Abstract

We propose a two-ring resonator configuration that can provide optical switching with high extinction ratio (ER), large modulation depth (MD) and low switching threshold, and compare it with two other conventional one-ring configurations. The achievable input threshold is n2IIN ~10-5, while maintaining a large ER (> 10dB) and MD (~ 1) over a 10-GHz (0.1 nm) optical bandwidth. This performance can also be achieved by the ring-enhanced Mach-Zehnder interferometer, and is one to two orders of magnitude better than the simple bus-coupled one-ring structures, because of the use of asymmetric Fano resonance as opposed to the usual symmetric resonance of a single ring. The sharpness and the asymmetricity of the Fano resonance are linked to the low switching threshold and the high extinction ratio, respectively, and also accounts for the different dependence on ring dimensions between the one- and two-ring structures.

© 2006 Optical Society of America

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  1. B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
    [CrossRef]
  2. T. A. Ibrahim, R. Grover, L. -C. Kuo, S. Kanakaraju, L. C. Calhoun, P. -T. Ho, "All-optical AND/NAND logic gates using semiconductor microresonators," IEEE Photon. Technol. Lett. 15, 1422-1424 (2003).
    [CrossRef]
  3. J. Niehusmann, A. Vörckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, "Ultrahigh-quality-factor silicon-on-insulator microring resonator", Opt. Lett. 29, 2861-2863 (2004).
    [CrossRef]
  4. D. A. B. Miller, "Refractive Fabry-Perot Bistability with Linear Absorption: Theory of Operation and Cavity optimization," IEEE J. Quantum Electron,  17, 306-311 (1981).
    [CrossRef]
  5. F. Sanchez, "Optical bistability in a 2x2 coupler fiber ring resonator: parametric formulation," Opt. Commun. 142, 211 (1997).
    [CrossRef]
  6. Y. Dumeige, D. Arnaud, P. Feron, "Combining FDTD with coupled mode theories for bistability in micro-ring resonators," Opt. Commun. 250 (2005) 376-383.
    [CrossRef]
  7. Y. Dumeige, P. Feron, "Dispersive tristability in microring resonator," Phys. Rev. E,  72066609 (2005).
    [CrossRef]
  8. J. Danckaert, K. Fobelets, I. Veretennicoff, "Dispersive optical bistability in stratified structures," Phys. Rev. B,  44, 15, 8214 (1991).
    [CrossRef]
  9. B. Maes, P. Bienstman, R. Baets, "Switching in coupled nonlinear photonic crystal resonators," J. Opt. Soc. Am. B  22(8), 1778-1784 (2005).
    [CrossRef]
  10. V. R. Almeida and M. Lipson, "Optical bistability on a silicon chip," Opt. Lett. 29, 2387-2389 (2004).
    [CrossRef] [PubMed]
  11. S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators, "J. Opt. Soc. Am. A,  20(3), 569-572 (2003).
    [CrossRef]
  12. Y. Lu, J. Yao, X. Li, and P. Wang, "Tunable asymmetrical Fano resonance and bistability in a microcavity-resonator-coupled Mach Zehnder Interferometer," Opt. Lett. 30, 3069-3071 (2005).
    [CrossRef] [PubMed]
  13. L. B. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, "Tunable delay line with interacting whispering-gallery-mode resonator," Opt. Lett. 29, 626 (2004).
    [CrossRef] [PubMed]
  14. I. Chremmos, and N. Uzunoglu, "Reflective properties of double-ring resonator system coupled to a waveguide," IEEE Photon. Technol. Lett,  17, 2110-2112, 2005
    [CrossRef]
  15. Y. M. Landobasa, S. Darmawan, and M. K. Chin, "Matrix Analysis of 2-D Micro-resonator Lattice Optical Filters," IEEE J. Quantum Electronics 41, 1410-1418 (2005).
    [CrossRef]
  16. A. Yariv, "Critical coupling and its control in optical waveguide-resonator systems," IEEE Photon. Technol. Lett. 14, 483-485, 2002.
    [CrossRef]
  17. A.R. Cowan and J.F. Young, "Optical bistability involving photonic crystal microcavities and Fano line shapes," Phys. Rev. E 68046606 (2003)
    [CrossRef]
  18. V. Van, T. A. Ibrahim, P.P. Absil, F. G. Johnson, R. Grover, and P-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Quantum Electron. 8, 705-713 (2002).
    [CrossRef]
  19. B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64 (1994), 2773.
    [CrossRef]
  20. C. Y. Chao and L. J. Guo," Reduction of surface scattering loss in polymer mirorings using thermal-reflow technique," IEEE Photon. Technol. Lett. 16, 1498-1500 (2004).
    [CrossRef]
  21. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
    [CrossRef] [PubMed]

2005 (7)

Y. Dumeige, D. Arnaud, P. Feron, "Combining FDTD with coupled mode theories for bistability in micro-ring resonators," Opt. Commun. 250 (2005) 376-383.
[CrossRef]

Y. Dumeige, P. Feron, "Dispersive tristability in microring resonator," Phys. Rev. E,  72066609 (2005).
[CrossRef]

B. Maes, P. Bienstman, R. Baets, "Switching in coupled nonlinear photonic crystal resonators," J. Opt. Soc. Am. B  22(8), 1778-1784 (2005).
[CrossRef]

Y. Lu, J. Yao, X. Li, and P. Wang, "Tunable asymmetrical Fano resonance and bistability in a microcavity-resonator-coupled Mach Zehnder Interferometer," Opt. Lett. 30, 3069-3071 (2005).
[CrossRef] [PubMed]

I. Chremmos, and N. Uzunoglu, "Reflective properties of double-ring resonator system coupled to a waveguide," IEEE Photon. Technol. Lett,  17, 2110-2112, 2005
[CrossRef]

Y. M. Landobasa, S. Darmawan, and M. K. Chin, "Matrix Analysis of 2-D Micro-resonator Lattice Optical Filters," IEEE J. Quantum Electronics 41, 1410-1418 (2005).
[CrossRef]

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, "Optical bistable switching action of Si high-Q photonic-crystal nanocavities," Opt. Express 13, 2678-2687 (2005).
[CrossRef] [PubMed]

2004 (5)

L. B. Maleki, A. B. Matsko, A. A. Savchenkov, and V. S. Ilchenko, "Tunable delay line with interacting whispering-gallery-mode resonator," Opt. Lett. 29, 626 (2004).
[CrossRef] [PubMed]

C. Y. Chao and L. J. Guo," Reduction of surface scattering loss in polymer mirorings using thermal-reflow technique," IEEE Photon. Technol. Lett. 16, 1498-1500 (2004).
[CrossRef]

V. R. Almeida and M. Lipson, "Optical bistability on a silicon chip," Opt. Lett. 29, 2387-2389 (2004).
[CrossRef] [PubMed]

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

J. Niehusmann, A. Vörckel, P. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, "Ultrahigh-quality-factor silicon-on-insulator microring resonator", Opt. Lett. 29, 2861-2863 (2004).
[CrossRef]

2003 (3)

T. A. Ibrahim, R. Grover, L. -C. Kuo, S. Kanakaraju, L. C. Calhoun, P. -T. Ho, "All-optical AND/NAND logic gates using semiconductor microresonators," IEEE Photon. Technol. Lett. 15, 1422-1424 (2003).
[CrossRef]

S. Fan, W. Suh, and J. D. Joannopoulos, "Temporal coupled-mode theory for the Fano resonance in optical resonators, "J. Opt. Soc. Am. A,  20(3), 569-572 (2003).
[CrossRef]

A.R. Cowan and J.F. Young, "Optical bistability involving photonic crystal microcavities and Fano line shapes," Phys. Rev. E 68046606 (2003)
[CrossRef]

2002 (2)

V. Van, T. A. Ibrahim, P.P. Absil, F. G. Johnson, R. Grover, and P-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

A. Yariv, "Critical coupling and its control in optical waveguide-resonator systems," IEEE Photon. Technol. Lett. 14, 483-485, 2002.
[CrossRef]

1997 (1)

F. Sanchez, "Optical bistability in a 2x2 coupler fiber ring resonator: parametric formulation," Opt. Commun. 142, 211 (1997).
[CrossRef]

1994 (1)

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64 (1994), 2773.
[CrossRef]

1991 (1)

J. Danckaert, K. Fobelets, I. Veretennicoff, "Dispersive optical bistability in stratified structures," Phys. Rev. B,  44, 15, 8214 (1991).
[CrossRef]

1981 (1)

D. A. B. Miller, "Refractive Fabry-Perot Bistability with Linear Absorption: Theory of Operation and Cavity optimization," IEEE J. Quantum Electron,  17, 306-311 (1981).
[CrossRef]

Absil, P. P.

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Absil, P.P.

V. Van, T. A. Ibrahim, P.P. Absil, F. G. Johnson, R. Grover, and P-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Almeida, V. R.

Arnaud, D.

Y. Dumeige, D. Arnaud, P. Feron, "Combining FDTD with coupled mode theories for bistability in micro-ring resonators," Opt. Commun. 250 (2005) 376-383.
[CrossRef]

Baets, R.

Baker, G.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64 (1994), 2773.
[CrossRef]

Bienstman, P.

Bolivar, P. H.

Calhoun, L. C.

T. A. Ibrahim, R. Grover, L. -C. Kuo, S. Kanakaraju, L. C. Calhoun, P. -T. Ho, "All-optical AND/NAND logic gates using semiconductor microresonators," IEEE Photon. Technol. Lett. 15, 1422-1424 (2003).
[CrossRef]

Cha, M.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64 (1994), 2773.
[CrossRef]

Chao, C. Y.

C. Y. Chao and L. J. Guo," Reduction of surface scattering loss in polymer mirorings using thermal-reflow technique," IEEE Photon. Technol. Lett. 16, 1498-1500 (2004).
[CrossRef]

Chin, M. K.

Y. M. Landobasa, S. Darmawan, and M. K. Chin, "Matrix Analysis of 2-D Micro-resonator Lattice Optical Filters," IEEE J. Quantum Electronics 41, 1410-1418 (2005).
[CrossRef]

Chremmos, I.

I. Chremmos, and N. Uzunoglu, "Reflective properties of double-ring resonator system coupled to a waveguide," IEEE Photon. Technol. Lett,  17, 2110-2112, 2005
[CrossRef]

Chu, S. T.

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Cowan, A.R.

A.R. Cowan and J.F. Young, "Optical bistability involving photonic crystal microcavities and Fano line shapes," Phys. Rev. E 68046606 (2003)
[CrossRef]

Danckaert, J.

J. Danckaert, K. Fobelets, I. Veretennicoff, "Dispersive optical bistability in stratified structures," Phys. Rev. B,  44, 15, 8214 (1991).
[CrossRef]

Darmawan, S.

Y. M. Landobasa, S. Darmawan, and M. K. Chin, "Matrix Analysis of 2-D Micro-resonator Lattice Optical Filters," IEEE J. Quantum Electronics 41, 1410-1418 (2005).
[CrossRef]

Dumeige, Y.

Y. Dumeige, D. Arnaud, P. Feron, "Combining FDTD with coupled mode theories for bistability in micro-ring resonators," Opt. Commun. 250 (2005) 376-383.
[CrossRef]

Y. Dumeige, P. Feron, "Dispersive tristability in microring resonator," Phys. Rev. E,  72066609 (2005).
[CrossRef]

Etemad, S.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64 (1994), 2773.
[CrossRef]

Fan, S.

Feron, P.

Y. Dumeige, P. Feron, "Dispersive tristability in microring resonator," Phys. Rev. E,  72066609 (2005).
[CrossRef]

Y. Dumeige, D. Arnaud, P. Feron, "Combining FDTD with coupled mode theories for bistability in micro-ring resonators," Opt. Commun. 250 (2005) 376-383.
[CrossRef]

Fobelets, K.

J. Danckaert, K. Fobelets, I. Veretennicoff, "Dispersive optical bistability in stratified structures," Phys. Rev. B,  44, 15, 8214 (1991).
[CrossRef]

Gill, D.

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Grover, R.

T. A. Ibrahim, R. Grover, L. -C. Kuo, S. Kanakaraju, L. C. Calhoun, P. -T. Ho, "All-optical AND/NAND logic gates using semiconductor microresonators," IEEE Photon. Technol. Lett. 15, 1422-1424 (2003).
[CrossRef]

V. Van, T. A. Ibrahim, P.P. Absil, F. G. Johnson, R. Grover, and P-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Guo, L. J.

C. Y. Chao and L. J. Guo," Reduction of surface scattering loss in polymer mirorings using thermal-reflow technique," IEEE Photon. Technol. Lett. 16, 1498-1500 (2004).
[CrossRef]

Henschel, W.

Ho, P. -T.

T. A. Ibrahim, R. Grover, L. -C. Kuo, S. Kanakaraju, L. C. Calhoun, P. -T. Ho, "All-optical AND/NAND logic gates using semiconductor microresonators," IEEE Photon. Technol. Lett. 15, 1422-1424 (2003).
[CrossRef]

Ho, P-T.

V. Van, T. A. Ibrahim, P.P. Absil, F. G. Johnson, R. Grover, and P-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Hryniewicz, J. V.

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Ibrahim, T. A.

T. A. Ibrahim, R. Grover, L. -C. Kuo, S. Kanakaraju, L. C. Calhoun, P. -T. Ho, "All-optical AND/NAND logic gates using semiconductor microresonators," IEEE Photon. Technol. Lett. 15, 1422-1424 (2003).
[CrossRef]

V. Van, T. A. Ibrahim, P.P. Absil, F. G. Johnson, R. Grover, and P-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Ilchenko, V. S.

Joannopoulos, J. D.

Johnson, F. G.

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

V. Van, T. A. Ibrahim, P.P. Absil, F. G. Johnson, R. Grover, and P-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Kajzar, F.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64 (1994), 2773.
[CrossRef]

Kanakaraju, S.

T. A. Ibrahim, R. Grover, L. -C. Kuo, S. Kanakaraju, L. C. Calhoun, P. -T. Ho, "All-optical AND/NAND logic gates using semiconductor microresonators," IEEE Photon. Technol. Lett. 15, 1422-1424 (2003).
[CrossRef]

King, O.

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Kira, G.

Kuo, L. -C.

T. A. Ibrahim, R. Grover, L. -C. Kuo, S. Kanakaraju, L. C. Calhoun, P. -T. Ho, "All-optical AND/NAND logic gates using semiconductor microresonators," IEEE Photon. Technol. Lett. 15, 1422-1424 (2003).
[CrossRef]

Kuramochi, E.

Kurz, H.

Landobasa, Y. M.

Y. M. Landobasa, S. Darmawan, and M. K. Chin, "Matrix Analysis of 2-D Micro-resonator Lattice Optical Filters," IEEE J. Quantum Electronics 41, 1410-1418 (2005).
[CrossRef]

Lawrence, B. L.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64 (1994), 2773.
[CrossRef]

Li, X.

Lipson, M.

Little, B.E.

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Lu, Y.

Maes, B.

Maleki, L. B.

Matsko, A. B.

Miller, D. A. B.

D. A. B. Miller, "Refractive Fabry-Perot Bistability with Linear Absorption: Theory of Operation and Cavity optimization," IEEE J. Quantum Electron,  17, 306-311 (1981).
[CrossRef]

Mitsugi, S.

Niehusmann, J.

Notomi, M.

Sanchez, F.

F. Sanchez, "Optical bistability in a 2x2 coupler fiber ring resonator: parametric formulation," Opt. Commun. 142, 211 (1997).
[CrossRef]

Savchenkov, A. A.

Seiferth, F.

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Shinya, A.

Stegeman, G. I.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64 (1994), 2773.
[CrossRef]

Suh, W.

Tanabe, T.

Torruellas, W. E.

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64 (1994), 2773.
[CrossRef]

Trakalo, M.

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

Uzunoglu, N.

I. Chremmos, and N. Uzunoglu, "Reflective properties of double-ring resonator system coupled to a waveguide," IEEE Photon. Technol. Lett,  17, 2110-2112, 2005
[CrossRef]

Van, V.

B.E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, and M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
[CrossRef]

V. Van, T. A. Ibrahim, P.P. Absil, F. G. Johnson, R. Grover, and P-T. Ho, "Optical signal processing using nonlinear semiconductor microring resonators," IEEE J. Quantum Electron. 8, 705-713 (2002).
[CrossRef]

Veretennicoff, I.

J. Danckaert, K. Fobelets, I. Veretennicoff, "Dispersive optical bistability in stratified structures," Phys. Rev. B,  44, 15, 8214 (1991).
[CrossRef]

Vörckel, A.

Wahlbrink, T.

Wang, P.

Yao, J.

Yariv, A.

A. Yariv, "Critical coupling and its control in optical waveguide-resonator systems," IEEE Photon. Technol. Lett. 14, 483-485, 2002.
[CrossRef]

Young, J.F.

A.R. Cowan and J.F. Young, "Optical bistability involving photonic crystal microcavities and Fano line shapes," Phys. Rev. E 68046606 (2003)
[CrossRef]

Appl. Phys. Lett. (1)

B. L. Lawrence, M. Cha, W. E. Torruellas, G. I. Stegeman, S. Etemad, G. Baker, F. Kajzar, "Measurement of the complex nonlinear refractive index of single crystal p-toluene sulfonate at 1064 nm," Appl. Phys. Lett. 64 (1994), 2773.
[CrossRef]

IEEE J. Quantum Electron (1)

D. A. B. Miller, "Refractive Fabry-Perot Bistability with Linear Absorption: Theory of Operation and Cavity optimization," IEEE J. Quantum Electron,  17, 306-311 (1981).
[CrossRef]

IEEE J. Quantum Electron. (1)

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Figures (13)

Fig. 1.
Fig. 1.

Schematic of a ring resonator coupled to one bus waveguide.

Fig. 2.
Fig. 2.

The transmission as a function of incident power for a critically coupled ring for (a) r=a=0.95 for various near-resonant wavelengths, and (b) at a fixed wavelength, λ=1567 nm, for various losses under the critical coupling condition.

Fig. 3.
Fig. 3.

Schematic of a REMZI with phase bias Δϕ.

Fig. 4.
Fig. 4.

The Fano resonances for various values of Δϕ.

Fig. 5.
Fig. 5.

The Cross output transmission as a function of incident power for various phase biases. The inset shows a blow-up of the curves at the switch-off points.

Fig. 6.
Fig. 6.

The achievable bandwidth can be up to 20GHz for relatively high ER. The highest ER can be as much as 40dB, with phase bias Δϕ=0.2π and r=0.9.

Fig. 7.
Fig. 7.

The two ring resonator configuration with “through” (T) and “drop” (D) outputs. The fields at various points in the structure are indicated.

Fig. 8.
Fig. 8.

(a) Plot of Eq. 8 for two different γ values. The nonlinear region is due to the upper ring. (b) The resultant shifts and shape changes in the resonances as γ deviates from 1. For this calculation, we set a 1 and a 2 to be 1 and r 1,2=0.95.

Fig. 9.
Fig. 9.

The analytically calculated “Through” spectra of a linear two-ring structure for different γ values (r 1,2=0.95). The right panel shows the associated field distribution for each resonance calculated by FDTD.

Fig. 10.
Fig. 10.

Fano resonances in the “Drop” spectra with different asymmetricities can be obtained by adjusting r 1, with γ=1.05 and r 2=0.99.

Fig. 11.
Fig. 11.

T vs. n 2IIN curves: (a) For various wavelengths, with r 1,2=0.85,. and a 1,2=0.99. (b) For different asymmetricities, as defined by the different (r 1, r 2) combinations. The dotted curve shows the loss of bistability when the upper ring is under the critical coupling condition.

Fig. 12.
Fig. 12.

Extinction ratio as a function of a1, for both T and D outputs, and for various values of r1.

Fig. 13.
Fig. 13.

The switching characteristics of the two-ring (solid) and one-ring (dashed) configurations with different cavity sizes. The cavity length is varied from 0.5 to 2 times the original length in both configurations, and the λ in each case is adjusted to achieve the lowest threshold. The coupling coefficient in both configurations is fixed, r=r 2=0.95. The (γ, r 1) for each of the two-ring cases is different, and from 0.5× to 2×, are given by (1.005, 0.8), (1.05, 0.85), and (1.05, 0.75), respectively.

Equations (15)

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T = E OUT E IN 2 = a 2 2 r a cos δ + r 2 1 2 r a cos δ + r 2 a 2
δ = δ L + δ NL = k 0 ( n eff + n 2 I r η ) L c
I R I IN = 1 r 2 1 2 r a cos δ + r 2 a 2 B
φ = π δ tan 1 { r sin δ a r cos δ } tan 1 { a r sin δ 1 a r cos δ }
t = E T E IN = r 1 [ 1 a 1 T 2 exp ( i δ 1 ) ] [ 1 a 1 r 1 2 T 2 exp ( i δ 1 ) ]
d = E D E IN = t 1 2 a 1 T 2 exp ( i δ 1 2 ) [ 1 a 1 r 1 2 T 2 exp ( i δ 1 ) ]
t = r 1 ( 1 a exp ( i δ ) 1 a r 1 2 exp ( i δ ) )
δ = tan 1 { a 2 sin ( γ δ 1 ) r 2 a 2 cos ( γ δ 1 ) } tan 1 { a 2 r 2 sin ( γ δ 1 ) 1 a 2 r 2 cos ( γ δ 1 ) } δ 1
E D = i t 1 T 2 a 1 1 2 exp ( i γ NL 14 E 1 2 ) exp ( i δ 1 2 ) E 1
E T = [ 1 a 1 T 2 exp ( i δ 1 ) exp ( i γ NL 16 E 1 2 ) ] ( r 1 i t 1 ) E 1
E IN = [ 1 a 1 r 1 2 T 2 exp ( i δ 1 ) exp ( i γ NL 16 E 1 2 ) ] ( 1 i t 1 ) E 1
E 3 = [ r 2 a 2 exp ( i δ 2 ) exp ( i γ NL 98 E 9 2 ) ] E 9 i t 2
E 2 = [ 1 a 2 r 2 exp ( i δ 2 ) exp ( i γ NL 98 E 9 2 ) ] E 9 i t 2
E 2 2 a 1 1 2 = E 1 2 , T 2 = E 3 E 2 , a 1,2 = exp ( α 1,2 L 1,2 2 )
E R max ( T ) = T max T min = ( 1 + a 1 1 a 1 ) 2 ( 1 a 1 r 1 2 1 + a 1 r 1 2 ) 2 , E R max ( D ) = D max D min = ( 1 + a 1 r 1 2 1 a 1 r 1 2 ) 2

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