Abstract

We study the use of nonlinear self-phase modulation (SPM) in coupled optical microresonators for ultrasensitive refractive index sensing. SPM leads to a positive feedback enhancement of the resonance frequency shift caused by a perturbation of the index of refraction in a resonator. Moreover, the use of two resonators coupled through input and output waveguides leads to a further improvement in the sensitivity owing to constructive interference and feedback via the waveguides. For parameters based on Si microresonators, the sensitivity is more than 102 larger than a single resonator without SPM leading to a minimum detectable index change of 1011RIU with resonator Q-factors of 104. We show that the nonlinearly enhanced system is robust with respect to laser noise when operated at input powers below the onset of bistability.

© 2013 Optical Society of America

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References

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  1. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, Anal. Chem. Acta 620, 8 (2008).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, S. K. Y. Tang, R. Illic, and M. Loncar, Conference on Laser and Electro Optics (Optical Society of America, 2011), paper QThH6.
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    [CrossRef]
  9. H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
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    [CrossRef]

2012

2011

2009

N. Jokerst, M. Royal, S. Palit, L. Luan, S. Dhar, and T. Tyler, J. Biophotonics 2, 212 (2009).
[CrossRef]

2008

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, Anal. Chem. Acta 620, 8 (2008).

I. M. White and X. Fan, Opt. Express 16, 1020 (2008).
[CrossRef]

Y. Xiao, V. Gaddam, and L. Yang, Opt. Express 16, 12538 (2008).
[CrossRef]

2006

2004

2002

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
[CrossRef]

1997

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Almeida, V. R.

Álvarez, M.

M. C. Estevez, M. Álvarez, and L. M. Lechuga, Laser Photonics Rev. 6, 463 (2012).
[CrossRef]

Asghari, M.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
[CrossRef]

Burgess, I. B.

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, Opt. Express 19, 22191 (2011).
[CrossRef]

Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, S. K. Y. Tang, R. Illic, and M. Loncar, Conference on Laser and Electro Optics (Optical Society of America, 2011), paper QThH6.

Chin, M. K.

Chrostowski, L.

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Cretu, E.

Darmawan, S.

Day, I. E.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
[CrossRef]

Deotare, P. B.

Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, S. K. Y. Tang, R. Illic, and M. Loncar, Conference on Laser and Electro Optics (Optical Society of America, 2011), paper QThH6.

Dhar, S.

N. Jokerst, M. Royal, S. Palit, L. Luan, S. Dhar, and T. Tyler, J. Biophotonics 2, 212 (2009).
[CrossRef]

Drake, J.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
[CrossRef]

Estevez, M. C.

M. C. Estevez, M. Álvarez, and L. M. Lechuga, Laser Photonics Rev. 6, 463 (2012).
[CrossRef]

Fan, X.

I. M. White and X. Fan, Opt. Express 16, 1020 (2008).
[CrossRef]

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, Anal. Chem. Acta 620, 8 (2008).

Floyd, D. L.

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Frank, I. W.

Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, S. K. Y. Tang, R. Illic, and M. Loncar, Conference on Laser and Electro Optics (Optical Society of America, 2011), paper QThH6.

Gaddam, V.

Guillen-Torres, M. A.

Harpin, A.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
[CrossRef]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Illic, R.

Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, S. K. Y. Tang, R. Illic, and M. Loncar, Conference on Laser and Electro Optics (Optical Society of America, 2011), paper QThH6.

Jaeger, N. A. F.

Jokerst, N.

N. Jokerst, M. Royal, S. Palit, L. Luan, S. Dhar, and T. Tyler, J. Biophotonics 2, 212 (2009).
[CrossRef]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Lechuga, L. M.

M. C. Estevez, M. Álvarez, and L. M. Lechuga, Laser Photonics Rev. 6, 463 (2012).
[CrossRef]

Liang, T. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
[CrossRef]

Lipson, M.

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

Loncar, M.

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, Opt. Express 19, 22191 (2011).
[CrossRef]

Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, S. K. Y. Tang, R. Illic, and M. Loncar, Conference on Laser and Electro Optics (Optical Society of America, 2011), paper QThH6.

Luan, L.

N. Jokerst, M. Royal, S. Palit, L. Luan, S. Dhar, and T. Tyler, J. Biophotonics 2, 212 (2009).
[CrossRef]

Mario, L. Y.

Palit, S.

N. Jokerst, M. Royal, S. Palit, L. Luan, S. Dhar, and T. Tyler, J. Biophotonics 2, 212 (2009).
[CrossRef]

Quan, Q.

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, Opt. Express 19, 22191 (2011).
[CrossRef]

Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, S. K. Y. Tang, R. Illic, and M. Loncar, Conference on Laser and Electro Optics (Optical Society of America, 2011), paper QThH6.

Roberts, S. W.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
[CrossRef]

Royal, M.

N. Jokerst, M. Royal, S. Palit, L. Luan, S. Dhar, and T. Tyler, J. Biophotonics 2, 212 (2009).
[CrossRef]

Shopova, S. I.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, Anal. Chem. Acta 620, 8 (2008).

Sun, Y.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, Anal. Chem. Acta 620, 8 (2008).

Suter, J. D.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, Anal. Chem. Acta 620, 8 (2008).

Tang, S. K. Y.

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, Opt. Express 19, 22191 (2011).
[CrossRef]

Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, S. K. Y. Tang, R. Illic, and M. Loncar, Conference on Laser and Electro Optics (Optical Society of America, 2011), paper QThH6.

Tsang, H. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
[CrossRef]

Tyler, T.

N. Jokerst, M. Royal, S. Palit, L. Luan, S. Dhar, and T. Tyler, J. Biophotonics 2, 212 (2009).
[CrossRef]

Vollmer, F.

Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, S. K. Y. Tang, R. Illic, and M. Loncar, Conference on Laser and Electro Optics (Optical Society of America, 2011), paper QThH6.

White, I. M.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, Anal. Chem. Acta 620, 8 (2008).

I. M. White and X. Fan, Opt. Express 16, 1020 (2008).
[CrossRef]

Wong, C. S.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
[CrossRef]

Xiao, Y.

Xu, Q.

Yang, L.

Zhu, H.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, Anal. Chem. Acta 620, 8 (2008).

Anal. Chem. Acta

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, Anal. Chem. Acta 620, 8 (2008).

Appl. Phys. Lett.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, Appl. Phys. Lett. 80, 416 (2002).
[CrossRef]

J. Biophotonics

N. Jokerst, M. Royal, S. Palit, L. Luan, S. Dhar, and T. Tyler, J. Biophotonics 2, 212 (2009).
[CrossRef]

J. Lightwave Technol.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997).
[CrossRef]

M. A. Guillen-Torres, E. Cretu, N. A. F. Jaeger, and L. Chrostowski, J. Lightwave Technol. 30, 1802 (2012).
[CrossRef]

Laser Photonics Rev.

M. C. Estevez, M. Álvarez, and L. M. Lechuga, Laser Photonics Rev. 6, 463 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Other

Q. Quan, F. Vollmer, I. B. Burgess, P. B. Deotare, I. W. Frank, S. K. Y. Tang, R. Illic, and M. Loncar, Conference on Laser and Electro Optics (Optical Society of America, 2011), paper QThH6.

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Figures (5)

Fig. 1.
Fig. 1.

Diagram of the double resonator system in an add–drop geometry. The dashed border line indicates the single resonator subsystem. The distance between the centers of the resonators is L=2πR(m/m)>2R, where m is an integer and m the axial mode number of the resonators.

Fig. 2.
Fig. 2.

Phase diagram indicating the bistable region of a single resonator with SPM for Δω=0.4. The inset shows the corresponding drop port power versus input power for nonlinear (red line) and linear (black line) cases.

Fig. 3.
Fig. 3.

Drop port power (red lines, left y axis) and sensitivity (black lines, right y axis) for nonlinear (solid lines) and linear (dashed lines) systems with Δω=0.4. (a) Pin=0.001 and (b) Pin=0.00502. The inset of (b) shows sensitivity as a function of Pin for ωn=0.263.

Fig. 4.
Fig. 4.

Drop port power and sensitivity for a double ring system with (solid lines) and without (dashed lines) SPM for (a) ϕn=0 and (b) ϕn=ϕ0(δn/n0) in the waveguides. The inset of (a) shows the drop port resonance of the linear system. The inset of (b) is the sensitivity ratio of nonlinear versus linear systems. For all graphs, Pin=0.01721 and Δω=0.4.

Fig. 5.
Fig. 5.

Drop port power and sensitivity of SPM double resonator system for ωn<0. Pin=0.01721 and Δω=0.05. The inset is a bistability phase diagram for Δω=0.05.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

dξjdt=i[δωωnα|ξj|2]ξjiμ(Ej-in+Ej-add)μ2ξjω02Qiξj,
Pin=U4κ2[(ΔωωnγU)2+(κ2+q)2],
S=1Pin|dPdropdωn|.
Pin=U[(ΔωωnγUκ2sinϕ)2+(κ2+κ2cosϕ+q)2]2(1+cosϕ)κ2.
δnsn0=ς1νfω0Smax(δPdropPin),

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