Abstract

The Kerr effect in silicon ring resonators (RRs) is widely used for switching and regeneration of optical communications signals. In addition, it has been shown to considerably limit the performance of refractive index sensors based on high quality-factor RRs. While the Kerr effect's impact on output signals of silicon RRs is well known, its influence on the properties of the output noise is yet to be explored. In this work, we analytically and numerically analyze the noise properties of Kerr effect in silicon RRs. We show that the input power, RR's bandwidth, and input optical signal to noise ratio (OSNR) have significant influence on the power and distribution of the output noise. We use the developed noise model to evaluate the RR's noise figure and output noise distribution for optical communications and sensing applications. These noise properties can be used for the design and performance evaluation of optical communications systems and sensors using silicon photonic RRs.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Photon pair generation in a silicon micro-ring resonator with reverse bias enhancement

Erman Engin, Damien Bonneau, Chandra M. Natarajan, Alex S. Clark, M. G. Tanner, R. H. Hadfield, Sanders N. Dorenbos, Val Zwiller, Kazuya Ohira, Nobuo Suzuki, Haruhiko Yoshida, Norio Iizuka, Mizunori Ezaki, Jeremy L. O’Brien, and Mark G. Thompson
Opt. Express 21(23) 27826-27834 (2013)

Numerical analysis of the performance of Mach-Zehnder interferometric logic gates enhanced with coupled nonlinear ring- resonators

Francisco Cuesta-Soto, Alejandro Martínez, J. Blasco, and Javier Martí
Opt. Express 15(5) 2323-2335 (2007)

All-optical tunable photonic crystal nor gate based on the nonlinear Kerr effect in a silicon nanocavity

Shirin Afzal, Vahid Ahmadi, and Majid Ebnali-Heidari
J. Opt. Soc. Am. B 30(9) 2535-2539 (2013)

References

  • View by:
  • |
  • |
  • |

  1. J. E. Heebner and R. W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt. Lett. 24(12), 847–849 (1999).
    [PubMed]
  2. S. Blair, J. E. Heebner, and R. W. Boyd, “Beyond the absorption-limited nonlinear phase shift with microring resonators,” Opt. Lett. 27(5), 357–359 (2002).
    [PubMed]
  3. Y. Chen and S. Blair, “Nonlinear phase shift of cascaded microring resonators,” J. Opt. Soc. Am. B 20(10), 2125–2132 (2003).
  4. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).
  5. 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).
    [PubMed]
  6. N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 2885 (2013).
    [PubMed]
  7. L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
    [PubMed]
  8. Q. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15(3), 924–929 (2007).
    [PubMed]
  9. Y. Lu, F. Liu, M. Qiu, and Y. Su, “All-optical format conversions from NRZ to BPSK and QPSK based on nonlinear responses in silicon microring resonators,” Opt. Express 15(21), 14275–14282 (2007).
    [PubMed]
  10. T. Ye, C. Yan, Y. Lu, F. Liu, and Y. Su, “All-optical regenerative NRZ-to-RZ format conversion using coupled ring-resonator optical waveguide,” Opt. Express 16(20), 15325–15331 (2008).
    [PubMed]
  11. C. Yan, T. Ye, and Y. Su, “All-optical regenerative NRZ-OOK-to-RZ-BPSK format conversion using silicon waveguides,” Opt. Lett. 34(1), 58–60 (2009).
    [PubMed]
  12. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007).
    [PubMed]
  13. J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express 16(6), 4296–4301 (2008).
    [PubMed]
  14. G. D. Kim, H. S. Lee, C. H. Park, S. S. Lee, B. T. Lim, H. K. Bae, and W. G. Lee, “Silicon photonic temperature sensor employing a ring resonator manufactured using a standard CMOS process,” Opt. Express 18(21), 22215–22221 (2010).
    [PubMed]
  15. A. Fernández Gavela, D. Grajales García, J. C. Ramirez, and L. M. Lechuga, “Last Advances in Silicon-Based Optical Biosensors,” Sensors (Basel) 16(3), 285 (2016).
    [PubMed]
  16. H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive silicon microring sensor with sharp asymmetrical resonance,” Opt. Express 18(3), 2967–2972 (2010).
    [PubMed]
  17. J. Hu, X. Sun, A. Agarwal, and L. C. Kimerling, “Design guidelines for optical resonator biochemical sensors,” J. Opt. Soc. Am. B 26(5), 1032–1041 (2009).
  18. X. Zhou, L. Zhang, and W. Pang, “Performance and noise analysis of optical microresonator-based biochemical sensors using intensity detection,” Opt. Express 24(16), 18197–18208 (2016).
    [PubMed]
  19. K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
    [PubMed]
  20. A. Van den Bos, “The multivariate complex normal distribution-a generalization,” IEEE Trans. Inf. Theory 41(2), 537–539 (1995).
  21. B. Picinbono, “Second-Order Complex Random Vectors and Normal Distributions,” IEEE Trans. Signal Process. 44(10), 2637–2640 (1996).
  22. L. Yin and G. P. Agrawal, “Impact of two-photon absorption on self-phase modulation in silicon waveguides,” Opt. Lett. 32(14), 2031–2033 (2007).
    [PubMed]
  23. R. W. Boyd, Nonlinear Optics (Academic, 2010).
  24. T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997).
  25. H. Rong, Y. H. Kuo, A. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14(3), 1182–1188 (2006).
    [PubMed]
  26. 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(7), 4881–4887 (2008).
    [PubMed]
  27. K. Padmaraju and K. Bergman, “Resolving the thermal challenges for silicon microring resonator devices,” Nanophotonics 3(4–5), 269–281 (2013).
  28. G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).
  29. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
  30. J. G. Proakis and M. Salehi, Digital Communications (McGraw Hill, 2008).
  31. C. Manolatou and M. Lipson, “All-optical silicon modulators based on carrier injection by two-photon absorption,” J. Lightwave Technol. 24, 1433 (2006).
  32. R. G. Gallager, Stochastic Processes, Theory for Applications (Cambridge University, 2013), Chap. 8.
  33. H. Xu, M. Hafezi, J. Fan, J. M. Taylor, G. F. Strouse, and Z. Ahmed, “Ultra-sensitive chip-based photonic temperature sensor using ring resonator structures,” Opt. Express 22(3), 3098–3104 (2014).
    [PubMed]

2016 (2)

A. Fernández Gavela, D. Grajales García, J. C. Ramirez, and L. M. Lechuga, “Last Advances in Silicon-Based Optical Biosensors,” Sensors (Basel) 16(3), 285 (2016).
[PubMed]

X. Zhou, L. Zhang, and W. Pang, “Performance and noise analysis of optical microresonator-based biochemical sensors using intensity detection,” Opt. Express 24(16), 18197–18208 (2016).
[PubMed]

2014 (1)

2013 (2)

K. Padmaraju and K. Bergman, “Resolving the thermal challenges for silicon microring resonator devices,” Nanophotonics 3(4–5), 269–281 (2013).

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 2885 (2013).
[PubMed]

2012 (2)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
[PubMed]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

2010 (3)

2009 (2)

2008 (3)

2007 (4)

2006 (2)

2005 (1)

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).

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).
[PubMed]

2003 (2)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[PubMed]

Y. Chen and S. Blair, “Nonlinear phase shift of cascaded microring resonators,” J. Opt. Soc. Am. B 20(10), 2125–2132 (2003).

2002 (1)

1999 (1)

1997 (1)

T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997).

1996 (1)

B. Picinbono, “Second-Order Complex Random Vectors and Normal Distributions,” IEEE Trans. Signal Process. 44(10), 2637–2640 (1996).

1995 (1)

A. Van den Bos, “The multivariate complex normal distribution-a generalization,” IEEE Trans. Inf. Theory 41(2), 537–539 (1995).

Agarwal, A.

Agrawal, G. P.

Ahmed, Z.

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).
[PubMed]

Badding, J. V.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 2885 (2013).
[PubMed]

Bae, H. K.

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007).
[PubMed]

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).
[PubMed]

Bartolozzi, I.

Bergman, K.

K. Padmaraju and K. Bergman, “Resolving the thermal challenges for silicon microring resonator devices,” Nanophotonics 3(4–5), 269–281 (2013).

Besnard, P.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).

Bienstman, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007).
[PubMed]

Blair, S.

Blin, S.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).

Bogaerts, W.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

Boyd, R. W.

Brabec, T.

T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997).

Chen, L.

Chen, Y.

Citrin, D. S.

Claes, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

Cohen, O.

Day, T. D.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 2885 (2013).
[PubMed]

De Heyn, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

De Vos, K.

Derevyanko, S. A.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[PubMed]

DeVos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

Fan, J.

Fan, L.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
[PubMed]

Fernández Gavela, A.

A. Fernández Gavela, D. Grajales García, J. C. Ramirez, and L. M. Lechuga, “Last Advances in Silicon-Based Optical Biosensors,” Sensors (Basel) 16(3), 285 (2016).
[PubMed]

Foster, M. A.

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).

Gaeta, A. L.

Grajales García, D.

A. Fernández Gavela, D. Grajales García, J. C. Ramirez, and L. M. Lechuga, “Last Advances in Silicon-Based Optical Biosensors,” Sensors (Basel) 16(3), 285 (2016).
[PubMed]

Hafezi, M.

Healy, N.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 2885 (2013).
[PubMed]

Heebner, J. E.

Hu, J.

Kim, G. D.

Kimerling, L. C.

Koos, C.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).

Krausz, F.

T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997).

Kuo, Y. H.

Lechuga, L. M.

A. Fernández Gavela, D. Grajales García, J. C. Ramirez, and L. M. Lechuga, “Last Advances in Silicon-Based Optical Biosensors,” Sensors (Basel) 16(3), 285 (2016).
[PubMed]

Lee, H. S.

Lee, S. S.

Lee, W. G.

Leuthold, J.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).

Lim, B. T.

Lipson, M.

Liu, A.

Liu, F.

Lu, Y.

Manolatou, C.

Mehta, P.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 2885 (2013).
[PubMed]

Niu, B.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
[PubMed]

Padmaraju, K.

K. Padmaraju and K. Bergman, “Resolving the thermal challenges for silicon microring resonator devices,” Nanophotonics 3(4–5), 269–281 (2013).

Panepucci, R. 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).
[PubMed]

Pang, W.

Paniccia, M.

Park, C. H.

Peacock, A. C.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 2885 (2013).
[PubMed]

Picinbono, B.

B. Picinbono, “Second-Order Complex Random Vectors and Normal Distributions,” IEEE Trans. Signal Process. 44(10), 2637–2640 (1996).

Qi, M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
[PubMed]

Qiu, M.

Ramirez, J. C.

A. Fernández Gavela, D. Grajales García, J. C. Ramirez, and L. M. Lechuga, “Last Advances in Silicon-Based Optical Biosensors,” Sensors (Basel) 16(3), 285 (2016).
[PubMed]

Robinson, J. T.

Rong, H.

Schacht, E.

Selvaraja, S. K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

Shen, H.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
[PubMed]

Stéphan, G. M.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).

Strouse, G. F.

Su, Y.

Suhailin, F. H.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 2885 (2013).
[PubMed]

Sun, X.

Tam, T. T.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).

Taylor, J. M.

Têtu, M.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).

Turitsyn, K. S.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[PubMed]

Turitsyn, S. K.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[PubMed]

Turner, A. C.

Van den Bos, A.

A. Van den Bos, “The multivariate complex normal distribution-a generalization,” IEEE Trans. Inf. Theory 41(2), 537–539 (1995).

Van Thourhout, D.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

Van Vaerenbergh, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

Varghese, L. T.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
[PubMed]

Vukovic, N.

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 2885 (2013).
[PubMed]

Wang, J.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
[PubMed]

Weiner, A. M.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
[PubMed]

Xu, H.

Xu, Q.

Xuan, Y.

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
[PubMed]

Yan, C.

Ye, T.

Yi, H.

Yin, L.

Yurkevich, I. V.

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[PubMed]

Zhang, L.

Zhou, X.

Zhou, Z.

IEEE Trans. Inf. Theory (1)

A. Van den Bos, “The multivariate complex normal distribution-a generalization,” IEEE Trans. Inf. Theory 41(2), 537–539 (1995).

IEEE Trans. Signal Process. (1)

B. Picinbono, “Second-Order Complex Random Vectors and Normal Distributions,” IEEE Trans. Signal Process. 44(10), 2637–2640 (1996).

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Laser Photonics Rev. (1)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photonics Rev. 20(10), 47–73 (2012).

Nanophotonics (1)

K. Padmaraju and K. Bergman, “Resolving the thermal challenges for silicon microring resonator devices,” Nanophotonics 3(4–5), 269–281 (2013).

Nat. Photonics (1)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).

Nature (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).
[PubMed]

Opt. Express (11)

H. Rong, Y. H. Kuo, A. Liu, M. Paniccia, and O. Cohen, “High efficiency wavelength conversion of 10 Gb/s data in silicon waveguides,” Opt. Express 14(3), 1182–1188 (2006).
[PubMed]

H. Yi, D. S. Citrin, and Z. Zhou, “Highly sensitive silicon microring sensor with sharp asymmetrical resonance,” Opt. Express 18(3), 2967–2972 (2010).
[PubMed]

G. D. Kim, H. S. Lee, C. H. Park, S. S. Lee, B. T. Lim, H. K. Bae, and W. G. Lee, “Silicon photonic temperature sensor employing a ring resonator manufactured using a standard CMOS process,” Opt. Express 18(21), 22215–22221 (2010).
[PubMed]

H. Xu, M. Hafezi, J. Fan, J. M. Taylor, G. F. Strouse, and Z. Ahmed, “Ultra-sensitive chip-based photonic temperature sensor using ring resonator structures,” Opt. Express 22(3), 3098–3104 (2014).
[PubMed]

X. Zhou, L. Zhang, and W. Pang, “Performance and noise analysis of optical microresonator-based biochemical sensors using intensity detection,” Opt. Express 24(16), 18197–18208 (2016).
[PubMed]

Q. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express 15(3), 924–929 (2007).
[PubMed]

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007).
[PubMed]

Y. Lu, F. Liu, M. Qiu, and Y. Su, “All-optical format conversions from NRZ to BPSK and QPSK based on nonlinear responses in silicon microring resonators,” Opt. Express 15(21), 14275–14282 (2007).
[PubMed]

J. T. Robinson, L. Chen, and M. Lipson, “On-chip gas detection in silicon optical microcavities,” Opt. Express 16(6), 4296–4301 (2008).
[PubMed]

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(7), 4881–4887 (2008).
[PubMed]

T. Ye, C. Yan, Y. Lu, F. Liu, and Y. Su, “All-optical regenerative NRZ-to-RZ format conversion using coupled ring-resonator optical waveguide,” Opt. Express 16(20), 15325–15331 (2008).
[PubMed]

Opt. Lett. (4)

Phys. Rev. A (1)

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).

Phys. Rev. Lett. (2)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, and S. K. Turitsyn, “Information capacity of optical fiber channels with zero average dispersion,” Phys. Rev. Lett. 91(20), 203901 (2003).
[PubMed]

T. Brabec and F. Krausz, “Nonlinear Optical Pulse Propagation in the Single-Cycle Regime,” Phys. Rev. Lett. 78(17), 3282–3285 (1997).

Sci. Rep. (1)

N. Vukovic, N. Healy, F. H. Suhailin, P. Mehta, T. D. Day, J. V. Badding, and A. C. Peacock, “Ultrafast optical control using the Kerr nonlinearity in hydrogenated amorphous silicon microcylindrical resonators,” Sci. Rep. 3, 2885 (2013).
[PubMed]

Science (1)

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “All-Silicon Passive Optical Diode,” Science 335(6067), 447–450 (2012).
[PubMed]

Sensors (Basel) (1)

A. Fernández Gavela, D. Grajales García, J. C. Ramirez, and L. M. Lechuga, “Last Advances in Silicon-Based Optical Biosensors,” Sensors (Basel) 16(3), 285 (2016).
[PubMed]

Other (3)

R. W. Boyd, Nonlinear Optics (Academic, 2010).

J. G. Proakis and M. Salehi, Digital Communications (McGraw Hill, 2008).

R. G. Gallager, Stochastic Processes, Theory for Applications (Cambridge University, 2013), Chap. 8.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1 Silicon notch ring resonator.
Fig. 2
Fig. 2 (a). Power and phase of the RR's ensemble average output field at the presence of the Kerr effect. (b) without the Kerr effect.
Fig. 3
Fig. 3 (a) Output pulse's power enhancement ratio and phase shift with respect to a RR without Kerr effect. (b). Output noise power enhancement ratio with respect to a RR without Kerr effect.
Fig. 4
Fig. 4 RR's noise figure with Kerr effect and when only linear effects take place.
Fig. 5
Fig. 5 The axes ratio and angle rotation of the ellipse defined by the equal-probability density contours of the output noise's probability density function. Inset: Output noise distribution obtained from the Monte Carlo simulation for input power of 10dBm.
Fig. 6
Fig. 6 (a). Coupling ratio of the RR vs. the input power. (b) Deviation of the phase between E 2 and E 1 from its value at the absence of the Kerr effect vs. the input power.
Fig. 7
Fig. 7 (a). RR's noise figure with Kerr effect and when only linear effects take place, vs. the RR's FWHM. (b). The parameters of the ellipse defined by the output noise's PDF, vs. the RR's FWHM
Fig. 8
Fig. 8 (a). RR's noise figure with Kerr effect and when only linear effects take place, vs. the input OSNR. (b). The parameters of the ellipse defined by the output noise's PDF, vs. the input OSNR. Inset: Output noise distribution obtained by the Monte Carlo simulation for input OSNR of 5dB/0.1nm.
Fig. 9
Fig. 9 (a). Output noise power enhancement ratio vs. the input power. (b). Output noise power enhancement ratio vs. the RR's FWHM. (c). Output noise power enhancement ratio vs. the input OSNR.
Fig. 10
Fig. 10 Power spectral density of the output noise for the linear and nonlinear cases.

Tables (1)

Tables Icon

Table 1 Simulated ring resonator parameters

Equations (34)

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

E 3 ( t )=r E 1 ( t )+is E 2 ( t )
E 4 ( t )=is E 1 ( t )+r E 2 ( t )
E 2 ( t )=a( t ) e iϕ( t ) E 4 ( tΔt )
E z =i k 0 n 2 n 0 ( 1+iK ) | E | 2 E α l E 2
a( t )= exp( α l L/2 ) 1+b I 4 ( tΔt )
ϕ( t )= k 0 L+ 1 2K ln[ 1+b I 4 ( tΔt ) ]
E 4 ( t )=is E 1 ( t )+ra( t ) e iϕ( t ) E 4 ( tΔt ) =is E 1 ( t )+v exp{ j 2K ln[ 1+b I 4 ( tΔt ) ] } 1+b I 4 ( tΔt ) E 4 ( tΔt )
g( x ) exp{ i 2K ln[ 1+x ] } 1+x
E 4 ( t )=is E 1 ( t )+v m=0 M a ˜ m | E 4 ( tΔt ) | 2m E 4 ( tΔt )
| E 4 | 2m E 4 = ( E ¯ 4 + n 4 ) m+1 ( E ¯ 4 * + n 4 * ) m =[ l=0 m+1 ( m+1 l ) E ¯ 4 m+1l n 4 l ][ p=0 m ( m p ) ( E ¯ 4 * ) mp ( n 4 * ) p ]
| E 4 | 2m E 4 | E ¯ 4 | 2m E ¯ 4 +m | E ¯ 4 | 2( m1 ) E ¯ 4 2 n 4 * +( m+1 ) | E ¯ 4 | 2m n 4
E 4 ( t )=is E 1 ( t )+v m=0 M a ˜ m [ | E ¯ 4 ( tΔt ) | 2m E ¯ 4 ( tΔt )+ +m | E ¯ 4 ( tΔt ) | 2( m1 ) E ¯ 4 2 ( tΔt ) n 4 * ( tΔt ) + ( m+1 ) | E ¯ 4 ( tΔt ) | 2m n 4 ( tΔt ) ]
E ¯ 4 ( t )=is E ¯ 1 ( t )+v m=0 M a ˜ m | E ¯ 4 ( tΔt ) | 2m E ¯ 4 ( tΔt )
n 4 ( t )=is n 1 ( t )+v m=0 M a ˜ m [ m | E ¯ 4 ( tΔt ) | 2( m1 ) E ¯ 4 2 ( tΔt ) n 4 * ( tΔt )+ + ( m+1 ) | E ¯ 4 ( tΔt ) | 2m n 4 ( tΔt ) ]
d 1 =is d 2,l ( t )=v m=0 M a ˜ m m | E ¯ 4 ( tlΔt ) | 2( m1 ) E ¯ 4 2 ( tlΔt ) d 3,l ( t )=v m=0 M a ˜ m ( m+1 ) | E ¯ 4 ( tlΔt ) | 2m
lim | E 1 ( tlΔt ) | 2 0 d 2,l ( t )=0 lim | E 1 ( tlΔt ) | 2 0 d 3,l ( t )=v
n 4 ( t )= d 1 n 1 ( t )+ d 2,1 ( t ) n 4 * ( tΔt )+ d 3,1 ( t ) n 4 ( tΔt )
n 4 ( t )= p=0 N α p ( t ) n 1 ( tpΔt )+ β p ( t ) n 1 * ( tpΔt )
α p ( t )= α p1 ( t ) d 3,p ( t ) β p1 ( t ) d 2,p * ( t ), α 0 ( t )= d 1 β p ( t )= β p1 ( t ) d 3,p * ( t ) α p1 ( t ) d 2,p ( t ), β 0 ( t )=0
N= τ p c L n 0
lim | E 1 | 2 0 α p ( t )=is v p lim | E 1 | 2 0 β p ( t )=0
n 4,lin ( t )= lim | E 1 | 2 0 n 4 ( t )=is p=0 N v p n 1 ( tpΔt )
R 4 ( t 1 , t 2 )=E[ n 4 ( t 1 ) n 4 * ( t 2 ) ] = p,k=0 N α p ( t 1 ) α k * ( t 2 ) R 1 ( ( kp )Δt+τ )+ β p ( t 1 ) β k * ( t 2 ) R 1 * ( ( kp )Δt+τ )
σ 4 2 ( t )=E[ | n 4 ( t ) | 2 ] = p,k=0 N α p ( t ) α k * ( t ) R 1 ( ( kp )Δt )+ β p ( t ) β k * ( t ) R 1 * ( ( kp )Δt )
C 4 ( t 1 , t 2 )=E[ n 4 ( t 1 ) n 4 ( t 2 ) ] = p,k=0 N α p ( t 1 ) β k ( t 2 ) R 1 ( ( kp )Δt+τ )+ α k ( t 2 ) β p ( t 1 ) R 1 * ( ( kp )Δt+τ )
R 1,4 ( t 1 , t 2 )=E[ n 1 ( t 1 ) n 4 * ( t 2 ) ]= p=0 N α p * ( t 2 ) R 1 ( τ+pΔt )
C 1,4 ( t 1 , t 2 )=E[ n 1 ( t 1 ) n 4 ( t 2 ) ]= p=0 N β p ( t 2 ) R 1 ( τ+pΔt )
R 2 ( t 1 , t 2 )= 1 r 2 [ R 4 ( t 1 , t 2 )+is R 1,4 * ( t 2 , t 1 )is R 1,4 ( t 1 , t 2 )+ s 2 R 1 ( τ ) ]
σ 2 2 ( t )= 1 r 2 [ σ 4 2 ( t )+2sIm{ R 1,4 ( t,t ) }+ s 2 σ 1 2 ]
C 2 ( t 1 , t 2 )= 1 r 2 [ C 4 ( t 1 , t 2 )is C 1,4 ( t 2 , t 1 )is C 1,4 ( t 1 , t 2 ) ]
R 3 ( t 1 , t 2 )= 1 r 2 [ R 1 ( τ )is R 1,4 ( t 1 , t 2 )+is R 1,4 * ( t 2 , t 1 )+ s 2 R 4 ( t 1 , t 2 ) ]
σ 3 2 ( t )= 1 r 2 [ σ 1 2 +2sIm{ R 1,4 ( t,t ) }+ s 2 σ 4 2 ( t ) ]
C 3 ( t 1 , t 2 )= 1 r 2 [ is C 1,4 ( t 1 , t 2 )+is C 1,4 ( t 2 , t 1 ) s 2 C 4 ( t 1 , t 2 ) ]
Couplingratio= | s E 2 | 2 | r E 1 | 2

Metrics