Abstract

The inelastic emission spectrum of a single fluorescent microsphere (bead) exhibits resonances arising from whispering gallery modes. Two beads in close proximity form a coupled bisphere. Coherent coupling arises from each bead’s evanescent field and leads to resonance splitting. Here we collect emission spectra of two coupled beads, with nearly identical diameters, as spacing between beads is varied. Using these size-matched beads allows us to probe resonance splitting under strong coupling conditions.

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References

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  1. C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124(6), 1807–1809 (1961).
    [CrossRef]
  2. H. Chew, “Transition rates of atoms near spherical surfaces,” J. Chem. Phys. 87(2), 1355–1360 (1987).
    [CrossRef]
  3. H. Chew, “Radiation and lifetimes of atoms inside dielectric particles,” Phys. Rev. A 38(7), 3410–3416 (1988).
    [CrossRef] [PubMed]
  4. J. A. Stratton, Electromagnetic Theory (McGraw Hill, New York, 1941), 554–567.
  5. A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38(23), 1351–1354 (1977).
    [CrossRef]
  6. R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structural resonances in the fluorescence spectra from microsphere,” Phys. Rev. Lett. 44(7), 475–478 (1980).
    [CrossRef]
  7. M. Kuwata-Gonokami and K. Takeda, “Polymer whispering gallery mode lasers,” Opt. Mater. 9(1-4), 12–17 (1998).
    [CrossRef]
  8. P. G. Schiro and A. S. Kwok, “Cavity-enhanced emission from a dye-coated microsphere,” Opt. Express 12(13), 2857–2863 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. S. Arnold, J. Comunale, W. B. Whitten, J. M. Ramsey, and K. A. Fuller, “Room-temperature microparticle-based persistent hole-burning spectroscopy,” J. Opt. Soc. Am. B 9(5), 819–824 (1992).
    [CrossRef]
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  12. M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
    [CrossRef]
  13. T. Mukaiyama, K Takeda, H Miyazaki, Y Jimba, and M Kuwata-Gonokami, “Tightbinding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
    [CrossRef]
  14. V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107(1-2), 41–48 (1994).
    [CrossRef]
  15. B. Möller, U. Woggon, and M. V. Artemyev, “Photons in coupled microsphere resonators,” J. Opt. A, Pure Appl. Opt. 8(4), S113–S121 (2006).
    [CrossRef]
  16. M. L. Povinelli, S. G. Johnson, M. Lonèar, M. Ibanescu, E. J. Smythe, F. Capasso, and J. Joannopoulos, “High-Q enhancement of attractive and repulsive optical forces between coupled whispering-gallery- mode resonators,” Opt. Express 13(20), 8286–8295 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
  18. J. Ng, C. T. Chan, P. Sheng, and Z. Lin, “Strong optical force induced by morphology-dependent resonances,” Opt. Lett. 30(15), 1956–1958 (2005).
    [CrossRef] [PubMed]

2007 (1)

P. Zijlstra, K. L. Van Der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90(16), 161101 (2007).
[CrossRef]

2006 (1)

B. Möller, U. Woggon, and M. V. Artemyev, “Photons in coupled microsphere resonators,” J. Opt. A, Pure Appl. Opt. 8(4), S113–S121 (2006).
[CrossRef]

2005 (2)

2004 (1)

2002 (1)

J. Bechhoefer and S. Wilson, “Faster, cheaper, safer optical tweezers for the undergraduate laboratory,” Am. J. Phys. 70(4), 393–400 (2002).
[CrossRef]

1999 (1)

T. Mukaiyama, K Takeda, H Miyazaki, Y Jimba, and M Kuwata-Gonokami, “Tightbinding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

1998 (2)

M. Kuwata-Gonokami and K. Takeda, “Polymer whispering gallery mode lasers,” Opt. Mater. 9(1-4), 12–17 (1998).
[CrossRef]

M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[CrossRef]

1994 (1)

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107(1-2), 41–48 (1994).
[CrossRef]

1992 (1)

1988 (1)

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

1987 (1)

H. Chew, “Transition rates of atoms near spherical surfaces,” J. Chem. Phys. 87(2), 1355–1360 (1987).
[CrossRef]

1980 (1)

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structural resonances in the fluorescence spectra from microsphere,” Phys. Rev. Lett. 44(7), 475–478 (1980).
[CrossRef]

1977 (1)

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38(23), 1351–1354 (1977).
[CrossRef]

1961 (1)

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124(6), 1807–1809 (1961).
[CrossRef]

Arnold, S.

Artemyev, M. V.

B. Möller, U. Woggon, and M. V. Artemyev, “Photons in coupled microsphere resonators,” J. Opt. A, Pure Appl. Opt. 8(4), S113–S121 (2006).
[CrossRef]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38(23), 1351–1354 (1977).
[CrossRef]

Barber, P. W.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structural resonances in the fluorescence spectra from microsphere,” Phys. Rev. Lett. 44(7), 475–478 (1980).
[CrossRef]

Bayer, M.

M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[CrossRef]

Bechhoefer, J.

J. Bechhoefer and S. Wilson, “Faster, cheaper, safer optical tweezers for the undergraduate laboratory,” Am. J. Phys. 70(4), 393–400 (2002).
[CrossRef]

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structural resonances in the fluorescence spectra from microsphere,” Phys. Rev. Lett. 44(7), 475–478 (1980).
[CrossRef]

Bond, W. L.

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124(6), 1807–1809 (1961).
[CrossRef]

Capasso, F.

Chan, C. T.

Chang, R. K.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structural resonances in the fluorescence spectra from microsphere,” Phys. Rev. Lett. 44(7), 475–478 (1980).
[CrossRef]

Chew, H.

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

H. Chew, “Transition rates of atoms near spherical surfaces,” J. Chem. Phys. 87(2), 1355–1360 (1987).
[CrossRef]

Comunale, J.

Dremin, A. A.

M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[CrossRef]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38(23), 1351–1354 (1977).
[CrossRef]

Forchel, A.

M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[CrossRef]

Fuller, K. A.

Garrett, C. G. B.

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124(6), 1807–1809 (1961).
[CrossRef]

Gorodetsky, M. L.

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107(1-2), 41–48 (1994).
[CrossRef]

Gutrod, T.

M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[CrossRef]

Ibanescu, M.

Ilchenko, V. S.

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107(1-2), 41–48 (1994).
[CrossRef]

Jimba, Y

T. Mukaiyama, K Takeda, H Miyazaki, Y Jimba, and M Kuwata-Gonokami, “Tightbinding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Joannopoulos, J.

Johnson, S. G.

Kaiser, W.

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124(6), 1807–1809 (1961).
[CrossRef]

Knipp, P. A.

M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[CrossRef]

Kulakovskii, V. D.

M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[CrossRef]

Kuwata-Gonokami, M

T. Mukaiyama, K Takeda, H Miyazaki, Y Jimba, and M Kuwata-Gonokami, “Tightbinding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Kuwata-Gonokami, M.

M. Kuwata-Gonokami and K. Takeda, “Polymer whispering gallery mode lasers,” Opt. Mater. 9(1-4), 12–17 (1998).
[CrossRef]

Kwok, A. S.

Lin, Z.

Lonèar, M.

Miyazaki, H

T. Mukaiyama, K Takeda, H Miyazaki, Y Jimba, and M Kuwata-Gonokami, “Tightbinding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Möller, B.

B. Möller, U. Woggon, and M. V. Artemyev, “Photons in coupled microsphere resonators,” J. Opt. A, Pure Appl. Opt. 8(4), S113–S121 (2006).
[CrossRef]

Mosk, A. P.

P. Zijlstra, K. L. Van Der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90(16), 161101 (2007).
[CrossRef]

Mukaiyama, T.

T. Mukaiyama, K Takeda, H Miyazaki, Y Jimba, and M Kuwata-Gonokami, “Tightbinding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Ng, J.

Owen, J. F.

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structural resonances in the fluorescence spectra from microsphere,” Phys. Rev. Lett. 44(7), 475–478 (1980).
[CrossRef]

Povinelli, M. L.

Ramsey, J. M.

Reinecke, T. L.

M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[CrossRef]

Reithmaier, J. P.

M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[CrossRef]

Schiro, P. G.

Sheng, P.

Smythe, E. J.

Takeda, K

T. Mukaiyama, K Takeda, H Miyazaki, Y Jimba, and M Kuwata-Gonokami, “Tightbinding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Takeda, K.

M. Kuwata-Gonokami and K. Takeda, “Polymer whispering gallery mode lasers,” Opt. Mater. 9(1-4), 12–17 (1998).
[CrossRef]

Van Der Molen, K. L.

P. Zijlstra, K. L. Van Der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90(16), 161101 (2007).
[CrossRef]

Vyatchanin, S. P.

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107(1-2), 41–48 (1994).
[CrossRef]

Whitten, W. B.

Wilson, S.

J. Bechhoefer and S. Wilson, “Faster, cheaper, safer optical tweezers for the undergraduate laboratory,” Am. J. Phys. 70(4), 393–400 (2002).
[CrossRef]

Woggon, U.

B. Möller, U. Woggon, and M. V. Artemyev, “Photons in coupled microsphere resonators,” J. Opt. A, Pure Appl. Opt. 8(4), S113–S121 (2006).
[CrossRef]

Zijlstra, P.

P. Zijlstra, K. L. Van Der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90(16), 161101 (2007).
[CrossRef]

Am. J. Phys. (1)

J. Bechhoefer and S. Wilson, “Faster, cheaper, safer optical tweezers for the undergraduate laboratory,” Am. J. Phys. 70(4), 393–400 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

P. Zijlstra, K. L. Van Der Molen, and A. P. Mosk, “Spatial refractive index sensor using whispering gallery modes in an optically trapped microsphere,” Appl. Phys. Lett. 90(16), 161101 (2007).
[CrossRef]

J. Chem. Phys. (1)

H. Chew, “Transition rates of atoms near spherical surfaces,” J. Chem. Phys. 87(2), 1355–1360 (1987).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

B. Möller, U. Woggon, and M. V. Artemyev, “Photons in coupled microsphere resonators,” J. Opt. A, Pure Appl. Opt. 8(4), S113–S121 (2006).
[CrossRef]

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

Opt. Commun. (1)

V. S. Ilchenko, M. L. Gorodetsky, and S. P. Vyatchanin, “Coupling and tunability of optical whispering-gallery modes: a basis for coordinate meter,” Opt. Commun. 107(1-2), 41–48 (1994).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Mater. (1)

M. Kuwata-Gonokami and K. Takeda, “Polymer whispering gallery mode lasers,” Opt. Mater. 9(1-4), 12–17 (1998).
[CrossRef]

Phys. Rev. (1)

C. G. B. Garrett, W. Kaiser, and W. L. Bond, “Stimulated emission into optical whispering modes of spheres,” Phys. Rev. 124(6), 1807–1809 (1961).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. Lett. (4)

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38(23), 1351–1354 (1977).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structural resonances in the fluorescence spectra from microsphere,” Phys. Rev. Lett. 44(7), 475–478 (1980).
[CrossRef]

M. Bayer, T. Gutrod, J. P. Reithmaier, A. Forchel, T. L. Reinecke, P. A. Knipp, A. A. Dremin, and V. D. Kulakovskii, “Optical Modes in Photonic Molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[CrossRef]

T. Mukaiyama, K Takeda, H Miyazaki, Y Jimba, and M Kuwata-Gonokami, “Tightbinding photonic molecule modes of resonant bispheres,” Phys. Rev. Lett. 82, 4623–4626 (1999).
[CrossRef]

Other (2)

J. A. Stratton, Electromagnetic Theory (McGraw Hill, New York, 1941), 554–567.

S. Arnold, and O. Gaathon, “Spectroscopy of photonic atoms: a means for ultra-sensitive specific sensing of bio-molecules,” in NATO Sci. Ser. II Math.231, B. di Bartolo and O. Forte, eds. (Springer, Netherlands, 2006).

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Figures (6)

Fig. 1
Fig. 1

Experiment schematic. Elements include: (A) IR trapping laser, (B) blue excitation laser, (C) polarized beamsplitters, (D) mirrors in motorized kinematic mounts, (E) dichroic mirror (reflect blue, transmit IR), (F) dichroic mirror (reflect blue and IR), (G) objective lens, (H) tube lens, (J) 30% reflecting mirror, (K) camera, (L) optic fiber connected to spectrometer. Telescopes and filters referred to in text are not shown.

Fig. 2
Fig. 2

Photographs of fluorescence emission from isolated beads matched in size. Photograph (a) shows the bead held stationary in Fig. 4, and photograph (b) shows the bead that is moved in Fig. 4.

Fig. 3
Fig. 3

Inelastic emission spectra of isolated beads shown in Fig. 2. The top spectrum corresponds to bead (a) with diameter 10.063 μm, and the bottom spectrum corresponds to bead (b) with diameter 10.065 μm. Resonance mode assignments are indicated.

Fig. 4
Fig. 4

Photographs of fluorescence emission from two beads matched in size. The top photograph shows the beads in contact, and the bottom photograph shows the beads close together but not in contact. To aid visualization in this article, a thin green ring has been overlaid upon the moving bead’s zero-order diffraction ring. The vertical arrow on the left (right) in each photograph identifies the left (right) edge of the beads’ first-order diffraction rings. The horizontal spacing between these edges is three pixels wider for the bottom photograph, compared to the top photograph. Thus, in the bottom photograph the beads are separated by 3 pixels x 0.114 μm/pixel = 0.34 μm.

Fig. 5
Fig. 5

Inelastic emission spectra of the stationary bead shown in Fig. 4, collected as the other bead is separated from it. The separation distance between beads for each spectrum is (a) 0, (b) 0.04 μm, (c) 0.19 μm, (d) 0.26 μm, (e) 0.38 μm, and (f) 0.98 μm.

Fig. 6
Fig. 6

Average TM and TE resonance splittings vs. bead separation distance. The square data points correspond to TM resonance splittings, and the circle data points correspond to TE resonance splittings, determined from the spectra in Fig. 5. The solid curves represent exponential decay functions Δλ = α exp (-x/r*) fitted to the TM and the TE data. These fits produced values r* = 0.69 μm for the TM data and r* = 0.70 μm for the TE data.

Equations (3)

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Δ λ / λ = 1 2 α .
α = ζ α n 3 2 exp ( x / r * ) ,
r * = λ / ( 2 π n p 2 n w 2 )

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