Abstract

We model the nonlinear response of a silica toroid microcavity using coupled-mode theory and a finite-element method, and successfully obtain Kerr bistable operation that does not suffer from the thermo-optic effect by optimizing the fiber-cavity coupling. Our rigorous analysis reveals the possibility of demonstrating a Kerr bistable memory with a memory holding time of 500 ns at an extremely low energy consumption.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (2)

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[CrossRef]

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef]

2011 (4)

J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1  dB/mpropagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011).
[CrossRef]

I. Razdolskiy, S. Berneschi, G. N. Conti, S. Pelli, T. V. Murzina, G. C. Righini, and S. Soria, “Hybrid microspheres for nonlinear Kerr switching devices,” Opt. Express 19, 9523–9528 (2011).
[CrossRef]

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[CrossRef]

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[CrossRef]

2010 (2)

2009 (1)

2008 (3)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[CrossRef]

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008).
[CrossRef]

2007 (4)

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theor. Tech. 55, 1209–1218 (2007).
[CrossRef]

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51, 1376–1380 (2007).
[CrossRef]

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[CrossRef]

2005 (4)

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (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]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
[CrossRef]

2004 (6)

V. Almeida, and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29, 2387–2389 (2004).
[CrossRef]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
[CrossRef]

H. Rokhsari and K. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[CrossRef]

T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[CrossRef]

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
[CrossRef]

2003 (5)

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[CrossRef]

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef]

K. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[CrossRef]

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef]

2002 (1)

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

2000 (1)

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef]

1999 (1)

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

1993 (1)

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

1990 (1)

H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of 2 optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[CrossRef]

1979 (1)

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef]

Almeida, V.

Armani, D.

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef]

Asano, T.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef]

Barclay, P.

Barton, J. S.

Bauters, J. F.

Bazin, M.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[CrossRef]

Berneschi, S.

Blumenthal, D. J.

Bowers, J. E.

Bruinink, C. M.

Brune, M.

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Cai, M.

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef]

Chen, T.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef]

Claudon, J.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[CrossRef]

Collot, L.

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Conti, G. N.

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef]

Ctistis, G.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[CrossRef]

Deppe, D.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Dominguez-Juarez, J. L.

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[CrossRef]

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008).
[CrossRef]

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Fainman, Y.

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51, 1376–1380 (2007).
[CrossRef]

Fan, S.

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[CrossRef]

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Fink, Y.

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Fukuda, H.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[CrossRef]

Gerard, J.-M.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[CrossRef]

Gibbs, H.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

H. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

Goh, K.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[CrossRef]

Haret, L.-D.

Haroche, S.

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Hartsuiker, A.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[CrossRef]

Haus, H.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Heck, M. J. R.

Heideman, R. G.

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Hosaka, T.

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[CrossRef]

Ibanescu, M.

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Ikeda, K.

K. Ikeda and Y. Fainman, “Material and structural criteria for ultra-fast Kerr nonlinear switching in optical resonant cavities,” Solid-State Electron. 51, 1376–1380 (2007).
[CrossRef]

Ilchenko, V.

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Itabashi, S.-i.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[CrossRef]

Joannopoulos, J.

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

John, D. D.

Johnson, S.

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Kakitsuka, T.

Kawaguchi, Y.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[CrossRef]

Khan, M.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Khanzadeh, M.

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Kimble, H.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[CrossRef]

Kippenberg, T.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[CrossRef]

T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[CrossRef]

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef]

Kira, G.

Kozyreff, G.

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[CrossRef]

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008).
[CrossRef]

Kuramochi, E.

Kurokawa, T.

H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of 2 optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[CrossRef]

Lee, H.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef]

Lefevreseguin, V.

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Leinse, A.

Li, J.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef]

Lipson, M.

Maleki, L.

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Manolatou, C.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Martorell, J.

J. L. Dominguez-Juarez, G. Kozyreff, and J. Martorell, “Whispering gallery microresonators for second harmonic light generation from a low number of small molecules,” Nat. Commun. 2, 254 (2011).
[CrossRef]

G. Kozyreff, J. L. Dominguez-Juarez, and J. Martorell, “Whispering-gallery-mode phase matching for surface second-order nonlinear optical processes in spherical microresonators,” Phys. Rev. A 77, 043817 (2008).
[CrossRef]

Matsko, A.

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Matsuo, S.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[CrossRef]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[CrossRef]

Mitsugi, S.

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]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

Miya, T.

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[CrossRef]

Miyashita, T.

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[CrossRef]

Murzina, T. V.

Noda, S.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef]

Notomi, M.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[CrossRef]

L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21108–21117 (2009).
[CrossRef]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[CrossRef]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (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]

Nozaki, K.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[CrossRef]

O’Brien, J. L.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef]

Oxborrow, M.

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theor. Tech. 55, 1209–1218 (2007).
[CrossRef]

Painter, O.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef]

P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
[CrossRef]

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef]

Pelli, S.

Politi, A.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef]

Pöllinger, M.

Raimond, J.

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef]

Rauschenbeutel, A.

Razdolskiy, I.

Righini, G. C.

Rokhsari, H.

H. Rokhsari and K. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[CrossRef]

H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
[CrossRef]

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Sato, T.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[CrossRef]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[CrossRef]

Savchenkov, A.

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804 (2004).
[CrossRef]

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Segawa, T.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[CrossRef]

Shafiei, M.

Shchekin, O.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Shinya, A.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[CrossRef]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[CrossRef]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (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]

Soljacic, M.

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[CrossRef]

M. Soljacic, M. Ibanescu, S. Johnson, Y. Fink, and J. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601 (2002).
[CrossRef]

Song, B.

Y. Akahane, T. Asano, B. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef]

Soria, S.

Spillane, S.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[CrossRef]

H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
[CrossRef]

T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[CrossRef]

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef]

Srinivasan, K.

Suzaki, Y.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[CrossRef]

Takahashi, R.

K. Nozaki, A. Shinya, S. Matsuo, Y. Suzaki, T. Segawa, T. Sato, Y. Kawaguchi, R. Takahashi, and M. Notomi, “Ultralow-power all-optical RAM based on nanocavities,” Nat. Photonics 6, 248–252 (2012).
[CrossRef]

Takesue, H.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[CrossRef]

Tanabe, T.

L.-D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21108–21117 (2009).
[CrossRef]

A. Shinya, S. Matsuo, Yosia, T. Tanabe, E. Kuramochi, T. Sato, T. Kakitsuka, and M. Notomi, “All-optical on-chip bit memory based on ultra high Q InGaAsP photonic crystal,” Opt. Express 16, 19382–19387 (2008).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[CrossRef]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (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]

W. Yoshiki and T. Tanabe, “Analysis of four-port system for bistable memory in silica toroid microcavity,” in The 2nd International Symposium on Photonics and Electronics Convergence (ISPEC2012) (ISPEC, 2012), paper C-4.

Taniyama, H.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
[CrossRef]

Terunuma, Y.

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[CrossRef]

Tokura, Y.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[CrossRef]

Tsuchizawa, T.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[CrossRef]

Tsuda, H.

H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of 2 optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[CrossRef]

Vahala, K.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[CrossRef]

T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[CrossRef]

H. Rokhsari and K. Vahala, “Ultralow loss, high Q, four port resonant couplers for quantum optics and photonics,” Phys. Rev. Lett. 92, 253905 (2004).
[CrossRef]

H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
[CrossRef]

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[CrossRef]

D. Armani, T. Kippenberg, S. Spillane, and K. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef]

K. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[CrossRef]

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[CrossRef]

Vahala, K. J.

H. Lee, T. Chen, J. Li, O. Painter, and K. J. Vahala, “Ultra-low-loss optical delay line on a silicon chip,” Nat. Commun. 3, 867 (2012).
[CrossRef]

Villeneuve, P.

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Vos, W. L.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[CrossRef]

Watanabe, T.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[CrossRef]

Wilcut, E.

S. Spillane, T. Kippenberg, K. Vahala, K. Goh, E. Wilcut, and H. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71, 013817 (2005).
[CrossRef]

Yamada, K.

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[CrossRef]

Yanik, M.

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
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Yariv, A.

A. Yariv, Optical Electronics in Modern Communications (Oxford University, 1997).

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432, 200–203 (2004).
[CrossRef]

Yoshiki, W.

W. Yoshiki and T. Tanabe, “Analysis of four-port system for bistable memory in silica toroid microcavity,” in The 2nd International Symposium on Photonics and Electronics Convergence (ISPEC2012) (ISPEC, 2012), paper C-4.

Yosia,

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[CrossRef]

Yuce, E.

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[CrossRef]

Appl. Phys. Lett. (7)

H. Tsuda and T. Kurokawa, “Construction of an all-optical flip-flop by combination of 2 optical triodes,” Appl. Phys. Lett. 57, 1724–1726 (1990).
[CrossRef]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “All-optical switches on a silicon chip realized using photonic crystal nanocavities,” Appl. Phys. Lett. 87, 151112 (2005).
[CrossRef]

H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S.-i. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett. 91, 201108 (2007).
[CrossRef]

G. Ctistis, E. Yuce, A. Hartsuiker, J. Claudon, M. Bazin, J.-M. Gerard, and W. L. Vos, “Ultimate fast optical switching of a planar microcavity in the telecom wavelength range,” Appl. Phys. Lett. 98, 161114 (2011).
[CrossRef]

M. Yanik, S. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83, 2739–2741 (2003).
[CrossRef]

H. Rokhsari, S. Spillane, and K. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85, 3029–3031 (2004).
[CrossRef]

T. Kippenberg, S. Spillane, and K. Vahala, “Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip,” Appl. Phys. Lett. 85, 6113–6115 (2004).
[CrossRef]

Electron. Lett. (1)

T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low-loss single-mode fibre at 1.55 μm,” Electron. Lett. 15, 106–108 (1979).
[CrossRef]

Europhys. Lett. (1)

L. Collot, V. Lefevreseguin, M. Brune, J. Raimond, and S. Haroche, “Very high-Q whispering-gallery mode resonances observed on fused-silica microspheres,” Europhys. Lett. 23, 327–334 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. Manolatou, M. Khan, S. Fan, P. Villeneuve, H. Haus, and J. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (1)

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theor. Tech. 55, 1209–1218 (2007).
[CrossRef]

Nat. Commun. (2)

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T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photon. 1, 49–52 (2007).
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Figures (5)

Fig. 1.
Fig. 1.

(a) Cavity structure used for numerical analysis. (b) Cross section of the mode-intensity profile of a toroid microcavity [32].

Fig. 2.
Fig. 2.

Figures obtained in an ideal case where the absorption loss in the cavity is determined only by the material. (a) ΔnKerr and ΔnTO versus time when a 6 μW rectangular pulse is input. The wavelength detuning δ between the input light and the initial cavity resonance is 27 fm. τcoup2 is set equal to τint. (b) Pout1 versus Pin of a triangular input pulse with different δ values, where Pout1=|sout1|2. (c) Pout2 versus Pin with different δ, where Pout2=|sout2|2. δ=13, 20, and 27 fm correspond to (3/2)ΔλFWHM, (33/4)ΔλFWHM, and 3ΔλFWHM, respectively. ΔλFWHM is the full-width at half-maximum of the cavity resonant spectrum width. (ΔλFWHM15fm). (d) Optical bistable memory operation. The solid, dotted, and dashed curves represent Pin, Pout1, and Pout2, respectively.

Fig. 3.
Fig. 3.

ΔnKerr (solid curve) and ΔnTO (dashed curve) versus time for different τcoup2 values in a realistic case. The input pulse power is set at 500×(Qtotτcoup2=τint/100/Qtot)2 in microwatts. The detuning δ is set at 3ΔλFWHM, where ΔλFWHM is 15 fm, 85 fm, and 782 pm when τcoup2 is τint, τint/10, and τint/100, respectively.

Fig. 4.
Fig. 4.

Input–output response of a triangular pulse input in a realistic case. (a) Pout1 versus Pin for different τcoup2. (b) Pout2 versus Pin for different τcoup2. The x-axis and y-axis are normalized as Pout1max=Pout2max=Pinmax=1. The detuning δ is set at 3ΔλFWHM. The input pulsewidth is 15 μs, 3 μs, and 0.3 μs and the pulse height is 4.5 μW, 160 μW, and 15 mW when τcoup2 is τint, τint/10, and τint/100, respectively.

Fig. 5.
Fig. 5.

Optical memory operation in a realistic case, when δ is 3ΔFWHM. The input power of the drive light is 2 μW, 80 μW, and 7.3 mW, when τcoup2 is τint, τint/10, and τint/100, respectively. The horizontal axis is normalized with the photon lifetime τtot and the vertical axes are normalized as Pout1max=Pout2max=Pinmax=1.

Tables (1)

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Table 1. Comparison of the Power Consumption of Different Systems

Equations (25)

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U=14εE02V,
I=2cn0UV,
ΔnKerr=n2I=2n2cn0UV,
ΔnTO=n0ξT.
ΔnTO=n0ξCρ1VUabs,
ΔnKerrΔnTO=2n2cρCn02ξUUabs>1.
{U(t)=U0dUabs(t)dt=1τdiffUabs+1τabsU(t),
t<2n2cρCn02ξτabs.
t<3.84τabs.
dadt=[jω012(1τabs+1τloss+1τcoup1+1τcoup2)]a+1τcoup1exp(jθ)sin,
θ=4π2n0(R+r)(1λ01λ).
sout1=exp(jβ1d)×[sin1τcoup1exp(jθ1)a],
sout2=exp(jβ2d)1τcoup2a,
a(t)=A(t)exp(jωt),
sin(t)=Sin(t)exp(jωt),
dA(t)dt=[j2πcn0(1λ01λ)12(1τabs+1τloss+1τcoup1+1τcoup2)]A(t)+1τcoup1exp(jθ)Sin(t).
δλ(t)=Δn(t)n0λ0,
dA(t)dt=[j2πcn0+Δn(t)(1λ0+δλ(t)1λ)12(1τabs+1τloss+1τcoup1+1τcoup2)]A(t)+1τcoup1exp(jθ)Sin(t),
θ=4π2(n0+Δn(t))(R+r)(1λ0+δλ(t)1λ).
ΔnKerr(x,y,t)=n2I(x,y,t)=2n2cn0U˜p(x,y,t),
U˜p(x,y,t)=Up(t)2πRI˜(x,y),
ΔnTO(x,y,t)=nξ[T(x,y,t)300[K]].
Q(x,y,t)={τabs1U˜p(x,y,t),in cavity,0,in air,
Δn(t)=[ΔnTO(x,y,t)+ΔnKerr(x,y,t)]I˜(x,y)dxdyI˜(x,y)dxdy.
τtot=(τmat1+τwater1+τcont1+τrad1+τsurf1+τcoup11+τcoup21)1,

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