## The impact of nonlinear losses in the silicon micro-ring cavities on CW pumping correlated photon pair generation |

Optics Express, Vol. 22, Issue 3, pp. 2620-2631 (2014)

http://dx.doi.org/10.1364/OE.22.002620

Acrobat PDF (1045 KB)

### 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 × 10^{4}. 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

## 1. Introduction

## 2. Experiment of correlated photon pair generation in a silicon micro-ring cavity under CW pumping

^{4}, estimated by the ratio between the resonance wavelength and the FWHM.

*η*is the collection and detection efficiency at signal side, including the detection efficiency of the SPD and the transmission efficiency between the output end of the bus waveguide and the SPD. C’

_{s}_{s}has the same unit as the measured signal side count rate (denoted by C

_{s}) and is calculated byWhere, d

_{s}and τ

_{s}are the dark count rate and the dead time of the signal side SPD, respectively. It can be seen that C’

_{s}is a modified signal side count rate proportional to R

_{s}, in which the impacts of dead time and dark count of the SPD are taken out. The blue dots in Fig. 3 are the calculated C’

_{s}according to the measured signal side count rate. It can be seen that C’

_{s}is close to C

_{s}at low pump level, while far higher than C

_{s}at high pump level.

_{s}, which is determined by the collection and detection efficiencies of the generated idler side photons. However, the coincidence count reduces rapidly with decreasing pump level when pump power is low due to the impact of dark counts of the SPD1. It also reduces with increasing pump level when pump power is high, which may be due to the impact of the dead time of the SPD2. On the other hand, the accidental coincidence count is proportional to the signal side count rate.

## 3. The impact of nonlinear losses in silicon micro-ring cavities on the CW pumping correlated photon pair generation

18. S. Azzini, D. Grassani, M. Galli, L. C. Andreani, M. Sorel, M. J. Strain, L. G. Helt, J. E. Sipe, M. Liscidini, and D. Bajoni, “From classical four-wave mixing to parametric fluorescence in silicon microring resonators,” Opt. Lett. **37**(18), 3807–3809 (2012). [CrossRef] [PubMed]

19. L. G. Helt, M. Liscidini, and J. E. Sipe, “How does it scale? comparing quantum and classical nonlinear optical processes in integrated devices,” J. Opt. Soc. Am. B **29**(8), 2199–2212 (2012). [CrossRef]

*α*, has three contributions: the first one is the linear loss, which is expressed by a linear loss coefficient

_{eff}*α.*The second one is the two-photon absorption (TPA) effect of silicon, which is expressed by the TPA coefficient

*β.*The last one is the free carrier absorption (FCA) effect of silicon, which can be expressed through the FCA cross section

*σ*and free carrier recombination life

*τ*.

*A*are the effective area of the silicon waveguide, the light frequency and the Planck constant, respectively.

_{eff,}ν, h20. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring Resonator Channel Dropping Filters,” J. Lightwave Technol. **15**(6), 998–1005 (1997). [CrossRef]

*Q*and

_{0}*Q*are the intrinsic and external Q factor of the cavity mode, respectively.

_{e}*Q*can be calculated by Eq. (6), in which

_{0}*α*is the effective loss coefficient of the waveguide in the cavity, v

_{eff}*is the group velocity of the light propagating in the cavity and*

_{g}*ω*is the angular frequency of the light.

*Q*can be calculated by Eq. (7), in which

_{e}*κ*is the coupling coefficient between the cavity and the bus waveguide,

*L*is the circumference of the cavity, while

*L*/v

_{g}is the round trip time of the light in the cavity

*Q>>1*), it can be estimated by the ratio between the resonance wavelength

*λ*and line width

*Δλ*of the dip shown in the spectrum

*Q*and

_{0}*Q*are far higher than 1, it can be deduced that the extinction ratio (denoted by Γ) can be expressed as (the derivation is shown in the appendix)Hence, after the estimation of Q factor by Eq. (8), the

_{e}*Q*and

_{0}*Q*of the mode also can be calculated according to the transmission spectrum through Eqs. (5) and (9). For the micro-ring cavity sample used in our experiment, the

_{e}*Q*,

*Q*and

_{0}*Q*of the specific mode can be calculated according to the measured transmission spectrum shown in Fig. 1(c), which are 8.1 × 10

_{e}^{4}, 14.6 × 10

^{4}and 18.3 × 10

^{4}, respectively. However, this method can’t be used to analyze the cavity under high light power due to strong light field enhancement effect in the cavity. On one hand, it will lead to obvious nonlinear losses in the cavity, which will change the intrinsic Q factor of the cavity. On the other hand, the index of the silicon waveguide in the cavity also changes under high light power, leading to a resonance wavelength shift of the cavity mode.

*Q*under different pump level according to the parameters of micro-ring cavity sample and parameters of TPA and FCA in silicon material. Equation (6) shows the relation between the

_{0}*Q*and the effective loss coefficient

_{0}*α*, which includes the contribution of nonlinear losses. The definition of

_{eff}*α*is shown in Eq. (4). In the following calculation,

_{eff}*β*

**,**

*σ*and

*τ*are set as 6.7 × 10

^{−12}m/W 、1.97 × 10

^{−21}m

^{2}and 4ns respectively according to the parameters of bulk silicon material [21

21. A. R. Motamedi, A. H. Nejadmalayeri, A. Khilo, F. X. Kärtner, and E. P. Ippen, “Ultrafast nonlinear optical studies of silicon nanowaveguides,” Opt. Express **20**(4), 4085–4101 (2012). [CrossRef] [PubMed]

*A*is 0.1μm

_{eff}^{2}, calculated according to the parameters of the waveguide cross section. ν is frequency of the pump light.

*α*is the linear loss coefficient. Under low light power, nonlinear losses can be neglected and the

*α*is simplified to

_{eff}*α*. Hence, according to the measured

*Q*under low light power,

_{0}*α*of the waveguide in the cavity can be calculated as 1.14dB/cm by Eq. (4). In the calculation, v

_{g}is c/4.12 calculated by the expression of v

_{g}= c/n

_{g}= c × L × Δλ

_{FSR}/λ

^{2}[22], where c is the light speed in vacuum, the cavity circumference L is 132.5μm, Δλ

_{FSR}is the free spectrum region (FSR) of the cavity, which is measured as 4.4nm.

*P*is the light power in the bus waveguide before coupled to the ring.

_{in}*F(ω)*is the field enhancement factor of the cavity [23] under the light frequency

*ω*. If the input light is close to resonance wavelength, it can be expressed asConsidering that the pump light in the experiment is always on resonance, the field enhancement factor of the pump light, which is denoted by

*F*, can be expressed asWhere

_{p}*ω*is the angular frequency of the pump light.

_{p}*Q*is determined by the coupling coefficient κ, which does not change with the pump level. Substituting the expression of

_{e}*P*(Eqs. (10) and (12)) into Eq. (3) and Eq. (4), it can be seen that the nonlinear loss coefficient

_{c}*α*in the cavity is a function of

_{eff}*P*and

_{in}*Q*. Substituting this expression of

_{0}*α*into Eq. (6), the relation between

_{eff}*P*and

_{in}*Q*can be derived and

_{0}*Q*under different pump level can be calculated. Figure 6 shows the calculated

_{0}*Q*,

_{0}*Q*and

*Q*under different input pump power, which are plotted as the lines with squares, circles and triangles, respectively. In this figure, the power of the pump source is used as the horizontal axis, which is 2.8dB higher than

_{e}*P*estimated by the coupling efficiency between the input lensed fiber and the bus waveguide. It can be seen that due to the nonlinear losses in the micro-ring cavity,

_{in}*Q*decreases with increasing pump level, while,

_{0}*Q*is unchanged. As a result, the total

_{e}*Q*also decreases with increasing pump level due to the nonlinear losses in the cavity.

*Q*is lower than

_{0}*Q*under all the pump levels, showing that the cavity used in the experiment is under-coupling.

_{e}*F*is calculated by Eq. (12).

_{p}*γ*is the nonlinear coefficient of the silicon waveguide,

*T*is the bandwidth of the generated photons by SFWM. In the case of micro-ring cavities,

^{−1}*T*is calculated byunder the assumption that

*ω*. Considering that the signal frequency

_{s}≈ω_{i}≈ω_{p}= ω_{0}*ω*and idler frequency

_{s}*ω*satisfy that

_{i}*ω*,

_{s}+ ω_{i}= 2ω_{p}*Δω*is defined as

*Δω*=

*ω*- ω

_{s}_{0,s}=

*ω*,

_{0,i}- ω_{i}*ω*and

_{0,s}*ω*are resonance frequency of the cavity modes for the signal and idler photons, respectively. Substituting Eq. (11) into Eq. (13) and Eq. (14), it can be calculated that,Hence,

_{0,i}*R ∝P*.

_{I}∝P_{p}^{2}Q^{7}*Q*

_{0}**=**

*Q*, this relation would be simplified to

_{e}*R ∝P*. Another simplification usually used in some condition is to ignore the intrinsic loss of the cavity, i.e.

_{p}^{2}Q^{3}*Q*

**=**

*Q*, it also leads to

_{e}*R ∝P*. In both cases, it is supposed that Q factor of the cavity is constant and the nonlinear losses in the cavity are not considered.

_{p}^{2}Q^{3}*R*. Figure 3 has shown that

*R ∝P*does not make a decent description of the relation between the photon pair generation rate and pump level when the pump power is high. The theoretical analysis in this section shows that under high pump level, the reduction of the Q factor due to the nonlinear losses in the cavity should be considered, leading to the relation of

_{p}^{2}Q^{3}*R ∝P*. To demonstrate it, the C’ measured under an input pump power lower than 0.1mW are fitted by the function of

_{p}^{2}Q^{7}*C’ = BP*. B is the fitting parameter. The value of

_{p}^{2}Q^{7}*Q*utilizes the calculated results shown in Fig. 6, in which the nonlinear losses due to the FCA and TPA in the cavity are considered. The fitting result is shown in Fig. 7, while the fitting result of C’ = A

*P*in Fig. 3 is also plotted for comparison. It can be seen that compared with the results of C’ = A

_{p}^{2}Q^{3}*P*the fitting result of

_{p}^{2}Q^{3},*C’ = BP*not only has a high precision at low pump level, but also agrees well with the C’ at high pump level. The comparison shows that under high pump level, the relation between the photon pair generation rate and pump level should be described by Eq. (15) or

_{p}^{2}Q^{7}*R ∝P*, in which the Q factor reduces with increasing pump level due to the nonlinear losses in the cavity.

_{p}^{2}Q^{7}## 4. Conclusion

## 5. Appendix

*β*is the light propagation constant in the micro-ring cavity.

*t*is the field straight-through coupling coefficient and Λ is the round trip loss coefficient of resonator. In a high Q cavity, they can be simplified as

^{2}<<1 and

*α*L/2 << 1, where κ is the field cross-coupling coefficient.

_{eff}## Acknowledgment

## References and links

1. | 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 |

2. | Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: modeling and applications,” Opt. Express |

3. | 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 |

4. | K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Frequency and Polarization Characteristics of Correlated Photon-Pair Generation Using a Silicon Wire Waveguide,” IEEE J. Sel. Top. Quantum Electron. |

5. | A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics |

6. | Q. Lin and G. P. Agrawal, “Silicon waveguides for creating quantum-correlated photon pairs,” Opt. Lett. |

7. | S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature |

8. | M. J. Thorpe, K. D. Moll, R. J. Jones, B. Safdi, and J. Ye, “Broadband cavity ringdown spectroscopy for sensitive and rapid molecular detection,” Science |

9. | D. G. Rabus, Z. Bian, and A. Shakouri, “A GaInAsP-InP double-ring resonator coupled laser,” IEEE Photon. Technol. Lett. |

10. | 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, and M. G. Thompson, “Photon pair generation in a silicon micro-ring resonator with reverse bias enhancement,” Opt. Express |

11. | W. C. Jiang, X. Lu, J. Zhang, O. Painter, and Q. Lin, “A silicon-chip source of bright photon-pair comb.” (2012). arXiv preprint arXiv:1210.4455 |

12. | L. G. Helt, Z. Yang, M. Liscidini, and J. E. Sipe, “Spontaneous four-wave mixing in microring resonators,” Opt. Lett. |

13. | 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 |

14. | S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics |

15. | S. Azzini, D. Grassani, M. J. Strain, M. Sorel, L. G. Helt, J. E. Sipe, M. Liscidini, M. Galli, and D. Bajoni, “Ultra-low power generation of twin photons in a compact silicon ring resonator,” Opt. Express |

16. | S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express |

17. | N. M. Wright, D. J. Thomson, K. L. Litvinenko, W. R. Headley, A. J. Smith, A. P. Knights, J. H. B. Deane, F. Y. Gardes, G. Z. Mashanovich, R. Gwilliam, and G. T. Reed, “Free carrier lifetime modification for silicon waveguide based devices,” Opt. Express |

18. | S. Azzini, D. Grassani, M. Galli, L. C. Andreani, M. Sorel, M. J. Strain, L. G. Helt, J. E. Sipe, M. Liscidini, and D. Bajoni, “From classical four-wave mixing to parametric fluorescence in silicon microring resonators,” Opt. Lett. |

19. | L. G. Helt, M. Liscidini, and J. E. Sipe, “How does it scale? comparing quantum and classical nonlinear optical processes in integrated devices,” J. Opt. Soc. Am. B |

20. | B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring Resonator Channel Dropping Filters,” J. Lightwave Technol. |

21. | A. R. Motamedi, A. H. Nejadmalayeri, A. Khilo, F. X. Kärtner, and E. P. Ippen, “Ultrafast nonlinear optical studies of silicon nanowaveguides,” Opt. Express |

22. | D. G. Rabus, Integrated ring resonators (Springer, Berlin, 2007). |

23. | M. Soltani, Novel integrated silicon nanophotonic structures using ultra-high Q resonator, Ph.D. dissertation, Georgia Institute of Technology, 2009. |

24. | M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics |

25. | 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. |

**OCIS Codes**

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: October 24, 2013

Revised Manuscript: December 6, 2013

Manuscript Accepted: January 27, 2014

Published: January 30, 2014

**Citation**

Yuan Guo, Wei Zhang, Ning Lv, Qiang Zhou, Yidong Huang, and Jiangde Peng, "The impact of nonlinear losses in the silicon micro-ring cavities on CW pumping correlated photon pair generation," Opt. Express **22**, 2620-2631 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-3-2620

Sort: Year | Journal | Reset

### References

- 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). [CrossRef] [PubMed]
- 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]
- A. J. Shields, “Semiconductor quantum light sources,” Nat. Photonics 1(4), 215–223 (2007). [CrossRef]
- Q. Lin, G. P. Agrawal, “Silicon waveguides for creating quantum-correlated photon pairs,” Opt. Lett. 31(21), 3140–3142 (2006). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- 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]
- W. C. Jiang, X. Lu, J. Zhang, O. Painter, and Q. Lin, “A silicon-chip source of bright photon-pair comb.” (2012). arXiv preprint arXiv:1210.4455
- 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]
- A. C. Turner, M. A. Foster, A. L. Gaeta, M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008). [CrossRef] [PubMed]
- S. F. Preble, Q. Xu, M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics 1, 1293–1296 (2007).
- 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). [CrossRef] [PubMed]
- S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, P. Emplit, S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express 17(19), 16558–16570 (2009). [CrossRef] [PubMed]
- N. M. Wright, D. J. Thomson, K. L. Litvinenko, W. R. Headley, A. J. Smith, A. P. Knights, J. H. B. Deane, F. Y. Gardes, G. Z. Mashanovich, R. Gwilliam, G. T. Reed, “Free carrier lifetime modification for silicon waveguide based devices,” Opt. Express 16(24), 19779–19784 (2008). [CrossRef] [PubMed]
- S. Azzini, D. Grassani, M. Galli, L. C. Andreani, M. Sorel, M. J. Strain, L. G. Helt, J. E. Sipe, M. Liscidini, D. Bajoni, “From classical four-wave mixing to parametric fluorescence in silicon microring resonators,” Opt. Lett. 37(18), 3807–3809 (2012). [CrossRef] [PubMed]
- L. G. Helt, M. Liscidini, J. E. Sipe, “How does it scale? comparing quantum and classical nonlinear optical processes in integrated devices,” J. Opt. Soc. Am. B 29(8), 2199–2212 (2012). [CrossRef]
- 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]
- A. R. Motamedi, A. H. Nejadmalayeri, A. Khilo, F. X. Kärtner, E. P. Ippen, “Ultrafast nonlinear optical studies of silicon nanowaveguides,” Opt. Express 20(4), 4085–4101 (2012). [CrossRef] [PubMed]
- D. G. Rabus, Integrated ring resonators (Springer, Berlin, 2007).
- M. Soltani, Novel integrated silicon nanophotonic structures using ultra-high Q resonator, Ph.D. dissertation, Georgia Institute of Technology, 2009.
- 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]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.