Abstract

We present a dynamical analysis of lossless intensity modulation in two different ring resonator geometries. In both geometries, we demonstrate modulation schemes that result in a symmetrical output with an infinite on/off ratio. The systems behave as lossless intensity modulators where the time-averaged output optical power is equal to the time-averaged input optical power.

© 2012 Optical Society of America

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References

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  1. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
    [Crossref]
  2. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
    [Crossref] [PubMed]
  3. L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13, 3129–3135 (2005).
    [Crossref] [PubMed]
  4. L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
    [Crossref]
  5. A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
    [Crossref] [PubMed]
  6. X. Chen, Y.-S. Chen, Y. Zhao, W. Jiang, and R. T. Chen, “Capacitor-embedded 0.54 pj/bit silicon-slot photonic crystal waveguide modulator,” Opt. Lett. 34, 602–604 (2009).
    [Crossref] [PubMed]
  7. H.-W. Chen, Y.-H. Kuo, and J. E. Bowers, “25 Gb/s hybrid silicon switch using a capacitively loaded traveling wave electrode,” Opt. Express 18, 1070–1075 (2010).
    [Crossref] [PubMed]
  8. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
    [Crossref] [PubMed]
  9. D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
    [Crossref]
  10. T. Tanabe, K. Nishiguchi, E. Kuramochi, and M. Notomi, “Low power and fast electro-optic silicon modulator with lateral p-i-n embedded photonic crystal nanocavity,” Opt. Express 17, 22505–22513 (2009).
    [Crossref]
  11. S. Manipatruni, K. Preston, L. Chen, and M. Lipson, “Ultra-low voltage, ultra-small mode volume silicon microring modulator,” Opt. Express 18, 18235–18242 (2010).
    [Crossref] [PubMed]
  12. A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
    [Crossref]
  13. W. D. Sacher and J. K. S. Poon, “Characteristics of microring resonators with waveguide-resonator coupling modulation,” J. Lightwave Technol. 27, 3800–3811 (2009).
    [Crossref]
  14. T. Ye and X. Cai, “On power consumption of silicon-microring-based optical modulators,” J. Lightwave Technol. 28, 1615–1623 (2010).
    [Crossref]
  15. Z. Pan, S. Chandel, and C. Yu, “Ultrahigh-speed optical pulse generation using a phase modulator and two stages of delayed Mach-Zehnder interferometers,” Opt. Eng. 46, 075001 (2007).
    [Crossref]
  16. C. Schmidt-Langhorst and H.-G. Weber, “Optical sampling techniques,” J. Opt. Fiber Commun. Rep. 2, 86–114 (2005).
    [Crossref]
  17. W. D. Sacher and J. K. S. Poon, “Dynamics of microring resonator modulators,” Opt. Express 16, 15741–15753 (2008).
    [Crossref] [PubMed]
  18. M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92, 083901 (2004).
    [Crossref] [PubMed]
  19. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  20. Q. Reed, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3, 406–410 (2007).
    [Crossref]
  21. M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23, 4222 – 4238 (2005).
    [Crossref]
  22. Q. Xu, “Silicon dual-ring modulator,” Opt. Express 17, 20783–20793 (2009).
    [Crossref] [PubMed]

2010 (4)

2009 (5)

2008 (1)

2007 (4)

Z. Pan, S. Chandel, and C. Yu, “Ultrahigh-speed optical pulse generation using a phase modulator and two stages of delayed Mach-Zehnder interferometers,” Opt. Eng. 46, 075001 (2007).
[Crossref]

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

Q. Reed, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3, 406–410 (2007).
[Crossref]

2005 (4)

M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23, 4222 – 4238 (2005).
[Crossref]

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13, 3129–3135 (2005).
[Crossref] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

C. Schmidt-Langhorst and H.-G. Weber, “Optical sampling techniques,” J. Opt. Fiber Commun. Rep. 2, 86–114 (2005).
[Crossref]

2004 (2)

M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92, 083901 (2004).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

2002 (1)

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
[Crossref]

Basak, J.

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

Beattie, J.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Bowers, J. E.

Cai, X.

Carothers, D.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Chandel, S.

Z. Pan, S. Chandel, and C. Yu, “Ultrahigh-speed optical pulse generation using a phase modulator and two stages of delayed Mach-Zehnder interferometers,” Opt. Eng. 46, 075001 (2007).
[Crossref]

Chen, H.-W.

Chen, L.

Chen, R. T.

Chen, X.

Chen, Y.-K.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Chen, Y.-S.

Chetrit, Y.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

Ciftcioglu, B.

Cohen, O.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Cohen, R.

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

Dong, P.

Q. Reed, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3, 406–410 (2007).
[Crossref]

Fan, S.

M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92, 083901 (2004).
[Crossref] [PubMed]

Franck, T.

Gardes, F. Y.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

Gill, D. M.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Hill, C.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Hodge, D.

Izhaky, N.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

Jiang, W.

Jones, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Kamocsai, R.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Keil, U.

Kuo, Y.-H.

Kuramochi, E.

Liao, L.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13, 3129–3135 (2005).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Lipson, M.

S. Manipatruni, K. Preston, L. Chen, and M. Lipson, “Ultra-low voltage, ultra-small mode volume silicon microring modulator,” Opt. Express 18, 18235–18242 (2010).
[Crossref] [PubMed]

Q. Reed, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3, 406–410 (2007).
[Crossref]

M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23, 4222 – 4238 (2005).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

Liu, A.

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13, 3129–3135 (2005).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Manipatruni, S.

Mashanovich, G.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

Morse, M.

Nguyen, H.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

Nicolaescu, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Nishiguchi, K.

Notomi, M.

Pan, Z.

Z. Pan, S. Chandel, and C. Yu, “Ultrahigh-speed optical pulse generation using a phase modulator and two stages of delayed Mach-Zehnder interferometers,” Opt. Eng. 46, 075001 (2007).
[Crossref]

Paniccia, M.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Patel, S. S.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Pomerene, A.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Poon, J. K. S.

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

Preston, K.

Rasras, M.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Reed, G. T.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

Reed, Q.

Q. Reed, P. Dong, and M. Lipson, “Breaking the delay-bandwidth limit in a photonic structure,” Nat. Phys. 3, 406–410 (2007).
[Crossref]

Rubin, D.

A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and M. Paniccia, “High-speed optical modulation based on carrier depletion in a silicon waveguide,” Opt. Express 15, 660–668 (2007).
[Crossref] [PubMed]

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13, 3129–3135 (2005).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Sacher, W. D.

Samara-Rubio, D.

L. Liao, D. Samara-Rubio, M. Morse, A. Liu, D. Hodge, D. Rubin, U. Keil, and T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express 13, 3129–3135 (2005).
[Crossref] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

Schmidt-Langhorst, C.

C. Schmidt-Langhorst and H.-G. Weber, “Optical sampling techniques,” J. Opt. Fiber Commun. Rep. 2, 86–114 (2005).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Tanabe, T.

Thomson, D. J.

G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photonics 4, 518–526 (2010).
[Crossref]

Tu, K.-Y.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Weber, H.-G.

C. Schmidt-Langhorst and H.-G. Weber, “Optical sampling techniques,” J. Opt. Fiber Commun. Rep. 2, 86–114 (2005).
[Crossref]

White, A. E.

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

Xu, Q.

Q. Xu, “Silicon dual-ring modulator,” Opt. Express 17, 20783–20793 (2009).
[Crossref] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

Yanik, M. F.

M. F. Yanik and S. Fan, “Stopping light all optically,” Phys. Rev. Lett. 92, 083901 (2004).
[Crossref] [PubMed]

Yariv, A.

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
[Crossref]

Ye, T.

Yu, C.

Z. Pan, S. Chandel, and C. Yu, “Ultrahigh-speed optical pulse generation using a phase modulator and two stages of delayed Mach-Zehnder interferometers,” Opt. Eng. 46, 075001 (2007).
[Crossref]

Zhao, Y.

Electron. Lett. (1)

L. Liao, A. Liu, J. Basak, H. Nguyen, M. Paniccia, D. Rubin, Y. Chetrit, R. Cohen, and N. Izhaky, “40 Gbit/s silicon optical modulator for highspeed applications,” Electron. Lett. 43, 1196–1197 (2007).
[Crossref]

IEEE Photon. Technol. Lett. (2)

D. M. Gill, M. Rasras, K.-Y. Tu, Y.-K. Chen, A. E. White, S. S. Patel, D. Carothers, A. Pomerene, R. Kamocsai, C. Hill, and J. Beattie, “Internal bandwidth equalization in a CMOS-compatible Si-ring modulator,” IEEE Photon. Technol. Lett. 21, 200–202 (2009).
[Crossref]

A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems,” IEEE Photon. Technol. Lett. 14, 483–485 (2002).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Fiber Commun. Rep. (1)

C. Schmidt-Langhorst and H.-G. Weber, “Optical sampling techniques,” J. Opt. Fiber Commun. Rep. 2, 86–114 (2005).
[Crossref]

Nat. Photonics (1)

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Nature (2)

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Figures (7)

Fig. 1
Fig. 1 Conventional way of describing intensity modulation which is only valid in the adiabatic regime: (a) transmission T of system as a function of some system parameter x, (b) modulation performed on x as a function of time, (c) resultant modulation of the system transmission T as a function of time.

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Fig. 2
Fig. 2 Analysis of a single-ring system: (a) shows the schematic of the system where a(t) is the ring modal amplitude, ωo is the ring resonance frequency, Sin(t) [Sout(t)] are the incoming [outgoing] waveguide modal amplitude and γcoup(t) is the waveguide coupling rate. (b) and (c) show the system output power at t ≫ 1 γ o for a modulated coupling rate γcoup(t) = [0.069 + 0.025sin(Ωt)]Ω and γcoup(t) = [6.43 + 2.92sin(Ωt)]Ω, respectively. In both (b) and (c), ωo = 2π(193THz), Sin = exp(jωot) and Ω = 2π(20GHz). Circles in (b) show the output power using the approximation of Eq. (5).

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Fig. 3
Fig. 3 Example implementation of waveguide coupling rate modulation in a single-ring system using a composite interferometer (CI) [12]. The CI consists of a Mach-Zehnder interferometer (MZI) sandwiched between two 3dB couplers. The MZI is driven in a push-pull configuration with modulated propagation phases ±Δθ(t) that modulate the waveguide coupling rate.

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Fig. 4
Fig. 4 Schematic of the coupled-three-ring system where a(t), p(t) and q(t) are the rings’ modal amplitudes, Sin(t) [Sout(t)] is the incoming [outgoing] waveguide modal amplitude, κ is the inter-ring coupling rate, γcoup is the waveguide coupling rate, ωo is the central ring resonance frequency, and Δ(t) is the side ring detuning.

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Fig. 5
Fig. 5 Plots of the normalized spectra of energy |a(ω)|2 of the central ring resonator in the coupled-three-ring system (Fig. 4) from both FDTD simulations (circles) and the CMT model (solid line). The three spectras are at different side ring detunings Δ.

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Fig. 6
Fig. 6 Plot showing the 40GHz modulated output power for the coupled-three-ring system (Fig. 4) at t ≫ 1/γcoup from both CMT (solid line) and FDTD (circles) simulations. The side ring resonance frequency detuning Δ(t) is modulated at a frequency 20GHz and amplitude δω = 2π(27.65GHz), while the other parameters are as follows: κ = 2π(17.9GHz), γcoup = 2π(18.7GHz), ωo = 2π(193THz), and Sin(t) = exp(jωot).

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Fig. 7
Fig. 7 Coupled-three-ring system electric field plots from FDTD simulations around the (a) maximum output power state, (b) dark state, and (c) zero output power state in Fig. 6. The electric field is polarized normal to the page.

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Equations (9)

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d a ( t ) d t = j ω o a ( t ) − [ γ coup ( t ) + γ loss ] a ( t ) + j 2 γ coup ( t ) S in ( t ) S out ( t ) = S in ( t ) + j 2 γ coup ( t ) a ( t ) .
T ( ω ) = S out S in = ω − ω o + j ( γ coup − γ loss ) ω − ω o − j ( γ coup + γ loss ) .
S out ( t ) = [ 1 + B ( t ) ] exp ( j ω o t ) ,
B ( t ) = j 2 γ coup ( t ) A ( t ) , A ( t ) = j exp [ − ∫ 0 t γ coup ( t ′ ) d t ′ ] ∫ 0 t 2 γ coup ( τ ) exp [ ∫ 0 τ γ coup ( t ′ ) d t ′ ] d τ ,
γ coup ( t ) = γ o + Δ γ sin ( Ω t )
B ( t ) ≈ 2 γ coup ( t ) γ o [ ( Δ γ 4 γ o ) 2 − 1 ] .
d a ( t ) d t = j ω o a ( t ) + j κ [ p ( t ) + q ( t ) ] − ( γ coup + γ loss ) a ( t ) + j 2 γ coup S in ( t ) d p ( t ) d t = j [ ω o + Δ ( t ) ] p ( t ) + j κ a ( t ) − γ loss p ( t ) d q ( t ) d t = j [ ω o − Δ ( t ) ] q ( t ) + j κ a ( t ) − γ loss q ( t ) S out ( t ) = S in ( t ) + j 2 γ coup a ( t ) .
T ( ω ) = S out S in = ω − ω o + y + j ( γ coup − γ loss ) ω − ω o + y − j ( γ coup + γ loss ) y = 2 κ 2 ( ω − ω o − j γ loss ) Δ 2 − ( ω − ω o − j γ loss ) 2 .
Δ ( t ) = δ ω sin ( Ω t )

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