Abstract

This paper presents a methodology for the incorporation of actively configurable interference-based optical elements into a circuit-level optoelectronic simulator. The self-consistent optoelectronic simulator is based on modified nodal analysis. The paper uses ring-resonator-based devices as examples of configurable devices. Construction of compact models of these devices from optical scattering and the waveguide elements using fundamental principles is presented in detail. In the results section, accuracy of the compact model of the ring resonator is first confirmed for static devices for steady-state and transient conditions. Last, the devices are placed in a complex optical circuit and used to modulate an optical carrier and select a particular channel from a multichannel optical signal. The modelling framework proposed proved to be robust and efficient for transient simulation of configurable elements in a self-consistent optoelectronic simulation engine.

© 2011 Optical Society of America

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References

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  1. R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
    [CrossRef]
  2. L. Tsybeskov, D. Lockwood, and M. Ichikawa, “Silicon photonics: CMOS going optical,” Proc. IEEE 97, 1161–l1165 (2009).
    [CrossRef]
  3. A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
    [CrossRef]
  4. T. Quarles, A. Newton, D. Pederson, and A. Sangiovanni-Vincentelli, “SPICE 3 Version 3F5 User’s Manual,” Department of Electrical Engineering and Computer Sciences, University of California, Berkeley.
  5. C.-W. Ho, A. Ruehli, and P. Brennan, “The modified nodal approach to network analysis,” IEEE Trans. Circuits Syst. 22, 504–509 (1975).
    [CrossRef]
  6. U. Wali, R. Pal, and B. Chatterjee, “On the modified nodal approach to network analysis,” Proc. IEEE 73, 485–487(1985).
    [CrossRef]
  7. P. Gunupudi, T. Smy, J. Klein, and Z. J. Jakubczyk, “Self-consistent simulation of opto-electronic circuits using a modified nodal analysis formulation,” IEEE Trans. Adv. Packaging 33, 979–993 (2010).
    [CrossRef]
  8. B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
    [CrossRef]
  9. J. Vlach and K. Singhal, Computer Methods for Circuit Analysis and Design (Van Nostrand Reinhold, 1993).
  10. J. D. Jackson, Classical Electrodynamics (Academic, 1998).
  11. T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, 1995).
  12. T. Smy and P. Gunupudi, “Robust simulation of opto-electronic systems by alternating complex envelope representations,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., doc. ID TCAD 6410 (to be published).
    [CrossRef]
  13. P. Gunupudi, T. Smy, J. Klein, and J. Jakubczyk, “Multi-disciplinary simulation of electro-opto-thermal networks using a SPICE-like framework,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008), paper ITuE3.
  14. D. G. Rabus, Integrated Ring Resonators (Springer, 2007).
  15. Q. Xu, B. Schmidt, J. Shakya, and M. Lipson, “Cascaded silicon micro-ring modulators for WDM optical interconnection,” Opt. Express 14, 9431–9435 (2006).
    [CrossRef] [PubMed]
  16. D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
    [CrossRef]
  17. G. T. Reed, G. Mashanovich, F. Y. Gardes, and D. J. Thomson, “Silicon optical modulators,” Nat. Photon. 4, 518–526 (2010).
    [CrossRef]
  18. M. Hammer, “HCMT models of optical microring-resonator circuits,” J. Opt. Soc. Am. B 27, 2237–2246 (2010).
    [CrossRef]
  19. D. Gallagher, “Modelling photonic integrated circuits using TDTW,” in Asia Optical Fiber Communication and Optoelectronic Exposition and Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper SuQ4.

2010 (3)

P. Gunupudi, T. Smy, J. Klein, and Z. J. Jakubczyk, “Self-consistent simulation of opto-electronic circuits using a modified nodal analysis formulation,” IEEE Trans. Adv. Packaging 33, 979–993 (2010).
[CrossRef]

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

M. Hammer, “HCMT models of optical microring-resonator circuits,” J. Opt. Soc. Am. B 27, 2237–2246 (2010).
[CrossRef]

2009 (3)

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

L. Tsybeskov, D. Lockwood, and M. Ichikawa, “Silicon photonics: CMOS going optical,” Proc. IEEE 97, 1161–l1165 (2009).
[CrossRef]

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

2006 (2)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
[CrossRef]

Q. Xu, B. Schmidt, J. Shakya, and M. Lipson, “Cascaded silicon micro-ring modulators for WDM optical interconnection,” Opt. Express 14, 9431–9435 (2006).
[CrossRef] [PubMed]

1997 (1)

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

1985 (1)

U. Wali, R. Pal, and B. Chatterjee, “On the modified nodal approach to network analysis,” Proc. IEEE 73, 485–487(1985).
[CrossRef]

1975 (1)

C.-W. Ho, A. Ruehli, and P. Brennan, “The modified nodal approach to network analysis,” IEEE Trans. Circuits Syst. 22, 504–509 (1975).
[CrossRef]

Brennan, P.

C.-W. Ho, A. Ruehli, and P. Brennan, “The modified nodal approach to network analysis,” IEEE Trans. Circuits Syst. 22, 504–509 (1975).
[CrossRef]

Cassan, E.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Chatterjee, B.

U. Wali, R. Pal, and B. Chatterjee, “On the modified nodal approach to network analysis,” Proc. IEEE 73, 485–487(1985).
[CrossRef]

Chu, S.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Crozat, P.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Cunningham, J.

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

Fedeli, J.-M.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Foresi, J.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Gallagher, D.

D. Gallagher, “Modelling photonic integrated circuits using TDTW,” in Asia Optical Fiber Communication and Optoelectronic Exposition and Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper SuQ4.

Gardes, F. Y.

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

Gunupudi, P.

P. Gunupudi, T. Smy, J. Klein, and Z. J. Jakubczyk, “Self-consistent simulation of opto-electronic circuits using a modified nodal analysis formulation,” IEEE Trans. Adv. Packaging 33, 979–993 (2010).
[CrossRef]

T. Smy and P. Gunupudi, “Robust simulation of opto-electronic systems by alternating complex envelope representations,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., doc. ID TCAD 6410 (to be published).
[CrossRef]

P. Gunupudi, T. Smy, J. Klein, and J. Jakubczyk, “Multi-disciplinary simulation of electro-opto-thermal networks using a SPICE-like framework,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008), paper ITuE3.

Halbwax, M.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Hammer, M.

Haus, H.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Ho, C.-W.

C.-W. Ho, A. Ruehli, and P. Brennan, “The modified nodal approach to network analysis,” IEEE Trans. Circuits Syst. 22, 504–509 (1975).
[CrossRef]

Ho, R.

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

Ichikawa, M.

L. Tsybeskov, D. Lockwood, and M. Ichikawa, “Silicon photonics: CMOS going optical,” Proc. IEEE 97, 1161–l1165 (2009).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Academic, 1998).

Jakubczyk, J.

P. Gunupudi, T. Smy, J. Klein, and J. Jakubczyk, “Multi-disciplinary simulation of electro-opto-thermal networks using a SPICE-like framework,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008), paper ITuE3.

Jakubczyk, Z. J.

P. Gunupudi, T. Smy, J. Klein, and Z. J. Jakubczyk, “Self-consistent simulation of opto-electronic circuits using a modified nodal analysis formulation,” IEEE Trans. Adv. Packaging 33, 979–993 (2010).
[CrossRef]

Klein, J.

P. Gunupudi, T. Smy, J. Klein, and Z. J. Jakubczyk, “Self-consistent simulation of opto-electronic circuits using a modified nodal analysis formulation,” IEEE Trans. Adv. Packaging 33, 979–993 (2010).
[CrossRef]

P. Gunupudi, T. Smy, J. Klein, and J. Jakubczyk, “Multi-disciplinary simulation of electro-opto-thermal networks using a SPICE-like framework,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008), paper ITuE3.

Koka, P.

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

Krishnamoorthy, A.

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

Laine, J.-P.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Laval, S.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Le Roux, X.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Lexau, J.

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

Li, G.

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

Lipson, M.

Little, B.

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

Lockwood, D.

L. Tsybeskov, D. Lockwood, and M. Ichikawa, “Silicon photonics: CMOS going optical,” Proc. IEEE 97, 1161–l1165 (2009).
[CrossRef]

Lupu, A.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Lyan, P.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Maine, S.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Marris-Morini, D.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Mashanovich, G.

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

Newton, A.

T. Quarles, A. Newton, D. Pederson, and A. Sangiovanni-Vincentelli, “SPICE 3 Version 3F5 User’s Manual,” Department of Electrical Engineering and Computer Sciences, University of California, Berkeley.

Pal, R.

U. Wali, R. Pal, and B. Chatterjee, “On the modified nodal approach to network analysis,” Proc. IEEE 73, 485–487(1985).
[CrossRef]

Pederson, D.

T. Quarles, A. Newton, D. Pederson, and A. Sangiovanni-Vincentelli, “SPICE 3 Version 3F5 User’s Manual,” Department of Electrical Engineering and Computer Sciences, University of California, Berkeley.

Quarles, T.

T. Quarles, A. Newton, D. Pederson, and A. Sangiovanni-Vincentelli, “SPICE 3 Version 3F5 User’s Manual,” Department of Electrical Engineering and Computer Sciences, University of California, Berkeley.

Rabus, D. G.

D. G. Rabus, Integrated Ring Resonators (Springer, 2007).

Rasigade, G.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Reed, G. T.

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

Rivallin, P.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Ruehli, A.

C.-W. Ho, A. Ruehli, and P. Brennan, “The modified nodal approach to network analysis,” IEEE Trans. Circuits Syst. 22, 504–509 (1975).
[CrossRef]

Sangiovanni-Vincentelli, A.

T. Quarles, A. Newton, D. Pederson, and A. Sangiovanni-Vincentelli, “SPICE 3 Version 3F5 User’s Manual,” Department of Electrical Engineering and Computer Sciences, University of California, Berkeley.

Schmidt, B.

Schwetman, H.

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

Shakya, J.

Shubin, I.

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

Singhal, K.

J. Vlach and K. Singhal, Computer Methods for Circuit Analysis and Design (Van Nostrand Reinhold, 1993).

Smy, T.

P. Gunupudi, T. Smy, J. Klein, and Z. J. Jakubczyk, “Self-consistent simulation of opto-electronic circuits using a modified nodal analysis formulation,” IEEE Trans. Adv. Packaging 33, 979–993 (2010).
[CrossRef]

T. Smy and P. Gunupudi, “Robust simulation of opto-electronic systems by alternating complex envelope representations,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., doc. ID TCAD 6410 (to be published).
[CrossRef]

P. Gunupudi, T. Smy, J. Klein, and J. Jakubczyk, “Multi-disciplinary simulation of electro-opto-thermal networks using a SPICE-like framework,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008), paper ITuE3.

Soref, R.

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
[CrossRef]

Tamir, T.

T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, 1995).

Thomson, D. J.

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

Tsybeskov, L.

L. Tsybeskov, D. Lockwood, and M. Ichikawa, “Silicon photonics: CMOS going optical,” Proc. IEEE 97, 1161–l1165 (2009).
[CrossRef]

Vivien, L.

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

Vlach, J.

J. Vlach and K. Singhal, Computer Methods for Circuit Analysis and Design (Van Nostrand Reinhold, 1993).

Wali, U.

U. Wali, R. Pal, and B. Chatterjee, “On the modified nodal approach to network analysis,” Proc. IEEE 73, 485–487(1985).
[CrossRef]

Xu, Q.

Zheng, X.

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
[CrossRef]

IEEE Trans. Adv. Packaging (1)

P. Gunupudi, T. Smy, J. Klein, and Z. J. Jakubczyk, “Self-consistent simulation of opto-electronic circuits using a modified nodal analysis formulation,” IEEE Trans. Adv. Packaging 33, 979–993 (2010).
[CrossRef]

IEEE Trans. Circuits Syst. (1)

C.-W. Ho, A. Ruehli, and P. Brennan, “The modified nodal approach to network analysis,” IEEE Trans. Circuits Syst. 22, 504–509 (1975).
[CrossRef]

J. Lightwave Technol. (1)

B. Little, S. Chu, H. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Photon. (1)

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

Opt. Express (1)

Proc. IEEE (4)

D. Marris-Morini, L. Vivien, G. Rasigade, J.-M. Fedeli, E. Cassan, X. Le Roux, P. Crozat, S. Maine, A. Lupu, P. Lyan, P. Rivallin, M. Halbwax, and S. Laval, “Recent progress in high-speed silicon-based optical modulators,” Proc. IEEE 97, 1199–1215(2009).
[CrossRef]

U. Wali, R. Pal, and B. Chatterjee, “On the modified nodal approach to network analysis,” Proc. IEEE 73, 485–487(1985).
[CrossRef]

L. Tsybeskov, D. Lockwood, and M. Ichikawa, “Silicon photonics: CMOS going optical,” Proc. IEEE 97, 1161–l1165 (2009).
[CrossRef]

A. Krishnamoorthy, R. Ho, X. Zheng, H. Schwetman, J. Lexau, P. Koka, G. Li, I. Shubin, and J. Cunningham, “Computer systems based on silicon photonic interconnects,” Proc. IEEE 97, 1337–1361 (2009).
[CrossRef]

Other (8)

T. Quarles, A. Newton, D. Pederson, and A. Sangiovanni-Vincentelli, “SPICE 3 Version 3F5 User’s Manual,” Department of Electrical Engineering and Computer Sciences, University of California, Berkeley.

D. Gallagher, “Modelling photonic integrated circuits using TDTW,” in Asia Optical Fiber Communication and Optoelectronic Exposition and Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper SuQ4.

J. Vlach and K. Singhal, Computer Methods for Circuit Analysis and Design (Van Nostrand Reinhold, 1993).

J. D. Jackson, Classical Electrodynamics (Academic, 1998).

T. Tamir, Guided-Wave Optoelectronics (Springer-Verlag, 1995).

T. Smy and P. Gunupudi, “Robust simulation of opto-electronic systems by alternating complex envelope representations,” IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., doc. ID TCAD 6410 (to be published).
[CrossRef]

P. Gunupudi, T. Smy, J. Klein, and J. Jakubczyk, “Multi-disciplinary simulation of electro-opto-thermal networks using a SPICE-like framework,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008), paper ITuE3.

D. G. Rabus, Integrated Ring Resonators (Springer, 2007).

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Figures (11)

Fig. 1
Fig. 1

Four-port configurable optical ring structure.

Fig. 2
Fig. 2

Four-port ring model consisting of two cross-couplers and WEs. Each WE in the ring would include time delays, phase shifts, and signal attenuation.

Fig. 3
Fig. 3

(a) Physical structure of the optical waveguide. (b) Waveguide model showing time delay ( Δ t w ) of phase and magnitude signals and phase shift ( Δ ϕ ) due to carrier wave phase offset and attenuation of the signal magnitude.

Fig. 4
Fig. 4

History of an input signal I ( t ) and the two cases used to determine the value of a delayed signal I ( t ) . The first case is when the time of interest t 0 Δ t 1 falls in the current time step, and the second is when it does not.

Fig. 5
Fig. 5

Simple device characterization circuit comprising a CW source, an optical ring, and a mirror. The CW source allows for voltage control of the carrier wavelength (λ) and the optical phase (ϕ) and magnitude (M).

Fig. 6
Fig. 6

Four-port ring though port response obtained by sweeping the carrier frequency of an optical signal with a constant magnitude and phase. Shown are two simulations; one with a nominal ring index of 3.00 and the second with index increased by 0.0002. Analytical theory is plotted as a solid curve.

Fig. 7
Fig. 7

Port responses of a four-port ring. (a) Transient simulation for a sinusoidal magnitude modulation at increasing frequencies. (b) Comparison of results for both ports obtained by phase and magnitude modulation with theory.

Fig. 8
Fig. 8

Four-port ring response to pulse excitation. (a)  10 ps Gaussian pulse showing the inherent delay due to energy storage in the ring. FFT results are shown as solid curve for the two ports. (b)  100 fs pulse showing the production of a train of pulses from the through port.

Fig. 9
Fig. 9

Ring-resonator-based WDM system schematic showing two four-port rings used as a modulator and a filter for adding/dropping channels. PD-1, photodiode 1; PD-2, photodiode 2.

Fig. 10
Fig. 10

Ring-resonator-based WDM system. (a) Optical field response at photodiode inputs. (b) Field response for the leading edge bits (shows response for both the full ring model configuration and without the time delays present). (c) Single-bit response as function of index modulation. (d) Single-bit response for different modulating pulse shapes ( Δ n = 0.0002 ).

Fig. 11
Fig. 11

Transient simulation showing bit stream routing using a configurable ring filter in the circuit of Fig. 9. Topmost plot shows the change in the index of ring R-2. Second plot shows the optical bit stream produced by the ring modulator R-1. Third plot shows the optical signals at the through port (solid) and drop port (dotted). Fourth plot presents the two output voltages V o 1 (dotted) and V o 2 (solid).

Tables (1)

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Table 1 Optical Signal Attenuation Due to a Linear Phase Variation a

Equations (26)

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C d x d t + Gx + F ( x ) = B ( t ) ,
E ( x , y , z , t ) = E ( t ) S i ( x , y ) e i ( n k z ω t + ϕ ( t ) ) ,
E ¯ ( t , z 0 ) = E f ( t ) e i ϕ f ( t ) e i ω t + E r ( t ) e i ϕ r ( t ) e i ω t ,
O ^ 1 O ^ 2 = t r r * t * I ^ 1 I ^ 2 ,
O 1 M f = O 1 r f 2 + O 1 i f 2 , O 1 ϕ f = arctan ( O 1 i f O 1 r f ) ,
O 1 r f = t I 1 M f cos ( I 1 ϕ f ) r I 2 M f sin ( I 2 ϕ f ) , O 1 i f = t I 1 M f cos ( I 1 ϕ f ) + r I 2 M f cos ( I 2 ϕ f ) ,
O M f X = 1 O M f ( O r f O r f X + O i f O i f X ) , O ϕ f X = 1 1 + ( O r f / O i f ) 2 ( 1 O r f O i f X O i f O r f 2 O r f X ) ,
O ^ f ( t ) = I M f ( t Δ t ) e α l e i I ϕ f ( t Δ t ) e i ω ( t Δ t ) = I M f ( t Δ t ) e α l e i ( I ϕ f ( t Δ t ) + Δ ϕ ) e i ω t .
n ( T , V ) = n 0 n V ( V ) n T ( T ) , κ ( T , V ) = κ 0 κ V ( V ) κ T ( T ) ,
Δ t = ( L / c ) n 0 n v ( V ) n T ( T ) .
O ( t 0 ) = I ( t Δ t 1 ) = [ I ( t 0 ) I ( t 1 ) ] Δ t δ t 0 + I ( t 1 ) ,
O ( t ) I ( t ) = Δ t δ t 0 .
Δ t T = L / c n 0 n T T n V , Δ t V = L / c n 0 n T n V V .
O ( t ) Δ t = I ( t ) I ( t δ t 1 ) δ t 1 .
O ( t ) T = L / c n 0 n T T n V I ( t ) I ( t δ t 1 ) δ t 1 ,
O ( t ) V = L / c n 0 n T n V V I ( t ) I ( t δ t 1 ) δ t 1 .
O ( t 0 ) = I ( t Δ t 2 ) = [ I ( t j ) I ( t j 1 ) ] Δ t t j t j t j 1 + I ( t j 1 ) ,
O ( t ) I ( t ) = 0.
O ( t ) Δ t = I ( t δ t j ) I ( t δ t j 1 ) δ t 1 .
O ( t ) T = L / c n 0 n T T n V I ( t δ t j ) I ( t δ t j 1 ) δ t 1 , O ( t ) V = L / c n 0 n T n V V I ( t δ t j ) I ( t δ t j 1 ) δ t 1 .
O ϕ = I ϕ ω Δ t ( V , T ) ,
O ϕ T = ω Δ t T = ω L / c n 0 n T T n V , O ϕ V = ω Δ t V = ω L / c n 0 n V V n T .
O M = I M e L κ ( V , T ) .
O M I M = e L κ ( V , T ) , O M T = I M e L κ ( V , T ) L κ T , O M V = I M e L κ ( V , T ) L κ V .
E ^ ( t ) = E 0 e i ( ω c + Δ ω ) t = E 0 e i Δ ω t · e i ω c t
E ^ ( t ) = E 0 2 ( e i ( ω c + ω m ) t e i ( ω c ω m ) t ) ,

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