Critical conditions of control light for a silicon-based photonic crystal bistable switching

Chao Li; Hong Wang; Jun-Fang Wu; Wen-Cheng Xu

doi:10.1364/OE.18.017313

Critical conditions of control light for a silicon-based photonic crystal bistable switching

Chao Li, Hong Wang, Jun-Fang Wu, and Wen-Cheng Xu

Optics Express
Vol. 18,
Issue 16,
pp. 17313-17321
(2010)
•https://doi.org/10.1364/OE.18.017313

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Chao Li, Hong Wang, Jun-Fang Wu, and Wen-Cheng Xu, "Critical conditions of control light for a silicon-based photonic crystal bistable switching," Opt. Express 18, 17313-17321 (2010)

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Related Topics
Table of Contents Category
- Photonic Crystals and Devices
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Bistability (190.1450)
- All-optical devices (230.1150)
- Photonic crystals (230.5298)

About this Article
History
- Original Manuscript: July 12, 2010
- Manuscript Accepted: July 22, 2010
- Published: July 29, 2010

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Open Access

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.

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References

View by:
Article Order
|
Year
|
Author
|
Publication

K. Ogusu and K. Takayama, “Optical bistability in photonic crystal microrings with nonlinear dielectric materials,” Opt. Express 16(10), 7525–7539 (2008).
[Crossref] [PubMed]
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]
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]
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]
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]
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]
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]
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]
H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, New Jersey, 1984).
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]
A. Taflove, and S. C. Hagness, Computational Electrodynamics (Artech House, Norwood, MA, 2000)

2010 (2)

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 (1)

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 (2)

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]

K. Ogusu and K. Takayama, “Optical bistability in photonic crystal microrings with nonlinear dielectric materials,” Opt. Express 16(10), 7525–7539 (2008).
[Crossref] [PubMed]

2007 (1)

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 (1)

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 (1)

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 (1)

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 (1)

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.

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.

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.

Ibanescu, M.

Joannopoulos, J. D.

Johnson, S. G.

Kim, M. K.

Kim, S. H.

Kuramochi, E.

Lee, Y. H.

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.

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.

Ogusu, K.

K. Ogusu and K. Takayama, “Optical bistability in photonic crystal microrings with nonlinear dielectric materials,” Opt. Express 16(10), 7525–7539 (2008).
[Crossref] [PubMed]

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.

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]

Takayama, K.

K. Ogusu and K. Takayama, “Optical bistability in photonic crystal microrings with nonlinear dielectric materials,” Opt. Express 16(10), 7525–7539 (2008).
[Crossref] [PubMed]

Tanabe, T.

Wu, J. F.

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]

Xu, W. C.

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]

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. (1)

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]

Appl. Phys. Lett. (3)

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]

J. Appl. Phys. (1)

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. (1)

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 (2)

K. Ogusu and K. Takayama, “Optical bistability in photonic crystal microrings with nonlinear dielectric materials,” Opt. Express 16(10), 7525–7539 (2008).
[Crossref] [PubMed]

Phys. Rev. B (1)

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. (1)

Other (2)

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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Fig. 1

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

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Fig. 2

Working principle diagram of a bistable switching

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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.

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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).

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Tables (2)

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

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

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Equations (18)

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{\begin{cases} \frac{d A}{d t} = [j (ω_{0} - γ \frac{{| s_{T} |}^{2}}{p_{0}}) - γ] A + \sqrt{2 γ_{1}} (s_{s} + s_{x}) \\ γ = γ_{0} + γ_{1} + γ_{2} + γ_{T P A} \\ s_{T} = \sqrt{2 γ_{2}} A \\ s_{s} + s_{x} + s_{R} = \sqrt{2 γ_{1}} A \end{cases},

γ_{T P A} = k γ_{1} {| s_{T} |}^{2},

A = \frac{\sqrt{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} \cdot e^{i ω_{0} t}]

S_{T} = \frac{\sqrt{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} \cdot e^{i ω_{0} t}),

| A |^{2} (t) = \frac{{(\sqrt{p_{s}} + \sqrt{p_{x}})}^{2} / 2 γ_{2}}{{(1 + k η {| s_{T} |}^{2} / 2)}^{2}} \cdot \frac{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) = \frac{| s_{T} |^{2}}{| s_{s} |^{2}} = \frac{{(\sqrt{p_{s}} + \sqrt{p_{x}})}^{2} / p_{s}}{{(1 + k η {| s_{T} |}^{2} / 2)}^{2}} \cdot \frac{η}{{(δ - {| s_{T} |}^{2} / p_{0})}^{2} + 1} [e^{- 2 γ t} - 2 e^{- γ t} \cos (ω_{0} - ω) t + 1],

{(\sqrt{p_{1}} + \sqrt{p_{x}})}^{2} \geq p_{2},

p_{x} \geq {(\sqrt{p_{2}} - \sqrt{p_{1}})}^{2} .

{| A |}^{2} \geq p_{1} T_{1} / (2 γ_{2}) .

\frac{{(\sqrt{p_{s}} + \sqrt{p_{x}})}^{2}}{{(1 + k η {| s_{T} |}^{2} / 2)}^{2}} \cdot \frac{η}{{(δ - {| s_{T} |}^{2} / p_{0})}^{2} + 1} [e^{- 2 γ t} - 2 e^{- γ t} \cos (ω_{0} - ω) t + 1] \geq T_{s} p_{s},

{(\sqrt{p_{1}} + \sqrt{p_{x}})}^{2} = p_{2} .

\frac{p_{2} / p_{1}}{{(1 + k η {| s_{T} |}^{2} / 2)}^{2}} \cdot \frac{η}{{(δ - {| s_{T} |}^{2} / p_{0})}^{2} + 1} [e^{- 2 γ t} - 2 e^{- γ t} \cos (ω_{0} - ω) t + 1] \geq T_{1} .

T (t) \geq T_{1} .

p_{i n} = {(\sqrt{p_{s}} + \sum_{i = 1}^{N} \sqrt{p_{x_{i}}})}^{2},

{(\sum_{i = 1}^{N} \sqrt{p_{x_{i}}})}^{2} \geq {(\sqrt{p_{2}} - \sqrt{p_{1}})}^{2} .

f (t) \exp (i ω_{0} t)

\sum_{i = 1}^{N} p_{x_{i}} \leq {(\sqrt{p_{2}} - \sqrt{p_{1}})}^{2} .

f (t) \exp (i ω_{0} t) = \sum_{i} g (ω_{i}) \exp (i ω_{i} t) Δ ω,

δ	p ₁ (kW/μm)	p ₂ (kW/μm)	$p_{x}^{T h e o r y}$ (kW/μm)	$p_{x}^{F D T D}$ (kW/μm)	$p_{x}^{T h e o r y}$ / $p_{x}^{F D T D}$
4.3478	0.120	0.215	0.0136	0.0135	1.007
8.695	0.353	1.517	0.402	0.386	1.041
13.04	0.741	5.63	2.28	2.13	1.07
17.39	1.341	14.78	7.217	7.21	1.001

δ	p ₁ (kW/μm)	p _x (kW/μm)	$t_{s}^{T h e o r y}$ (ps)	$t_{s}^{F D T D}$ (ps)	$t_{s}^{T h e o r y} / t_{s}^{F D T D}$
4.3478	0.120	0.014	11.74	11.07	1.061
8.695	0.353	0.402	5.47	5.47	1.000
13.04	0.741	2.280	2.51	2.45	1.024
17.39	1.341	7.217	1.56	1.52	1.026

δ	p ₁ (kW/μm)	p ₂ (kW/μm)	$p_{x}^{T h e o r y}$ (kW/μm)	$p_{x}^{F D T D}$ (kW/μm)	$p_{x}^{T h e o r y}$ / $p_{x}^{F D T D}$
4.3478	0.120	0.215	0.0136	0.0135	1.007
8.695	0.353	1.517	0.402	0.386	1.041
13.04	0.741	5.63	2.28	2.13	1.07
17.39	1.341	14.78	7.217	7.21	1.001

δ	p ₁ (kW/μm)	p _x (kW/μm)	$t_{s}^{T h e o r y}$ (ps)	$t_{s}^{F D T D}$ (ps)	$t_{s}^{T h e o r y} / t_{s}^{F D T D}$
4.3478	0.120	0.014	11.74	11.07	1.061
8.695	0.353	0.402	5.47	5.47	1.000
13.04	0.741	2.280	2.51	2.45	1.024
17.39	1.341	7.217	1.56	1.52	1.026

Abstract

References

2010 (2)

2009 (1)

2008 (2)

2007 (1)

2006 (1)

2005 (1)

2003 (1)

2002 (1)

Andreani, L. C.

Baets, R.

Belotti, M.

Bienstman, P.

Brissinger, D.

Chang, H. J.

Chen, Y.

Cluzel, B.

Coillet, A.

De Angelis, S.

de Fornel, F.

Dumas, C.

Fan, S. H.

Fink, Y.

Galisteo Lòpez, J. F.

Galli, M.

Grelu, P.

Hwang, I. K.

Ibanescu, M.

Joannopoulos, J. D.

Johnson, S. G.

Kim, M. K.

Kim, S. H.

Kuramochi, E.

Lee, Y. H.

Li, C.

Maksymov, I.

Mitsugi, S.

Morthier, G.

Notomi, M.

Ogusu, K.

Peyrade, D.

Priem, G.

Shinya, A.

Soljacic, M.

Takayama, K.

Tanabe, T.

Wu, J. F.

Xu, W. C.

Yanik, M. F.

Appl. Opt. (1)

Appl. Phys. Lett. (3)

J. Appl. Phys. (1)

Opt. Commun. (1)

Opt. Express (2)

Phys. Rev. B (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

Other (2)

Cited By

Figures (4)

Tables (2)

Equations (18)

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