Abstract

We examine properties of whispering gallery modes (WGMs) in a dielectric microsphere coated with a high-refractive-index layer. With an increase in layer thickness, the photonic field of a WGM moves near the sphere’s surface, while the peak in its radial distribution narrows, followed by backtracking and broadening. During these changes, the resonance frequency decreases. The radial compression exposes a stronger evanescent field to the surroundings, yet the mode retains a sharp resonance peak in the frequency domain. The high-refractive-index layer will enhance the sensitivity of WGM frequency-shift sensors when used to detect adsorption of molecules and a change in refractive index in the surroundings. A possibility to match resonance shifts of different radial modes in the measurement of refractive indices is proposed.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Serpengüzel, S. Arnold, and G. Griffel, "Excitation of resonances of microspheres on an optical fiber," Opt. Lett. 20, 654-656 (1995).
    [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, 4057-4049 (2002).
    [CrossRef]
  3. F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and S. Arnold, "Multiplexed DNA detection by optical resonances in microspheres," Biophys. J. 85, 1974-1979 (2003).
    [CrossRef] [PubMed]
  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]
  5. E. Krioukov, D. J. W. Klunder, A. Driessen, J. Greve, and C. Otto, "Sensor based on an integrated optical microcavity," Opt. Lett. 27, 512-514 (2002).
    [CrossRef]
  6. M. 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]
  7. V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, "Strain-tunable high-Q optical microsphere resonator," Opt. Commun. 145, 86-90 (1998).
    [CrossRef]
  8. R. L. Hightower and C. B. Richardson, "Resonant Mie Scattering from a layered sphere," Appl. Opt. 27, 4850-4855 (1988).
    [CrossRef] [PubMed]
  9. D. Q. Chowdhury, S. C. Hill, and P. W. Barber, "Morphology-dependent resonances in radially inhomogeneous spheres," J. Opt. Soc. Am. A 8, 1702-1705 (1991).
    [CrossRef]
  10. 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]
  11. I. Teraoka and S. Arnold, "Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications," J. Opt. Soc. Am. B 23, 1381-1389 (2006).
    [CrossRef]
  12. M. Noto, I. Teraoka, D. Keng, and S. Arnold, are preparing a manuscript entitled "Polarization sensitive biosensing using whispering gallery modes."
  13. S. Arnold and S. Holler, "Microparticle photophysics: fluorescence microscopy and spectroscopy of a photonic atom," Exp. Methods Phys. Sci. 40, 227-253 (2002).
    [CrossRef]
  14. B. R. Johnson, "Theory of morphology-dependent resonances: shape resonances and width formulas," J. Opt. Soc. Am. A 10, 343-352 (1993).
    [CrossRef]
  15. 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]

2006 (1)

2005 (1)

2003 (4)

2002 (3)

S. Arnold and S. Holler, "Microparticle photophysics: fluorescence microscopy and spectroscopy of a photonic atom," Exp. Methods Phys. Sci. 40, 227-253 (2002).
[CrossRef]

E. Krioukov, D. J. W. Klunder, A. Driessen, J. Greve, and C. Otto, "Sensor based on an integrated optical microcavity," Opt. Lett. 27, 512-514 (2002).
[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, 4057-4049 (2002).
[CrossRef]

1998 (1)

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, "Strain-tunable high-Q optical microsphere resonator," Opt. Commun. 145, 86-90 (1998).
[CrossRef]

1995 (1)

1993 (1)

1991 (1)

1988 (1)

Arnold, S.

I. Teraoka and S. Arnold, "Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications," J. Opt. Soc. Am. B 23, 1381-1389 (2006).
[CrossRef]

M. 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]

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and S. Arnold, "Multiplexed DNA detection by optical resonances in microspheres," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

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, S. Arnold, D. Braun, I. Teraoka, and S. Arnold, "Multiplexed DNA detection by optical resonances in microspheres," Biophys. J. 85, 1974-1979 (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]

S. Arnold and S. Holler, "Microparticle photophysics: fluorescence microscopy and spectroscopy of a photonic atom," Exp. Methods Phys. Sci. 40, 227-253 (2002).
[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, 4057-4049 (2002).
[CrossRef]

A. Serpengüzel, S. Arnold, and G. Griffel, "Excitation of resonances of microspheres on an optical fiber," Opt. Lett. 20, 654-656 (1995).
[CrossRef] [PubMed]

M. Noto, I. Teraoka, D. Keng, and S. Arnold, are preparing a manuscript entitled "Polarization sensitive biosensing using whispering gallery modes."

Barber, P. W.

Braun, D.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and S. Arnold, "Multiplexed DNA detection by optical resonances in microspheres," 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, 4057-4049 (2002).
[CrossRef]

Chowdhury, D. Q.

Driessen, A.

Greve, J.

Griffel, G.

Haroche, S.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, "Strain-tunable high-Q optical microsphere resonator," Opt. Commun. 145, 86-90 (1998).
[CrossRef]

Hightower, R. L.

Hill, S. C.

Holler, S.

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]

S. Arnold and S. Holler, "Microparticle photophysics: fluorescence microscopy and spectroscopy of a photonic atom," Exp. Methods Phys. Sci. 40, 227-253 (2002).
[CrossRef]

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]

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, "Strain-tunable high-Q optical microsphere resonator," Opt. Commun. 145, 86-90 (1998).
[CrossRef]

Johnson, B. R.

Keng, D.

M. 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]

M. Noto, I. Teraoka, D. Keng, and S. Arnold, are preparing a manuscript entitled "Polarization sensitive biosensing using whispering gallery modes."

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, 4057-4049 (2002).
[CrossRef]

Klunder, D. J. W.

Krioukov, E.

Lefèvre-Seguin, V.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, "Strain-tunable high-Q optical microsphere resonator," Opt. Commun. 145, 86-90 (1998).
[CrossRef]

Libchaber, A.

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, 4057-4049 (2002).
[CrossRef]

Maleki, L.

Matsko, A. B.

Noto, M.

M. 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]

M. Noto, I. Teraoka, D. Keng, and S. Arnold, are preparing a manuscript entitled "Polarization sensitive biosensing using whispering gallery modes."

Otto, C.

Raimond, J.-M.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, "Strain-tunable high-Q optical microsphere resonator," Opt. Commun. 145, 86-90 (1998).
[CrossRef]

Richardson, C. B.

Savchenkov, A. A.

Serpengüzel, A.

Teraoka, I.

Treussart, F.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, "Strain-tunable high-Q optical microsphere resonator," Opt. Commun. 145, 86-90 (1998).
[CrossRef]

Velichansky, V. L.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, "Strain-tunable high-Q optical microsphere resonator," Opt. Commun. 145, 86-90 (1998).
[CrossRef]

Volikov, P. S.

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, "Strain-tunable high-Q optical microsphere resonator," Opt. Commun. 145, 86-90 (1998).
[CrossRef]

Vollmer, F.

Appl. Opt. (1)

Appl. Phys. Lett. (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, 4057-4049 (2002).
[CrossRef]

Biophys. J. (1)

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and S. Arnold, "Multiplexed DNA detection by optical resonances in microspheres," Biophys. J. 85, 1974-1979 (2003).
[CrossRef] [PubMed]

Exp. Methods Phys. Sci. (1)

S. Arnold and S. Holler, "Microparticle photophysics: fluorescence microscopy and spectroscopy of a photonic atom," Exp. Methods Phys. Sci. 40, 227-253 (2002).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

Opt. Commun. (1)

V. S. Ilchenko, P. S. Volikov, V. L. Velichansky, F. Treussart, V. Lefèvre-Seguin, J.-M. Raimond, and S. Haroche, "Strain-tunable high-Q optical microsphere resonator," Opt. Commun. 145, 86-90 (1998).
[CrossRef]

Opt. Lett. (4)

Other (1)

M. Noto, I. Teraoka, D. Keng, and S. Arnold, are preparing a manuscript entitled "Polarization sensitive biosensing using whispering gallery modes."

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 (8)

Fig. 1
Fig. 1

Radial function S l ( r ) compared for three radial modes ( v = 1 , 2 , 3 ) of a WGM in a microsphere ( n 1 = 1.452 ) of radius a = 100 μ m in water ( n 2 = 1.320 ) coupled to a laser operating at λ = 1.34 μ m . The mode numbers are l = 666 , 654 , 644 for v = 1 , 2 , 3 , respectively. To facilitate the comparison, S l ( r ) was normalized to have a unit height at r = a .

Fig. 2
Fig. 2

Variation of resonant wave vector k of a WGM with thickness t of the dielectric layer in a microsphere of n 1 = 1.452 (total radius, a = 100 μ m ). Refractive index n 3 of the layer is indicated adjacent to each curve. The mode orders are (a) v = 1 and (b) v = 2 .

Fig. 3
Fig. 3

Variation of decay rate Γ in the evanescent field with thickness t of the dielectric layer in a microsphere of n 1 = 1.452 (total radius, a = 100 μ m ) for the first radial mode. The refractive index n 3 of the layer is indicated adjacent to each curve.

Fig. 4
Fig. 4

Radial function S l ( r ) ( A l = 1 ) of the first radial mode in a microsphere with a dielectric layer of refractive index n 3 = 1.6 and a total radius of 100 μ m . The thickness t of the layer is indicated adjacent to each curve. The coating of t = 100 μ m indicates a plain microsphere of uniform refractive index n 3 .

Fig. 5
Fig. 5

Radial function S l ( r ) ( A l = 1 ) of the second radial mode in a microsphere with a dielectric layer of refractive index n 3 = 1.6 and a total radius of 100 μ m . Layer thickness t is indicated adjacent to each curve.

Fig. 6
Fig. 6

Responses (a) G RI and (b) G ads of a WGM to a uniform refractive-index change in the surround and adsorption of small particles at a low density, respectively, in a microsphere coated with a 0.1 μ m thick layer, plotted as a function of refractive index n 3 of the layer. The radial modes are 1, (solid curves), 2 (dotted curves), and 3 (dashed–dotted line).

Fig. 7
Fig. 7

Response G RI of a WGM resonance to a uniform refractive-index change in the surround in a coated microsphere, plotted as a function of layer thickness t. (a) First radial mode ( v = 1 ) , (b) second radial mode ( v = 2 ) . The refractive indices of the coating layer are 1.5, 1.55, 1.6, 1.65, and 1.7 in increasing order of height of the left-hand peak.

Fig. 8
Fig. 8

Response G RI in a microsphere of n 1 = 1.51 immersed in a medium of n 2 = 1.32 , plotted as a function of thickness t of coating layer n 3 = 1.7 . The radial modes are 1 (solid curve), 2 (dotted curve), and 3 (dashed–dotted curve).

Equations (31)

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

δ k k 0 = V p δ ϵ r E 0 * E p d r 2 V ϵ r E 0 * E 0 d r ,
Γ ( n 1 2 n 2 2 ) 1 2 k 0 ,
V p δ ϵ r E 0 * E p d r = E 0 ( r = a ) 2 V p β δ ϵ r d r ,
V p δ ϵ r E 0 * E p d r = β δ ϵ r V p E 0 ( r ) 2 d r .
E = exp ( i m φ ) k r S l ( r ) X l m ( θ ) ,
[ d 2 d r 2 l ( l + 1 ) r 2 ] S l = [ n ( r ) ] 2 k 2 S l ,
X l m ( θ ) = i m sin θ P l m ( cos θ ) e ̂ θ θ P l m ( cos θ ) e ̂ φ ,
n ( r ) = { n 1 r < a t n 3 a t < r < a n 2 a < r } .
S l ( r ) = { A l ψ l ( n 1 k r ) r < a t C l ψ l ( n 3 k r ) + D l χ l ( n 3 k r ) a t < r < a B l χ l ( n 2 k r ) a < r } ,
n 2 n 3 χ l ( n 2 k a ) χ l ( n 2 k a ) = ( C l D l ) ψ l ( n 3 k a ) + χ l ( n 3 k a ) ( C l D l ) ψ l ( n 3 k a ) + χ l ( n 3 k a ) ,
C l D l = n 3 ψ l ( z 1 ) χ l ( z 3 ) n 1 ψ l ( z 1 ) χ l ( z 3 ) n 3 ψ l ( z 1 ) ψ l ( z 3 ) + n 1 ψ l ( z 1 ) ψ l ( z 3 ) ,
w = 2 ( d γ d k ) k = k 0 ,
V ϵ r E 0 * d r = W k 2 0 [ n ( r ) S l ( r ) ] 2 d r ,
0 [ n ( r ) S l ( r ) ] 2 d r = n 1 2 I 1 + n 3 2 I 3 + n 2 2 I 2 ,
I 1 0 a t A l 2 [ ψ l ( n 1 k r ) ] 2 d r ,
I 3 = a t a [ C l ψ l ( n 3 k r ) + D l χ l ( n 3 k r ) ] 2 d r ,
I 2 0 B l 2 [ χ l ( n 2 k r ) ] 2 d r .
I 1 = ( A l 2 n 1 k ) Ψ l [ n 1 k ( a t ) ] ,
I 2 = ( B l 2 n 2 k ) X l ( n 2 k a ) ,
Ψ l ( z ) 0 z [ ψ l ( x ) ] 2 d x = { z ψ l 2 + [ l ( l + 1 ) z z ] ψ l 2 + ψ l ψ l } 2 ,
X l ( z ) z [ χ l ( x ) ] 2 d x = { z χ l 2 + [ l ( l + 1 ) z z ] χ l 2 + χ l χ l } 2 .
I 3 = I 3 a + I 3 b + I 3 c ,
I 3 a C l 2 a t a [ ψ l ( n 3 k r ) ] 2 d r = ( C l 2 n 3 k ) { Ψ l ( n 3 k a ) Ψ l [ n 3 k ( a t ) ] } ,
I 3 b 2 C l D l a t a ψ l ( n 3 k r ) χ l ( n 3 k r ) d r = ( 2 C l D l n 3 k ) { Ξ l ( n 3 k a ) Ξ l [ n 3 k ( a t ) ] } ,
I 3 c D l 2 a t a [ χ l ( n 3 k r ) ] 2 d r = ( D l 2 n 3 k ) { X l [ n 3 k ( a t ) ] X l ( n 3 k a ) } ,
Ξ l ( z ) ψ l ( z ) χ l ( z ) d z = const . + { [ z l ( l + 1 ) z ] ψ l χ l ( ψ l χ l + ψ l χ l ) 2 + z χ l ψ l } 2 .
V p δ ϵ r E 0 * E p d r = W k 2 δ ( n 2 ) l 2 .
G RI δ k k 0 δ ( n 2 ) = I 2 2 ( n 1 2 I 1 + n 3 2 I 3 + n 2 2 I 2 ) .
V p δ ϵ r E 0 * E p d r = 3 n 2 2 ( n p 2 n 2 2 ) n p 2 + 2 n 2 2 V p E 0 ( a , θ , ϕ ) 2 .
V p δ ϵ r E 0 * E p d r = 3 n 2 2 ( n p 2 n 2 2 ) n p 2 + 2 n 2 2 V p N p 4 π E 0 ( a , Ω ) 2 d Ω ,
G ads δ k k 0 [ 3 n 2 2 ( n p 2 n 2 2 ) n p 2 + 2 n 2 2 V p N p 4 π a 3 ] 1 = a [ S l ( a ) ] 2 2 ( n 1 2 I 1 + n 3 2 I 3 + n 2 2 I 2 ) .

Metrics