Abstract

We present a quantum-mechanical theory to describe narrow-band photon-pair generation via four-wave mixing in a Silicon-on-Insulator (SOI) micro-resonator. We also provide design principles for efficient photon-pair generation in an SOI micro-resonator through extensive numerical simulations. Microring cavities are shown to have a much wider dispersion-compensated frequency range than straight cavities. A microring with an inner radius of 8 μm can output an entangled photon comb of 21 pairwise-correlated peaks (42 comb lines) spanning from 1.3 μm to 1.8 μm. Such on-chip quantum photonic devices offer a path toward future integrated quantum photonics and quantum integrated circuits.

© 2011 Optical Society of America

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  13. J. Chen, A. Pearlman, A. Ling, J. Fan, and A. Migdall, “A versatile waveguide source of photon pairs for chipscale quantum information processing,” Opt. Express 17, 6727 (2009).
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    [CrossRef]
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  23. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15, 16604 (2007).
    [CrossRef] [PubMed]
  24. We note that the optical modes in our proposed microring resonators are not ideal whispering gallery modes, in the sense that the modes have non-zero interatction with the inner wall of the ring resonators. However, the electric field strength at the inner wall is typically no more than 1% of its peak value near the outer wall (see Fig. 2). Even though this interaction is negligibly small, we used the numerically determined modes in our calculations, rather than analytical expressions of ideal whispering gallery modes. We still refer to our modes as whispering gallery modes throughout the text, but we recognize this is an approximation.
  25. M. Scholtz, L. Koch, and O. Benson, “Analytical treatment of spectral properties and signal-idler intensity correlations for a double-resonant optical parametric oscillator far below threshold,” Opt. Commun. 282, 3518 (2009).
    [CrossRef]
  26. J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82, 2594 (1999).
    [CrossRef]
  27. C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304 (2000).
    [CrossRef] [PubMed]
  28. S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
    [CrossRef]
  29. L. Olislager, J. Cussey, A. T. Nguyen, P. Emplit, S. Massar, J.-M. Merolla, and K. P. Huy, “Frequency-bin entangled photons,” Phys. Rev. A 82, 013804 (2010).
    [CrossRef]
  30. L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295 (2006).
    [CrossRef] [PubMed]
  31. A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguide,” Opt. Express 14, 4357 (2006).
    [CrossRef] [PubMed]
  32. 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, 1904 (2010).
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    [CrossRef]
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  35. http://www.comsol.com
  36. Certain trade names and company products are mentioned in the text or identified in an illustration in order to specify adequately the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it necessarily imply that the products are the best available for the purpose.
  37. 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, 10596 (2008).
    [CrossRef] [PubMed]
  38. I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
    [CrossRef]
  39. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theory Tech. 55, 1209 (2007).
    [CrossRef]
  40. Private communications with M. Oxborrow and P. Del’Haye,

2010 (3)

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302 (2010).
[CrossRef]

L. Olislager, J. Cussey, A. T. Nguyen, P. Emplit, S. Massar, J.-M. Merolla, and K. P. Huy, “Frequency-bin entangled photons,” Phys. Rev. A 82, 013804 (2010).
[CrossRef]

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, 1904 (2010).

2009 (5)

M. Scholtz, L. Koch, and O. Benson, “Analytical treatment of spectral properties and signal-idler intensity correlations for a double-resonant optical parametric oscillator far below threshold,” Opt. Commun. 282, 3518 (2009).
[CrossRef]

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[CrossRef]

J. Chen, A. Pearlman, A. Ling, J. Fan, and A. Migdall, “A versatile waveguide source of photon pairs for chipscale quantum information processing,” Opt. Express 17, 6727 (2009).
[CrossRef] [PubMed]

T. Zhong, F. N. C. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fibercoupled periodically poled KTiOPO4 waveguide,” Opt. Express 17, 12019 (2009).
[CrossRef] [PubMed]

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558 (2009).
[CrossRef] [PubMed]

2008 (5)

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, 4881 (2008).
[CrossRef] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon waveguide quantum circuits,” Science 320, 646 (2008).
[CrossRef] [PubMed]

H. J. Kimble, “The quantum internet,” Nature 453, 1023 (2008).
[CrossRef] [PubMed]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368 (2008).
[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, 10596 (2008).
[CrossRef] [PubMed]

2007 (4)

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[CrossRef]

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theory Tech. 55, 1209 (2007).
[CrossRef]

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

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479 (2007).
[CrossRef] [PubMed]

2006 (4)

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388 (2006).
[CrossRef] [PubMed]

Q. Lin, and G. P. Agrawal, “Silicon waveguides for creating quantum-correlated photon pairs,” Opt. Lett. 31, 3140 (2006).
[CrossRef] [PubMed]

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguide,” Opt. Express 14, 4357 (2006).
[CrossRef] [PubMed]

2005 (4)

J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Phys. Rev. A 72, 033801 (2005).
[CrossRef]

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-Fiber Source of Polarization-Entangled Photons in the 1550 nm Telecom Band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

J. Fan, A. Migdall, and L. J. Wang, “Efficient generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. 30, 3368 (2005).
[CrossRef]

J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534 (2005).
[CrossRef] [PubMed]

2004 (1)

. H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802(R) (2004).
[CrossRef]

2002 (1)

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983 (2002).
[CrossRef]

2001 (1)

K. Banaszek, “A. B. U’Ren, and I. A.Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett. 26, 1367 (2001).
[CrossRef]

2000 (2)

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554 (2000).
[CrossRef]

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

1999 (1)

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82, 2594 (1999).
[CrossRef]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

1993 (1)

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Type-II Parametric Down-conversion,” Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

1975 (1)

M. Heiblum, and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75 (1975).
[CrossRef]

Absil, P. P.

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554 (2000).
[CrossRef]

Agha, I. H.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Agrawal, G. P.

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

Q. Lin, and G. P. Agrawal, “Silicon waveguides for creating quantum-correlated photon pairs,” Opt. Lett. 31, 3140 (2006).
[CrossRef] [PubMed]

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295 (2006).
[CrossRef] [PubMed]

Alley, C. O.

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Type-II Parametric Down-conversion,” Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

Baets, R. G.

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558 (2009).
[CrossRef] [PubMed]

Banaszek, K.

K. Banaszek, “A. B. U’Ren, and I. A.Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett. 26, 1367 (2001).
[CrossRef]

Battle, P.

T. Zhong, F. N. C. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fibercoupled periodically poled KTiOPO4 waveguide,” Opt. Express 17, 12019 (2009).
[CrossRef] [PubMed]

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479 (2007).
[CrossRef] [PubMed]

Beausoleil, R. G.

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479 (2007).
[CrossRef] [PubMed]

Benson, O.

M. Scholtz, L. Koch, and O. Benson, “Analytical treatment of spectral properties and signal-idler intensity correlations for a double-resonant optical parametric oscillator far below threshold,” Opt. Commun. 282, 3518 (2009).
[CrossRef]

Bogaerts, W.

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558 (2009).
[CrossRef] [PubMed]

Brendel, J.

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82, 2594 (1999).
[CrossRef]

Chen, J.

J. Chen, A. Pearlman, A. Ling, J. Fan, and A. Migdall, “A versatile waveguide source of photon pairs for chipscale quantum information processing,” Opt. Express 17, 6727 (2009).
[CrossRef] [PubMed]

J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Phys. Rev. A 72, 033801 (2005).
[CrossRef]

Cho, P. S.

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554 (2000).
[CrossRef]

Clemmen, S.

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558 (2009).
[CrossRef] [PubMed]

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon waveguide quantum circuits,” Science 320, 646 (2008).
[CrossRef] [PubMed]

Cussey, J.

L. Olislager, J. Cussey, A. T. Nguyen, P. Emplit, S. Massar, J.-M. Merolla, and K. P. Huy, “Frequency-bin entangled photons,” Phys. Rev. A 82, 013804 (2010).
[CrossRef]

Duligall, J.

J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534 (2005).
[CrossRef] [PubMed]

Dwir, B.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302 (2010).
[CrossRef]

Eberly, J. H.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

Emplit, P.

L. Olislager, J. Cussey, A. T. Nguyen, P. Emplit, S. Massar, J.-M. Merolla, and K. P. Huy, “Frequency-bin entangled photons,” Phys. Rev. A 82, 013804 (2010).
[CrossRef]

Emplit, Ph.

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558 (2009).
[CrossRef] [PubMed]

Faist, J.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302 (2010).
[CrossRef]

Fan, J.

J. Chen, A. Pearlman, A. Ling, J. Fan, and A. Migdall, “A versatile waveguide source of photon pairs for chipscale quantum information processing,” Opt. Express 17, 6727 (2009).
[CrossRef] [PubMed]

J. Fan, A. Migdall, and L. J. Wang, “Efficient generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. 30, 3368 (2005).
[CrossRef]

Fedrizzi, A.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[CrossRef]

Felici, M.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302 (2010).
[CrossRef]

Fiorentino, M.

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479 (2007).
[CrossRef] [PubMed]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983 (2002).
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Foster, M. A.

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, 1904 (2010).

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, 4881 (2008).
[CrossRef] [PubMed]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[CrossRef]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguide,” Opt. Express 14, 4357 (2006).
[CrossRef] [PubMed]

Fukuda, H.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368 (2008).
[CrossRef] [PubMed]

Fulconis, J.

J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534 (2005).
[CrossRef] [PubMed]

Gaeta, A. L.

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, 1904 (2010).

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, 4881 (2008).
[CrossRef] [PubMed]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[CrossRef]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguide,” Opt. Express 14, 4357 (2006).
[CrossRef] [PubMed]

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A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302 (2010).
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J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82, 2594 (1999).
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K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368 (2008).
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P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554 (2000).
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P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554 (2000).
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L. Olislager, J. Cussey, A. T. Nguyen, P. Emplit, S. Massar, J.-M. Merolla, and K. P. Huy, “Frequency-bin entangled photons,” Phys. Rev. A 82, 013804 (2010).
[CrossRef]

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558 (2009).
[CrossRef] [PubMed]

Inoue, K.

. H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802(R) (2004).
[CrossRef]

Itabashi, S.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368 (2008).
[CrossRef] [PubMed]

Johnson, T. J.

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, 10596 (2008).
[CrossRef] [PubMed]

Joneckis, L. G.

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554 (2000).
[CrossRef]

Kapon, E.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302 (2010).
[CrossRef]

Kiess, T. E.

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Type-II Parametric Down-conversion,” Phys. Rev. Lett. 71, 3893 (1993).
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H. J. Kimble, “The quantum internet,” Nature 453, 1023 (2008).
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M. Scholtz, L. Koch, and O. Benson, “Analytical treatment of spectral properties and signal-idler intensity correlations for a double-resonant optical parametric oscillator far below threshold,” Opt. Commun. 282, 3518 (2009).
[CrossRef]

Kumar, P.

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388 (2006).
[CrossRef] [PubMed]

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-Fiber Source of Polarization-Entangled Photons in the 1550 nm Telecom Band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Phys. Rev. A 72, 033801 (2005).
[CrossRef]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983 (2002).
[CrossRef]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Langford, N. K.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[CrossRef]

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C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304 (2000).
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J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388 (2006).
[CrossRef] [PubMed]

Li, X.

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-Fiber Source of Polarization-Entangled Photons in the 1550 nm Telecom Band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Phys. Rev. A 72, 033801 (2005).
[CrossRef]

Lin, Q.

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, 10596 (2008).
[CrossRef] [PubMed]

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15, 16604 (2007).
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Q. Lin, and G. P. Agrawal, “Silicon waveguides for creating quantum-correlated photon pairs,” Opt. Lett. 31, 3140 (2006).
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L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295 (2006).
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Ling, A.

J. Chen, A. Pearlman, A. Ling, J. Fan, and A. Migdall, “A versatile waveguide source of photon pairs for chipscale quantum information processing,” Opt. Express 17, 6727 (2009).
[CrossRef] [PubMed]

Lipson, M.

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, 1904 (2010).

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, 4881 (2008).
[CrossRef] [PubMed]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguide,” Opt. Express 14, 4357 (2006).
[CrossRef] [PubMed]

Little, B. E.

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554 (2000).
[CrossRef]

Manolatou, C.

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguide,” Opt. Express 14, 4357 (2006).
[CrossRef] [PubMed]

Massar, S.

L. Olislager, J. Cussey, A. T. Nguyen, P. Emplit, S. Massar, J.-M. Merolla, and K. P. Huy, “Frequency-bin entangled photons,” Phys. Rev. A 82, 013804 (2010).
[CrossRef]

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558 (2009).
[CrossRef] [PubMed]

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Merolla, J.-M.

L. Olislager, J. Cussey, A. T. Nguyen, P. Emplit, S. Massar, J.-M. Merolla, and K. P. Huy, “Frequency-bin entangled photons,” Phys. Rev. A 82, 013804 (2010).
[CrossRef]

Michael, C. P.

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, 10596 (2008).
[CrossRef] [PubMed]

Migdall, A.

J. Chen, A. Pearlman, A. Ling, J. Fan, and A. Migdall, “A versatile waveguide source of photon pairs for chipscale quantum information processing,” Opt. Express 17, 6727 (2009).
[CrossRef] [PubMed]

J. Fan, A. Migdall, and L. J. Wang, “Efficient generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. 30, 3368 (2005).
[CrossRef]

Mohan, A.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302 (2010).
[CrossRef]

Munro, M. W.

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479 (2007).
[CrossRef] [PubMed]

Nguyen, A. T.

L. Olislager, J. Cussey, A. T. Nguyen, P. Emplit, S. Massar, J.-M. Merolla, and K. P. Huy, “Frequency-bin entangled photons,” Phys. Rev. A 82, 013804 (2010).
[CrossRef]

O’Brien, J. L.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon waveguide quantum circuits,” Science 320, 646 (2008).
[CrossRef] [PubMed]

Okawachi, Y.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Olislager, L.

L. Olislager, J. Cussey, A. T. Nguyen, P. Emplit, S. Massar, J.-M. Merolla, and K. P. Huy, “Frequency-bin entangled photons,” Phys. Rev. A 82, 013804 (2010).
[CrossRef]

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M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theory Tech. 55, 1209 (2007).
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Painter, O. J.

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, 10596 (2008).
[CrossRef] [PubMed]

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

Pearlman, A.

J. Chen, A. Pearlman, A. Ling, J. Fan, and A. Migdall, “A versatile waveguide source of photon pairs for chipscale quantum information processing,” Opt. Express 17, 6727 (2009).
[CrossRef] [PubMed]

Perahia, R.

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, 10596 (2008).
[CrossRef] [PubMed]

Politi, A.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon waveguide quantum circuits,” Science 320, 646 (2008).
[CrossRef] [PubMed]

Ramelow, S.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[CrossRef]

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon waveguide quantum circuits,” Science 320, 646 (2008).
[CrossRef] [PubMed]

J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534 (2005).
[CrossRef] [PubMed]

Ratschbacher, L.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[CrossRef]

Roberts, T. D.

T. Zhong, F. N. C. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fibercoupled periodically poled KTiOPO4 waveguide,” Opt. Express 17, 12019 (2009).
[CrossRef] [PubMed]

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479 (2007).
[CrossRef] [PubMed]

Rudra, A.

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302 (2010).
[CrossRef]

Russell, P. S.

J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534 (2005).
[CrossRef] [PubMed]

Salem, R.

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, 1904 (2010).

Schmidt, B. S.

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguide,” Opt. Express 14, 4357 (2006).
[CrossRef] [PubMed]

Scholtz, M.

M. Scholtz, L. Koch, and O. Benson, “Analytical treatment of spectral properties and signal-idler intensity correlations for a double-resonant optical parametric oscillator far below threshold,” Opt. Commun. 282, 3518 (2009).
[CrossRef]

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Type-II Parametric Down-conversion,” Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

Sharping, J. E.

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[CrossRef]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguide,” Opt. Express 14, 4357 (2006).
[CrossRef] [PubMed]

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-Fiber Source of Polarization-Entangled Photons in the 1550 nm Telecom Band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983 (2002).
[CrossRef]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Shih, Y. H.

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Type-II Parametric Down-conversion,” Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

Spillane, S. M.

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479 (2007).
[CrossRef] [PubMed]

Takesue, H.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368 (2008).
[CrossRef] [PubMed]

. H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802(R) (2004).
[CrossRef]

Tittel, W.

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82, 2594 (1999).
[CrossRef]

Tokura, Y.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368 (2008).
[CrossRef] [PubMed]

Tsuchizawa, T.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368 (2008).
[CrossRef] [PubMed]

Turner, A. C.

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, 4881 (2008).
[CrossRef] [PubMed]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388 (2006).
[CrossRef] [PubMed]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguide,” Opt. Express 14, 4357 (2006).
[CrossRef] [PubMed]

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, 1904 (2010).

Voss, P. L.

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-Fiber Source of Polarization-Entangled Photons in the 1550 nm Telecom Band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983 (2002).
[CrossRef]

Wadsworth, W. J.

J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534 (2005).
[CrossRef] [PubMed]

Walmsley, I. A.

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

Wang, L. J.

J. Fan, A. Migdall, and L. J. Wang, “Efficient generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. 30, 3368 (2005).
[CrossRef]

Watanabe, T.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368 (2008).
[CrossRef] [PubMed]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Wilson, R. A.

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554 (2000).
[CrossRef]

Wong, F. N. C.

T. Zhong, F. N. C. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fibercoupled periodically poled KTiOPO4 waveguide,” Opt. Express 17, 12019 (2009).
[CrossRef] [PubMed]

Yamada, K.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368 (2008).
[CrossRef] [PubMed]

Yin, L.

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295 (2006).
[CrossRef] [PubMed]

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon waveguide quantum circuits,” Science 320, 646 (2008).
[CrossRef] [PubMed]

Zbinden, H.

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82, 2594 (1999).
[CrossRef]

Zeilinger, A.

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[CrossRef]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

Zhong, T.

T. Zhong, F. N. C. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fibercoupled periodically poled KTiOPO4 waveguide,” Opt. Express 17, 12019 (2009).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

M. Heiblum, and J. H. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. 11, 75 (1975).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett. 14, 983 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theory Tech. 55, 1209 (2007).
[CrossRef]

Nat. Photonics (1)

A. Mohan, M. Felici, P. Gallo, B. Dwir, A. Rudra, J. Faist, and E. Kapon, “Polarization-entangled photons produced with high-symmetry site-controlled quantum dots,” Nat. Photonics 4, 302 (2010).
[CrossRef]

Nature (1)

H. J. Kimble, “The quantum internet,” Nature 453, 1023 (2008).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Scholtz, L. Koch, and O. Benson, “Analytical treatment of spectral properties and signal-idler intensity correlations for a double-resonant optical parametric oscillator far below threshold,” Opt. Commun. 282, 3518 (2009).
[CrossRef]

Opt. Express (12)

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

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Tailored anomalous group-velocity dispersion in silicon channel waveguide,” Opt. Express 14, 4357 (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, 1904 (2010).

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, 4881 (2008).
[CrossRef] [PubMed]

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, “Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals,” Opt. Express 15, 7479 (2007).
[CrossRef] [PubMed]

J. Chen, A. Pearlman, A. Ling, J. Fan, and A. Migdall, “A versatile waveguide source of photon pairs for chipscale quantum information processing,” Opt. Express 17, 6727 (2009).
[CrossRef] [PubMed]

T. Zhong, F. N. C. Wong, T. D. Roberts, and P. Battle, “High performance photon-pair source based on a fibercoupled periodically poled KTiOPO4 waveguide,” Opt. Express 17, 12019 (2009).
[CrossRef] [PubMed]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14, 12388 (2006).
[CrossRef] [PubMed]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16, 20368 (2008).
[CrossRef] [PubMed]

S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17, 16558 (2009).
[CrossRef] [PubMed]

J. G. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13, 534 (2005).
[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, 10596 (2008).
[CrossRef] [PubMed]

Opt. Lett. (5)

J. Fan, A. Migdall, and L. J. Wang, “Efficient generation of correlated photon pairs in a microstructure fiber,” Opt. Lett. 30, 3368 (2005).
[CrossRef]

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25, 554 (2000).
[CrossRef]

Q. Lin, and G. P. Agrawal, “Silicon waveguides for creating quantum-correlated photon pairs,” Opt. Lett. 31, 3140 (2006).
[CrossRef] [PubMed]

K. Banaszek, “A. B. U’Ren, and I. A.Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett. 26, 1367 (2001).
[CrossRef]

L. Yin, Q. Lin, and G. P. Agrawal, “Dispersion tailoring and soliton propagation in silicon waveguides,” Opt. Lett. 31, 1295 (2006).
[CrossRef] [PubMed]

Phys. Rev. A (4)

L. Olislager, J. Cussey, A. T. Nguyen, P. Emplit, S. Massar, J.-M. Merolla, and K. P. Huy, “Frequency-bin entangled photons,” Phys. Rev. A 82, 013804 (2010).
[CrossRef]

J. Chen, X. Li, and P. Kumar, “Two-photon-state generation via four-wave mixing in optical fibers,” Phys. Rev. A 72, 033801 (2005).
[CrossRef]

. H. Takesue and K. Inoue, “Generation of polarization-entangled photon pairs and violation of Bell’s inequality using spontaneous four-wave mixing in a fiber loop,” Phys. Rev. A 70, 031802(R) (2004).
[CrossRef]

I. H. Agha, Y. Okawachi, M. A. Foster, J. E. Sharping, and A. L. Gaeta, “Four-wave-mixing parametric oscillations in dispersion-compensated high-Q silica microspheres,” Phys. Rev. A 76, 043837 (2007).
[CrossRef]

Phys. Rev. Lett. (6)

X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-Fiber Source of Polarization-Entangled Photons in the 1550 nm Telecom Band,” Phys. Rev. Lett. 94, 053601 (2005).
[CrossRef] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New High-Intensity Source of Polarization-Entangled Photon Pairs,” Phys. Rev. Lett. 75, 4337 (1995).
[CrossRef] [PubMed]

T. E. Kiess, Y. H. Shih, A. V. Sergienko, and C. O. Alley, “Einstein-Podolsky-Rosen-Bohm Experiment Using Pairs of Light Quanta Produced by Type-II Parametric Down-conversion,” Phys. Rev. Lett. 71, 3893 (1993).
[CrossRef] [PubMed]

J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, “Pulsed energy-time entangled twin-photon source for quantum communication,” Phys. Rev. Lett. 82, 2594 (1999).
[CrossRef]

C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite Hilbert space and entropy control,” Phys. Rev. Lett. 84, 5304 (2000).
[CrossRef] [PubMed]

S. Ramelow, L. Ratschbacher, A. Fedrizzi, N. K. Langford, and A. Zeilinger, “Discrete tunable color entanglement,” Phys. Rev. Lett. 103, 253601 (2009).
[CrossRef]

Science (1)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-Silicon waveguide quantum circuits,” Science 320, 646 (2008).
[CrossRef] [PubMed]

Other (6)

D. Bouwmeester, A. K. Ekert, and A. Zeilinger, The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation, 1st Ed., (Springer 2000).
[PubMed]

We note that the optical modes in our proposed microring resonators are not ideal whispering gallery modes, in the sense that the modes have non-zero interatction with the inner wall of the ring resonators. However, the electric field strength at the inner wall is typically no more than 1% of its peak value near the outer wall (see Fig. 2). Even though this interaction is negligibly small, we used the numerically determined modes in our calculations, rather than analytical expressions of ideal whispering gallery modes. We still refer to our modes as whispering gallery modes throughout the text, but we recognize this is an approximation.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press 1985), p. 548.

http://www.comsol.com

Certain trade names and company products are mentioned in the text or identified in an illustration in order to specify adequately the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it necessarily imply that the products are the best available for the purpose.

Private communications with M. Oxborrow and P. Del’Haye,

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of a microring resonator side-coupled to a bus waveguide, both integrated on a SOI chip. (b) Top-down view of photon pair production in the SOI device shown in (a). Pump is injected into the microring via the bus waveguide; copolarized photon pairs are generated and resonantly enhanced and evanescently coupled out of the microring. Waves propagate in the z direction in the bus waveguide. Inside the microring, there exist two polarization eigenmodes: TM (Electric field perpendicular to the plane of propagation) and TE (Electric field in the plane of propagation but perpendicular to the propagation direction). R1, inner ring radius; R2, outer ring radius. (c) Cross section of both the microring and the bus waveguide. The crystallographic axes are designated for the bus waveguide only. (d) An entangled comb of photon pairs is generated when pump frequency is tuned to mode number Mp. A signal photon occupying mode ms can always find its partner idler photon symmetrically placed around pump occupying mode mi = ms. Also shown is the simulated signal output with a relative mode number ms = 1, which has a full width at half-maximum of 20 GHz for a cavity damping rate of 31.25 GHz.

Fig. 5
Fig. 5

(a) Frequency mismatch for TM modes for a microring resonator of R1 = 8μm. Blue, λp = 1.498 μm with Mp = 114; red, λp = 1.555 μm with Mp = 109; black, λp = 1.616 μm with Mp = 104. One can see that Mp = 109 corresponds to the optimal pump mode. Frequency mismatch when pump is chosen optimally for TE (black) and TM (red) for several different bending radii: (b) R1 = 8μm, Mp = 111 for TE, Mp = 109 for TM; (c) R1 = 7μm, Mp = 97 for TE, Mp = 96 for TM; and (d) R1 = 5μm, Mp = 69 for TE, Mp = 68 for TM. Optimal pump wavelengths are labelled on the figures.

Fig. 2
Fig. 2

Conformal transformation from a bent waveguide to its equivalent straight waveguide, along with the fundamental TE mode shape (R 1 = 8μm, λ = 1.528 μm) in its corresponding coordinate.

Fig. 3
Fig. 3

Numerically simulated group index ng and group velocity dispersion k″ for (a) straight waveguide, (b) bent waveguide with R1 = 8μm, and (c) bent waveguide with R1 = 3μm. TE mode: black; TM mode: red. The curves for bulk Si are plotted in blue for reference.

Fig. 4
Fig. 4

Zero-dispersion wavelength vs. the inverse of the bending radius of an SOI waveguide for both TE (black dots) and TM (red squares) modes.

Fig. 6
Fig. 6

Frequency mismatch in a straight cavity for quasi-TE modes with λp = 1.407 μm (solid blue), 1.516 μm (solid red), and 1.649 μm (solid black), and quasi-TM modes with λp = 1.405 μm (hollow blue), 1.514 μm (hollow red), and 1.646 μm (hollow black).

Equations (23)

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E p ( + ) ( z , t ) = E p e i [ k p ( ω p ) z ω p t ] e i Γ P z ,
E s ( ) ( z , t ) = h ¯ ω s 2 ɛ 0 n s c A eff , s γ s Δ ω s 2 π m s d Ω s a s ( ω s , m s + Ω s ) γ s / 2 i Ω s e i [ k s z ( ω s , m s + Ω s ) t ] .
| Ψ = η L m s m i d Ω s d Ω i γ s γ i δ ( m s Δ ω s + m i Δ ω i + Ω s + Ω i ) ( γ s / 2 i Ω s ) ( γ i / 2 i Ω i ) e i L [ k 4 ( m s Δ ω s Ω s ) 2 + k 4 ( m i Δ ω i + Ω i ) 2 + Γ P ] a s ( ω s , m s + Ω s ) a i ( ω i , m i + Ω i ) | 0 sinc { L [ k 4 ( m s Δ ω s Ω s ) 2 + k 4 ( m i Δ ω i + Ω i ) 2 + Γ P ] } ,
e i u t d t = 2 π δ ( u ) ,
L 0 e i β x d x = L e i β L / 2 sinc ( β L / 2 ) .
| Ψ = η L m d Ω γ s γ i e i L [ k ( m Δ ω Ω ) 2 / 2 + Γ P ] ( γ s / 2 i Ω ) ( γ i / 2 + i Ω ) sinc { L [ k ( m Δ ω Ω ) 2 / 2 + Γ P ] } a s ( ω p m Δ ω + Ω ) a i ( ω p + m Δ ω Ω ) | 0 .
S ( ω s ) = ( η L ) 2 m γ s γ i sinc 2 { L [ k ( ω p ω s ) 2 / 2 + Γ P ] } | γ s / 2 i ( ω s ω p + m Δ ω ) | 2 | γ i / 2 + i ( ω s ω p + m Δ ω ) | 2 .
S ( ω i ) = Ψ | a i ( ω i ) a i ( ω i ) | Ψ = ( η L ) 2 m γ s γ i sinc 2 { L [ k ( ω i ω p ) 2 / 2 + Γ P ] } | γ s / 2 i ( ω p ω i + m Δ ω ) | 2 | γ i / 2 + i ( ω p ω i + m Δ ω ) | 2 .
u = R 2 ln ( ρ / R 2 ) ,
v = R 2 θ .
n Air = 1 ,
n SiO 2 = 1 + 0.6961663 λ 2 λ 2 0.0684043 2 + 0.4079426 λ 2 λ 2 0.1162414 2 + 0.8974794 λ 2 λ 2 9.896161 2 ,
n Si = 3.41906 + 0.123172 λ 2 0.028 + 0.0265456 ( λ 2 0.028 ) 2 2.66511 × 10 8 λ 2 + 5.45852 × 10 14 λ 2 ,
Δ = 1 2 π ( 2 ω 0 p ω 0 s ω 0 i ) ,
Δ nl = 2 n 2 I n ( ω p ) ω p 2 π ,
R ijkl ( 3 ) ( τ ) = γ e δ ( τ ) [ σ 3 ( δ ij δ kl + δ ik δ jl + δ il δ jk ) + ( 1 σ ) δ ij δ jk δ kl ] + γ R h R ( τ ) ( δ ik δ jl + δ il δ jk 2 δ ij δ jk δ kl ) .
[ a x a ρ a θ ] = [ M xx M xy M xz M ρ x M ρ y M ρ z M θ x M θ y M θ z ] [ a x a y a z ] ,
[ M xx M xy M xz M ρ x M ρ y M ρ z M θ x M θ y M θ z ] = [ 1 0 0 0 cos θ sin θ 0 sin θ ρ cos θ ρ ] .
R ρ ρ ρ ρ ( 3 ) = γ e δ ( τ ) ( cos 4 θ + sin 4 θ + 2 σ sin 2 θ cos 2 θ ) + 4 γ R h R ( τ ) sin 2 θ cos 2 θ ,
R xxxx ( 3 ) = γ e δ ( τ ) ,
R x ρ ρ x ( 3 ) = R ρ xx ρ ( 3 ) = σ 3 γ e δ ( τ ) + γ R h R ( τ ) .
n g L = M λ ,
ω d k d ω = 2 π M L .

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