Abstract

Whispering gallery modes (WGMs) in dielectric microcylinders are investigated numerically as sensitive probes of the surrounding medium, for applications in chemical sensing and biosensing. We consider a geometry where WGMs are exited via frustrated total internal reflection from a planar dielectric substrate, as reported in recent experiments. The optical coupling between the substrate and the cylinder yields a WGM broadening exponentially decreasing with increasing distance between the cylinder and the substrate. We also consider a separation layer between the substrate and the cylinder that results in a WGM broadening and shift depending on the index mismatch between the layer and the surrounding medium, and find that Q values >105 are possible for a mismatch in the few percent range. For biosensing applications we calculate the effect of single and multiple cylinder-shaped particles of different sizes attached to the cylinder surface to simulate biological analytes. We find not only WGM shifts but also broadenings and splittings acting as sensitive indicators of different properties of the analytes. In particular, in the case of a single particle, both particle size and refractive index can be determined from the WGM shift and broadening, opening the perspective to a new modality of biosensing applicable to single objects such as viruses or bacteria. In the multiparticle case, the results are statistically analyzed in terms of their surface coverage.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Noto, F. Vollmer, D. Keng, I. Teraoka, and S. Arnold, “Nanolayer characterization through wavelength multiplexing of a microsphere resonator,” Opt. Lett. 30, 510-512 (2005).
    [CrossRef] [PubMed]
  2. F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057-4059 (2002).
    [CrossRef]
  3. F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libshaber, “Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities,” Biophys. J. 85, 1974-1979 (2003).
    [CrossRef] [PubMed]
  4. M. Hosodaa and T. Shigaki, “Degeneracy breaking of optical resonance modes in rolled-up spiral microtubes,” Appl. Phys. Lett. 90, 181107 (2007).
    [CrossRef]
  5. T. Ling and L. J. Guo, “A unique resonance mode observed in a prismcoupled microtube resonator sensor with superior index sensitivity,” Opt. Express 15, 17424-17432 (2007).
    [CrossRef] [PubMed]
  6. M. Sumetsky, R. S. Windeler, Y. Dulashko, and X. Fan, “Optical liquid ring resonator sensor,” Opt. Express 15, 14376-14381 (2007).
    [CrossRef] [PubMed]
  7. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783-787 (2007).
    [CrossRef] [PubMed]
  8. H.-C. Ren, F. Vollmer, S. Arnold, and A. Libchaber, “High-Q microsphere biosensor-analysis for adsorption of rodlike bacteria,” Opt. Express 15, 17410-17422 (2007).
    [CrossRef] [PubMed]
  9. C.-M. Yuan, “Efficient light scattering modeling for alignment, metrology, and resist exposure in photolithography,” IEEE Trans. Electron Devices 39, 1588-1598 (1992).
    [CrossRef]
  10. N. I. Nikolaev and A. Erdmann, “Rigorous simulation of alignment for microlithography,” J. Microlithogr., Microfabr., Microsyst. 2, 220-226 (2003).
    [CrossRef]
  11. M. G. Moharam, D. A. Pommet, and E. B. Grann, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077-1086 (1995).
    [CrossRef]
  12. J. A. Stratton, Electro Magnetic Theory (McGraw-Hill, 1941).
  13. D. Meschede, Optics, Light and Lasers (Wiley VCH, 2003).
  14. This assumes that the divergence of the Gaussian beam θdiv=λ/(πw0nb) is much less than π/2−θ.
  15. M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-q whispering-gallery modes,” J. Opt. Soc. Am. B 16, 147-154 (1999).
    [CrossRef]
  16. The coupling to the substrate also breaks the rotational symmetry, but we have verified that in the simulations the mode splitting is dominated by the numerical discretization.
  17. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272-274 (2003).
    [CrossRef] [PubMed]
  18. I. Teraoka, S. Arnold, and F. Vollmer, “Perturbation approach to resonance shifts of whispering-gallery modes in a dielectric microsphere as a probe of a surrounding medium,” J. Opt. Soc. Am. B 20, 1937-1946 (2003).
    [CrossRef]
  19. M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74-77 (2000).
    [CrossRef] [PubMed]
  20. J. Lutti, W. Langbein, and P. Borri, “High Q optical resonances of polystyrene microspheres in water controlled by optical,” Appl. Phys. Lett. 91, 141116 (2007).
    [CrossRef]
  21. H. J. Coles, B. R. Jennings, and V. J. Morris, “Refractive index increment measurement of bacterial suspensions,” Phys. Med. Biol. 20, 310-313 (1975).
    [CrossRef] [PubMed]
  22. K. R. Hiremath and V. N. Astratov, “Perturbations of whispering gallery modes by nanoparticles embedded in microcavities,” Opt. Express 16, 5421-5426 (2008).
    [CrossRef] [PubMed]

2008 (1)

2007 (6)

M. Sumetsky, R. S. Windeler, Y. Dulashko, and X. Fan, “Optical liquid ring resonator sensor,” Opt. Express 15, 14376-14381 (2007).
[CrossRef] [PubMed]

H.-C. Ren, F. Vollmer, S. Arnold, and A. Libchaber, “High-Q microsphere biosensor-analysis for adsorption of rodlike bacteria,” Opt. Express 15, 17410-17422 (2007).
[CrossRef] [PubMed]

T. Ling and L. J. Guo, “A unique resonance mode observed in a prismcoupled microtube resonator sensor with superior index sensitivity,” Opt. Express 15, 17424-17432 (2007).
[CrossRef] [PubMed]

M. Hosodaa and T. Shigaki, “Degeneracy breaking of optical resonance modes in rolled-up spiral microtubes,” Appl. Phys. Lett. 90, 181107 (2007).
[CrossRef]

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783-787 (2007).
[CrossRef] [PubMed]

J. Lutti, W. Langbein, and P. Borri, “High Q optical resonances of polystyrene microspheres in water controlled by optical,” Appl. Phys. Lett. 91, 141116 (2007).
[CrossRef]

2005 (1)

2003 (4)

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272-274 (2003).
[CrossRef] [PubMed]

I. Teraoka, S. Arnold, and F. Vollmer, “Perturbation approach to resonance shifts of whispering-gallery modes in a dielectric microsphere as a probe of a surrounding medium,” J. Opt. Soc. Am. B 20, 1937-1946 (2003).
[CrossRef]

N. I. Nikolaev and A. Erdmann, “Rigorous simulation of alignment for microlithography,” J. Microlithogr., Microfabr., Microsyst. 2, 220-226 (2003).
[CrossRef]

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libshaber, “Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities,” Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

2002 (1)

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

2000 (1)

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

1999 (1)

1995 (1)

1992 (1)

C.-M. Yuan, “Efficient light scattering modeling for alignment, metrology, and resist exposure in photolithography,” IEEE Trans. Electron Devices 39, 1588-1598 (1992).
[CrossRef]

1975 (1)

H. J. Coles, B. R. Jennings, and V. J. Morris, “Refractive index increment measurement of bacterial suspensions,” Phys. Med. Biol. 20, 310-313 (1975).
[CrossRef] [PubMed]

Armani, A. M.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783-787 (2007).
[CrossRef] [PubMed]

Arnold, S.

Astratov, V. N.

Borri, P.

J. Lutti, W. Langbein, and P. Borri, “High Q optical resonances of polystyrene microspheres in water controlled by optical,” Appl. Phys. Lett. 91, 141116 (2007).
[CrossRef]

Braun, D.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libshaber, “Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities,” Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Coles, H. J.

H. J. Coles, B. R. Jennings, and V. J. Morris, “Refractive index increment measurement of bacterial suspensions,” Phys. Med. Biol. 20, 310-313 (1975).
[CrossRef] [PubMed]

Dulashko, Y.

Erdmann, A.

N. I. Nikolaev and A. Erdmann, “Rigorous simulation of alignment for microlithography,” J. Microlithogr., Microfabr., Microsyst. 2, 220-226 (2003).
[CrossRef]

Fan, X.

Flagan, R. C.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783-787 (2007).
[CrossRef] [PubMed]

Fraser, S. E.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783-787 (2007).
[CrossRef] [PubMed]

Gorodetsky, M. L.

Grann, E. B.

Guo, L. J.

Hiremath, K. R.

Holler, S.

Hosodaa, M.

M. Hosodaa and T. Shigaki, “Degeneracy breaking of optical resonance modes in rolled-up spiral microtubes,” Appl. Phys. Lett. 90, 181107 (2007).
[CrossRef]

Ilchenko, V. S.

Jennings, B. R.

H. J. Coles, B. R. Jennings, and V. J. Morris, “Refractive index increment measurement of bacterial suspensions,” Phys. Med. Biol. 20, 310-313 (1975).
[CrossRef] [PubMed]

Keng, D.

Khoshsima, M.

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272-274 (2003).
[CrossRef] [PubMed]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Kulkarni, R. P.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783-787 (2007).
[CrossRef] [PubMed]

Langbein, W.

J. Lutti, W. Langbein, and P. Borri, “High Q optical resonances of polystyrene microspheres in water controlled by optical,” Appl. Phys. Lett. 91, 141116 (2007).
[CrossRef]

Libchaber, A.

H.-C. Ren, F. Vollmer, S. Arnold, and A. Libchaber, “High-Q microsphere biosensor-analysis for adsorption of rodlike bacteria,” Opt. Express 15, 17410-17422 (2007).
[CrossRef] [PubMed]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Libshaber, A.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libshaber, “Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities,” Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Ling, T.

Lutti, J.

J. Lutti, W. Langbein, and P. Borri, “High Q optical resonances of polystyrene microspheres in water controlled by optical,” Appl. Phys. Lett. 91, 141116 (2007).
[CrossRef]

Meschede, D.

D. Meschede, Optics, Light and Lasers (Wiley VCH, 2003).

Moharam, M. G.

Morris, V. J.

H. J. Coles, B. R. Jennings, and V. J. Morris, “Refractive index increment measurement of bacterial suspensions,” Phys. Med. Biol. 20, 310-313 (1975).
[CrossRef] [PubMed]

Nikolaev, N. I.

N. I. Nikolaev and A. Erdmann, “Rigorous simulation of alignment for microlithography,” J. Microlithogr., Microfabr., Microsyst. 2, 220-226 (2003).
[CrossRef]

Noto, N.

Painter, O.

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Pommet, D. A.

Ren, H.-C.

Shigaki, T.

M. Hosodaa and T. Shigaki, “Degeneracy breaking of optical resonance modes in rolled-up spiral microtubes,” Appl. Phys. Lett. 90, 181107 (2007).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electro Magnetic Theory (McGraw-Hill, 1941).

Sumetsky, M.

Teraoka, I.

Vahala, K. J.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783-787 (2007).
[CrossRef] [PubMed]

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Vollmer, F.

Windeler, R. S.

Yuan, C.-M.

C.-M. Yuan, “Efficient light scattering modeling for alignment, metrology, and resist exposure in photolithography,” IEEE Trans. Electron Devices 39, 1588-1598 (1992).
[CrossRef]

Appl. Phys. Lett. (3)

M. Hosodaa and T. Shigaki, “Degeneracy breaking of optical resonance modes in rolled-up spiral microtubes,” Appl. Phys. Lett. 90, 181107 (2007).
[CrossRef]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

J. Lutti, W. Langbein, and P. Borri, “High Q optical resonances of polystyrene microspheres in water controlled by optical,” Appl. Phys. Lett. 91, 141116 (2007).
[CrossRef]

Biophys. J. (1)

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libshaber, “Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities,” Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

IEEE Trans. Electron Devices (1)

C.-M. Yuan, “Efficient light scattering modeling for alignment, metrology, and resist exposure in photolithography,” IEEE Trans. Electron Devices 39, 1588-1598 (1992).
[CrossRef]

J. Microlithogr., Microfabr., Microsyst. (1)

N. I. Nikolaev and A. Erdmann, “Rigorous simulation of alignment for microlithography,” J. Microlithogr., Microfabr., Microsyst. 2, 220-226 (2003).
[CrossRef]

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

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

Opt. Express (4)

Opt. Lett. (2)

Phys. Med. Biol. (1)

H. J. Coles, B. R. Jennings, and V. J. Morris, “Refractive index increment measurement of bacterial suspensions,” Phys. Med. Biol. 20, 310-313 (1975).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

M. Cai, O. Painter, and K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74-77 (2000).
[CrossRef] [PubMed]

Science (1)

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783-787 (2007).
[CrossRef] [PubMed]

Other (4)

J. A. Stratton, Electro Magnetic Theory (McGraw-Hill, 1941).

D. Meschede, Optics, Light and Lasers (Wiley VCH, 2003).

This assumes that the divergence of the Gaussian beam θdiv=λ/(πw0nb) is much less than π/2−θ.

The coupling to the substrate also breaks the rotational symmetry, but we have verified that in the simulations the mode splitting is dominated by the numerical discretization.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Scheme of the simulation region composed of a substrate (index n b ), a separation layer (thickness d s , index n s ), and a resonator (cylinder, radius r c , index n c ) surrounded by a medium (e.g., water, index n w ). The counterpropagating modes m = ± l , a standing wave for l = 10 , and the excitation beam geometry (red arrows in the substrate) are also indicated.

Fig. 2
Fig. 2

Electric field distribution E ( x , y ) for different excitation wavelengths λ and sizes w 0 at d s = 0.4 μ m . (a) Phase and (b) amplitude on resonance λ = 0.767386 μ m and w 0 = 5 μ m . (c) amplitude off-resonance λ = 0.767486 μ m (detuning 0.21 meV ), otherwise as (a). (d) Amplitude for optimal size w 0 = 1.12 μ m , otherwise as (a). Phase on a gray scale π π (set to zero for small amplitudes for clarity). Amplitude on a logarithmic color scale (see scale bars).

Fig. 3
Fig. 3

(a) T m spectra for d s = 0.3 and 0.0 μ m , as labeled. Dotted lines: analytical wavelengths of TE n l . (b) T m spectra around TE 1 122 at varying d s (labeled in micrometers). Inset: linewidth γ versus d s , and fit (red solid curve; see text). Dashed curves are offset and exponential decay of the fit. (c) Phase of T m corresponding to (b). (d) T spectra corresponding to (b).

Fig. 4
Fig. 4

(a) Shift ν ̃ (red triangles) and broadening γ ̃ (black circles) of the TE 1 122 WGM versus versus index mismatch n ̃ s between the separation layer and the medium for d s = 0.6 μ m . Dotted lines correspond to n ̃ eff = n eff n w and n ̃ c = n c n w , as labeled. The intensity distribution of the WGM at the separation layer surface is shown as a shaded area. (b) Zoom of (a) with n ̃ s 1 on a double-log scale (open symbols) and for d s = 0.8 μ m (filled symbols). (c) Mode transmission spectra for various n ̃ s as labeled.

Fig. 5
Fig. 5

Effect of a particle attached to the resonator on the TE 1 122 WGM, versus the radius of the attached particle r p , for an index mismatch n ̃ p = 0.05 (black squares), 0.1 (red circles), and 0.2 (blue triangles). A sketch of the geometry is shown. (a) Shift ν ̃ normalized to n ̃ p . (b) Broadening γ ̃ normalized to n ̃ p 2 . Green dashed lines are fits (see text). The values are averaged over the two SW WGMs. Inset (a): splitting Δ and the scattering potentials P p ( 2 n eff k 0 ) and P l p ( 2 n eff k 0 ) . Inset (b): ratio between normalized broadening and normalized shift.

Fig. 6
Fig. 6

Calculated electric field amplitude E ( x , y ) for resonant excitation of the TE 1 122 WGM at a distance d s = 0.6 μ m (see also Fig. 2). A single attached particle is present, with n p = 1.53 and r p of 1000 nm in (a) and of 100 nm in (b). Logarithmic color scale over two decades (see scale bar).

Fig. 7
Fig. 7

Shift ν ̃ in (a) and splitting Δ in (b) of the TE 1 122 WGM versus the number N p of randomly attached particles with r p = 50 nm . Shown are average values, with error bars indicating the SD over different position realizations (see text). The refractive index n p of the particles is 1.53 (blue triangles), 1.43 (red circles), and 1.38 (black squares). Solid lines (curves) correspond to fits η in (a) and η ( 1 η ) in (b). In (a) the attachment geometry is shown and the inset shows T m in amplitude and phase for a single realization of N = 200 and n = 1.53 , indicated by the arrow.

Fig. 8
Fig. 8

Same as Fig. 7 for particles of r p = 200 nm . Background of (a): sketch of particles with the three considered radii on the resonator surface, the WGM intensity decay length z 0 , and the effective WGM wavelength λ n eff .

Fig. 9
Fig. 9

Shift ν ̃ (a) and broadening γ ̃ (b) of the TE 1 122 WGM versus the number N p of randomly attached particles with r p = 1000 nm . Shown are average values, with error bars indicating the SD over different position realizations (see text). The refractive index n p of the particles is 1.53 (blue triangles), 1.43 (red circles), and 1.38 (black squares). Solid lines correspond to fits η .

Equations (7)

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

k c J l ( k c r c ) J l ( k c r c ) = k w H l ( 1 ) ( k w r c ) H l ( 1 ) ( k w r c ) ,
T m = 1 P 0 T E T E 0 T * d y , T = P T P 0 T ,
P T = E T 2 d y , P 0 T = E 0 T 2 d y .
ν ̃ = C 1 n ̃ p x 2 + x 1 2 ,
x = 2 r p C 2 ,
γ ̃ = C 1 n ̃ p 2 ( x 1 + x 1 4 ) 4 ,
x = 2 r p C 2 ,

Metrics