Abstract

In this paper, 1.5μm correlated photon pairs are generated under continuous wave (CW) pumping in a silicon micro-ring cavity with a Q factor of 8.1 × 104. The ratio of coincidences to accidental coincidences (CAR) is up to 200 under a coincidence time bin width of 5ns. The experiment result of single side photon count shows that the generation rate does not increase as the square of the pump level due to the nonlinear losses in the cavity which reduce the Q factor and impact the field enhancement effect in the cavity under high pump level. Theoretical analysis shows that the photon pair generation rate in the cavity is proportional to the seventh power of the Q factor, which agrees well with the experiment result. It provides a way to analyze the performance of CW pumping correlated photon pair generation in silicon micro-ring cavities under high pump levels.

© 2014 Optical Society of America

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2012 (4)

2010 (2)

L. G. Helt, Z. Yang, M. Liscidini, J. E. Sipe, “Spontaneous four-wave mixing in microring resonators,” Opt. Lett. 35(18), 3006–3008 (2010).
[CrossRef] [PubMed]

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[CrossRef]

2009 (1)

2008 (4)

2007 (3)

S. F. Preble, Q. Xu, M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 1293–1296 (2007).

A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics 1(4), 215–223 (2007).
[CrossRef]

Q. Lin, O. J. Painter, G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (1)

D. G. Rabus, Z. Bian, A. Shakouri, “A GaInAsP-InP double-ring resonator coupled laser,” IEEE Photon. Technol. Lett. 17(9), 1770–1772 (2005).
[CrossRef]

2002 (1)

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[CrossRef] [PubMed]

2000 (1)

1997 (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring Resonator Channel Dropping Filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Absil, P. P.

Agrawal, G. P.

Andreani, L. C.

Azzini, S.

Baets, R. G.

Bajoni, D.

Bian, Z.

D. G. Rabus, Z. Bian, A. Shakouri, “A GaInAsP-InP double-ring resonator coupled laser,” IEEE Photon. Technol. Lett. 17(9), 1770–1772 (2005).
[CrossRef]

Bogaerts, W.

Bonneau, D.

Cho, P. S.

Chu, S.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[CrossRef]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring Resonator Channel Dropping Filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Clark, A. S.

Clemmen, S.

Deane, J. H. B.

Dorenbos, S. N.

Duchesne, D.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[CrossRef]

Emplit, P.

Engin, E.

Ezaki, M.

Ferrera, M.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[CrossRef]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring Resonator Channel Dropping Filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Foster, M. A.

Fukuda, H.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Frequency and Polarization Characteristics of Correlated Photon-Pair Generation Using a Silicon Wire Waveguide,” IEEE J. Sel. Top. Quantum Electron. 16(1), 325–331 (2010).
[CrossRef]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008).
[CrossRef] [PubMed]

Gaeta, A. L.

Galli, M.

Gardes, F. Y.

Grassani, D.

Gwilliam, R.

Hadfield, R. H.

Harada, K.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Frequency and Polarization Characteristics of Correlated Photon-Pair Generation Using a Silicon Wire Waveguide,” IEEE J. Sel. Top. Quantum Electron. 16(1), 325–331 (2010).
[CrossRef]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008).
[CrossRef] [PubMed]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring Resonator Channel Dropping Filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Headley, W. R.

Helt, L. G.

Ho, P. T.

Hryniewicz, J. V.

Huy, K. P.

Iizuka, N.

Ippen, E. P.

Itabashi, S.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Frequency and Polarization Characteristics of Correlated Photon-Pair Generation Using a Silicon Wire Waveguide,” IEEE J. Sel. Top. Quantum Electron. 16(1), 325–331 (2010).
[CrossRef]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008).
[CrossRef] [PubMed]

Joneckis, L. G.

Jones, R. J.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311(5767), 1595–1599 (2006).
[CrossRef] [PubMed]

Kärtner, F. X.

Khilo, A.

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[CrossRef] [PubMed]

Knights, A. P.

Kumar, P.

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring Resonator Channel Dropping Filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Lee, K. F.

Lin, Q.

Lipson, M.

Liscidini, M.

Little, B. E.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[CrossRef]

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, P. T. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett. 25(8), 554–556 (2000).
[CrossRef] [PubMed]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring Resonator Channel Dropping Filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

Litvinenko, K. L.

Mashanovich, G. Z.

Massar, S.

Moll, K. D.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311(5767), 1595–1599 (2006).
[CrossRef] [PubMed]

Morandotti, R.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[CrossRef]

Moss, D. J.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[CrossRef]

Motamedi, A. R.

Natarajan, C. M.

Nejadmalayeri, A. H.

O’Brien, J. L.

Ohira, K.

Painter, O. J.

Preble, S. F.

S. F. Preble, Q. Xu, M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 1293–1296 (2007).

Rabus, D. G.

D. G. Rabus, Z. Bian, A. Shakouri, “A GaInAsP-InP double-ring resonator coupled laser,” IEEE Photon. Technol. Lett. 17(9), 1770–1772 (2005).
[CrossRef]

Razzari, L.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[CrossRef]

Reed, G. T.

Safdi, B.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311(5767), 1595–1599 (2006).
[CrossRef] [PubMed]

Schmidt, B. S.

Shakouri, A.

D. G. Rabus, Z. Bian, A. Shakouri, “A GaInAsP-InP double-ring resonator coupled laser,” IEEE Photon. Technol. Lett. 17(9), 1770–1772 (2005).
[CrossRef]

Sharping, J. E.

Shields, A. J.

A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics 1(4), 215–223 (2007).
[CrossRef]

Sipe, J. E.

Smith, A. J.

Sorel, M.

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[CrossRef] [PubMed]

Strain, M. J.

Suzuki, N.

Takesue, H.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Frequency and Polarization Characteristics of Correlated Photon-Pair Generation Using a Silicon Wire Waveguide,” IEEE J. Sel. Top. Quantum Electron. 16(1), 325–331 (2010).
[CrossRef]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008).
[CrossRef] [PubMed]

Tanner, M. G.

Thompson, M. G.

Thomson, D. J.

Thorpe, M. J.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311(5767), 1595–1599 (2006).
[CrossRef] [PubMed]

Tokura, Y.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Frequency and Polarization Characteristics of Correlated Photon-Pair Generation Using a Silicon Wire Waveguide,” IEEE J. Sel. Top. Quantum Electron. 16(1), 325–331 (2010).
[CrossRef]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008).
[CrossRef] [PubMed]

Tsuchizawa, T.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Frequency and Polarization Characteristics of Correlated Photon-Pair Generation Using a Silicon Wire Waveguide,” IEEE J. Sel. Top. Quantum Electron. 16(1), 325–331 (2010).
[CrossRef]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008).
[CrossRef] [PubMed]

Turner, A. C.

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[CrossRef] [PubMed]

Watanabe, T.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Frequency and Polarization Characteristics of Correlated Photon-Pair Generation Using a Silicon Wire Waveguide,” IEEE J. Sel. Top. Quantum Electron. 16(1), 325–331 (2010).
[CrossRef]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008).
[CrossRef] [PubMed]

Wilson, R. A.

Wright, N. M.

Xu, Q.

S. F. Preble, Q. Xu, M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 1293–1296 (2007).

Yamada, K.

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Frequency and Polarization Characteristics of Correlated Photon-Pair Generation Using a Silicon Wire Waveguide,” IEEE J. Sel. Top. Quantum Electron. 16(1), 325–331 (2010).
[CrossRef]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008).
[CrossRef] [PubMed]

Yang, Z.

L. G. Helt, Z. Yang, M. Liscidini, J. E. Sipe, “Spontaneous four-wave mixing in microring resonators,” Opt. Lett. 35(18), 3006–3008 (2010).
[CrossRef] [PubMed]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[CrossRef]

Ye, J.

M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science 311(5767), 1595–1599 (2006).
[CrossRef] [PubMed]

Yoshida, H.

Zwiller, V.

IEEE J. Sel. Top. Quantum Electron. (1)

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Frequency and Polarization Characteristics of Correlated Photon-Pair Generation Using a Silicon Wire Waveguide,” IEEE J. Sel. Top. Quantum Electron. 16(1), 325–331 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

D. G. Rabus, Z. Bian, A. Shakouri, “A GaInAsP-InP double-ring resonator coupled laser,” IEEE Photon. Technol. Lett. 17(9), 1770–1772 (2005).
[CrossRef]

J. Lightwave Technol. (1)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, “Microring Resonator Channel Dropping Filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Photonics (3)

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[CrossRef]

S. F. Preble, Q. Xu, M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 1293–1296 (2007).

A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics 1(4), 215–223 (2007).
[CrossRef]

Nature (1)

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[CrossRef] [PubMed]

Opt. Express (9)

E. Engin, D. Bonneau, C. M. Natarajan, A. S. Clark, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, J. L. O’Brien, M. G. Thompson, “Photon pair generation in a silicon micro-ring resonator with reverse bias enhancement,” Opt. Express 21(23), 27826–27834 (2013).
[CrossRef]

J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express 14(25), 12388–12393 (2006).
[CrossRef] [PubMed]

Q. Lin, O. J. Painter, G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express 15(25), 16604–16644 (2007).
[CrossRef] [PubMed]

K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, S. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express 16(25), 20368–20373 (2008).
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S. Azzini, D. Grassani, M. J. Strain, M. Sorel, L. G. Helt, J. E. Sipe, M. Liscidini, M. Galli, D. Bajoni, “Ultra-low power generation of twin photons in a compact silicon ring resonator,” Opt. Express 20(21), 23100–23107 (2012).
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Opt. Lett. (4)

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Figures (7)

Fig. 1
Fig. 1

The micro-ring cavity used in the experiment. (a) The sketch of the cavity, (b) The cross section of the bus waveguide and the waveguide in the cavity. (c) The transmission spectrum of the quasi-TE mode near the resonance wavelength of a specific cavity mode.

Fig. 2
Fig. 2

The experiment setup for the correlated photon pair generation in the micro-ring cavity. PC, polarization controller; TOBF, tunable optical band-pass filter; SPD, single photon detector; CWDM, coarse wavelength division multiplexer.

Fig. 3
Fig. 3

Signal side photon count rates under different input pump power. The black squares: measured count rate Cs; The blue dots: modified count rate C’s. The red line: the fitting curve of the C’s with an input pump power lower than 0.1mW utilizing APp2Q3.The inset figure: the detail fitting result at low pump level.

Fig. 4
Fig. 4

Measured results of the coincidence count and accidental coincidence count. (a) a typical result of a coincidence count measurement; (b) Coincidence and accidental coincidence counts under different signal side count rate; Black triangles: the coincidence counts; Blue triangles: the accidental coincidence counts.

Fig. 5
Fig. 5

The measured CAR under different signal side count rate.

Fig. 6
Fig. 6

Calculated Q, Q0 and Qe under different input pump power.

Fig. 7
Fig. 7

Fitting results of the modified signal side photon count rates under different input pump power. The blue triangle: modified count rate Cs’. The red dots and magenta triangles: the fitting result of C’ = APp2Q3 and C’ = BPp2Q7, respectively.

Equations (17)

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R s = C s / η s
C s = C s d s 1 C s τ s
dP dz = α eff P
α eff =α+ βP A eff + τβσ P 2 2hv A eff
1/Q=1/ Q e +1/ Q 0
Q 0 = ω α eff v g
Q e = ωL | κ | 2 v g
Q= λ Δλ
Γ | Q e Q 0 Q e + Q 0 | 2
P c = P in | F( ω ) | 2
| F( ω ) | 2 = ν g Lω 4/ Q e ( ω ω 0 ) 2 / ω 0 2 + ( 1/ Q e +1/ Q 0 ) 2
| F p | 2 = v g L ω p 4/ Q e ( 1/ Q e +1/ Q 0 ) 2
P I = h ω p T ( γ P in L ) 2 | F p | 4
T= 2π dΔω | F( ω 0 Δω ) | 2 | F( ω 0 +Δω ) | 2
T= Q e 2 L 2 ω p0 4π v g 2 Q 3 hence , P I = 2 ( γ P in ) 2 v g 4 Q 7 L 2 ω p 2 Q e 4
Γ= | t-Λexp( iβL ) 1-Λtexp( iβL ) | 2
Γ= | tΛ 1Λt | 2 | exp( α eff L 2 ) 1 | κ | 2 1exp( α eff L 2 )· 1 | κ | 2 | 2 | α eff L 2 | κ | 2 2 1( 1 α eff L 2 | κ | 2 2 + α eff L 2 · | κ | 2 2 ) | 2 | α eff L | κ | 2 α eff L+ | κ | 2 | 2 = | Q e Q 0 Q e + Q 0 | 2

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