Abstract

We analyze the effect of the nonlinear Kerr index of refraction and two-photon absorption (TPA) in a rotating silicon microring resonator coupled to waveguides in an add–drop configuration. The nonlinear index of refraction leads to a bifurcation of the intensities of two counterpropagating modes in the nonrotating state. This bifurcation also significantly enhances the intensity difference between these modes due to the Sagnac-induced frequency splitting of the modes in the rotating resonator. Although silicon resonators have a very large Kerr index, they also suffer from large TPA at telecom wavelengths. It is shown that despite TPA, the Kerr nonlinear enhancement to the rotation sensitivity is still of the order of 104. An analysis of typical detector noise indicates that a detection limit of <1deg/h in a 1.4 mm radius resonator is achievable.

© 2014 Optical Society of America

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  1. W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2014

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, J. Eur. Opt. Soc. Rapid Publ. 9, 14013 (2014).
[CrossRef]

D. Kalantarov and C. P. Search, Opt. Lett. 39, 985 (2014).
[CrossRef]

2012

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

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

B. A. Daniel and G. P. Agrawal, J. Opt. Soc. Am. B 29, 2288 (2012).
[CrossRef]

2010

2009

M. Terrel, M. J. F. Digonnet, and S. Fan, Laser Photon. Rev. 3, 452 (2009).
[CrossRef]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, Opt. Express 17, 22124 (2009).
[CrossRef]

2007

A. D. Bristow, N. Rotenberg, and H. M. van Driel, Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

2005

2003

S. M. Weiss, M. Molinari, and P. M. Fauchet, Appl. Phys. Lett. 83, 1980 (2003).
[CrossRef]

1986

K. Iwatsuki, K. Hotate, and M. Higashiguchi, J. Lightwave Technol. 4, 645 (1986).
[CrossRef]

1984

1982

A. E. Kaplan and P. Meystre, Opt. Commun. 40, 229 (1982).
[CrossRef]

1981

Agrawal, G. P.

Armenise, M. N.

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, J. Eur. Opt. Soc. Rapid Publ. 9, 14013 (2014).
[CrossRef]

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, Adv. Opt. Photon. 2, 370 (2010).
[CrossRef]

Baets, R.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Bienstman, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Bogaerts, W.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Campanella, C. E.

Chrostowski, L.

Ciminelli, C.

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, J. Eur. Opt. Soc. Rapid Publ. 9, 14013 (2014).
[CrossRef]

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, Adv. Opt. Photon. 2, 370 (2010).
[CrossRef]

Claes, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Cretu, E.

Daniel, B. A.

De Heyn, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Dell’Olio, F.

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, J. Eur. Opt. Soc. Rapid Publ. 9, 14013 (2014).
[CrossRef]

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, Adv. Opt. Photon. 2, 370 (2010).
[CrossRef]

DeVos, K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Digonnet, M. J. F.

M. Terrel, M. J. F. Digonnet, and S. Fan, Laser Photon. Rev. 3, 452 (2009).
[CrossRef]

Dumon, P.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Fan, S.

M. Terrel, M. J. F. Digonnet, and S. Fan, Laser Photon. Rev. 3, 452 (2009).
[CrossRef]

Fauchet, P. M.

S. M. Weiss, M. Molinari, and P. M. Fauchet, Appl. Phys. Lett. 83, 1980 (2003).
[CrossRef]

Foster, M. A.

Freude, W.

J. Leuthold, C. Koos, and W. Freude, Nat. Photonics 4, 535 (2010).
[CrossRef]

Gaeta, A. L.

Green, W. M. J.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, Nat. Photonics 4, 557 (2010).
[CrossRef]

Guillen-Torres, M. A.

Higashiguchi, M.

K. Iwatsuki, K. Hotate, and M. Higashiguchi, J. Lightwave Technol. 4, 645 (1986).
[CrossRef]

K. Iwatsuki, K. Hotate, and M. Higashiguchi, Appl. Opt. 23, 3916 (1984).
[CrossRef]

Hotate, K.

K. Iwatsuki, K. Hotate, and M. Higashiguchi, J. Lightwave Technol. 4, 645 (1986).
[CrossRef]

K. Iwatsuki, K. Hotate, and M. Higashiguchi, Appl. Opt. 23, 3916 (1984).
[CrossRef]

Iwatsuki, K.

K. Iwatsuki, K. Hotate, and M. Higashiguchi, J. Lightwave Technol. 4, 645 (1986).
[CrossRef]

K. Iwatsuki, K. Hotate, and M. Higashiguchi, Appl. Opt. 23, 3916 (1984).
[CrossRef]

Jaeger, N. A. F.

Kalantarov, D.

Kaplan, A. E.

A. E. Kaplan and P. Meystre, Opt. Commun. 40, 229 (1982).
[CrossRef]

A. E. Kaplan and P. Meystre, Opt. Lett. 6, 590 (1981).
[CrossRef]

Koos, C.

J. Leuthold, C. Koos, and W. Freude, Nat. Photonics 4, 535 (2010).
[CrossRef]

Leuthold, J.

J. Leuthold, C. Koos, and W. Freude, Nat. Photonics 4, 535 (2010).
[CrossRef]

Levy, J. S.

Lipson, M.

Liu, X.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, Nat. Photonics 4, 557 (2010).
[CrossRef]

Meystre, P.

A. E. Kaplan and P. Meystre, Opt. Commun. 40, 229 (1982).
[CrossRef]

A. E. Kaplan and P. Meystre, Opt. Lett. 6, 590 (1981).
[CrossRef]

Molinari, M.

S. M. Weiss, M. Molinari, and P. M. Fauchet, Appl. Phys. Lett. 83, 1980 (2003).
[CrossRef]

Osgood, R. M.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, Nat. Photonics 4, 557 (2010).
[CrossRef]

Poitras, C. B.

Preble, S. F.

Premaratne, M.

Rotenberg, N.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Rukhlenko, I. D.

Salem, R.

Schmidt, B. S.

Search, C. P.

Selvaraja, S. K.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Tatoli, T.

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, J. Eur. Opt. Soc. Rapid Publ. 9, 14013 (2014).
[CrossRef]

Terrel, M.

M. Terrel, M. J. F. Digonnet, and S. Fan, Laser Photon. Rev. 3, 452 (2009).
[CrossRef]

Turner-Foster, A. C.

van Driel, H. M.

A. D. Bristow, N. Rotenberg, and H. M. van Driel, Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

Van Thourhout, D.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Van Vaerenbergh, T.

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Vlasov, Y. A.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, Nat. Photonics 4, 557 (2010).
[CrossRef]

Weiss, S. M.

S. M. Weiss, M. Molinari, and P. M. Fauchet, Appl. Phys. Lett. 83, 1980 (2003).
[CrossRef]

Xu, Q.

Adv. Opt. Photon.

Appl. Opt.

Appl. Phys. Lett.

S. M. Weiss, M. Molinari, and P. M. Fauchet, Appl. Phys. Lett. 83, 1980 (2003).
[CrossRef]

A. D. Bristow, N. Rotenberg, and H. M. van Driel, Appl. Phys. Lett. 90, 191104 (2007).
[CrossRef]

J. Eur. Opt. Soc. Rapid Publ.

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, J. Eur. Opt. Soc. Rapid Publ. 9, 14013 (2014).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Laser Photon. Rev.

M. Terrel, M. J. F. Digonnet, and S. Fan, Laser Photon. Rev. 3, 452 (2009).
[CrossRef]

W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. DeVos, S. K. Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Laser Photon. Rev. 6, 47 (2012).
[CrossRef]

Nat. Photonics

J. Leuthold, C. Koos, and W. Freude, Nat. Photonics 4, 535 (2010).
[CrossRef]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, Nat. Photonics 4, 557 (2010).
[CrossRef]

Opt. Commun.

A. E. Kaplan and P. Meystre, Opt. Commun. 40, 229 (1982).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (5)

Fig. 1.
Fig. 1.

SOI microresonator gyroscope. Light from the laser is split by a 3 dB coupler and excites counterpropagating modes in the resonator. The modes are then coupled out into the output waveguide leading to photodetectors D1 and D2. The device is rotated about an axis perpendicular to the resonator’s plane at the rate ωR.

Fig. 2.
Fig. 2.

Dimensionless resonator intensities I1 and I2 as a function of the dimensionless input intensity Iin for Ω=0. The curves correspond to: η=0 (red), η=0.05 (green), and η=0.1 (blue). Solid lines are solutions of Eq. (4), while dashed lines are solution of Eq. (3). The inset shows Δth as a function of η as well as Ith. Here, Δ=2.24.

Fig. 3.
Fig. 3.

I1 and I2 versus Iin for the nonlinear resonator for Δ=2.24=Δth(η=0.1)0.01 and Ith=7.11. The four curves illustrate mode splitting with increasing Ω. The inset shows ΔI=I1I2 versus Iin for the nonlinear (solid lines) and linear (dashed lines) resonators. The curves are Ω=0 (black line), Ω=106 (red), Ω=5×106 (green), and Ω=105 (blue).

Fig. 4.
Fig. 4.

Enhancement factor Γ as a function of Iin for Δ<Δth. (a) η=0 and Δ=1.74=Δth0.01 and (b) η=0.1 and Δ=2.24=Δth0.01. The inset of (b) shows the power difference ΔP=P1P2 at the photodetectors D1 and D2 as a function of ωR.

Fig. 5.
Fig. 5.

Enhancement factor Γ as a function of Iin for Δ>Δth. (a) η=0 and Δ=1.72=Δth+0.01 and (b) η=0.1 and Δ=2.22=Δth+0.01. Solid lines are from Eq. (6), while circles are numerically calculated from Eq. (2). The inset shows the power difference ΔP=P1P2 at the photodetectors as a function of ωR.

Equations (6)

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

dEjdt=μEin[i(ωω0+(1)jωs)+γ]Ejiω0χ(1iη)(|Ej|2+2|E3j|2)Ej,
Ij=Iin[1+η(Ij+2I3j)]2+[Δ+(1)jΩ+(Ij+2I3j)]2.
Iin=I0[(1+η3I0)2+(Δ+3I0)2].
(1+Δ2)+2(Δ+η)M+(1+η2)M2=(1+η2)Iin2(Δ+η)+3(1+η2)M,N=Iin2(Δ+η)+3(1+η2)M.
S=1Iind|I1I2|dΩ.
Γ=4I0(Δ+3I0)Iin[(Δ+I0)(Δ+3I0)+(1+ηI0)(1+3ηI0)]4|Δ|(1+Δ2)2.

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