Abstract

In this paper, we investigate the critical conditions of control light for a silicon-based photonic crystal bistable switching. By establishing a time-dependent evolution equation, the critical pump power and pump time of the control light are derived, respectively. It is found that with the increase of the frequency detuning of the incident light, the critical power of the control light will rise, while the corresponding critical time will be shortened. It is also revealed that under the same conditions, the critical total power of the multiple-beam control light is less than the one of the single-beam control light. The theoretical predictions show perfect agreement with the simulation results.

© 2010 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. M. K. Kim, I. K. Hwang, S. H. Kim, H. J. Chang, and Y. H. Lee, “All-optical bistable switching in curved microfiber-coupled photonic crystal resonators,” Appl. Phys. Lett. 90(16), 161118 (2007).
    [CrossRef]
  4. M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
    [CrossRef]
  5. M. Belotti, J. F. Galisteo Lòpez, S. De Angelis, M. Galli, I. Maksymov, L. C. Andreani, D. Peyrade, and Y. Chen, “All-optical switching in 2D silicon photonic crystals with low loss waveguides and optical cavities,” Opt. Express 16(15), 11624–11636 (2008).
    [PubMed]
  6. 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(15), 151112 (2005).
    [CrossRef]
  7. G. Priem, P. Bienstman, G. Morthier, and R. Baets, “Impact of absorption mechanisms on Kerr-nonlinear resonator behavior,” J. Appl. Phys. 99(6), 063103 (2006).
    [CrossRef]
  8. D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. de Fornel, “Near-field control of optical bistability in a nanocavity,” Phys. Rev. B 80(3), 033103 (2009).
    [CrossRef]
  9. C. Li, J. F. Wu, and W. C. Xu, “Influence of two-photon absorption on bistable switching in a silicon photonic crystal microcavity,” Opt. Commun. 283(14), 2957–2960 (2010).
    [CrossRef]
  10. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, New Jersey, 1984).
  11. C. Li, J. F. Wu, and W. C. Xu, “Precise control of light frequency via a linear photonic crystal microcavity,” Appl. Opt. 49(14), 2597–2600 (2010).
    [CrossRef]
  12. A. Taflove, and S. C. Hagness, Computational Electrodynamics (Artech House, Norwood, MA, 2000)

2010

C. Li, J. F. Wu, and W. C. Xu, “Influence of two-photon absorption on bistable switching in a silicon photonic crystal microcavity,” Opt. Commun. 283(14), 2957–2960 (2010).
[CrossRef]

C. Li, J. F. Wu, and W. C. Xu, “Precise control of light frequency via a linear photonic crystal microcavity,” Appl. Opt. 49(14), 2597–2600 (2010).
[CrossRef]

2009

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. de Fornel, “Near-field control of optical bistability in a nanocavity,” Phys. Rev. B 80(3), 033103 (2009).
[CrossRef]

2008

2007

M. K. Kim, I. K. Hwang, S. H. Kim, H. J. Chang, and Y. H. Lee, “All-optical bistable switching in curved microfiber-coupled photonic crystal resonators,” Appl. Phys. Lett. 90(16), 161118 (2007).
[CrossRef]

2006

G. Priem, P. Bienstman, G. Morthier, and R. Baets, “Impact of absorption mechanisms on Kerr-nonlinear resonator behavior,” J. Appl. Phys. 99(6), 063103 (2006).
[CrossRef]

2005

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(15), 151112 (2005).
[CrossRef]

2003

M. F. Yanik, S. H. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83(14), 2739–2741 (2003).
[CrossRef]

2002

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[CrossRef]

Andreani, L. C.

Baets, R.

G. Priem, P. Bienstman, G. Morthier, and R. Baets, “Impact of absorption mechanisms on Kerr-nonlinear resonator behavior,” J. Appl. Phys. 99(6), 063103 (2006).
[CrossRef]

Belotti, M.

Bienstman, P.

G. Priem, P. Bienstman, G. Morthier, and R. Baets, “Impact of absorption mechanisms on Kerr-nonlinear resonator behavior,” J. Appl. Phys. 99(6), 063103 (2006).
[CrossRef]

Brissinger, D.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. de Fornel, “Near-field control of optical bistability in a nanocavity,” Phys. Rev. B 80(3), 033103 (2009).
[CrossRef]

Chang, H. J.

M. K. Kim, I. K. Hwang, S. H. Kim, H. J. Chang, and Y. H. Lee, “All-optical bistable switching in curved microfiber-coupled photonic crystal resonators,” Appl. Phys. Lett. 90(16), 161118 (2007).
[CrossRef]

Chen, Y.

Cluzel, B.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. de Fornel, “Near-field control of optical bistability in a nanocavity,” Phys. Rev. B 80(3), 033103 (2009).
[CrossRef]

Coillet, A.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. de Fornel, “Near-field control of optical bistability in a nanocavity,” Phys. Rev. B 80(3), 033103 (2009).
[CrossRef]

De Angelis, S.

de Fornel, F.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. de Fornel, “Near-field control of optical bistability in a nanocavity,” Phys. Rev. B 80(3), 033103 (2009).
[CrossRef]

Dumas, C.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. de Fornel, “Near-field control of optical bistability in a nanocavity,” Phys. Rev. B 80(3), 033103 (2009).
[CrossRef]

Fan, S. H.

M. F. Yanik, S. H. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83(14), 2739–2741 (2003).
[CrossRef]

Fink, Y.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[CrossRef]

Galisteo Lòpez, J. F.

Galli, M.

Grelu, P.

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. de Fornel, “Near-field control of optical bistability in a nanocavity,” Phys. Rev. B 80(3), 033103 (2009).
[CrossRef]

Hwang, I. K.

M. K. Kim, I. K. Hwang, S. H. Kim, H. J. Chang, and Y. H. Lee, “All-optical bistable switching in curved microfiber-coupled photonic crystal resonators,” Appl. Phys. Lett. 90(16), 161118 (2007).
[CrossRef]

Ibanescu, M.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[CrossRef]

Joannopoulos, J. D.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[CrossRef]

Johnson, S. G.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[CrossRef]

Kim, M. K.

M. K. Kim, I. K. Hwang, S. H. Kim, H. J. Chang, and Y. H. Lee, “All-optical bistable switching in curved microfiber-coupled photonic crystal resonators,” Appl. Phys. Lett. 90(16), 161118 (2007).
[CrossRef]

Kim, S. H.

M. K. Kim, I. K. Hwang, S. H. Kim, H. J. Chang, and Y. H. Lee, “All-optical bistable switching in curved microfiber-coupled photonic crystal resonators,” Appl. Phys. Lett. 90(16), 161118 (2007).
[CrossRef]

Kuramochi, E.

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(15), 151112 (2005).
[CrossRef]

Lee, Y. H.

M. K. Kim, I. K. Hwang, S. H. Kim, H. J. Chang, and Y. H. Lee, “All-optical bistable switching in curved microfiber-coupled photonic crystal resonators,” Appl. Phys. Lett. 90(16), 161118 (2007).
[CrossRef]

Li, C.

C. Li, J. F. Wu, and W. C. Xu, “Influence of two-photon absorption on bistable switching in a silicon photonic crystal microcavity,” Opt. Commun. 283(14), 2957–2960 (2010).
[CrossRef]

C. Li, J. F. Wu, and W. C. Xu, “Precise control of light frequency via a linear photonic crystal microcavity,” Appl. Opt. 49(14), 2597–2600 (2010).
[CrossRef]

Maksymov, I.

Mitsugi, S.

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(15), 151112 (2005).
[CrossRef]

Morthier, G.

G. Priem, P. Bienstman, G. Morthier, and R. Baets, “Impact of absorption mechanisms on Kerr-nonlinear resonator behavior,” J. Appl. Phys. 99(6), 063103 (2006).
[CrossRef]

Notomi, M.

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(15), 151112 (2005).
[CrossRef]

Ogusu, K.

Peyrade, D.

Priem, G.

G. Priem, P. Bienstman, G. Morthier, and R. Baets, “Impact of absorption mechanisms on Kerr-nonlinear resonator behavior,” J. Appl. Phys. 99(6), 063103 (2006).
[CrossRef]

Shinya, A.

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(15), 151112 (2005).
[CrossRef]

Soljacic, M.

M. F. Yanik, S. H. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83(14), 2739–2741 (2003).
[CrossRef]

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[CrossRef]

Takayama, K.

Tanabe, T.

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(15), 151112 (2005).
[CrossRef]

Wu, J. F.

C. Li, J. F. Wu, and W. C. Xu, “Precise control of light frequency via a linear photonic crystal microcavity,” Appl. Opt. 49(14), 2597–2600 (2010).
[CrossRef]

C. Li, J. F. Wu, and W. C. Xu, “Influence of two-photon absorption on bistable switching in a silicon photonic crystal microcavity,” Opt. Commun. 283(14), 2957–2960 (2010).
[CrossRef]

Xu, W. C.

C. Li, J. F. Wu, and W. C. Xu, “Influence of two-photon absorption on bistable switching in a silicon photonic crystal microcavity,” Opt. Commun. 283(14), 2957–2960 (2010).
[CrossRef]

C. Li, J. F. Wu, and W. C. Xu, “Precise control of light frequency via a linear photonic crystal microcavity,” Appl. Opt. 49(14), 2597–2600 (2010).
[CrossRef]

Yanik, M. F.

M. F. Yanik, S. H. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83(14), 2739–2741 (2003).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

M. F. Yanik, S. H. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83(14), 2739–2741 (2003).
[CrossRef]

M. K. Kim, I. K. Hwang, S. H. Kim, H. J. Chang, and Y. H. Lee, “All-optical bistable switching in curved microfiber-coupled photonic crystal resonators,” Appl. Phys. Lett. 90(16), 161118 (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(15), 151112 (2005).
[CrossRef]

J. Appl. Phys.

G. Priem, P. Bienstman, G. Morthier, and R. Baets, “Impact of absorption mechanisms on Kerr-nonlinear resonator behavior,” J. Appl. Phys. 99(6), 063103 (2006).
[CrossRef]

Opt. Commun.

C. Li, J. F. Wu, and W. C. Xu, “Influence of two-photon absorption on bistable switching in a silicon photonic crystal microcavity,” Opt. Commun. 283(14), 2957–2960 (2010).
[CrossRef]

Opt. Express

Phys. Rev. B

D. Brissinger, B. Cluzel, A. Coillet, C. Dumas, P. Grelu, and F. de Fornel, “Near-field control of optical bistability in a nanocavity,” Phys. Rev. B 80(3), 033103 (2009).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002).
[CrossRef]

Other

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, New Jersey, 1984).

A. Taflove, and S. C. Hagness, Computational Electrodynamics (Artech House, Norwood, MA, 2000)

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Figures (4)

Fig. 1
Fig. 1

Sketch of a typical bistable switching composed of a resonator cavity coupled to both input and output WGs.

Fig. 2
Fig. 2

Working principle diagram of a bistable switching

Fig. 3
Fig. 3

Evolvement curves of bistable switching for different pump power of the control light. The upper curve: p x = 0.0136 kW/μm; The lower curve: p x = 0.0132 kW/μm.

Fig. 4
Fig. 4

Critical pump time of the control light for δ = 4.3478. (a) Illustration for how to obtain the critical pump time of the control light. (b) Evolvement curve of transmission when the control light is shut off at t = 3522(a/c).

Tables (2)

Tables Icon

Table 1 Critical pump power of the control light with respect to different frequency detuning.

Tables Icon

Table 2 Critical pump time of the control light with respect to different frequency detuning.

Equations (18)

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{ d A d t = [ j ( ω 0 γ | s T | 2 p 0 ) γ ] A + 2 γ 1 ( s s + s x ) γ = γ 0 + γ 1 + γ 2 + γ T P A s T = 2 γ 2 A s s + s x + s R = 2 γ 1 A ,
γ T P A = k γ 1 | s T | 2 ,
A = 2 γ 1 ( | s s | + | s x | ) i ( ω ω 0 + γ | s T | 2 / p 0 ) + γ [ e i ω t e γ t e i ω 0 t ]
S T = 4 γ 1 γ 2 ( | s s | + | s x | ) i ( ω ω 0 + γ | s T | 2 / p 0 ) + γ ( e i ω t e γ t e i ω 0 t ) ,
| A | 2 ( t ) = ( p s + p x ) 2 / 2 γ 2 ( 1 + k η | s T | 2 / 2 ) 2 η ( δ | s T | 2 / p 0 ) 2 + 1 [ e 2 γ t 2 e γ t cos ( ω 0 ω ) t + 1 ] ,
T ( t ) = | s T | 2 | s s | 2 = ( p s + p x ) 2 / p s ( 1 + k η | s T | 2 / 2 ) 2 η ( δ | s T | 2 / p 0 ) 2 + 1 [ e 2 γ t 2 e γ t cos ( ω 0 ω ) t + 1 ] ,
( p 1 + p x ) 2 p 2 ,
p x ( p 2 p 1 ) 2 .
| A | 2 p 1 T 1 / ( 2 γ 2 ) .
( p s + p x ) 2 ( 1 + k η | s T | 2 / 2 ) 2 η ( δ | s T | 2 / p 0 ) 2 + 1 [ e 2 γ t 2 e γ t cos ( ω 0 ω ) t + 1 ] T s p s ,
( p 1 + p x ) 2 = p 2 .
p 2 / p 1 ( 1 + k η | s T | 2 / 2 ) 2 η ( δ | s T | 2 / p 0 ) 2 + 1 [ e 2 γ t 2 e γ t cos ( ω 0 ω ) t + 1 ] T 1 .
T ( t ) T 1 .
p i n = ( p s + i = 1 N p x i ) 2 ,
( i = 1 N p x i ) 2 ( p 2 p 1 ) 2 .
f ( t ) exp ( i ω 0 t )
i = 1 N p x i ( p 2 p 1 ) 2 .
f ( t ) exp ( i ω 0 t ) = i g ( ω i ) exp ( i ω i t ) Δ ω ,

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