Abstract

By modifying the resonance condition of optical microfiber resonator while considering the strong coupling effect, we theoretically investigate the influence of coupling on the resonant wavelength and refractive index sensitivity, and compare our results with the previously published results. Numerical calculation shows significant difference in resonant wavelength and sensitivity for different coupling strengths. By considering coupling effect, the resonant peak position can be shifted as far as 3.89 nm and the sensitivity can be modified by as much as 83 nm/RIU. This suggests a method to tune the resonant wavelength and sensitivity, by varying the pitch and the coupling between two adjacent microfibers in the coupling area.

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References

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  1. G. Brambilla, “Optical fiber nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010).
    [CrossRef]
  2. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
    [CrossRef] [PubMed]
  3. L. Tong, “Brief introduction to optical microfibers and nanofibers,” Front. Optoelectron. China 3(1), 54–60 (2010).
    [CrossRef]
  4. G. Brambilla, V. Finazzi, and D. J. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express 12(10), 2258–2263 (2004).
    [CrossRef] [PubMed]
  5. G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon. 1(1), 107–161 (2009).
    [CrossRef]
  6. K. S. Lim, S. W. Harun, S. S. A. Damanhuri, A. A. Jasim, C. K. Tio, and H. Ahmad, “Current sensor based on microfiber knot resonator,” Sens. Actuators A Phys. 167(1), 60–62 (2011).
    [CrossRef]
  7. X. Jiang, Y. Chen, G. Vienne, and L. Tong, “All-fiber add-drop filters based on microfiber knot resonators,” Opt. Lett. 32(12), 1710–1712 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. F. Xu, Q. Wang, J.-F. Zhou, W. Hu, and Y.-Q. Lu, “Dispersion study of optical nanowire microcoil resonators,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1102–1106 (2011).
    [CrossRef]
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    [CrossRef] [PubMed]
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2011 (3)

K. S. Lim, S. W. Harun, S. S. A. Damanhuri, A. A. Jasim, C. K. Tio, and H. Ahmad, “Current sensor based on microfiber knot resonator,” Sens. Actuators A Phys. 167(1), 60–62 (2011).
[CrossRef]

T. Lee, N. G. R. Broderick, and G. Brambilla, “Berry phase magnification in optical microcoil resonators,” Opt. Lett. 36(15), 2839–2841 (2011).
[CrossRef] [PubMed]

F. Xu, Q. Wang, J.-F. Zhou, W. Hu, and Y.-Q. Lu, “Dispersion study of optical nanowire microcoil resonators,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1102–1106 (2011).
[CrossRef]

2010 (3)

J. Yongmin, G. S. Murugan, G. Brambilla, and D. J. Richardson, “Embedded optical microfiber coil resonator with enhanced high Q,” IEEE Photon. Technol. Lett. 22, 1638–1640 (2010).

G. Brambilla, “Optical fiber nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010).
[CrossRef]

L. Tong, “Brief introduction to optical microfibers and nanofibers,” Front. Optoelectron. China 3(1), 54–60 (2010).
[CrossRef]

2009 (2)

2008 (3)

2007 (4)

2005 (1)

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86(16), 161108 (2005).
[CrossRef]

2004 (2)

2003 (1)

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Ahmad, H.

K. S. Lim, S. W. Harun, S. S. A. Damanhuri, A. A. Jasim, C. K. Tio, and H. Ahmad, “Current sensor based on microfiber knot resonator,” Sens. Actuators A Phys. 167(1), 60–62 (2011).
[CrossRef]

Ashcom, J. B.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Brambilla, G.

T. Lee, N. G. R. Broderick, and G. Brambilla, “Berry phase magnification in optical microcoil resonators,” Opt. Lett. 36(15), 2839–2841 (2011).
[CrossRef] [PubMed]

J. Yongmin, G. S. Murugan, G. Brambilla, and D. J. Richardson, “Embedded optical microfiber coil resonator with enhanced high Q,” IEEE Photon. Technol. Lett. 22, 1638–1640 (2010).

G. Brambilla, “Optical fiber nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010).
[CrossRef]

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon. 1(1), 107–161 (2009).
[CrossRef]

F. Xu and G. Brambilla, “Demonstration of a refractometric sensor based on optical microfiber coil resonator,” Appl. Phys. Lett. 92, 101126 (2008).

F. Xu, V. Pruneri, V. Finazzi, and G. Brambilla, “An embedded optical nanowire loop resonator refractometric sensor,” Opt. Express 16(2), 1062–1067 (2008).
[CrossRef] [PubMed]

F. Xu and G. Brambilla, “Embedding optical microfiber coil resonators in Teflon,” Opt. Lett. 32(15), 2164–2166 (2007).
[CrossRef] [PubMed]

F. Xu, P. Horak, and G. Brambilla, “Conical and biconical ultra-high-Q optical-fiber nanowire microcoil resonator,” Appl. Opt. 46(4), 570–573 (2007).
[CrossRef] [PubMed]

G. Brambilla, V. Finazzi, and D. J. Richardson, “Ultra-low-loss optical fiber nanotapers,” Opt. Express 12(10), 2258–2263 (2004).
[CrossRef] [PubMed]

Broderick, N. G. R.

Chen, Y.

Damanhuri, S. S. A.

K. S. Lim, S. W. Harun, S. S. A. Damanhuri, A. A. Jasim, C. K. Tio, and H. Ahmad, “Current sensor based on microfiber knot resonator,” Sens. Actuators A Phys. 167(1), 60–62 (2011).
[CrossRef]

Dulashko, Y.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86(16), 161108 (2005).
[CrossRef]

Feng, X.

Finazzi, V.

Fini, J. M.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86(16), 161108 (2005).
[CrossRef]

Gattass, R. R.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Guo, X.

Hale, A.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86(16), 161108 (2005).
[CrossRef]

Harun, S. W.

K. S. Lim, S. W. Harun, S. S. A. Damanhuri, A. A. Jasim, C. K. Tio, and H. Ahmad, “Current sensor based on microfiber knot resonator,” Sens. Actuators A Phys. 167(1), 60–62 (2011).
[CrossRef]

He, S. L.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Horak, P.

Hu, W.

F. Xu, Q. Wang, J.-F. Zhou, W. Hu, and Y.-Q. Lu, “Dispersion study of optical nanowire microcoil resonators,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1102–1106 (2011).
[CrossRef]

Huang, K.

Jasim, A. A.

K. S. Lim, S. W. Harun, S. S. A. Damanhuri, A. A. Jasim, C. K. Tio, and H. Ahmad, “Current sensor based on microfiber knot resonator,” Sens. Actuators A Phys. 167(1), 60–62 (2011).
[CrossRef]

Jiang, X.

Jung, Y.

Knox, W. H.

P. Pal and W. H. Knox, “Fabrication and characterization of fused microfiber resonators,” IEEE Photon. Technol. Lett. 21(12), 766–768 (2009).
[CrossRef]

Koizumi, F.

Koukharenko, E.

Lee, T.

Lim, K. S.

K. S. Lim, S. W. Harun, S. S. A. Damanhuri, A. A. Jasim, C. K. Tio, and H. Ahmad, “Current sensor based on microfiber knot resonator,” Sens. Actuators A Phys. 167(1), 60–62 (2011).
[CrossRef]

Lou, J. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Lu, Y.-Q.

F. Xu, Q. Wang, J.-F. Zhou, W. Hu, and Y.-Q. Lu, “Dispersion study of optical nanowire microcoil resonators,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1102–1106 (2011).
[CrossRef]

Maxwell, I.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Mazur, E.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Murugan, G. S.

J. Yongmin, G. S. Murugan, G. Brambilla, and D. J. Richardson, “Embedded optical microfiber coil resonator with enhanced high Q,” IEEE Photon. Technol. Lett. 22, 1638–1640 (2010).

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. P. Sessions, E. Koukharenko, X. Feng, G. S. Murugan, J. S. Wilkinson, and D. J. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon. 1(1), 107–161 (2009).
[CrossRef]

Pal, P.

P. Pal and W. H. Knox, “Fabrication and characterization of fused microfiber resonators,” IEEE Photon. Technol. Lett. 21(12), 766–768 (2009).
[CrossRef]

Pruneri, V.

Richardson, D. J.

Sessions, N. P.

Shen, M. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Sumetsky, M.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86(16), 161108 (2005).
[CrossRef]

M. Sumetsky, “Optical fiber microcoil resonators,” Opt. Express 12(10), 2303–2316 (2004).
[CrossRef] [PubMed]

Tio, C. K.

K. S. Lim, S. W. Harun, S. S. A. Damanhuri, A. A. Jasim, C. K. Tio, and H. Ahmad, “Current sensor based on microfiber knot resonator,” Sens. Actuators A Phys. 167(1), 60–62 (2011).
[CrossRef]

Tong, L.

Tong, L. M.

X. Guo and L. M. Tong, “Supported microfiber loops for optical sensing,” Opt. Express 16(19), 14429–14434 (2008).
[CrossRef] [PubMed]

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Vienne, G.

Wang, Q.

F. Xu, Q. Wang, J.-F. Zhou, W. Hu, and Y.-Q. Lu, “Dispersion study of optical nanowire microcoil resonators,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1102–1106 (2011).
[CrossRef]

Wilkinson, J. S.

Xu, F.

Yang, S.

Yongmin, J.

J. Yongmin, G. S. Murugan, G. Brambilla, and D. J. Richardson, “Embedded optical microfiber coil resonator with enhanced high Q,” IEEE Photon. Technol. Lett. 22, 1638–1640 (2010).

Zhou, J.-F.

F. Xu, Q. Wang, J.-F. Zhou, W. Hu, and Y.-Q. Lu, “Dispersion study of optical nanowire microcoil resonators,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1102–1106 (2011).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (2)

Appl. Phys. Lett. (2)

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, “Optical microfiber loop resonator,” Appl. Phys. Lett. 86(16), 161108 (2005).
[CrossRef]

F. Xu and G. Brambilla, “Demonstration of a refractometric sensor based on optical microfiber coil resonator,” Appl. Phys. Lett. 92, 101126 (2008).

Front. Optoelectron. China (1)

L. Tong, “Brief introduction to optical microfibers and nanofibers,” Front. Optoelectron. China 3(1), 54–60 (2010).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

F. Xu, Q. Wang, J.-F. Zhou, W. Hu, and Y.-Q. Lu, “Dispersion study of optical nanowire microcoil resonators,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1102–1106 (2011).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

J. Yongmin, G. S. Murugan, G. Brambilla, and D. J. Richardson, “Embedded optical microfiber coil resonator with enhanced high Q,” IEEE Photon. Technol. Lett. 22, 1638–1640 (2010).

P. Pal and W. H. Knox, “Fabrication and characterization of fused microfiber resonators,” IEEE Photon. Technol. Lett. 21(12), 766–768 (2009).
[CrossRef]

J. Opt. (1)

G. Brambilla, “Optical fiber nanowires and microwires: a review,” J. Opt. 12(4), 043001 (2010).
[CrossRef]

Nature (1)

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, “Subwavelength-diameter silica wires for low-loss optical wave guiding,” Nature 426(6968), 816–819 (2003).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (3)

Sens. Actuators A Phys. (1)

K. S. Lim, S. W. Harun, S. S. A. Damanhuri, A. A. Jasim, C. K. Tio, and H. Ahmad, “Current sensor based on microfiber knot resonator,” Sens. Actuators A Phys. 167(1), 60–62 (2011).
[CrossRef]

Other (1)

K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Elsevier, 2006).

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Figures (4)

Fig. 1
Fig. 1

(a) Basic configuration of an MFR, (b) basic configuration of a two-turn all-coupling 3D MCR, and (c) cross-section of a coupling region.

Fig. 2
Fig. 2

The calculated (a) k, (b) c, (c) χ and (d) M profiles of a resonator with different diameter d and different pitch P.

Fig. 3
Fig. 3

Calculated ∆λR profiles of an MFR for different values of diameter d and pitch P.

Fig. 4
Fig. 4

Calculated (a) Sn and (b) Sk profiles of an MFR with different values of diameter d and pitch P.

Equations (10)

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

{ dA dz + c 12 dB dz +j χ 1 A+j κ 12 B=0 dB dz + c 21 dA dz +j χ 2 B+j κ 21 A=0
κ pq = ω ε 0 + + ( N 2 N q 2 ) E p * E q dxdy + + u z ( E p * × H p + E p × H p * )dxdy c pq = + + u z ( E p * × H q + E q × H p * )dxdy + + u z ( E p * × H p + E p × H p * )dxdy χ p = ω ε 0 + + ( N 2 N p 2 ) E p * E p dxdy + + u z ( E p * × H p + E p × H p * )dxdy
{ dA dz +jkB=0 dB dz +jkA=0
βL=2mπm=1,2,3
{ A(z)= C 1 exp[i(M+N)z] C 2 exp[i(MN)z] B(z)= C 1 exp[i(M+N)z]+ C 2 exp[i(MN)z]
{ C 1 = 1exp[i( λ 2 T+βL)] {2exp[i( λ 1 T+βL)]exp[i( λ 2 T+βL)]} C 2 = exp[i( λ 2 T+βL)]1 {2exp[i( λ 1 T+βL)]exp[i( λ 2 T+βL)]}
βL+MT=2mπm=1,2,3
S= λ R n sur
S= λ R n sur = S n + S k
{ S n = 2π β n eff n sur S k =α λ β M n sur

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