Abstract

New 3D geometries of the optical nanowire microcoil resonator are suggested and investigated theoretically. The dependence of the Q factor on coupling parameters is calculated and compared for three different profiles. Results suggest that ultra-high-Q resonators can be fabricated more easily when the nanowire microcoil resonator has a biconical profile.

© 2007 Optical Society of America

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  1. B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, "Quality-factor and nonlinear properties of optical whispering-gallery modes," Phys. Lett. A 137, 393-397 (1989).
    [CrossRef]
  2. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitation of whispering-gallery mode resonances by a fiber taper," Opt. Lett. 22, 1129-1131 (1997).
    [CrossRef] [PubMed]
  3. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Dispersion compensation in whispering-gallery modes," J. Opt. Soc. Am. A 20, 157-162 (2003).
    [CrossRef]
  4. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 04902 (2003).
    [CrossRef]
  5. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
    [CrossRef]
  6. D. Rafizadeh, J. P. Zhang, S. C. Hagness, A. Taflove, K. A. Stair, and S. T. Ho, "Waveguide-coupled AlGaAs/GaAs microcavity ring and disk resonators with high finesse and 21.6-nm free spectral range," Opt. Lett. 22, 1244-1246 (1997).
    [CrossRef] [PubMed]
  7. S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, "An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid," IEEE Photon. Technol. Lett. 11, 691-693 (1999).
    [CrossRef]
  8. J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
    [CrossRef]
  9. R. K. Painter, A. Lee, A. Scherer, J. D. Yariv, P. O'Brien, D. Dapkus, and I. Kim, "Two-dimensional photonic bandgap defect mode laser," Science 284, 1819-1821 (1999).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. G. Brambilla, F. Xu, and X. Feng, "Fabrication of optical fibre nanowires and their optical and mechanical characterization," Electron. Lett. 42, 517-519 (2006).
    [CrossRef]
  13. K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
    [CrossRef] [PubMed]
  14. O. Schwelb, "Transmission, group delay, and dispersion in single-ring optical resonators and add/drop filters--a tutorial overview," J. Lightwave Technol. 22, 1380-1394 (2004).
    [CrossRef]

2006 (1)

G. Brambilla, F. Xu, and X. Feng, "Fabrication of optical fibre nanowires and their optical and mechanical characterization," Electron. Lett. 42, 517-519 (2006).
[CrossRef]

2005 (1)

2004 (2)

2003 (3)

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Dispersion compensation in whispering-gallery modes," J. Opt. Soc. Am. A 20, 157-162 (2003).
[CrossRef]

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 04902 (2003).
[CrossRef]

1999 (2)

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, "An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid," IEEE Photon. Technol. Lett. 11, 691-693 (1999).
[CrossRef]

R. K. Painter, A. Lee, A. Scherer, J. D. Yariv, P. O'Brien, D. Dapkus, and I. Kim, "Two-dimensional photonic bandgap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

1997 (3)

1996 (1)

J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
[CrossRef]

1989 (1)

B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, "Quality-factor and nonlinear properties of optical whispering-gallery modes," Phys. Lett. A 137, 393-397 (1989).
[CrossRef]

Barrier, D.

J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
[CrossRef]

Birks, T. A.

Braginsky, B.

B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, "Quality-factor and nonlinear properties of optical whispering-gallery modes," Phys. Lett. A 137, 393-397 (1989).
[CrossRef]

Brambilla, G.

G. Brambilla, F. Xu, and X. Feng, "Fabrication of optical fibre nanowires and their optical and mechanical characterization," Electron. Lett. 42, 517-519 (2006).
[CrossRef]

Cheung, G.

Chu, S. T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, "An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid," IEEE Photon. Technol. Lett. 11, 691-693 (1999).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Costard, E.

J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
[CrossRef]

Dapkus, D.

R. K. Painter, A. Lee, A. Scherer, J. D. Yariv, P. O'Brien, D. Dapkus, and I. Kim, "Two-dimensional photonic bandgap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Feng, X.

G. Brambilla, F. Xu, and X. Feng, "Fabrication of optical fibre nanowires and their optical and mechanical characterization," Electron. Lett. 42, 517-519 (2006).
[CrossRef]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Gerard, J. M.

J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
[CrossRef]

Gorodetsky, M. L.

B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, "Quality-factor and nonlinear properties of optical whispering-gallery modes," Phys. Lett. A 137, 393-397 (1989).
[CrossRef]

Hagness, S. C.

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Ho, S. T.

Ilchenko, V. S.

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Dispersion compensation in whispering-gallery modes," J. Opt. Soc. Am. A 20, 157-162 (2003).
[CrossRef]

B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, "Quality-factor and nonlinear properties of optical whispering-gallery modes," Phys. Lett. A 137, 393-397 (1989).
[CrossRef]

Jacques, F.

Kaneko, T.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, "An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid," IEEE Photon. Technol. Lett. 11, 691-693 (1999).
[CrossRef]

Kim, I.

R. K. Painter, A. Lee, A. Scherer, J. D. Yariv, P. O'Brien, D. Dapkus, and I. Kim, "Two-dimensional photonic bandgap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 04902 (2003).
[CrossRef]

Knight, J. C.

Kokubun, Y.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, "An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid," IEEE Photon. Technol. Lett. 11, 691-693 (1999).
[CrossRef]

Kuszelewicz, R.

J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
[CrossRef]

Laine, J. P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Lee, A.

R. K. Painter, A. Lee, A. Scherer, J. D. Yariv, P. O'Brien, D. Dapkus, and I. Kim, "Two-dimensional photonic bandgap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Little, B. E.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, "An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid," IEEE Photon. Technol. Lett. 11, 691-693 (1999).
[CrossRef]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

Maleki, L.

Manin, L.

J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
[CrossRef]

Marzin, J. Y.

J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
[CrossRef]

Matsko, A. B.

O'Brien, P.

R. K. Painter, A. Lee, A. Scherer, J. D. Yariv, P. O'Brien, D. Dapkus, and I. Kim, "Two-dimensional photonic bandgap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Painter, O. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 04902 (2003).
[CrossRef]

Painter, R. K.

R. K. Painter, A. Lee, A. Scherer, J. D. Yariv, P. O'Brien, D. Dapkus, and I. Kim, "Two-dimensional photonic bandgap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Pan, W.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, "An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid," IEEE Photon. Technol. Lett. 11, 691-693 (1999).
[CrossRef]

Rafizadeh, D.

Rivera, T.

J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
[CrossRef]

Sato, S.

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, "An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid," IEEE Photon. Technol. Lett. 11, 691-693 (1999).
[CrossRef]

Savchenkov, A. A.

Scherer, A.

R. K. Painter, A. Lee, A. Scherer, J. D. Yariv, P. O'Brien, D. Dapkus, and I. Kim, "Two-dimensional photonic bandgap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Schwelb, O.

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 04902 (2003).
[CrossRef]

Stair, K. A.

Sumetsky, M.

Taflove, A.

Thierry-Mieg, V.

J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
[CrossRef]

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 04902 (2003).
[CrossRef]

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

Xu, F.

G. Brambilla, F. Xu, and X. Feng, "Fabrication of optical fibre nanowires and their optical and mechanical characterization," Electron. Lett. 42, 517-519 (2006).
[CrossRef]

Yariv, J. D.

R. K. Painter, A. Lee, A. Scherer, J. D. Yariv, P. O'Brien, D. Dapkus, and I. Kim, "Two-dimensional photonic bandgap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

Zhang, J. P.

Appl. Phys. Lett. (1)

J. M. Gerard, D. Barrier, J. Y. Marzin, R. Kuszelewicz, L. Manin, E. Costard, V. Thierry-Mieg, and T. Rivera, "Quantum boxes as active probes for photonic microstructures: The pillar microcavity case," Appl. Phys. Lett. 69, 449-451 (1996).
[CrossRef]

Electron. Lett. (1)

G. Brambilla, F. Xu, and X. Feng, "Fabrication of optical fibre nanowires and their optical and mechanical characterization," Electron. Lett. 42, 517-519 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. T. Chu, B. E. Little, W. Pan, T. Kaneko, S. Sato, and Y. Kokubun, "An eight-channel add-drop filter using vertically coupled microring resonators over a cross grid," IEEE Photon. Technol. Lett. 11, 691-693 (1999).
[CrossRef]

J. Lightwave Technol. (2)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," J. Lightwave Technol. 15, 998-1005 (1997).
[CrossRef]

O. Schwelb, "Transmission, group delay, and dispersion in single-ring optical resonators and add/drop filters--a tutorial overview," J. Lightwave Technol. 22, 1380-1394 (2004).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nature (1)

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Phys. Lett. A (1)

B. Braginsky, M. L. Gorodetsky, and V. S. Ilchenko, "Quality-factor and nonlinear properties of optical whispering-gallery modes," Phys. Lett. A 137, 393-397 (1989).
[CrossRef]

Phys. Rev. Lett. (1)

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 04902 (2003).
[CrossRef]

Science (1)

R. K. Painter, A. Lee, A. Scherer, J. D. Yariv, P. O'Brien, D. Dapkus, and I. Kim, "Two-dimensional photonic bandgap defect mode laser," Science 284, 1819-1821 (1999).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Illustration of an ONMR in cylindrical coordinates.

Fig. 2
Fig. 2

Illustration of three types of fundamental profiles of ONMRs: H (uniform), V (conical), and X (biconical).

Fig. 3
Fig. 3

FWHM dependency on the average coupling parameter K near λ 0 = 1550   nm in three-turn ONMRs for three types of profile: H (dashed lines), V (dotted lines) and X (solid lines). (a) Linear scaling, K = 0 20 ; (b) logarithmic scaling, K = 14 20 .

Fig. 4
Fig. 4

Dependence of the tolerance ratio (defined as the percentage of the average coupling parameter K where the FWHM is below 0.01   nm ) near K M (14–20, 16–20, and 18–20) on the number of turns M in a microcoil resonator for three types of profile: H (squares), V (triangles), and X (circles).

Fig. 5
Fig. 5

Tolerance ratio near K M (K = 10–20, 14–20, and 18–20) versus dR in the x-profile three-turn ONMR.

Equations (8)

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

d d θ ( A 1 A 2 A m A M 1 A M ) = i ( 0 R 2 ( θ ) χ 21 ( θ ) 0 0 0 0 R 1 ( θ ) χ 12 ( θ ) 0 R 3 ( θ ) χ 32 ( θ ) 0 0 0 0 R 2 ( θ ) χ 23 ( θ ) 0 0 0 0 0 0 0 0 R M 1 ( θ ) χ M 2 M 1 ( θ ) 0 0 0 0 R M 2 ( θ ) χ M 1 M 2 ( θ ) 0 R M ( θ ) χ M M 1 ( θ ) 0 0 0 0 R M 1 ( θ ) χ M 1 M ( θ ) 0 ) ( A 1 A 2 A m A M 1 A M ) ,
R m + 1 ( 0 ) = R m ( 2 π ) ,
A m + 1 ( 0 ) = A m ( 2 π ) exp { i 0 2 π β R m ( θ ) d s } ,
m = 1 , 2 , , M 1.
T = A M ( 2 π ) A 1 ( 0 )  exp { i 0 2 π β R M ( θ ) d θ } .
H ( uniform ) : R m ( θ ) = R 0 ,
V ( conical ) : R m ( θ ) = R 0 + M 2  d R + ( m 1 + θ 2 π ) d R ,
X ( biconical ) : R m ( θ ) = R 0 + | ( M + 1 2 m θ π 2 π ) | ×d R M 4  d R ,

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