Abstract

Due to ultra high quality factor (106 − 109), axisymmetric optical microcavities are popular platforms for biosensing applications. It has been recently demonstrated that a microcavity biosensor can track a biodetection event as a function of its quality factor by using phase shift cavity ring down spectroscopy (PS-CRDS). However, to achieve maximum sensitivity, it is necessary to optimize the microcavity parameters for a given sensing application. Here, we introduce an improved finite element model which allows us to determine the optimized geometry for the PS-CRDS sensor. The improved model not only provides fast and accurate determination of quality factors but also determines the tunneling distance of axisymmetric resonators. The improved model is validated numerically, analytically, and experimentally.

© 2013 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
  32. S. Scheurich, S. Belle, R. Hellmann, S. So, I.J.G. Sparrow, and G. Emmerson, “Application of a silica-on-silicon planar optical waveguide Bragg grating sensor for organic liquid compound detection,” Proc. SPIE7356 (2009)
    [CrossRef]
  33. M. Gallignani, S. Garrigues, and M. Guardia, “Direct determination of ethanol in all types of alcoholic beverages by near-infrared derivative spectrometry,”Analyst118, (1993).
    [CrossRef]
  34. A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations (Springer, 1997).
  35. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Dispersion compensation in whispering-gallery modes,” J. Opt. Soc. Am. A20, 157–162, (2003).
    [CrossRef]
  36. A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, “Ultra-high-Q microcavity operation in H2O and D2O, Appl. Phys. Lett.87, (2005).
    [CrossRef]

2012 (4)

F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics267–291 (2012).

M. Oxborrow, J. D. Breeze, and N. M. Alford, “Room-temperature solid-state maser,” Nature488, 353–356 (2012).
[CrossRef] [PubMed]

C. Shi, H. S. Choi, and A. M. Armani, “Optical microcavities with a thiol-functionalized gold nanoparticle polymer thin film coating,” Appl. Phys. Lett.100, 013305 (2012).
[CrossRef]

M. I. Cheema, S. Mehrabani, A. A. Hayat, Y. A. Peter, A. M. Armani, and A. G. Kirk, “Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy,” Opt. Express20, 9090–9098 (2012).
[CrossRef] [PubMed]

2011 (1)

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. (2011).
[CrossRef]

2010 (3)

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902, (2010).
[CrossRef]

A. Arbabi, Y. M. Kang, and L. L. Goddard, “Analysis and Design of a Microring Inline Single Wavelength Reflector,” in FIO, October24, 2010.

M. Soltani, Q. Li, S. Yegnanarayanan, and A. Adibi, “Toward ultimate miniaturization of high Q silicon traveling-wave microresonators,” Opt. Express18, 19541–19557 (2010).
[CrossRef] [PubMed]

2009 (3)

M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micropillar cavity quality factors calculated with finite element methods,” Opt. Express2, (2009).

M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express17, 19160 (2009).
[CrossRef]

S. Scheurich, S. Belle, R. Hellmann, S. So, I.J.G. Sparrow, and G. Emmerson, “Application of a silica-on-silicon planar optical waveguide Bragg grating sensor for organic liquid compound detection,” Proc. SPIE7356 (2009)
[CrossRef]

2008 (2)

2007 (1)

M. Oxborrow, “Traceable 2-D finite element simulation of the whispering gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. on Microwave Theory Tech.55, 1209–1218 (2007).
[CrossRef]

2006 (1)

2005 (3)

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, “Ultra-high-Q microcavity operation in H2O and D2O, Appl. Phys. Lett.87, (2005).
[CrossRef]

O. Chinellato, P. Arbenz, M. Streiff, and A. Witzig, “Computation of optical modes in axisymmetric open cavity resonators,” Future Gener. Comp. Sy.21, 1263–1274 (2005).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, “Chaos-assisted tunneling in dielectric microcavities,” Opt. Lett.30, (2005).
[CrossRef] [PubMed]

2003 (3)

J. R. Buck and H. J. Kimble, “Optimal sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A67033806 (2003).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Dispersion compensation in whispering-gallery modes,” J. Opt. Soc. Am. A20, 157–162, (2003).
[CrossRef]

2002 (1)

J. L. Nadeau, V. S. Ilchenko, D. Kossakovski, G. H. Bearman, and L. Maleki, “High-Q whispering-gallery mode sensor in liquids,” Proc. SPIE4629, 72 (2002).

2000 (1)

P. Pereyra, “Closed formulas for tunneling time in superlattices,” Phys. Rev. Lett.84, 1772–1775 (2000).
[CrossRef] [PubMed]

1997 (1)

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett.7, 371–373, (1997).
[CrossRef]

1994 (2)

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett.73, 2308–2311, (1994).
[CrossRef] [PubMed]

R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villalva, G. J. Dick, D. G. Santiago, and R. T. Wang, “Azimuthally dependent finite element solution to the cylindrical resonator,”10th annual review of progress in applied computational electromagnetics1, 159–170, (1994).

1993 (2)

B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,”J. Opt. Soc. Am. A10, 2, (1993).
[CrossRef]

M. Gallignani, S. Garrigues, and M. Guardia, “Direct determination of ethanol in all types of alcoholic beverages by near-infrared derivative spectrometry,”Analyst118, (1993).
[CrossRef]

1992 (1)

V. V. Datsyuk, “Some characteristics of resonant electromagnetic modes in a dielectric sphere,”Appl. Phys.B54, 184–187, (1992).

1985 (1)

M. Koshiba, K. Hayata, and M. Suzuki, “Improved finite element formulation in terms of the magnetic field vector for dielectric waveguides,” IEEE Trans. on Microwave Theory Tech.33, 227–233, (1985).
[CrossRef]

Adibi, A.

Alford, N. M.

M. Oxborrow, J. D. Breeze, and N. M. Alford, “Room-temperature solid-state maser,” Nature488, 353–356 (2012).
[CrossRef] [PubMed]

Arbabi, A.

A. Arbabi, Y. M. Kang, and L. L. Goddard, “Analysis and Design of a Microring Inline Single Wavelength Reflector,” in FIO, October24, 2010.

Arbenz, P.

O. Chinellato, P. Arbenz, M. Streiff, and A. Witzig, “Computation of optical modes in axisymmetric open cavity resonators,” Future Gener. Comp. Sy.21, 1263–1274 (2005).
[CrossRef]

Armani, A. M.

M. I. Cheema, S. Mehrabani, A. A. Hayat, Y. A. Peter, A. M. Armani, and A. G. Kirk, “Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy,” Opt. Express20, 9090–9098 (2012).
[CrossRef] [PubMed]

C. Shi, H. S. Choi, and A. M. Armani, “Optical microcavities with a thiol-functionalized gold nanoparticle polymer thin film coating,” Appl. Phys. Lett.100, 013305 (2012).
[CrossRef]

A. M. Armani and K. J. Vahala, “Heavy water detection using ultra-high-q microcavities,” Opt. Lett.31, 1896–1898 (2006).
[CrossRef] [PubMed]

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, “Ultra-high-Q microcavity operation in H2O and D2O, Appl. Phys. Lett.87, (2005).
[CrossRef]

Armani, D. K.

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, “Ultra-high-Q microcavity operation in H2O and D2O, Appl. Phys. Lett.87, (2005).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

Barnes, J.

Bearman, G. H.

J. L. Nadeau, V. S. Ilchenko, D. Kossakovski, G. H. Bearman, and L. Maleki, “High-Q whispering-gallery mode sensor in liquids,” Proc. SPIE4629, 72 (2002).

Belle, S.

S. Scheurich, S. Belle, R. Hellmann, S. So, I.J.G. Sparrow, and G. Emmerson, “Application of a silica-on-silicon planar optical waveguide Bragg grating sensor for organic liquid compound detection,” Proc. SPIE7356 (2009)
[CrossRef]

Breeze, J. D.

M. Oxborrow, J. D. Breeze, and N. M. Alford, “Room-temperature solid-state maser,” Nature488, 353–356 (2012).
[CrossRef] [PubMed]

Buck, J. R.

J. R. Buck and H. J. Kimble, “Optimal sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A67033806 (2003).
[CrossRef]

Burger, S.

M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micropillar cavity quality factors calculated with finite element methods,” Opt. Express2, (2009).

Carmon, T.

Carver, B.

Cheema, M. I.

M. I. Cheema, S. Mehrabani, A. A. Hayat, Y. A. Peter, A. M. Armani, and A. G. Kirk, “Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy,” Opt. Express20, 9090–9098 (2012).
[CrossRef] [PubMed]

M. I. Cheema and A. G. Kirk, “Implementation of the perfectly matched layer to determine the quality factor of axisymmetric resonators in COMSOL,” in COMSOL conference,Boston, Oct 8 2010.

Chen, T.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. (2011).
[CrossRef]

Chew, W. C.

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett.7, 371–373, (1997).
[CrossRef]

Chinellato, O.

O. Chinellato, P. Arbenz, M. Streiff, and A. Witzig, “Computation of optical modes in axisymmetric open cavity resonators,” Future Gener. Comp. Sy.21, 1263–1274 (2005).
[CrossRef]

Choi, H. S.

C. Shi, H. S. Choi, and A. M. Armani, “Optical microcavities with a thiol-functionalized gold nanoparticle polymer thin film coating,” Appl. Phys. Lett.100, 013305 (2012).
[CrossRef]

Datsyuk, V. V.

V. V. Datsyuk, “Some characteristics of resonant electromagnetic modes in a dielectric sphere,”Appl. Phys.B54, 184–187, (1992).

Dick, G. J.

R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villalva, G. J. Dick, D. G. Santiago, and R. T. Wang, “Azimuthally dependent finite element solution to the cylindrical resonator,”10th annual review of progress in applied computational electromagnetics1, 159–170, (1994).

Dong, C. H.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902, (2010).
[CrossRef]

Emmerson, G.

S. Scheurich, S. Belle, R. Hellmann, S. So, I.J.G. Sparrow, and G. Emmerson, “Application of a silica-on-silicon planar optical waveguide Bragg grating sensor for organic liquid compound detection,” Proc. SPIE7356 (2009)
[CrossRef]

Fan, X.

X. Fan, I. M. White, S. I. Shopoua, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Analytica Chimica Acta620, 8–26 (2008)
[CrossRef]

Flagan, R. C.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. (2011).
[CrossRef]

Fraser, J. M.

Fraser, S. E.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. (2011).
[CrossRef]

Gagliardi, G.

Gallignani, M.

M. Gallignani, S. Garrigues, and M. Guardia, “Direct determination of ethanol in all types of alcoholic beverages by near-infrared derivative spectrometry,”Analyst118, (1993).
[CrossRef]

Garrigues, S.

M. Gallignani, S. Garrigues, and M. Guardia, “Direct determination of ethanol in all types of alcoholic beverages by near-infrared derivative spectrometry,”Analyst118, (1993).
[CrossRef]

Gil, L. M.

R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villalva, G. J. Dick, D. G. Santiago, and R. T. Wang, “Azimuthally dependent finite element solution to the cylindrical resonator,”10th annual review of progress in applied computational electromagnetics1, 159–170, (1994).

Goddard, L. L.

A. Arbabi, Y. M. Kang, and L. L. Goddard, “Analysis and Design of a Microring Inline Single Wavelength Reflector,” in FIO, October24, 2010.

Gong, Q.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902, (2010).
[CrossRef]

Guardia, M.

M. Gallignani, S. Garrigues, and M. Guardia, “Direct determination of ethanol in all types of alcoholic beverages by near-infrared derivative spectrometry,”Analyst118, (1993).
[CrossRef]

Han, Z. F.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902, (2010).
[CrossRef]

Hayat, A. A.

Hayata, K.

M. Koshiba, K. Hayata, and M. Suzuki, “Improved finite element formulation in terms of the magnetic field vector for dielectric waveguides,” IEEE Trans. on Microwave Theory Tech.33, 227–233, (1985).
[CrossRef]

Hellmann, R.

S. Scheurich, S. Belle, R. Hellmann, S. So, I.J.G. Sparrow, and G. Emmerson, “Application of a silica-on-silicon planar optical waveguide Bragg grating sensor for organic liquid compound detection,” Proc. SPIE7356 (2009)
[CrossRef]

Herchak, S.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. (2011).
[CrossRef]

Hetterich, M.

M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micropillar cavity quality factors calculated with finite element methods,” Opt. Express2, (2009).

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. A20, 157–162, (2003).
[CrossRef]

J. L. Nadeau, V. S. Ilchenko, D. Kossakovski, G. H. Bearman, and L. Maleki, “High-Q whispering-gallery mode sensor in liquids,” Proc. SPIE4629, 72 (2002).

L. Maleki and V. S. Ilchenko, “Techniques and devices for sensing a sample by using a whispering gallery mode resonator,” California Institute of Technology, US Patent 6,490,039, (2002).

Johnson, B. R.

B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,”J. Opt. Soc. Am. A10, 2, (1993).
[CrossRef]

Kalt, H.

M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micropillar cavity quality factors calculated with finite element methods,” Opt. Express2, (2009).

Kang, Y. M.

A. Arbabi, Y. M. Kang, and L. L. Goddard, “Analysis and Design of a Microring Inline Single Wavelength Reflector,” in FIO, October24, 2010.

Karl, M.

M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micropillar cavity quality factors calculated with finite element methods,” Opt. Express2, (2009).

Kettner, B.

M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micropillar cavity quality factors calculated with finite element methods,” Opt. Express2, (2009).

Kim, J. H.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. (2011).
[CrossRef]

Kimble, H. J.

J. R. Buck and H. J. Kimble, “Optimal sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A67033806 (2003).
[CrossRef]

Kippenberg, T. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

Kirk, A. G.

M. I. Cheema, S. Mehrabani, A. A. Hayat, Y. A. Peter, A. M. Armani, and A. G. Kirk, “Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy,” Opt. Express20, 9090–9098 (2012).
[CrossRef] [PubMed]

M. I. Cheema and A. G. Kirk, “Implementation of the perfectly matched layer to determine the quality factor of axisymmetric resonators in COMSOL,” in COMSOL conference,Boston, Oct 8 2010.

Koshiba, M.

M. Koshiba, K. Hayata, and M. Suzuki, “Improved finite element formulation in terms of the magnetic field vector for dielectric waveguides,” IEEE Trans. on Microwave Theory Tech.33, 227–233, (1985).
[CrossRef]

Kossakovski, D.

J. L. Nadeau, V. S. Ilchenko, D. Kossakovski, G. H. Bearman, and L. Maleki, “High-Q whispering-gallery mode sensor in liquids,” Proc. SPIE4629, 72 (2002).

Krausz, F.

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett.73, 2308–2311, (1994).
[CrossRef] [PubMed]

Lee, H.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. (2011).
[CrossRef]

Li, B. B.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902, (2010).
[CrossRef]

Li, Q.

Li, Y.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902, (2010).
[CrossRef]

Loock, H. P.

Lu, T.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. (2011).
[CrossRef]

Maleki, L.

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Dispersion compensation in whispering-gallery modes,” J. Opt. Soc. Am. A20, 157–162, (2003).
[CrossRef]

J. L. Nadeau, V. S. Ilchenko, D. Kossakovski, G. H. Bearman, and L. Maleki, “High-Q whispering-gallery mode sensor in liquids,” Proc. SPIE4629, 72 (2002).

L. Maleki and V. S. Ilchenko, “Techniques and devices for sensing a sample by using a whispering gallery mode resonator,” California Institute of Technology, US Patent 6,490,039, (2002).

Matsko, A. B.

Mehrabani, S.

Min, B.

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, “Ultra-high-Q microcavity operation in H2O and D2O, Appl. Phys. Lett.87, (2005).
[CrossRef]

Nadeau, J. L.

J. L. Nadeau, V. S. Ilchenko, D. Kossakovski, G. H. Bearman, and L. Maleki, “High-Q whispering-gallery mode sensor in liquids,” Proc. SPIE4629, 72 (2002).

Narimanov, E. E.

V. A. Podolskiy and E. E. Narimanov, “Chaos-assisted tunneling in dielectric microcavities,” Opt. Lett.30, (2005).
[CrossRef] [PubMed]

Osegueda, R. A.

R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villalva, G. J. Dick, D. G. Santiago, and R. T. Wang, “Azimuthally dependent finite element solution to the cylindrical resonator,”10th annual review of progress in applied computational electromagnetics1, 159–170, (1994).

Oxborrow, M.

M. Oxborrow, J. D. Breeze, and N. M. Alford, “Room-temperature solid-state maser,” Nature488, 353–356 (2012).
[CrossRef] [PubMed]

M. Oxborrow, “Traceable 2-D finite element simulation of the whispering gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. on Microwave Theory Tech.55, 1209–1218 (2007).
[CrossRef]

Pereyra, P.

P. Pereyra, “Closed formulas for tunneling time in superlattices,” Phys. Rev. Lett.84, 1772–1775 (2000).
[CrossRef] [PubMed]

Peter, Y. A.

Pierluissi, J. H.

R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villalva, G. J. Dick, D. G. Santiago, and R. T. Wang, “Azimuthally dependent finite element solution to the cylindrical resonator,”10th annual review of progress in applied computational electromagnetics1, 159–170, (1994).

Podolskiy, V. A.

V. A. Podolskiy and E. E. Narimanov, “Chaos-assisted tunneling in dielectric microcavities,” Opt. Lett.30, (2005).
[CrossRef] [PubMed]

Quarteroni, A.

A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations (Springer, 1997).

Revilla, A.

R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villalva, G. J. Dick, D. G. Santiago, and R. T. Wang, “Azimuthally dependent finite element solution to the cylindrical resonator,”10th annual review of progress in applied computational electromagnetics1, 159–170, (1994).

Santiago, D. G.

R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villalva, G. J. Dick, D. G. Santiago, and R. T. Wang, “Azimuthally dependent finite element solution to the cylindrical resonator,”10th annual review of progress in applied computational electromagnetics1, 159–170, (1994).

Savchenkov, A. A.

Scheurich, S.

S. Scheurich, S. Belle, R. Hellmann, S. So, I.J.G. Sparrow, and G. Emmerson, “Application of a silica-on-silicon planar optical waveguide Bragg grating sensor for organic liquid compound detection,” Proc. SPIE7356 (2009)
[CrossRef]

Schmidt, F.

M. Karl, B. Kettner, S. Burger, F. Schmidt, H. Kalt, and M. Hetterich, “Dependencies of micropillar cavity quality factors calculated with finite element methods,” Opt. Express2, (2009).

Shi, C.

C. Shi, H. S. Choi, and A. M. Armani, “Optical microcavities with a thiol-functionalized gold nanoparticle polymer thin film coating,” Appl. Phys. Lett.100, 013305 (2012).
[CrossRef]

Shopoua, S. I.

X. Fan, I. M. White, S. I. Shopoua, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Analytica Chimica Acta620, 8–26 (2008)
[CrossRef]

So, S.

S. Scheurich, S. Belle, R. Hellmann, S. So, I.J.G. Sparrow, and G. Emmerson, “Application of a silica-on-silicon planar optical waveguide Bragg grating sensor for organic liquid compound detection,” Proc. SPIE7356 (2009)
[CrossRef]

Soltani, M.

Sparrow, I.J.G.

S. Scheurich, S. Belle, R. Hellmann, S. So, I.J.G. Sparrow, and G. Emmerson, “Application of a silica-on-silicon planar optical waveguide Bragg grating sensor for organic liquid compound detection,” Proc. SPIE7356 (2009)
[CrossRef]

Spielmann, C.

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett.73, 2308–2311, (1994).
[CrossRef] [PubMed]

Spillane, S. M.

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, “Ultra-high-Q microcavity operation in H2O and D2O, Appl. Phys. Lett.87, (2005).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

S. M. Spillane, “Fiber-coupled ultra-high-Q microresonators for nonlinear and quantum optics,” PhD. thesis, CALTECH (2004)

Stingl, A.

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett.73, 2308–2311, (1994).
[CrossRef] [PubMed]

Streiff, M.

O. Chinellato, P. Arbenz, M. Streiff, and A. Witzig, “Computation of optical modes in axisymmetric open cavity resonators,” Future Gener. Comp. Sy.21, 1263–1274 (2005).
[CrossRef]

Sun, Y.

X. Fan, I. M. White, S. I. Shopoua, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Analytica Chimica Acta620, 8–26 (2008)
[CrossRef]

Suter, J. D.

X. Fan, I. M. White, S. I. Shopoua, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Analytica Chimica Acta620, 8–26 (2008)
[CrossRef]

Suzuki, M.

M. Koshiba, K. Hayata, and M. Suzuki, “Improved finite element formulation in terms of the magnetic field vector for dielectric waveguides,” IEEE Trans. on Microwave Theory Tech.33, 227–233, (1985).
[CrossRef]

Szipöcs, R.

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett.73, 2308–2311, (1994).
[CrossRef] [PubMed]

Teixeira, F. L.

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett.7, 371–373, (1997).
[CrossRef]

Tian, Z.

Tomes, M.

Vahala, K.

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. (2011).
[CrossRef]

Vahala, K. J.

M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express17, 19160 (2009).
[CrossRef]

A. M. Armani and K. J. Vahala, “Heavy water detection using ultra-high-q microcavities,” Opt. Lett.31, 1896–1898 (2006).
[CrossRef] [PubMed]

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, “Ultra-high-Q microcavity operation in H2O and D2O, Appl. Phys. Lett.87, (2005).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

Valli, A.

A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations (Springer, 1997).

Villalva, G. J.

R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villalva, G. J. Dick, D. G. Santiago, and R. T. Wang, “Azimuthally dependent finite element solution to the cylindrical resonator,”10th annual review of progress in applied computational electromagnetics1, 159–170, (1994).

Vollmer, F.

F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics267–291 (2012).

Wang, R. T.

R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villalva, G. J. Dick, D. G. Santiago, and R. T. Wang, “Azimuthally dependent finite element solution to the cylindrical resonator,”10th annual review of progress in applied computational electromagnetics1, 159–170, (1994).

Weinstein, L. A.

L. A. Weinstein, Open Resonators and Open Waveguides (The Golem Press, Boulder, Colorado, USA, 1969) pp. 298.

White, I. M.

X. Fan, I. M. White, S. I. Shopoua, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Analytica Chimica Acta620, 8–26 (2008)
[CrossRef]

Wilson, M. W. B.

Witzig, A.

O. Chinellato, P. Arbenz, M. Streiff, and A. Witzig, “Computation of optical modes in axisymmetric open cavity resonators,” Future Gener. Comp. Sy.21, 1263–1274 (2005).
[CrossRef]

Xiao, Y. F.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902, (2010).
[CrossRef]

Yam, S.

Yang, L.

F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics267–291 (2012).

Yastrubshak, O.

Yegnanarayanan, S.

Zhu, H.

X. Fan, I. M. White, S. I. Shopoua, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Analytica Chimica Acta620, 8–26 (2008)
[CrossRef]

Zou, C. L.

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902, (2010).
[CrossRef]

10th annual review of progress in applied computational electromagnetics (1)

R. A. Osegueda, J. H. Pierluissi, L. M. Gil, A. Revilla, G. J. Villalva, G. J. Dick, D. G. Santiago, and R. T. Wang, “Azimuthally dependent finite element solution to the cylindrical resonator,”10th annual review of progress in applied computational electromagnetics1, 159–170, (1994).

Analyst (1)

M. Gallignani, S. Garrigues, and M. Guardia, “Direct determination of ethanol in all types of alcoholic beverages by near-infrared derivative spectrometry,”Analyst118, (1993).
[CrossRef]

Analytica Chimica Acta (1)

X. Fan, I. M. White, S. I. Shopoua, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Analytica Chimica Acta620, 8–26 (2008)
[CrossRef]

Appl. Phys. (1)

V. V. Datsyuk, “Some characteristics of resonant electromagnetic modes in a dielectric sphere,”Appl. Phys.B54, 184–187, (1992).

Appl. Phys. Lett. (2)

C. Shi, H. S. Choi, and A. M. Armani, “Optical microcavities with a thiol-functionalized gold nanoparticle polymer thin film coating,” Appl. Phys. Lett.100, 013305 (2012).
[CrossRef]

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, “Ultra-high-Q microcavity operation in H2O and D2O, Appl. Phys. Lett.87, (2005).
[CrossRef]

FIO (1)

A. Arbabi, Y. M. Kang, and L. L. Goddard, “Analysis and Design of a Microring Inline Single Wavelength Reflector,” in FIO, October24, 2010.

Future Gener. Comp. Sy. (1)

O. Chinellato, P. Arbenz, M. Streiff, and A. Witzig, “Computation of optical modes in axisymmetric open cavity resonators,” Future Gener. Comp. Sy.21, 1263–1274 (2005).
[CrossRef]

IEEE Microwave Guided Wave Lett. (1)

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett.7, 371–373, (1997).
[CrossRef]

IEEE Trans. on Microwave Theory Tech. (2)

M. Oxborrow, “Traceable 2-D finite element simulation of the whispering gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. on Microwave Theory Tech.55, 1209–1218 (2007).
[CrossRef]

M. Koshiba, K. Hayata, and M. Suzuki, “Improved finite element formulation in terms of the magnetic field vector for dielectric waveguides,” IEEE Trans. on Microwave Theory Tech.33, 227–233, (1985).
[CrossRef]

J. Opt. Soc. Am. A (2)

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Dispersion compensation in whispering-gallery modes,” J. Opt. Soc. Am. A20, 157–162, (2003).
[CrossRef]

B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,”J. Opt. Soc. Am. A10, 2, (1993).
[CrossRef]

Nanophotonics (1)

F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics267–291 (2012).

Nature (2)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature421, 925–928 (2003).
[CrossRef] [PubMed]

M. Oxborrow, J. D. Breeze, and N. M. Alford, “Room-temperature solid-state maser,” Nature488, 353–356 (2012).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (2)

V. A. Podolskiy and E. E. Narimanov, “Chaos-assisted tunneling in dielectric microcavities,” Opt. Lett.30, (2005).
[CrossRef] [PubMed]

A. M. Armani and K. J. Vahala, “Heavy water detection using ultra-high-q microcavities,” Opt. Lett.31, 1896–1898 (2006).
[CrossRef] [PubMed]

Phys. Rev. A (1)

J. R. Buck and H. J. Kimble, “Optimal sizes of dielectric microspheres for cavity QED with strong coupling,” Phys. Rev. A67033806 (2003).
[CrossRef]

Phys. Rev. Lett. (3)

Y. F. Xiao, C. L. Zou, B. B. Li, Y. Li, C. H. Dong, Z. F. Han, and Q. Gong, “High-Q exterior whispering-gallery modes in a metal-coated microresonator,” Phys. Rev. Lett.105, 153902, (2010).
[CrossRef]

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett.73, 2308–2311, (1994).
[CrossRef] [PubMed]

P. Pereyra, “Closed formulas for tunneling time in superlattices,” Phys. Rev. Lett.84, 1772–1775 (2000).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. (1)

T. Lu, H. Lee, T. Chen, S. Herchak, J. H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. (2011).
[CrossRef]

Proc. SPIE (2)

S. Scheurich, S. Belle, R. Hellmann, S. So, I.J.G. Sparrow, and G. Emmerson, “Application of a silica-on-silicon planar optical waveguide Bragg grating sensor for organic liquid compound detection,” Proc. SPIE7356 (2009)
[CrossRef]

J. L. Nadeau, V. S. Ilchenko, D. Kossakovski, G. H. Bearman, and L. Maleki, “High-Q whispering-gallery mode sensor in liquids,” Proc. SPIE4629, 72 (2002).

Other (6)

L. Maleki and V. S. Ilchenko, “Techniques and devices for sensing a sample by using a whispering gallery mode resonator,” California Institute of Technology, US Patent 6,490,039, (2002).

S. M. Spillane, “Fiber-coupled ultra-high-Q microresonators for nonlinear and quantum optics,” PhD. thesis, CALTECH (2004)

L. A. Weinstein, Open Resonators and Open Waveguides (The Golem Press, Boulder, Colorado, USA, 1969) pp. 298.

A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations (Springer, 1997).

https://sites.google.com/site/axisymmetricmarkoxborrow/home

M. I. Cheema and A. G. Kirk, “Implementation of the perfectly matched layer to determine the quality factor of axisymmetric resonators in COMSOL,” in COMSOL conference,Boston, Oct 8 2010.

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