Abstract

Silicon microring resonators are being recently used for high-brightness and efficient photon-pair generation at telecommunication wavelengths. Here, based on detailed theoretical and numerical modeling, we study the impact on pair generation of increasing the optical pump power, which generally causes nonlinear impairments such as free-carrier and two-photon absorption in silicon micro-resonators. Contrary to expectation, the pair generation properties of such devices may seem to be preserved at increasing pump powers, although not better than at a moderate pump power. These results suggest that silicon microrings can be used for pair generation over a wide range of pump powers, which may benefit applications in remotely pumped architectures, where the pump level might not be known a priori.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (5)

L.-T. Feng, G.-C. Guo, and X.-F. Ren, “Progress on Integrated Quantum Photonic Sources with Silicon,” Adv. Quantum Technol. 3(2), 1900058 (2020).
[Crossref]

R. R. Kumar, X. Wu, and H. K. Tsang, “Compact high-extinction tunable CROW filters for integrated quantum photonic circuits,” Opt. Lett. 45(6), 1289–1292 (2020).
[Crossref]

C. Wu, Y. Liu, X. Gu, X. Yu, Y. Kong, Y. Wang, X. Qiang, J. Wu, Z. Zhu, X. Yang, and P. Xu, “Bright photon-pair source based on a silicon dual-Mach-Zehnder microring,” Sci. China: Phys., Mech. Astron. 63(2), 220362 (2020).
[Crossref]

B. Korzh, Q.-Y. Zhao, J. P. Allmaras, S. Frasca, T. M. Autry, E. A. Bersin, A. D. Beyer, R. M. Briggs, B. Bumble, M. Colangelo, G. M. Crouch, A. E. Dane, T. Gerrits, A. E. Lita, F. Marsili, G. Moody, C. Peña, E. Ramirez, J. D. Rezac, N. Sinclair, M. J. Stevens, A. E. Velasco, V. B. Verma, E. E. Wollman, S. Xie, D. Zhu, P. D. Hale, M. Spiropulu, K. L. Silverman, R. P. Mirin, S. W. Nam, A. G. Kozorezov, M. D. Shaw, and K. K. Berggren, “Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector,” Nat. Photonics 14(4), 250–255 (2020).
[Crossref]

X. Wang, A. E. Dane, K. K. Berggren, M. D. Shaw, S. Mookherjea, B. A. Korzh, P. O. Weigel, D. J. Nemchick, B. J. Drouin, W. Becker, Q.-Y. Zhao, D. Zhu, and M. Colangelo, “Oscilloscopic Capture of Greater-Than-100 GHz, Ultra-Low Power Optical Waveforms Enabled by Integrated Electrooptic Devices,” J. Lightwave Technol. 38(1), 166–173 (2020).
[Crossref]

2019 (2)

K. Guo, L. Yang, X. Shi, X. Liu, Y. Cao, J. Zhang, X. Wang, J. Yang, H. Ou, and Y. Zhao, “Nonclassical Optical Bistability and Resonance-Locked Regime of Photon-Pair Sources Using Silicon Microring Resonator,” Phys. Rev. Appl. 11(3), 034007 (2019).
[Crossref]

X. Shi, K. Guo, J. B. Christensen, M. A. U. Castaneda, X. Liu, H. Ou, and K. Rottwitt, “Multichannel Photon-Pair Generation with Strong and Uniform Spectral Correlation in a Silicon Microring Resonator,” Phys. Rev. Appl. 12(3), 034053 (2019).
[Crossref]

2018 (1)

C. Ma and S. Mookherjea, “Simultaneous dual-band entangled photon pair generation using a silicon photonic microring resonator,” Quantum Sci. Technol. 3(3), 034001 (2018).
[Crossref]

2017 (3)

2016 (3)

2015 (4)

M. Savanier, R. Kumar, and S. Mookherjea, “Optimizing photon-pair generation electronically using a p-i-n diode incorporated in a silicon microring resonator,” Appl. Phys. Lett. 107(13), 131101 (2015).
[Crossref]

J. W. Silverstone, R. Santagati, D. Bonneau, M. J. Strain, M. Sorel, J. L. O’Brien, and M. G. Thompson, “Qubit entanglement between ring-resonator photon-pair sources on a silicon chip,” Nat. Commun. 6(1), 7948 (2015).
[Crossref]

W. C. Jiang, X. Lu, J. Zhang, O. Painter, and Q. Lin, “Silicon-chip source of bright photon pairs,” Opt. Express 23(16), 20884–20904 (2015).
[Crossref]

C. M. Gentry, J. M. Shainline, M. T. Wade, M. J. Stevens, S. D. Dyer, X. Zeng, F. Pavanello, T. Gerrits, S. W. Nam, R. P. Mirin, and M. A. Popović, “Quantum-correlated photon pairs generated in a commercial 45 nm complementary metal-oxide semiconductor microelectronic chip,” Optica 2(12), 1065–1071 (2015).
[Crossref]

2014 (2)

Y. Guo, W. Zhang, N. Lv, Q. Zhou, Y. Huang, and J. Peng, “The impact of nonlinear losses in the silicon micro-ring cavities on CW pumping correlated photon pair generation,” Opt. Express 22(3), 2620–2631 (2014).
[Crossref]

N. C. Harris, D. Grassani, A. Simbula, M. Pant, M. Galli, T. Baehr-Jones, M. Hochberg, D. Englund, D. Bajoni, and C. Galland, “Integrated Source of Spectrally Filtered Correlated Photons for Large-Scale Quantum Photonic Systems,” Phys. Rev. X  4, 041047 (2014).
[Crossref]

2013 (2)

J. R. Ong, R. Kumar, R. Aguinaldo, and S. Mookherjea, “Efficient CW Four-Wave Mixing in Silicon-on-Insulator Micro-Rings With Active Carrier Removal,” IEEE Photonics Technol. Lett. 25(17), 1699–1702 (2013).
[Crossref]

J. R. Ong, R. Kumar, and S. Mookherjea, “Ultra-High-Contrast and Tunable-Bandwidth Filter Using Cascaded High-Order Silicon Microring Filters,” IEEE Photonics Technol. Lett. 25(16), 1543–1546 (2013).
[Crossref]

2011 (1)

Y.-P. Huang and P. Kumar, “Distilling quantum entanglement via mode-matched filtering,” Phys. Rev. A 84(3), 032315 (2011).
[Crossref]

2009 (1)

2008 (1)

X. Sang, E.-K. Tien, and O. Boyraz, “Applications of two-photon absorption in silicon,” J. Optoelectron. Adv. Mat. 11(1), 15–25 (2008).

2007 (1)

Y. Liu and H. K. Tsang, “Time dependent density of free carriers generated by two photon absorption in silicon waveguides,” Appl. Phys. Lett. 90(21), 211105 (2007).
[Crossref]

2006 (5)

2005 (1)

2004 (1)

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[Crossref]

2003 (1)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[Crossref]

2002 (2)

A. J. Sabbah and D. M. Riffe, “Femtosecond pump-probe reflectivity study of silicon carrier dynamics,” Phys. Rev. B 66(16), 165217 (2002).
[Crossref]

I. Marcikic, H. de Riedmatten, W. Tittel, V. Scarani, H. Zbinden, and N. Gisin, “Time-bin entangled qubits for quantum communication created by femtosecond pulses,” Phys. Rev. A 66(6), 062308 (2002).
[Crossref]

2001 (1)

P. P. Absil, J. V. Hryniewicz, B. E. Little, F. G. Johnson, K. J. Ritter, and P.-T. Ho, “Vertically coupled microring resonators using polymer wafer bonding,” IEEE Photonics Technol. Lett. 13(1), 49–51 (2001).
[Crossref]

1999 (1)

D. V. Tishinin, P. D. Dapkus, A. E. Bond, I. Kim, C. K. Lin, and J. O’Brien, “Vertical resonant couplers with precise coupling efficiency control fabricated by wafer bonding,” IEEE Photonics Technol. Lett. 11(8), 1003–1005 (1999).
[Crossref]

1987 (1)

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Absil, P. P.

P. P. Absil, J. V. Hryniewicz, B. E. Little, F. G. Johnson, K. J. Ritter, and P.-T. Ho, “Vertically coupled microring resonators using polymer wafer bonding,” IEEE Photonics Technol. Lett. 13(1), 49–51 (2001).
[Crossref]

Agrawal, G. P.

Aguinaldo, R.

J. R. Ong, R. Kumar, R. Aguinaldo, and S. Mookherjea, “Efficient CW Four-Wave Mixing in Silicon-on-Insulator Micro-Rings With Active Carrier Removal,” IEEE Photonics Technol. Lett. 25(17), 1699–1702 (2013).
[Crossref]

Allmaras, J. P.

B. Korzh, Q.-Y. Zhao, J. P. Allmaras, S. Frasca, T. M. Autry, E. A. Bersin, A. D. Beyer, R. M. Briggs, B. Bumble, M. Colangelo, G. M. Crouch, A. E. Dane, T. Gerrits, A. E. Lita, F. Marsili, G. Moody, C. Peña, E. Ramirez, J. D. Rezac, N. Sinclair, M. J. Stevens, A. E. Velasco, V. B. Verma, E. E. Wollman, S. Xie, D. Zhu, P. D. Hale, M. Spiropulu, K. L. Silverman, R. P. Mirin, S. W. Nam, A. G. Kozorezov, M. D. Shaw, and K. K. Berggren, “Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector,” Nat. Photonics 14(4), 250–255 (2020).
[Crossref]

Almeida, V. R.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[Crossref]

Alsing, P. M.

J. A. Steidle, C. C. Tison, M. L. Fanto, M. L. Fanto, S. F. Preble, and P. M. Alsing, “Highly Directional Silicon Microring Photon Pair Source,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2019) paper FTh1D.4.

Anant, V.

Autry, T. M.

B. Korzh, Q.-Y. Zhao, J. P. Allmaras, S. Frasca, T. M. Autry, E. A. Bersin, A. D. Beyer, R. M. Briggs, B. Bumble, M. Colangelo, G. M. Crouch, A. E. Dane, T. Gerrits, A. E. Lita, F. Marsili, G. Moody, C. Peña, E. Ramirez, J. D. Rezac, N. Sinclair, M. J. Stevens, A. E. Velasco, V. B. Verma, E. E. Wollman, S. Xie, D. Zhu, P. D. Hale, M. Spiropulu, K. L. Silverman, R. P. Mirin, S. W. Nam, A. G. Kozorezov, M. D. Shaw, and K. K. Berggren, “Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector,” Nat. Photonics 14(4), 250–255 (2020).
[Crossref]

Baehr-Jones, T.

N. C. Harris, D. Grassani, A. Simbula, M. Pant, M. Galli, T. Baehr-Jones, M. Hochberg, D. Englund, D. Bajoni, and C. Galland, “Integrated Source of Spectrally Filtered Correlated Photons for Large-Scale Quantum Photonic Systems,” Phys. Rev. X  4, 041047 (2014).
[Crossref]

Baets, R. G.

Bajoni, D.

L. Caspani, C. Xiong, B. J. Eggleton, D. Bajoni, M. Liscidini, M. Galli, R. Morandotti, and D. J. Moss, “Integrated sources of photon quantum states based on nonlinear optics,” Light: Sci. Appl. 6(11), e17100 (2017).
[Crossref]

N. C. Harris, D. Grassani, A. Simbula, M. Pant, M. Galli, T. Baehr-Jones, M. Hochberg, D. Englund, D. Bajoni, and C. Galland, “Integrated Source of Spectrally Filtered Correlated Photons for Large-Scale Quantum Photonic Systems,” Phys. Rev. X  4, 041047 (2014).
[Crossref]

F. A. Sabattoli, H. E. Dirani, F. Garrisi, S. Sam, C. Petit-Etienne, J. M. Hartmann, E. Pargon, C. Monat, M. Liscidini, C. Sciancalepore, M. Galli, and D. Bajoni, “A Source of Heralded Single Photon Using High Quality Factor Silicon Ring Resonators,” in 2019 21st International Conference on Transparent Optical Networks (ICTON)(IEEE, 2019), paper Th.C2.4.

Barrios, C. A.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004).
[Crossref]

Becker, W.

Bennett, B.

R. Soref and B. Bennett, “Electrooptical effects in silicon,” IEEE J. Quantum Electron. 23(1), 123–129 (1987).
[Crossref]

Berggren, K. K.

B. Korzh, Q.-Y. Zhao, J. P. Allmaras, S. Frasca, T. M. Autry, E. A. Bersin, A. D. Beyer, R. M. Briggs, B. Bumble, M. Colangelo, G. M. Crouch, A. E. Dane, T. Gerrits, A. E. Lita, F. Marsili, G. Moody, C. Peña, E. Ramirez, J. D. Rezac, N. Sinclair, M. J. Stevens, A. E. Velasco, V. B. Verma, E. E. Wollman, S. Xie, D. Zhu, P. D. Hale, M. Spiropulu, K. L. Silverman, R. P. Mirin, S. W. Nam, A. G. Kozorezov, M. D. Shaw, and K. K. Berggren, “Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector,” Nat. Photonics 14(4), 250–255 (2020).
[Crossref]

X. Wang, A. E. Dane, K. K. Berggren, M. D. Shaw, S. Mookherjea, B. A. Korzh, P. O. Weigel, D. J. Nemchick, B. J. Drouin, W. Becker, Q.-Y. Zhao, D. Zhu, and M. Colangelo, “Oscilloscopic Capture of Greater-Than-100 GHz, Ultra-Low Power Optical Waveforms Enabled by Integrated Electrooptic Devices,” J. Lightwave Technol. 38(1), 166–173 (2020).
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Figures (8)

Fig. 1.
Fig. 1. (a) Experimentally measured silicon microdisc resonator spectra, measured using a swept-wavelength tunable laser, at different input power levels. As the input power scales up, the resonance red shifts and extinction degrades. (b) Some of the physical processes impacting pair generation in a silicon photonic device when the pump power is high, which involves two-photon absorption (TPA), free carrier absorption (FCA), free carrier dispersion (FCD) and thermo-optic effect.
Fig. 2.
Fig. 2. (a) Schematic drawing of an optical ring resonator, where coefficients r and κ are the electric-field amplitude transmittance and cross-coupling coefficients, respectively. (b) Optical mode profile (magnitude of the transverse electrical field) for the transverse-electric (TE) mode in a typical single-mode silicon rib waveguide. The waveguide cross section is 220 nm thick and 500 nm wide, with a slab height of 70 nm.
Fig. 3.
Fig. 3. Change inside the microring cavity consisting of waveguide shown in Fig. 2(b), assuming a constant (amplitude) coupling strength in the coupling region of 0.01. (a) Loss composition as a function of input power. To start with, there is linear absorption losses such as material absorption loss and scattering loss. As the input power increases, TPA produces free carriers which induce FCA. FCA becomes dominant at high input power levels. (b) Intracavity resonant power and Q-factor of the cavity as a function of input power. The blue dash line is the resonant power in an ideal linear cavity. The blue solid line is the power inside a nonlinear cavity. As the input power increases, Q-factor of the cavity degrades, and the resonant enhancement effect is not as strong. The rate gap between a nonlinear and linear cavity widens.
Fig. 4.
Fig. 4. PGR inside the microring cavity consisting of waveguide shown in Fig. 2(b), when |κ|2 = 0.01. TPA and its-induced FCA prevent the intracavity power from scaling with the input power as fast as it is in a linear cavity, Thus the increase in the SPM term in phase matching term also slows down significantly, which prevents the sinc2 term to appear in the high power region. As the input power increases, the cavity changes from over-coupled to under-coupled, thus the extraction efficiency of the photon pairs are also compromised. The overall extracted PGR reaches a maximum of 55 MHz at the input power of 1.7 mW.
Fig. 5.
Fig. 5. Extracted PGR (a) (in Hz) and CAR (c) (in log scale) as a function of input power and |κ|2 in a TPA-free cavity. The right lower corner contains very fine and dense ripples representing the fast oscillating phase matching term (sinc2) induced by high intracavity power. Extracted PGR (b) and CAR (c) (in log scale) as a function of input power and |κ|2 in a nonlinear cavity. All calculations are based on the microring cavity consisting of waveguide shown in Fig. 2(b).
Fig. 6.
Fig. 6. Photon pair characteristics for the combinations of |κ|2 and P0 to maximize PGR. (a) Optimum |κ|2 as a function of input pump power to maximize the PGR (extracted). The dash lines are reference |κ|2 (dash blue) and PGR (dash orange) for a TPA-free resonator. The solid lines are reference |κ|2 (solid blue) and PGR (solid orange) for a nonlinear cavity where TPA can occur. (b) CAR and the resonance’s FWHM as a function of the input pump power for the maximized PGR (extracted). The dash lines are reference CAR (dash blue) and FWHM (dash orange) for a TPA-free cavity. The solid lines are reference CAR (solid blue) and FWHM (solid orange) for a nonlinear cavity where TPA can occur. The shaded area (light yellow) is where the extracted PGR is within half of its maximum for a TPA-enabled resonator.
Fig. 7.
Fig. 7. PGR (units: number of pairs per second, or Hz) as a function of input pump power P0 and waveguide-cavity coupling strength |κ|2 for different waveguide cross sections, labeled at the top of each sub-panel by the waveguide height x waveguide width. (The slab height is 70 nm.) The group velocity dispersion is shown in the upper-left corner of each subfigure. The dashed line in each subfigure is optimum |κ|2 to maximize PGR for each input pump power. The colorbar indicates the exponent of the PGR, i.e., values of 0 to 8 represent PGR values of 1 Hz to 1E8 Hz, respectively.
Fig. 8.
Fig. 8. (a)­(b) Maximum PGR (a) and its corresponding CAR (b) as a function of waveguide cross section geometry. The cells denoted by crosses correspond to waveguide cross sections whose fundamental mode is TM mode. (c) Maximum PGR for input pump power of 1 mW as a function of waveguide cross section geometry. (d) Maximum PGR as a function of each input pump power level for 220 nm-thick cross sections.

Tables (1)

Tables Icon

Table 1. Values of relevant parameters used in calculations.

Equations (24)

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γ = 2 π n 2 λ p A eff
R = Δ ν [ γ P res L eff res ] 2 sinc 2 ( β 2 Δ ω 2 L res 2 + γ P res L eff res )
P r e s ( λ ) = P 0 × 1 r 2 ( 1 r a ) 2 × ( λ p 2 Q ) 2 ( λ λ p ) 2 + λ p 2 Q
L res = L × F π
L eff res = 1 exp ( α L ) α × F π .
F = π r a 1 r a
Q = π n g L r a λ res ( 1 r a )
α TPA = β TPA I
α ¯ TPA = S i β TPA I 2 ( r ) d A I ( r ) d A β TPA P res A eff .
d N d t = β TPA I 2 2 h ν + D 2 N 2 x N τ c
N = β TPA I 2 τ 0 2 h ν .
α FC = e 3 λ 2 4 π 2 c 2 ϵ 0 n ( Δ N e m c e 2 μ e + Δ N h m c h 2 μ h ) = σ N ( z , t )
Δ n FC = e 2 λ 2 8 π 2 c 2 ϵ 0 n ( Δ N e m ce + Δ N h m ch ) 8.2 × 10 22 λ 2 N ( z , t )
α ¯ FC = S i σ N ( z , t ) I ( r ) d A I ( r ) d A = σ β TPA τ 0 2 h ν ( P res ) 2 A eff A eff
A eff = I ( r ) d A I 2 ( r ) d A Si I 3 ( r ) d A .
Δ n = d n d T Δ T
d Δ T d t = ( α TPA + α FC + α m ) I ρ Si C Si Δ T τ th
Δ T ( z , t ) = τ th ( α TPA + α FCA + α m ) ρ Si C Si I ( z , t ) = τ th ( β TPA I ( z , t ) + α FC + α m ) ρ Si C Si I ( z , t ) .
α total = ( α TPA + α FC + α m ) .
P 0 = P res ( 1 r a ) 2 1 r 2 .
η p = 1 ± ( T c ) 2
CAR = C cc C acc C cc
C c c = R pair η i η s
C a c c = Δ τ [ ( R i + R n,i ) η i + D i ] [ ( R s + R n,s ) η s + D s ]

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