Abstract

This paper investigates the Q-factor limits imposed on the far-field detection of the whispering gallery modes of active microspherical resonators. It is shown that the Q-factor measured for a given active microsphere in the far-field using a microscope is significantly lower than that measured using evanescent field collection through a taper. The discrepancy is attributed to the inevitable small asphericity of microspheres that results in mode-splitting which becomes unresolvable in the far-field. Analytic expressions quantifying the Q-factor limits due to small levels of asphericity are subsequently derived.

© 2015 Optical Society of America

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References

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  1. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21(7), 453–455 (1996).
    [Crossref] [PubMed]
  2. T. J. Kippenberg, Nonlinear optics in ultra-high-Q whispering-gallery optical microcavities (CIT, 2004).
  3. K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
    [Crossref] [PubMed]
  4. A. François, N. Riesen, H. Ji, S. Afshar V., and T. M. Monro, “Polymer based whispering gallery mode laser for biosensing applications,” Appl. Phys. Lett. 106(3), 031104 (2015).
    [Crossref]
  5. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
    [Crossref] [PubMed]
  6. M. Himmelhaus and A. François, “In-vitro sensing of biomechanical forces in live cells by a whispering gallery mode biosensor,” Biosens. Bioelectron. 25(2), 418–427 (2009).
    [Crossref] [PubMed]
  7. M. A. Gouveia, P. D. Avila, T. H. R. Marques, M. C. Torres, and C. M. B. Cordeiro, “Morphology dependent polymeric capillary optical resonator hydrostatic pressure sensor,” Opt. Express 23(8), 10643–10652 (2015).
    [Crossref] [PubMed]
  8. B. E. Little, J.-P. Laine, and H. A. Haus, “Analytic theory of coupling from tapered fibers and half-blocks into microsphere resonators,” J. Lightwave Technol. 17(4), 704–715 (1999).
    [Crossref]
  9. Y. Zhi, J. Valenta, and A. Meldrum, “Structure of whispering gallery mode spectrum of microspheres coated with fluorescent silicon quantum dots,” J. Opt. Soc. Am. B 30(11), 3079–3085 (2013).
    [Crossref]
  10. H. T. Beier, G. L. Coté, and K. E. Meissner, “Modeling whispering gallery modes in quantum dot embedded polystyrene microspheres,” J. Opt. Soc. Am. B 27(3), 536–543 (2010).
    [Crossref]
  11. Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
    [Crossref] [PubMed]
  12. H.-H. Yu, C.-H. Yi, and C.-M. Kim, “Mechanism of Q-spoiling in deformed optical microcavities,” Opt. Express 23(9), 11054–11062 (2015).
    [Crossref] [PubMed]
  13. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41(9), 5187–5198 (1990).
    [Crossref] [PubMed]
  14. G. Kurizki, A. Kofman, A. Kozhekin, and G. Harel, “Control of atomic state decay in cavities and microspheres,” New J. Phys. 2, 28 (2000).
    [Crossref]
  15. K. Srinivasan, O. Painter, A. Stintz, and S. Krishna, “Single quantum dot spectroscopy using a fiber taper waveguide near-field optic,” Appl. Phys. Lett. 91(9), 091102 (2007).
    [Crossref]
  16. B. Redding, E. Marchena, T. Creazzo, S. Shi, and D. W. Prather, “Comparison of raised-microdisk whispering-gallery-mode characterization techniques,” Opt. Lett. 35(7), 998–1000 (2010).
    [Crossref] [PubMed]
  17. N. Riesen, S. Afshar V., A. François, and T. M. Monro, “Material candidates for optical frequency comb generation in microspheres,” Opt. Express 23(11), 14784–14795 (2015).
    [Crossref] [PubMed]
  18. J. Zhang, L. Xue, and Y. Han, “Fabrication gradient surfaces by changing polystyrene microsphere topography,” Langmuir 21(1), 5–8 (2005).
    [Crossref] [PubMed]
  19. H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38(7), 3410–3416 (1988).
    [Crossref] [PubMed]
  20. T. Reynolds, M. R. Henderson, A. François, N. Riesen, J. M. M. Hall, S. Afshar V., S. J. Nicholls, and T. M. Monro, “Optimization of whispering gallery resonator design for biosensing applications,” Opt. Express 23(13), 17067–17076 (2015).
    [Crossref] [PubMed]
  21. M. J. Humphrey, E. Dale, A. Rosenberger, and D. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271(1), 124–131 (2007).
    [Crossref]

2015 (6)

2013 (1)

2010 (2)

2009 (1)

M. Himmelhaus and A. François, “In-vitro sensing of biomechanical forces in live cells by a whispering gallery mode biosensor,” Biosens. Bioelectron. 25(2), 418–427 (2009).
[Crossref] [PubMed]

2008 (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

2007 (2)

K. Srinivasan, O. Painter, A. Stintz, and S. Krishna, “Single quantum dot spectroscopy using a fiber taper waveguide near-field optic,” Appl. Phys. Lett. 91(9), 091102 (2007).
[Crossref]

M. J. Humphrey, E. Dale, A. Rosenberger, and D. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271(1), 124–131 (2007).
[Crossref]

2005 (1)

J. Zhang, L. Xue, and Y. Han, “Fabrication gradient surfaces by changing polystyrene microsphere topography,” Langmuir 21(1), 5–8 (2005).
[Crossref] [PubMed]

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

2000 (1)

G. Kurizki, A. Kofman, A. Kozhekin, and G. Harel, “Control of atomic state decay in cavities and microspheres,” New J. Phys. 2, 28 (2000).
[Crossref]

1999 (1)

1996 (1)

1990 (1)

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41(9), 5187–5198 (1990).
[Crossref] [PubMed]

1988 (1)

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38(7), 3410–3416 (1988).
[Crossref] [PubMed]

Afshar V., S.

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

Avila, P. D.

Baaske, M. D.

Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
[Crossref] [PubMed]

Ballard, Z.

Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
[Crossref] [PubMed]

Bandy, D.

M. J. Humphrey, E. Dale, A. Rosenberger, and D. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271(1), 124–131 (2007).
[Crossref]

Barber, P. W.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41(9), 5187–5198 (1990).
[Crossref] [PubMed]

Beier, H. T.

Chew, H.

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38(7), 3410–3416 (1988).
[Crossref] [PubMed]

Cordeiro, C. M. B.

Coté, G. L.

Creazzo, T.

Dale, E.

M. J. Humphrey, E. Dale, A. Rosenberger, and D. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271(1), 124–131 (2007).
[Crossref]

François, A.

A. François, N. Riesen, H. Ji, S. Afshar V., and T. M. Monro, “Polymer based whispering gallery mode laser for biosensing applications,” Appl. Phys. Lett. 106(3), 031104 (2015).
[Crossref]

N. Riesen, S. Afshar V., A. François, and T. M. Monro, “Material candidates for optical frequency comb generation in microspheres,” Opt. Express 23(11), 14784–14795 (2015).
[Crossref] [PubMed]

T. Reynolds, M. R. Henderson, A. François, N. Riesen, J. M. M. Hall, S. Afshar V., S. J. Nicholls, and T. M. Monro, “Optimization of whispering gallery resonator design for biosensing applications,” Opt. Express 23(13), 17067–17076 (2015).
[Crossref] [PubMed]

M. Himmelhaus and A. François, “In-vitro sensing of biomechanical forces in live cells by a whispering gallery mode biosensor,” Biosens. Bioelectron. 25(2), 418–427 (2009).
[Crossref] [PubMed]

Gorodetsky, M. L.

Gouveia, M. A.

Hall, J. M. M.

Han, Y.

J. Zhang, L. Xue, and Y. Han, “Fabrication gradient surfaces by changing polystyrene microsphere topography,” Langmuir 21(1), 5–8 (2005).
[Crossref] [PubMed]

Harel, G.

G. Kurizki, A. Kofman, A. Kozhekin, and G. Harel, “Control of atomic state decay in cavities and microspheres,” New J. Phys. 2, 28 (2000).
[Crossref]

Haus, H. A.

Henderson, M. R.

Hill, S. C.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41(9), 5187–5198 (1990).
[Crossref] [PubMed]

Himmelhaus, M.

M. Himmelhaus and A. François, “In-vitro sensing of biomechanical forces in live cells by a whispering gallery mode biosensor,” Biosens. Bioelectron. 25(2), 418–427 (2009).
[Crossref] [PubMed]

Humphrey, M. J.

M. J. Humphrey, E. Dale, A. Rosenberger, and D. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271(1), 124–131 (2007).
[Crossref]

Ilchenko, V. S.

Ji, H.

A. François, N. Riesen, H. Ji, S. Afshar V., and T. M. Monro, “Polymer based whispering gallery mode laser for biosensing applications,” Appl. Phys. Lett. 106(3), 031104 (2015).
[Crossref]

Kim, C.-M.

Kofman, A.

G. Kurizki, A. Kofman, A. Kozhekin, and G. Harel, “Control of atomic state decay in cavities and microspheres,” New J. Phys. 2, 28 (2000).
[Crossref]

Kozhekin, A.

G. Kurizki, A. Kofman, A. Kozhekin, and G. Harel, “Control of atomic state decay in cavities and microspheres,” New J. Phys. 2, 28 (2000).
[Crossref]

Krishna, S.

K. Srinivasan, O. Painter, A. Stintz, and S. Krishna, “Single quantum dot spectroscopy using a fiber taper waveguide near-field optic,” Appl. Phys. Lett. 91(9), 091102 (2007).
[Crossref]

Kurizki, G.

G. Kurizki, A. Kofman, A. Kozhekin, and G. Harel, “Control of atomic state decay in cavities and microspheres,” New J. Phys. 2, 28 (2000).
[Crossref]

Lai, H. M.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41(9), 5187–5198 (1990).
[Crossref] [PubMed]

Laine, J.-P.

Leung, P. T.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41(9), 5187–5198 (1990).
[Crossref] [PubMed]

Little, B. E.

Marchena, E.

Marques, T. H. R.

Meissner, K. E.

Meldrum, A.

Monro, T. M.

Nicholls, S. J.

Painter, O.

K. Srinivasan, O. Painter, A. Stintz, and S. Krishna, “Single quantum dot spectroscopy using a fiber taper waveguide near-field optic,” Appl. Phys. Lett. 91(9), 091102 (2007).
[Crossref]

Prather, D. W.

Redding, B.

Reynolds, T.

Riesen, N.

Rosenberger, A.

M. J. Humphrey, E. Dale, A. Rosenberger, and D. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271(1), 124–131 (2007).
[Crossref]

Savchenkov, A. A.

Shi, S.

Srinivasan, K.

K. Srinivasan, O. Painter, A. Stintz, and S. Krishna, “Single quantum dot spectroscopy using a fiber taper waveguide near-field optic,” Appl. Phys. Lett. 91(9), 091102 (2007).
[Crossref]

Stintz, A.

K. Srinivasan, O. Painter, A. Stintz, and S. Krishna, “Single quantum dot spectroscopy using a fiber taper waveguide near-field optic,” Appl. Phys. Lett. 91(9), 091102 (2007).
[Crossref]

Torres, M. C.

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

Valenta, J.

Vollmer, F.

Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
[Crossref] [PubMed]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

Xue, L.

J. Zhang, L. Xue, and Y. Han, “Fabrication gradient surfaces by changing polystyrene microsphere topography,” Langmuir 21(1), 5–8 (2005).
[Crossref] [PubMed]

Yi, C.-H.

Young, K.

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41(9), 5187–5198 (1990).
[Crossref] [PubMed]

Yu, H.-H.

Zhang, J.

J. Zhang, L. Xue, and Y. Han, “Fabrication gradient surfaces by changing polystyrene microsphere topography,” Langmuir 21(1), 5–8 (2005).
[Crossref] [PubMed]

Zhi, Y.

Appl. Phys. Lett. (2)

A. François, N. Riesen, H. Ji, S. Afshar V., and T. M. Monro, “Polymer based whispering gallery mode laser for biosensing applications,” Appl. Phys. Lett. 106(3), 031104 (2015).
[Crossref]

K. Srinivasan, O. Painter, A. Stintz, and S. Krishna, “Single quantum dot spectroscopy using a fiber taper waveguide near-field optic,” Appl. Phys. Lett. 91(9), 091102 (2007).
[Crossref]

Biosens. Bioelectron. (1)

M. Himmelhaus and A. François, “In-vitro sensing of biomechanical forces in live cells by a whispering gallery mode biosensor,” Biosens. Bioelectron. 25(2), 418–427 (2009).
[Crossref] [PubMed]

J. Lightwave Technol. (1)

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

Langmuir (1)

J. Zhang, L. Xue, and Y. Han, “Fabrication gradient surfaces by changing polystyrene microsphere topography,” Langmuir 21(1), 5–8 (2005).
[Crossref] [PubMed]

Nat. Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

Nature (1)

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

New J. Phys. (1)

G. Kurizki, A. Kofman, A. Kozhekin, and G. Harel, “Control of atomic state decay in cavities and microspheres,” New J. Phys. 2, 28 (2000).
[Crossref]

Opt. Commun. (1)

M. J. Humphrey, E. Dale, A. Rosenberger, and D. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. 271(1), 124–131 (2007).
[Crossref]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. A (2)

H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38(7), 3410–3416 (1988).
[Crossref] [PubMed]

H. M. Lai, P. T. Leung, K. Young, P. W. Barber, and S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41(9), 5187–5198 (1990).
[Crossref] [PubMed]

Sensors (Basel) (1)

Z. Ballard, M. D. Baaske, and F. Vollmer, “Stand-off biodetection with free-space coupled asymmetric microsphere cavities,” Sensors (Basel) 15(4), 8968–8980 (2015).
[Crossref] [PubMed]

Other (1)

T. J. Kippenberg, Nonlinear optics in ultra-high-Q whispering-gallery optical microcavities (CIT, 2004).

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Figures (4)

Fig. 1
Fig. 1 (a)-(b) Whispering gallery mode spectra sampled in the far-field (red) and via the taper (black) of the same dye-doped polystyrene microsphere excited with free-space illumination. The measurements were taken simultaneously at the same pump power. (c) A closer look at the whispering gallery mode spectra of the polystyrene microsphere, and signs of mode-splitting for far-field collection (inset). (d) Microscope images showing the taper and attached microsphere under free-space excitation.
Fig. 2
Fig. 2 (a) Whispering gallery mode spectra sampled in the far-field of the same dye-doped polystyrene microsphere excited with either the taper (green) or with free-space illumination (red). (b) Microscope images showing taper excitation of the microsphere with the pump wavelength removed using a dichroic filter.
Fig. 3
Fig. 3 (a) Depiction of the fiber taper and far-field collection of the WGM signal of the microsphere. Quantification of the spoiling of the Q-factor of an active microsphere when using far-field excitation and collection by (b) modelling the wavelength shift over a range of radii Δρ of a perfect microsphere or (c) the wavelength shift associated with mode-splitting for given levels of ellipticity ε. The inset of (b) shows the Q-factor spoiling occurring for a Gaussian distribution of radii with mean 7.5 μm and standard deviation σ = 0.5 nm modelled using the Chew model [19, 20]. Here the dark blue curve is the fundamental mode for a perfect sphere, whereas the light blue peaks are the non-degenerate fundamental (m = l) modes for an aspherical resonator, which overlap to yield linewidth broadening as suggested by the red Gaussian fit.
Fig. 4
Fig. 4 (a) Low resolution scanning electron microscope (SEM) image of a 15 µm polystyrene microsphere. Inset shows the same sphere when excited by the taper (b) Corresponding two color threshold image with an ellipse fit shown (red line).

Equations (2)

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Q FF = ω Δω ρ Δρ
Δω ω = ε 6 ( 3 m 2 l 2 1 )

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