and H. Garcia, Appl. Phys. Lett. 82, 2954 (2003).
[CrossRef]

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, Appl. Phys. Lett. 85, 3346 (2004).
[CrossRef]

Electron. Lett.

J. O’Dowd, W. H. Guo, M. Lynch, E. Flood, A. L. Bradley, and J. F. Donegan, Electron. Lett. 46, 854 (2010).
[CrossRef]

M. Krause, H. Renner, and E. Brinkmeyer, Electron. Lett. 44, 691 (2008).
[CrossRef]

IEEE J. Quantum Electron.

X. G. Chen, N. C. Panoiu, and R. M. Osgood, Jr., IEEE J. Quantum Electron. 42, 160 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

N. C. Panoiu, J. F. McMillan, and C. W. Wong, IEEE J. Sel. Top. Quantum Electron. 16, 257 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., IEEE Photon. Technol. Lett. 14, 65 (2002).
[CrossRef]

N. Vermeulen, J. E. Sipe, and H. Thienpont, IEEE Photon. Technol. Lett. 22, 1796 (2010).
[CrossRef]

J. Lightwave Technol.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, J. Lightwave Technol. 14, 58 (1996).
[CrossRef]

J. Kim, O. Boyraz, J. H. Lim, and M. N. Islam, J. Lightwave Technol. 19, 247 (2001).
[CrossRef]

Nat. Photon.

X. Liu, R. M. Osgood, Jr., Y. A. Vlasov, and W. M. J. Green, Nat. Photon. 4, 557 (2010).
[CrossRef]

Opt. Express

Other

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Elsevier, 2007).

N. Vermeulen, J. E. Sipe, C. Debaes, and H. Thienpont, in 2010 IEEE Photonics Society Summer Topical Meeting Series (IEEE, 2010), pp. 92–93.
[CrossRef]

D. G. Rabus, Integrated Ring Resonators, Vol. 127 of Springer Series in Optical Sciences (Springer, 2007).

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Figures (3)

Fig. 1
Fig. 1

(a) Initial orientation of SiNWG with respect to Si crystal, (b) γ versus Si crystal rotation (about the [ 001 ] direction) for a 220 nm × 500 nm SiNWG at λ = 1.55 μm . χ 1111 ( 3 ) / χ 1122 ( 3 ) = 2 , 2.15, 2.36, 2.75, and 3 are considered.

Fig. 2
Fig. 2

Nonlinear optical grating on-chip via (a) ring resonator or (b) CWBs. (c)  Δ n (as defined in inset) experienced by the pump formed by nonlinear grating versus P p . A copropagating signal would experience 2 Δ n due to cross-phase modulation [4]. (d)  Δ β compensated by a grating formed in a ring resonator or CWBs of varying R. Points 1, 2, and 3 give examples of phase matching with a 100 mW pump at λ p = 1.55 μm and R, λ s , and λ i of (1) 20.7, 2, and 1.265 μm ; (2) 100, 1.714, and 1.415 μm ; and (3) 900, 1.601, and 1.502 μm , respectively.

Fig. 3
Fig. 3

Conversion efficiency for varying λ s in CWBs with R = 47.98 μm and λ p = 1.55 μm . A 12 dB enhancement occurs for λ s = 1.78 μm . The inset plots the conversion efficiency enhancement as a function of pump power.

Equations (3)

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

Γ = A 0 A 0 e * ( ω ) · χ ( 3 ) ( r ; ω , ω , ω , ω ) e ( ω ) e * ( ω ) e ( ω ) d A ( A n 2 ( r ; ω ) | e ( r ; ω ) | 2 d A ) 2 ,
γ = ( 3 ω Γ ) / ( 4 ϵ 0 A 0 v g 2 ) ,
Λ NL = π R / 2 ,

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