Abstract

We model fluorescence images of single molecules in spherical dielectric microcavities. Molecules are treated as time-harmonic dipoles. Images are integrated over emission frequencies. Because of the strong refractive properties of the enclosing sphere, the fluorescence image depends on the refractive index of the sphere and the position, the orientation, and the emission frequency of the molecule. When the dipole’s emission is at the frequency of a microsphere resonance, the brightest regions in the images appear to originate from outside the sphere for some dipole positions. This type of calculation should help in interpreting images of molecules in microspheres.

© 1999 Optical Society of America

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    [CrossRef] [PubMed]
  2. J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
    [CrossRef]
  3. W. E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
    [CrossRef] [PubMed]
  4. D. J. Norris, M. Kuwata-Gonokami, and W. E. Moerner, “Excitation of a single molecule on the surface of a spherical microcavity,” Appl. Phys. Lett. 71, 297–299 (1997).
    [CrossRef]
  5. M. D. Barnes, K. C. Ng, K. P. McNamara, C.-Y. Kung, J. M. Ramsey, and S. C. Hill, “Fluorescence imaging of single molecules in polymer microspheres,” Cytometry 36, 169–175 (1999).
    [CrossRef] [PubMed]
  6. S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
    [CrossRef] [PubMed]
  7. J.-Z. Zhang, G. Chen, and R. K. Chang, “Pumping of stimulated Raman scattering by stimulated Brillouin scattering within a single liquid droplet: input laser linewidth effects,” J. Opt. Soc. Am. B 7, 108–115 (1990).
    [CrossRef]
  8. S. Arnold and L. M. Folan, “Microphotography of an electrodynamically levitated particle,” Proc. SPIE 1862, 218–222 (1993).
    [CrossRef]
  9. S. Arnold, S. Holler, and S. D. Druger, “Imaging enhanced energy transfer in a levitated aerosol particle,” J. Chem. Phys. 104, 7741–7748 (1996).
    [CrossRef]
  10. M. Winter and L. A. Melton, “Measurement of internal circulation in droplets using laser-induced fluorescence,” Appl. Opt. 29, 4574–4577 (1990).
    [CrossRef] [PubMed]
  11. S. R. Harris, W. R. Lempert, L. Hersch, C. L. Burcham, D. A. Saville, and R. B. Miles, “Quantitative measurements of internal circulation in droplets using flow tagging velocimetry,” AIAA J. 34, 449–454 (1996).
    [CrossRef]
  12. M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
    [CrossRef] [PubMed]
  13. J. A. Lock, “Theory of the observations made of high-order rainbows from a single water droplet,” Appl. Opt. 26, 5291–5298 (1987).
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  16. S. Arnold, S. Holler, J. H. Li, A. Serpenguzel, W. F. Auffermann, and S. C. Hill, “Aerosol particle microphotography and glare-spot absorption spectroscopy,” Opt. Lett 20, 773–775 (1995).
    [CrossRef] [PubMed]
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    [CrossRef]
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  20. M. D. Barnes, W. B. Whitten, S. Arnold, and J. M. Ramsey, “Homogeneous linewidths of rhodamine 6G at room temperature from cavity enhanced spontaneous emission rates,” J. Chem. Phys. 97, 7842–7845 (1992).
    [CrossRef]
  21. H.-B. Lin, J. D. Eversole, C. D. Merrit, and A. J. Campillo, “Cavity-modified spontaneous emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
    [CrossRef] [PubMed]
  22. N. Lermer, M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, and S. C. Hill, “Spatial photoselection of single molecules on the surface of a spherical microcavity,” Opt. Lett. 23, 951–953 (1998).
    [CrossRef]
  23. C.-Y. Kung, M. D. Barnes, N. Lermer, W. B. Whitten, and J. M. Ramsey, “Single molecule analysis of ultradilute solutions with guided streams of 1-μm water droplets,” Appl. Opt. 38, 1481–1487 (1999).
    [CrossRef]
  24. H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
    [CrossRef]
  25. S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency,” Appl. Opt. 35, 6278–6288 (1996).
    [CrossRef] [PubMed]
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  29. We obtain this Green function by rewriting Eq. (A7) of Ref. 25, eliminating fvG, gνG, cvH, and dvH using Eqs. (A4), (A5), (A10), and (A11), and eliminating the integral over source points.
  30. The advantage of choosing the z axis to pass through the dipole, and thereby limiting the required m to 0 and 1, is that it provides a way to obtain images for relatively large spheres without computation of the angular functions and coefficients for all m up to n (and without exceeding the available computer storage if these are saved). The disadvantage is that it requires more manipulation and coordinate transformations afterward.
  31. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999), p. 484.
  32. J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
    [CrossRef]
  33. E. E. M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chowdhury, “Near-resonance excitation of morphology dependent resonances with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
    [CrossRef] [PubMed]
  34. J. A. Lock, “Excitation efficiency of a morphology-dependent resonance by a focused Gaussian beam,” J. Opt. Soc. Am. A 15, 2986–2994 (1998).
    [CrossRef]
  35. H.-B. Lin, J. D. Eversole, A. J. Campillo, and J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. 23, 1921–1923 (1998).
    [CrossRef]
  36. S. C. Hill, G. Videen, and J. D. Pendleton, “Reciprocity method for obtaining the far fields generated by a source inside or near a scattering object,” J. Opt. Soc. Am. B 14, 2522–2529 (1997).
    [CrossRef]
  37. N. Velesco and G. Schweiger, “Geometrical optics calculations of inelastic scattering on large particles,” Appl. Opt. 38, 1046–1052 (1999).
    [CrossRef]
  38. If m=1 (i.e., there is no sphere) and Θ=165°, then by the lens law the image plane should be at zL2=3.52 mm. The calculated images have spot sizes that do not vary markedly between zL 2 values of 2.5 and 4.5 mm.

1999

W. E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
[CrossRef] [PubMed]

M. D. Barnes, K. C. Ng, K. P. McNamara, C.-Y. Kung, J. M. Ramsey, and S. C. Hill, “Fluorescence imaging of single molecules in polymer microspheres,” Cytometry 36, 169–175 (1999).
[CrossRef] [PubMed]

C.-Y. Kung, M. D. Barnes, N. Lermer, W. B. Whitten, and J. M. Ramsey, “Single molecule analysis of ultradilute solutions with guided streams of 1-μm water droplets,” Appl. Opt. 38, 1481–1487 (1999).
[CrossRef]

N. Velesco and G. Schweiger, “Geometrical optics calculations of inelastic scattering on large particles,” Appl. Opt. 38, 1046–1052 (1999).
[CrossRef]

1998

1997

S. C. Hill, G. Videen, and J. D. Pendleton, “Reciprocity method for obtaining the far fields generated by a source inside or near a scattering object,” J. Opt. Soc. Am. B 14, 2522–2529 (1997).
[CrossRef]

D. J. Norris, M. Kuwata-Gonokami, and W. E. Moerner, “Excitation of a single molecule on the surface of a spherical microcavity,” Appl. Phys. Lett. 71, 297–299 (1997).
[CrossRef]

1996

R. M. Dickson, D. J. Norris, Y.-L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

S. Arnold, S. Holler, and S. D. Druger, “Imaging enhanced energy transfer in a levitated aerosol particle,” J. Chem. Phys. 104, 7741–7748 (1996).
[CrossRef]

S. R. Harris, W. R. Lempert, L. Hersch, C. L. Burcham, D. A. Saville, and R. B. Miles, “Quantitative measurements of internal circulation in droplets using flow tagging velocimetry,” AIAA J. 34, 449–454 (1996).
[CrossRef]

M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
[CrossRef] [PubMed]

S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency,” Appl. Opt. 35, 6278–6288 (1996).
[CrossRef] [PubMed]

1995

S. Arnold, S. Holler, J. H. Li, A. Serpenguzel, W. F. Auffermann, and S. C. Hill, “Aerosol particle microphotography and glare-spot absorption spectroscopy,” Opt. Lett 20, 773–775 (1995).
[CrossRef] [PubMed]

1993

S. Arnold and L. M. Folan, “Microphotography of an electrodynamically levitated particle,” Proc. SPIE 1862, 218–222 (1993).
[CrossRef]

1992

S. A. Schaub, D. R. Alexander, and J. P. Barton, “Glare spot image calculations for a spherical particle illuminated by a tightly focused beam,” J. Opt. Soc. Am. A 9, 316–330 (1992).
[CrossRef]

E. E. M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chowdhury, “Near-resonance excitation of morphology dependent resonances with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
[CrossRef] [PubMed]

M. D. Barnes, W. B. Whitten, S. Arnold, and J. M. Ramsey, “Homogeneous linewidths of rhodamine 6G at room temperature from cavity enhanced spontaneous emission rates,” J. Chem. Phys. 97, 7842–7845 (1992).
[CrossRef]

H.-B. Lin, J. D. Eversole, C. D. Merrit, and A. J. Campillo, “Cavity-modified spontaneous emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
[CrossRef] [PubMed]

1991

1990

1989

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

1987

1986

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
[CrossRef] [PubMed]

1976

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

Alexander, D. R.

Arnold, S.

M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
[CrossRef] [PubMed]

S. Arnold, S. Holler, and S. D. Druger, “Imaging enhanced energy transfer in a levitated aerosol particle,” J. Chem. Phys. 104, 7741–7748 (1996).
[CrossRef]

S. Arnold, S. Holler, J. H. Li, A. Serpenguzel, W. F. Auffermann, and S. C. Hill, “Aerosol particle microphotography and glare-spot absorption spectroscopy,” Opt. Lett 20, 773–775 (1995).
[CrossRef] [PubMed]

S. Arnold and L. M. Folan, “Microphotography of an electrodynamically levitated particle,” Proc. SPIE 1862, 218–222 (1993).
[CrossRef]

M. D. Barnes, W. B. Whitten, S. Arnold, and J. M. Ramsey, “Homogeneous linewidths of rhodamine 6G at room temperature from cavity enhanced spontaneous emission rates,” J. Chem. Phys. 97, 7842–7845 (1992).
[CrossRef]

Auffermann, W. F.

S. Arnold, S. Holler, J. H. Li, A. Serpenguzel, W. F. Auffermann, and S. C. Hill, “Aerosol particle microphotography and glare-spot absorption spectroscopy,” Opt. Lett 20, 773–775 (1995).
[CrossRef] [PubMed]

Barber, P. W.

Barnes, M. D.

C.-Y. Kung, M. D. Barnes, N. Lermer, W. B. Whitten, and J. M. Ramsey, “Single molecule analysis of ultradilute solutions with guided streams of 1-μm water droplets,” Appl. Opt. 38, 1481–1487 (1999).
[CrossRef]

M. D. Barnes, K. C. Ng, K. P. McNamara, C.-Y. Kung, J. M. Ramsey, and S. C. Hill, “Fluorescence imaging of single molecules in polymer microspheres,” Cytometry 36, 169–175 (1999).
[CrossRef] [PubMed]

N. Lermer, M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, and S. C. Hill, “Spatial photoselection of single molecules on the surface of a spherical microcavity,” Opt. Lett. 23, 951–953 (1998).
[CrossRef]

S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency,” Appl. Opt. 35, 6278–6288 (1996).
[CrossRef] [PubMed]

M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
[CrossRef] [PubMed]

M. D. Barnes, W. B. Whitten, S. Arnold, and J. M. Ramsey, “Homogeneous linewidths of rhodamine 6G at room temperature from cavity enhanced spontaneous emission rates,” J. Chem. Phys. 97, 7842–7845 (1992).
[CrossRef]

Barton, J. P.

Brus, L. E.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

Burcham, C. L.

S. R. Harris, W. R. Lempert, L. Hersch, C. L. Burcham, D. A. Saville, and R. B. Miles, “Quantitative measurements of internal circulation in droplets using flow tagging velocimetry,” AIAA J. 34, 449–454 (1996).
[CrossRef]

Campillo, A. J.

H.-B. Lin, J. D. Eversole, A. J. Campillo, and J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. 23, 1921–1923 (1998).
[CrossRef]

H.-B. Lin, J. D. Eversole, C. D. Merrit, and A. J. Campillo, “Cavity-modified spontaneous emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
[CrossRef] [PubMed]

Chang, R. K.

Chen, G.

Chew, H.

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

Chowdhury, D. Q.

Dickson, R. M.

R. M. Dickson, D. J. Norris, Y.-L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

Druger, S. D.

S. Arnold, S. Holler, and S. D. Druger, “Imaging enhanced energy transfer in a levitated aerosol particle,” J. Chem. Phys. 104, 7741–7748 (1996).
[CrossRef]

Eversole, J. D.

H.-B. Lin, J. D. Eversole, A. J. Campillo, and J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. 23, 1921–1923 (1998).
[CrossRef]

H.-B. Lin, J. D. Eversole, C. D. Merrit, and A. J. Campillo, “Cavity-modified spontaneous emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
[CrossRef] [PubMed]

Folan, L. M.

S. Arnold and L. M. Folan, “Microphotography of an electrodynamically levitated particle,” Proc. SPIE 1862, 218–222 (1993).
[CrossRef]

Harris, S. R.

S. R. Harris, W. R. Lempert, L. Hersch, C. L. Burcham, D. A. Saville, and R. B. Miles, “Quantitative measurements of internal circulation in droplets using flow tagging velocimetry,” AIAA J. 34, 449–454 (1996).
[CrossRef]

Harris, T. D.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

Hersch, L.

S. R. Harris, W. R. Lempert, L. Hersch, C. L. Burcham, D. A. Saville, and R. B. Miles, “Quantitative measurements of internal circulation in droplets using flow tagging velocimetry,” AIAA J. 34, 449–454 (1996).
[CrossRef]

Hill, S. C.

Holler, S.

M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
[CrossRef] [PubMed]

S. Arnold, S. Holler, and S. D. Druger, “Imaging enhanced energy transfer in a levitated aerosol particle,” J. Chem. Phys. 104, 7741–7748 (1996).
[CrossRef]

S. Arnold, S. Holler, J. H. Li, A. Serpenguzel, W. F. Auffermann, and S. C. Hill, “Aerosol particle microphotography and glare-spot absorption spectroscopy,” Opt. Lett 20, 773–775 (1995).
[CrossRef] [PubMed]

Kerker, M.

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

Khaled, E. E. M.

Kung, C.-Y.

C.-Y. Kung, M. D. Barnes, N. Lermer, W. B. Whitten, and J. M. Ramsey, “Single molecule analysis of ultradilute solutions with guided streams of 1-μm water droplets,” Appl. Opt. 38, 1481–1487 (1999).
[CrossRef]

M. D. Barnes, K. C. Ng, K. P. McNamara, C.-Y. Kung, J. M. Ramsey, and S. C. Hill, “Fluorescence imaging of single molecules in polymer microspheres,” Cytometry 36, 169–175 (1999).
[CrossRef] [PubMed]

N. Lermer, M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, and S. C. Hill, “Spatial photoselection of single molecules on the surface of a spherical microcavity,” Opt. Lett. 23, 951–953 (1998).
[CrossRef]

M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
[CrossRef] [PubMed]

Kuwata-Gonokami, M.

D. J. Norris, M. Kuwata-Gonokami, and W. E. Moerner, “Excitation of a single molecule on the surface of a spherical microcavity,” Appl. Phys. Lett. 71, 297–299 (1997).
[CrossRef]

Lempert, W. R.

S. R. Harris, W. R. Lempert, L. Hersch, C. L. Burcham, D. A. Saville, and R. B. Miles, “Quantitative measurements of internal circulation in droplets using flow tagging velocimetry,” AIAA J. 34, 449–454 (1996).
[CrossRef]

Lermer, N.

Li, J. H.

S. Arnold, S. Holler, J. H. Li, A. Serpenguzel, W. F. Auffermann, and S. C. Hill, “Aerosol particle microphotography and glare-spot absorption spectroscopy,” Opt. Lett 20, 773–775 (1995).
[CrossRef] [PubMed]

Lin, H.-B.

H.-B. Lin, J. D. Eversole, A. J. Campillo, and J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. 23, 1921–1923 (1998).
[CrossRef]

H.-B. Lin, J. D. Eversole, C. D. Merrit, and A. J. Campillo, “Cavity-modified spontaneous emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
[CrossRef] [PubMed]

Lock, J. A.

Macklin, J. J.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

McNamara, K. P.

M. D. Barnes, K. C. Ng, K. P. McNamara, C.-Y. Kung, J. M. Ramsey, and S. C. Hill, “Fluorescence imaging of single molecules in polymer microspheres,” Cytometry 36, 169–175 (1999).
[CrossRef] [PubMed]

McNulty, P. J.

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

Melton, L. A.

M. Winter and L. A. Melton, “Measurement of internal circulation in droplets using laser-induced fluorescence,” Appl. Opt. 29, 4574–4577 (1990).
[CrossRef] [PubMed]

J. Zhang and L. A. Melton, “Numerical simulations and restorations of laser droplet-slicing images,” Appl. Opt. 334, 192–200 (1990).

Merrit, C. D.

H.-B. Lin, J. D. Eversole, C. D. Merrit, and A. J. Campillo, “Cavity-modified spontaneous emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
[CrossRef] [PubMed]

Miles, R. B.

S. R. Harris, W. R. Lempert, L. Hersch, C. L. Burcham, D. A. Saville, and R. B. Miles, “Quantitative measurements of internal circulation in droplets using flow tagging velocimetry,” AIAA J. 34, 449–454 (1996).
[CrossRef]

Moerner, W. E.

W. E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
[CrossRef] [PubMed]

D. J. Norris, M. Kuwata-Gonokami, and W. E. Moerner, “Excitation of a single molecule on the surface of a spherical microcavity,” Appl. Phys. Lett. 71, 297–299 (1997).
[CrossRef]

R. M. Dickson, D. J. Norris, Y.-L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

Ng, K. C.

M. D. Barnes, K. C. Ng, K. P. McNamara, C.-Y. Kung, J. M. Ramsey, and S. C. Hill, “Fluorescence imaging of single molecules in polymer microspheres,” Cytometry 36, 169–175 (1999).
[CrossRef] [PubMed]

Norris, D. J.

D. J. Norris, M. Kuwata-Gonokami, and W. E. Moerner, “Excitation of a single molecule on the surface of a spherical microcavity,” Appl. Phys. Lett. 71, 297–299 (1997).
[CrossRef]

R. M. Dickson, D. J. Norris, Y.-L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

Orrit, M.

W. E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
[CrossRef] [PubMed]

Pendleton, J. D.

Qian, S.-X.

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
[CrossRef] [PubMed]

Ramsey, J. M.

M. D. Barnes, K. C. Ng, K. P. McNamara, C.-Y. Kung, J. M. Ramsey, and S. C. Hill, “Fluorescence imaging of single molecules in polymer microspheres,” Cytometry 36, 169–175 (1999).
[CrossRef] [PubMed]

C.-Y. Kung, M. D. Barnes, N. Lermer, W. B. Whitten, and J. M. Ramsey, “Single molecule analysis of ultradilute solutions with guided streams of 1-μm water droplets,” Appl. Opt. 38, 1481–1487 (1999).
[CrossRef]

N. Lermer, M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, and S. C. Hill, “Spatial photoselection of single molecules on the surface of a spherical microcavity,” Opt. Lett. 23, 951–953 (1998).
[CrossRef]

S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency,” Appl. Opt. 35, 6278–6288 (1996).
[CrossRef] [PubMed]

M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
[CrossRef] [PubMed]

M. D. Barnes, W. B. Whitten, S. Arnold, and J. M. Ramsey, “Homogeneous linewidths of rhodamine 6G at room temperature from cavity enhanced spontaneous emission rates,” J. Chem. Phys. 97, 7842–7845 (1992).
[CrossRef]

Saleheen, H. I.

Saville, D. A.

S. R. Harris, W. R. Lempert, L. Hersch, C. L. Burcham, D. A. Saville, and R. B. Miles, “Quantitative measurements of internal circulation in droplets using flow tagging velocimetry,” AIAA J. 34, 449–454 (1996).
[CrossRef]

Schaub, S. A.

Schweiger, G.

Serpenguzel, A.

S. Arnold, S. Holler, J. H. Li, A. Serpenguzel, W. F. Auffermann, and S. C. Hill, “Aerosol particle microphotography and glare-spot absorption spectroscopy,” Opt. Lett 20, 773–775 (1995).
[CrossRef] [PubMed]

Snow, J. B.

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
[CrossRef] [PubMed]

Trautman, J. K.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

Tzeng, H.-M.

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
[CrossRef] [PubMed]

Tzeng, Y.-L.

R. M. Dickson, D. J. Norris, Y.-L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

van de Hulst, H. C.

Velesco, N.

Videen, G.

Wang, R. T.

Whitten, W. B.

Winter, M.

Zhang, J.

J. Zhang and L. A. Melton, “Numerical simulations and restorations of laser droplet-slicing images,” Appl. Opt. 334, 192–200 (1990).

Zhang, J.-Z.

AIAA J.

S. R. Harris, W. R. Lempert, L. Hersch, C. L. Burcham, D. A. Saville, and R. B. Miles, “Quantitative measurements of internal circulation in droplets using flow tagging velocimetry,” AIAA J. 34, 449–454 (1996).
[CrossRef]

Appl. Opt.

J. Zhang and L. A. Melton, “Numerical simulations and restorations of laser droplet-slicing images,” Appl. Opt. 334, 192–200 (1990).

J. A. Lock, “Theory of the observations made of high-order rainbows from a single water droplet,” Appl. Opt. 26, 5291–5298 (1987).
[CrossRef] [PubMed]

M. Winter and L. A. Melton, “Measurement of internal circulation in droplets using laser-induced fluorescence,” Appl. Opt. 29, 4574–4577 (1990).
[CrossRef] [PubMed]

H. C. van de Hulst and R. T. Wang, “Glare points,” Appl. Opt. 30, 4755–4763 (1991).
[CrossRef] [PubMed]

S. A. Schaub, D. R. Alexander, and J. P. Barton, “Theoretical model of the laser imaging of small aerosols: applications to aerosol sizing,” Appl. Opt. 30, 4777–4784 (1991).
[CrossRef] [PubMed]

N. Velesco and G. Schweiger, “Geometrical optics calculations of inelastic scattering on large particles,” Appl. Opt. 38, 1046–1052 (1999).
[CrossRef]

C.-Y. Kung, M. D. Barnes, N. Lermer, W. B. Whitten, and J. M. Ramsey, “Single molecule analysis of ultradilute solutions with guided streams of 1-μm water droplets,” Appl. Opt. 38, 1481–1487 (1999).
[CrossRef]

S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, and J. M. Ramsey, “Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency,” Appl. Opt. 35, 6278–6288 (1996).
[CrossRef] [PubMed]

E. E. M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chowdhury, “Near-resonance excitation of morphology dependent resonances with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
[CrossRef] [PubMed]

Appl. Phys. Lett.

D. J. Norris, M. Kuwata-Gonokami, and W. E. Moerner, “Excitation of a single molecule on the surface of a spherical microcavity,” Appl. Phys. Lett. 71, 297–299 (1997).
[CrossRef]

Cytometry

M. D. Barnes, K. C. Ng, K. P. McNamara, C.-Y. Kung, J. M. Ramsey, and S. C. Hill, “Fluorescence imaging of single molecules in polymer microspheres,” Cytometry 36, 169–175 (1999).
[CrossRef] [PubMed]

J. Appl. Phys.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

J. Chem. Phys.

S. Arnold, S. Holler, and S. D. Druger, “Imaging enhanced energy transfer in a levitated aerosol particle,” J. Chem. Phys. 104, 7741–7748 (1996).
[CrossRef]

M. D. Barnes, W. B. Whitten, S. Arnold, and J. M. Ramsey, “Homogeneous linewidths of rhodamine 6G at room temperature from cavity enhanced spontaneous emission rates,” J. Chem. Phys. 97, 7842–7845 (1992).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Lett

S. Arnold, S. Holler, J. H. Li, A. Serpenguzel, W. F. Auffermann, and S. C. Hill, “Aerosol particle microphotography and glare-spot absorption spectroscopy,” Opt. Lett 20, 773–775 (1995).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

H. Chew, P. J. McNulty, and M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

H.-B. Lin, J. D. Eversole, C. D. Merrit, and A. J. Campillo, “Cavity-modified spontaneous emission rates in liquid microdroplets,” Phys. Rev. A 45, 6756–6760 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett.

M. D. Barnes, C.-Y. Kung, W. B. Whitten, J. M. Ramsey, S. Arnold, and S. Holler, “Fluorescence of oriented molecules in a microcavity,” Phys. Rev. Lett. 76, 3931–3934 (1996).
[CrossRef] [PubMed]

Proc. SPIE

S. Arnold and L. M. Folan, “Microphotography of an electrodynamically levitated particle,” Proc. SPIE 1862, 218–222 (1993).
[CrossRef]

Science

S.-X. Qian, J. B. Snow, H.-M. Tzeng, and R. K. Chang, “Lasing droplets: highlighting the liquid–air interface by laser emission,” Science 231, 486–488 (1986).
[CrossRef] [PubMed]

R. M. Dickson, D. J. Norris, Y.-L. Tzeng, and W. E. Moerner, “Three-dimensional imaging of single molecules solvated in pores of poly(acrylamide) gels,” Science 274, 966–969 (1996).
[CrossRef] [PubMed]

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Imaging and time-resolved spectroscopy of single molecules at an interface,” Science 272, 255–258 (1996).
[CrossRef]

W. E. Moerner and M. Orrit, “Illuminating single molecules in condensed matter,” Science 283, 1670–1676 (1999).
[CrossRef] [PubMed]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1998), p. 128.

C. R. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), p. 89.

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), p. 84.

We obtain this Green function by rewriting Eq. (A7) of Ref. 25, eliminating fvG, gνG, cvH, and dvH using Eqs. (A4), (A5), (A10), and (A11), and eliminating the integral over source points.

The advantage of choosing the z axis to pass through the dipole, and thereby limiting the required m to 0 and 1, is that it provides a way to obtain images for relatively large spheres without computation of the angular functions and coefficients for all m up to n (and without exceeding the available computer storage if these are saved). The disadvantage is that it requires more manipulation and coordinate transformations afterward.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999), p. 484.

If m=1 (i.e., there is no sphere) and Θ=165°, then by the lens law the image plane should be at zL2=3.52 mm. The calculated images have spot sizes that do not vary markedly between zL 2 values of 2.5 and 4.5 mm.

R. K. Chang and A. J. Campillo, Optical Processes in Microcavities (World Scientific, Singapore, 1996).

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Figures (4)

Fig. 1
Fig. 1

Diagram in the y=0 plane that shows the sphere, the dipole (shown as short arrow), the lens, and the axes. The y-axis points into the page in all three coordinate systems. The lens converts the diverging spherical wave on S1 into the converging spherical wave on S2. The dipole is always on the z axis of the sphere/dipole system. The image is centered on the zL2 axis.

Fig. 2
Fig. 2

Calculated images of a dipole at r/a=0.9999 in a 5-µm-diameter sphere of refractive index 1.454. The lens (0.5 NA) is 90° from the z axis. The image plane is at the origin of the L2 coordinate system. The horizontal axis is yL2/aM, and the vertical axis is xL2/aM. The dotted circle in the top row, third column, shows where the edge of the sphere would be imaged in the geometrical optics limit. The dipole is polarized in the z (parallel to xL2), x (zL2), and y (yL2) directions, in the top, middle, and bottom rows, respectively. In the first column the emission is integrated over frequency from 16367 cm-1 to 16967 cm-1 (encompassing 5 MDR’s). The molecule’s emission is centered at 16667 cm-1 and has a Lorentzian linewidth (full width at half-maximum) of 100 cm-1. In the second column the single-frequency emission is at 16666.7 cm-1, which is not on a resonance. In the third column the emission is on the TM32,1 MDR (16559.7851 cm-1, with Q=104). In the fourth column the emission is on the TE33,1 MDR (16742.035 cm-1 with Q=2.2×104). The maximum values of the color scales have been adjusted to show the main variations: with the magnitude of the dipole held constant, peak values are 2 in columns 1 and 2, 110 in column 3, and 600 in column 4 (except for the top row of column 4, where it is only 10). The distance from the center of the sphere to the plane of the lens is 1 mm, and from the plane of the lens to the image is 40 mm.

Fig. 3
Fig. 3

Calculated images of a dipole in a sphere as in Fig. 2 but with the lens at Θ = 165° from the z axis. In the upper row the image plane is at the origin of the L2 coordinate system. In the lower row the image plane is at zL2=10 mm (i.e., 10 mm closer to the lens than in Fig. 2) so that the spot size is smaller.

Fig. 4
Fig. 4

Calculated images of a dipole in a sphere as in Fig. 2 except that the dipole’s polarization is p(r)=(ix+iy+iz)/3, and the lens is at Θ = 135° (left image) and Θ = 165° (right image). The images are integrated over emission frequency with the same parameters as in Fig. 2.

Equations (5)

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Es(kr)=iω2μkmπν=1Dν[ηnTEMν3(kr)Mν1(mkr)+ηnTMNν3(kr)Nν1(mkr)]·p(r),
Dv=m(2n+1)(n-m)!4n(n+1)(n+m)!,
ηnTE=i/mxjn(mx)[xhn(1)(x)]-[mxjn(mx)]hn(1)(x),
ηnTM=i/xm2jn(mx)[xhn(1)(x)]-[mxjn(mx)]hn(1)(x),
E(rI)=CS2E(rS2)exp(ik|rI-rS2|)|rI-rS2|×cos-rS2|rS2|·(rI-rS2)|rI-rS2|dA,

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