Abstract

Waveguide backscatter affects the resonance shape and quality factor (Q) of ring resonators. Our simple analytical expression predicts how waveguide backscatter spoils the Q and results in resonance splitting. We show that the effects of backscatter depend only on the finesse of the resonator and when it can safely be ignored. Finally, we describe the effects of backscatter in low-loss cavities using simple complex Lorentzian functions.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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  1. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
    [Crossref]
  2. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
    [Crossref]
  3. D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Splitting of high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. 20, 1835–1837 (1995).
    [Crossref] [PubMed]
  4. A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99, 173603 (2007).
    [Crossref] [PubMed]
  5. B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997).
    [Crossref] [PubMed]
  6. M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693–3695 (2004).
    [Crossref]
  7. A. Canciamilla, M. Torreggiani, C. Ferrari, F. Morichetti, R. Costa, and A. Melloni, “Backscatter in integrated optical waveguides and circuits,” Proc. SPIE 7218, 72180N (2009).
    [Crossref]
  8. F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010).
    [Crossref]
  9. G. Ballesteros, J. Matres, J. Martí, and C. Oton, “Characterizing and modeling backscattering in silicon microring resonators,” Opt. Express 19, 1005 (2011).
    [Crossref]
  10. A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
    [Crossref]
  11. A. E. Siegman, Lasers (Univ. Sci. books1986).
  12. Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32, 915–917 (2007).
    [Crossref] [PubMed]
  13. A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
    [Crossref]
  14. D. Melati, A. Melloni, and F. Morichetti, “Real photonic waveguides: guiding light through imperfections,” Adv. Opt. Photonics 6, 156 (2014).
    [Crossref]
  15. R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 29, 06F309 (2011).
    [Crossref]

2016 (1)

A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
[Crossref]

2014 (1)

D. Melati, A. Melloni, and F. Morichetti, “Real photonic waveguides: guiding light through imperfections,” Adv. Opt. Photonics 6, 156 (2014).
[Crossref]

2012 (1)

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

2011 (2)

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 29, 06F309 (2011).
[Crossref]

G. Ballesteros, J. Matres, J. Martí, and C. Oton, “Characterizing and modeling backscattering in silicon microring resonators,” Opt. Express 19, 1005 (2011).
[Crossref]

2010 (2)

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
[Crossref]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010).
[Crossref]

2009 (1)

A. Canciamilla, M. Torreggiani, C. Ferrari, F. Morichetti, R. Costa, and A. Melloni, “Backscatter in integrated optical waveguides and circuits,” Proc. SPIE 7218, 72180N (2009).
[Crossref]

2007 (2)

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref] [PubMed]

Z. Shi, R. W. Boyd, D. J. Gauthier, and C. C. Dudley, “Enhancing the spectral sensitivity of interferometers using slow-light media,” Opt. Lett. 32, 915–917 (2007).
[Crossref] [PubMed]

2004 (1)

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693–3695 (2004).
[Crossref]

1997 (2)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997).
[Crossref] [PubMed]

1995 (1)

Aida, Y.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 29, 06F309 (2011).
[Crossref]

Baehr-Jones, T.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 29, 06F309 (2011).
[Crossref]

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Ballesteros, G.

G. Ballesteros, J. Matres, J. Martí, and C. Oton, “Characterizing and modeling backscattering in silicon microring resonators,” Opt. Express 19, 1005 (2011).
[Crossref]

Barclay, P. E.

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693–3695 (2004).
[Crossref]

Benson, O.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref] [PubMed]

Bienstman, P.

A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
[Crossref]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Bogaerts, W.

A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
[Crossref]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Bojko, R. J.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 29, 06F309 (2011).
[Crossref]

Borselli, M.

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693–3695 (2004).
[Crossref]

Boyd, R. W.

Canciamilla, A.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
[Crossref]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010).
[Crossref]

A. Canciamilla, M. Torreggiani, C. Ferrari, F. Morichetti, R. Costa, and A. Melloni, “Backscatter in integrated optical waveguides and circuits,” Proc. SPIE 7218, 72180N (2009).
[Crossref]

Chu, S. T.

B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997).
[Crossref] [PubMed]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Claes, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Costa, R.

A. Canciamilla, M. Torreggiani, C. Ferrari, F. Morichetti, R. Costa, and A. Melloni, “Backscatter in integrated optical waveguides and circuits,” Proc. SPIE 7218, 72180N (2009).
[Crossref]

De Heyn, P.

A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
[Crossref]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

De La Rue, R.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
[Crossref]

De La Rue, R. M.

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010).
[Crossref]

De Vos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Dudley, C. C.

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Ferrari, C.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
[Crossref]

A. Canciamilla, M. Torreggiani, C. Ferrari, F. Morichetti, R. Costa, and A. Melloni, “Backscatter in integrated optical waveguides and circuits,” Proc. SPIE 7218, 72180N (2009).
[Crossref]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Gauthier, D. J.

Götzinger, S.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref] [PubMed]

Hare, J.

Haroche, S.

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

He, L.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 29, 06F309 (2011).
[Crossref]

Hochberg, M.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 29, 06F309 (2011).
[Crossref]

Krauss, T. F.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
[Crossref]

Kumar Selvaraja, S.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Laine, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Laine, J. P.

Lefèvre-Seguin, V.

Li, A.

A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
[Crossref]

Li, J.

R. J. Bojko, J. Li, L. He, T. Baehr-Jones, M. Hochberg, and Y. Aida, “Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides,” J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 29, 06F309 (2011).
[Crossref]

Little, B. E.

B. E. Little, J. P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997).
[Crossref] [PubMed]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. Laine, “Microring resonator channel dropping filter,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Martí, J.

G. Ballesteros, J. Matres, J. Martí, and C. Oton, “Characterizing and modeling backscattering in silicon microring resonators,” Opt. Express 19, 1005 (2011).
[Crossref]

Martinelli, M.

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010).
[Crossref]

Matres, J.

G. Ballesteros, J. Matres, J. Martí, and C. Oton, “Characterizing and modeling backscattering in silicon microring resonators,” Opt. Express 19, 1005 (2011).
[Crossref]

Mazzei, A.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref] [PubMed]

Melati, D.

D. Melati, A. Melloni, and F. Morichetti, “Real photonic waveguides: guiding light through imperfections,” Adv. Opt. Photonics 6, 156 (2014).
[Crossref]

Melloni, A.

D. Melati, A. Melloni, and F. Morichetti, “Real photonic waveguides: guiding light through imperfections,” Adv. Opt. Photonics 6, 156 (2014).
[Crossref]

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
[Crossref]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010).
[Crossref]

A. Canciamilla, M. Torreggiani, C. Ferrari, F. Morichetti, R. Costa, and A. Melloni, “Backscatter in integrated optical waveguides and circuits,” Proc. SPIE 7218, 72180N (2009).
[Crossref]

Menezes, L. de S.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref] [PubMed]

Morichetti, F.

D. Melati, A. Melloni, and F. Morichetti, “Real photonic waveguides: guiding light through imperfections,” Adv. Opt. Photonics 6, 156 (2014).
[Crossref]

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
[Crossref]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010).
[Crossref]

A. Canciamilla, M. Torreggiani, C. Ferrari, F. Morichetti, R. Costa, and A. Melloni, “Backscatter in integrated optical waveguides and circuits,” Proc. SPIE 7218, 72180N (2009).
[Crossref]

O’Faolain, L.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
[Crossref]

Oton, C.

G. Ballesteros, J. Matres, J. Martí, and C. Oton, “Characterizing and modeling backscattering in silicon microring resonators,” Opt. Express 19, 1005 (2011).
[Crossref]

Painter, O.

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693–3695 (2004).
[Crossref]

Raimond, J.-M.

Samarelli, A.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
[Crossref]

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010).
[Crossref]

Sandoghdar, V.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref] [PubMed]

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, “Splitting of high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. 20, 1835–1837 (1995).
[Crossref] [PubMed]

Shi, Z.

Siegman, A. E.

A. E. Siegman, Lasers (Univ. Sci. books1986).

Sorel, M.

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, “Coherent backscattering in optical microring resonators,” Appl. Phys. Lett. 96, 081112 (2010).
[Crossref]

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
[Crossref]

Srinivasan, K.

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693–3695 (2004).
[Crossref]

Torreggiani, M.

A. Canciamilla, M. Torreggiani, C. Ferrari, F. Morichetti, R. Costa, and A. Melloni, “Backscatter in integrated optical waveguides and circuits,” Proc. SPIE 7218, 72180N (2009).
[Crossref]

Van Thourhout, D.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

Van Vaerenbergh, T.

A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
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W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
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Zumofen, G.

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99, 173603 (2007).
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D. Melati, A. Melloni, and F. Morichetti, “Real photonic waveguides: guiding light through imperfections,” Adv. Opt. Photonics 6, 156 (2014).
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A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O’Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: Coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2, 181–194 (2010).
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W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, “Silicon microring resonators,” Laser Photon. Rev. 6, 47–73 (2012).
[Crossref]

A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, and W. Bogaerts, “Backscattering in silicon microring resonators: a quantitative analysis,” Laser Photon. Rev. 10, 420–431 (2016).
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Phys. Rev. Lett. (1)

A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99, 173603 (2007).
[Crossref] [PubMed]

Proc. SPIE (1)

A. Canciamilla, M. Torreggiani, C. Ferrari, F. Morichetti, R. Costa, and A. Melloni, “Backscatter in integrated optical waveguides and circuits,” Proc. SPIE 7218, 72180N (2009).
[Crossref]

Other (1)

A. E. Siegman, Lasers (Univ. Sci. books1986).

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Figures (6)

Fig. 1
Fig. 1 The ring resonator (right) reflects part of the light incident on the coupler (r1), in the same way that a mirror reflects r1 field in a Fabry Perot (left). The field inside the cavity (Ec) depends on the propagation loss per pass inside the cavity (tp1, tp2) together with the transmission (t1, t2) and reflection (r1, r2) of the couplers.
Fig. 2
Fig. 2 The round trip field transmission of a Fabry-Perot cavity (tc) combines the propagation loss (tp = tp1tp2) and the loss in the couplers (which act as mirrors) r1 and r2.
Fig. 3
Fig. 3 From the resonance width (Δλ) and depth (R0) we extract the cavity loss (δc) and coupling coefficient (δ1), approximating the resonance as a complex Lorentzian and assuming αbs = 0.
Fig. 4
Fig. 4 We consider a single reflector (i.e. back-scattering point) to model the two modes that build up inside the cavity.
Fig. 5
Fig. 5 Same ring resonator with different levels of back-scattering (Rbs): As the back-scatter increases, the forward and backward propagating modes interfere destructively and the resonance splits into two. F = 64 (δc = 9.8%)
Fig. 6
Fig. 6 Transmission (dB) versus wavelength (nm) resonances for a 5 μm radius ring. Fitting to the back-scatter model we extract reasonable coupling (δ1) and cavity loss in the ring (δc), while the model without back-scatter would only be valid for resonances lightly affected by back-scatter (middle figure).

Equations (35)

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R 1 = e δ 1
r 1 = R 1 t 1 = T 1
t c ( ω ) = E n + 1 E n = r 1 ( ω ) t p 1 ( ω ) t p 2 ( ω ) r 2 ( ω ) r 1 t p 1 t p 2 t 2 e j θ
T p = t p 2 = e δ p = e α p L c
θ = 2 π ( ν ν o ) FSR
FSR = 1 τ c = c n g L c
T c = | t c | 2 = R 1 R 2 T p = e δ 1 e δ 2 e δ p = e δ c
δ c = δ 1 + δ 2 + δ p
F = FSR Δ ν 2 π δ c
E 0 = j t 1 E in
E t = j t 2 t p 1 E c
E c = j t 1 E in + t c ( ω ) E c
H c ( ω ) = E c E in = j t 1 1 t c ( ω )
H r ( ω ) = E r E in = r 1 + j t 1 t c r 1 1 H c ( ω )
H t ( ω ) = E out E in = j t 2 t p 1 H c ( ω )
P c P in = | E c | 2 | E in | 2 = | H c ( ω ) | 2
L ( x ) = 1 1 + j x
x = 2 ω Δ ω o = 2 θ δ c
H c = E c E in j 2 δ 1 δ c L ( x )
H r = E r E in 1 2 δ 1 δ c L ( x )
H t = E out E in 2 δ 1 δ 2 δ c L ( x )
δ c 2 π F = 2 π m c Q
R o ( 1 2 δ 1 δ c ) 2
δ 1 δ c 2 ( 1 + R 0 )
δ p + δ 2 δ c 2 ( 1 R 0 )
t c ( ω ) = r 1 r 2 t p t bs e j θ
T c = | t c | 2 = R 1 R 2 T p T bs = e δ 1 e δ 2 e δ bs = e δ c
δ c = δ 1 + δ 2 + δ p + δ bs
E c = t c E c + j t 1 E in + j r bs t c t bs 2 E c b
E c b = t c E c b + j r bs E c
E c = j t 1 E in + j r bs t c t bs 2 E c b 1 t c
E c b = j r bs E c 1 t c
H c ( ω ) = E c E in = j t 1 ( 1 t c ) ( 1 + t c ( r bs t bs 1 1 t c ) 2 ) 1
t c ( r bs t bs 1 1 t c ) 2 4 R bs δ c 2 < 0.025
R bs < ( 1 2 F ) 2

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