Abstract

We present an algorithm that can be used to simultaneously determine the radius and the refractive index (with dispersion) of a spherical, homogeneous particle. This is accomplished by fitting characteristic resonances calculated using Mie scattering coefficients to the measured whispering gallery mode resonances. The advantage of this algorithm over those that have been presented previously is that a large portion of the search can be reduced to two dimensions (a search that includes radius and refractive index with dispersion will always be at least three dimensions). Using this algorithm, we analyze two large sets of cavity-enhanced Raman spectra from optically trapped aerosol particles. The speed of the algorithm allows for best fits to be found in real time. Precision is found to be limited by the resolution of the spectrograph.

© 2013 Optical Society of America

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  1. M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383, 802–804 (1996).
    [CrossRef]
  2. L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).
  3. T. Ioppolo, M. Kozhevnikov, V. Stepaniuk, M. V. Otügen, and V. Sheverev, “Micro-optical force sensor concept based on whispering gallery mode resonators,” Appl. Opt. 47, 3009–3014 (2008).
    [CrossRef]
  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]
  5. V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes–Part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2006).
    [CrossRef]
  6. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
    [CrossRef]
  7. U. K. Krieger, C. Marcolli, and J. P. Reid, “Exploring the complexity of aerosol particle properties and processes using single particle techniques,” Chem. Soc. Rev. 41, 6631–6662 (2012).
    [CrossRef]
  8. R. E. Benner, P. W. Barber, J. F. Owen, and R. K. Chang, “Observation of structure resonances in the fluorescence spectra from microspheres,” Phys. Rev. Lett. 44, 475–478 (1980).
    [CrossRef]
  9. J. B. Snow, S. X. Qian, and R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985).
    [CrossRef]
  10. R. Thurn and W. Kiefer, “Structural resonances observed in the Raman spectra of optically levitated liquid droplets,” Appl. Opt. 24, 1515–1519 (1985).
    [CrossRef]
  11. H. B. Lin, J. D. Eversole, and A. J. Campillo, “Continuous-wave stimulated Raman scattering in microdroplets,” Opt. Lett. 17, 828–830 (1992).
    [CrossRef]
  12. J. D. Eversole, H. B. Lin, A. L. Huston, A. J. Campillo, P. T. Leung, S. Y. Liu, and K. Young, “High-precision identification of morphology-dependent resonances in optical processes in microdroplets,” J. Opt. Soc. Am. B 10, 1955–1968 (1993).
    [CrossRef]
  13. R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: Principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474–487 (2004).
    [CrossRef]
  14. R. E. H. Miles, J. S. Walker, D. R. Burnham, and J. P. Reid, “Retrieval of the complex refractive index of aerosol droplets from optical tweezers measurements,” Phys. Chem. Chem. Phys. 14, 3037–3047 (2012).
    [CrossRef]
  15. A. A. Zardini and U. K. Krieger, “Evaporation kinetics of a non-spherical, levitated aerosol particle using optical resonance spectroscopy for precision sizing,” Opt. Express 17, 4659–4669 (2009).
    [CrossRef]
  16. G. Hargreaves, N.-O. A. Kwamena, Y. H. Zhang, J. R. Butler, S. Rushworth, S. L. Clegg, and J. P. Reid, “Measurements of the equilibrium size of supersaturated aqueous sodium chloride droplets at low relative humidity using aerosol optical tweezers and an electrodynamic balance,” J. Phys. Chem. A 114, 1806–1815 (2010).
    [CrossRef]
  17. H.-J. Tong, J. P. Reid, D. L. Bones, B. P. Luo, and U. K. Krieger, “Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature,” Atmos. Chem. Phys. 11, 4739–4754 (2011).
    [CrossRef]
  18. D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger, “Comparing the mechanism of water condensation and evaporation in glassy aerosol,” Proc. Natl. Acad. Sci. USA 109, 11613–11618 (2012).
    [CrossRef]
  19. B. J. Dennis-Smither, K. L. Hanford, N.-O. A. Kwamena, R. E. H. Miles, and J. P. Reid, “Phase, morphology, and hygroscopicity of mixed oleic acid/sodium chloride/water aerosol particles before and after ozonolysis,” J. Phys. Chem. A 116, 6159–6168 (2012).
    [CrossRef]
  20. B. J. Dennis-Smither, R. E. H. Miles, and J. P. Reid, “Oxidative aging of mixed oleic acid/sodium chloride aerosol particles,” J. Geophys. Res. 117, D20204 (2012).
    [CrossRef]
  21. S. Hill, C. Rushforth, R. Benner, and P. Conwell, “Sizing dielectric spheres and cylinders by aligning measured and computed resonance locations: algorithm for multiple orders,” Appl. Opt. 24, 2380–2390 (1985).
    [CrossRef]
  22. P. R. Conwell, C. K. Rushforth, R. E. Benner, and S. C. Hill, “Efficient automated algorithm for the sizing of dielectric microspheres using the resonance spectrum,” J. Opt. Soc. Am. A 1, 1181–1187 (1984).
    [CrossRef]
  23. X. Zheng and D. Carroll, “Exact resonant condition for dielectric spheres,” J. Opt. A 1, 168–172 (1999).
    [CrossRef]
  24. P. Chýlek, “Large-sphere limits of the Mie-scattering functions,” J. Opt. Soc. Am. 63, 699–706 (1973).
    [CrossRef]
  25. J. Probert-Jones, “Resonance component of backscattering by large dielectric spheres,” J. Opt. Soc. Am. A 1, 822–830 (1984).
    [CrossRef]
  26. B. Hunter, M. Box, and B. Maier, “Resonance structure in weakly absorbing spheres,” J. Opt. Soc. Am. A 5, 1281–1286 (1988).
    [CrossRef]
  27. P. Chýlek, “Partial-wave resonances and the ripple structure in the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1976).
    [CrossRef]
  28. P. Chýlek, “Resonance structure of Mie scattering: distance between resonances,” J. Opt. Soc. Am. A 7, 1609–1613 (1990).
    [CrossRef]
  29. R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys. 10, 391–398 (1939).
    [CrossRef]
  30. P. Debye, “Der lichtdruck auf kugeln von beliebigem material,” Ann. Phys. 335, 57–136 (1909).
    [CrossRef]
  31. R. Fuchs and K. Kliewer, “Optical modes of vibration in an ionic crystal sphere,” J. Opt. Soc. Am. 58, 319–330 (1968).
    [CrossRef]
  32. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), pp. 556–557.
  33. C. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Science Paperback, 1998), pp. 100–101.
  34. C. Lam, P. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992).
    [CrossRef]
  35. S. Schiller, “Asymptotic expansion of morphological resonance frequencies in Mie scattering,” Appl. Opt. 32, 2181–2185 (1993).
    [CrossRef]
  36. L. Mitchem, J. Buajarern, R. J. Hopkins, A. D. Ward, R. J. J. Gilham, R. L. Johnston, and J. P. Reid, “Spectroscopy of growing and evaporating water droplets: exploring the variation in equilibrium droplet size with relative humidity,” J. Phys. Chem. A 110, 8116–8125 (2006).
    [CrossRef]
  37. S. L. Clegg, P. Brimblecombe, and A. S. Wexler, “Thermodynamic model of the system H+-NH4+-Na+-SO42−-NO3−-Cl−-H2O at 298.15 K,” J. Phys. Chem. A 102, 2155–2171 (1998).
    [CrossRef]
  38. R. C. Millard and G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep Sea Res. Part A 37, 1909–1926 (1990).
    [CrossRef]
  39. G. Bernardo-Gil, M. Esquivel, and A. Ribeiro, “Densities and refractive indices of pure organic acids as a function of temperature,” J. Chem. Eng. Data 35, 202–204 (1990).
    [CrossRef]
  40. M. Daimon and A. Masumura, “Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region,” Appl. Opt. 46, 3811–3820 (2007).
    [CrossRef]

2012 (5)

U. K. Krieger, C. Marcolli, and J. P. Reid, “Exploring the complexity of aerosol particle properties and processes using single particle techniques,” Chem. Soc. Rev. 41, 6631–6662 (2012).
[CrossRef]

D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger, “Comparing the mechanism of water condensation and evaporation in glassy aerosol,” Proc. Natl. Acad. Sci. USA 109, 11613–11618 (2012).
[CrossRef]

B. J. Dennis-Smither, K. L. Hanford, N.-O. A. Kwamena, R. E. H. Miles, and J. P. Reid, “Phase, morphology, and hygroscopicity of mixed oleic acid/sodium chloride/water aerosol particles before and after ozonolysis,” J. Phys. Chem. A 116, 6159–6168 (2012).
[CrossRef]

B. J. Dennis-Smither, R. E. H. Miles, and J. P. Reid, “Oxidative aging of mixed oleic acid/sodium chloride aerosol particles,” J. Geophys. Res. 117, D20204 (2012).
[CrossRef]

R. E. H. Miles, J. S. Walker, D. R. Burnham, and J. P. Reid, “Retrieval of the complex refractive index of aerosol droplets from optical tweezers measurements,” Phys. Chem. Chem. Phys. 14, 3037–3047 (2012).
[CrossRef]

2011 (1)

H.-J. Tong, J. P. Reid, D. L. Bones, B. P. Luo, and U. K. Krieger, “Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature,” Atmos. Chem. Phys. 11, 4739–4754 (2011).
[CrossRef]

2010 (1)

G. Hargreaves, N.-O. A. Kwamena, Y. H. Zhang, J. R. Butler, S. Rushworth, S. L. Clegg, and J. P. Reid, “Measurements of the equilibrium size of supersaturated aqueous sodium chloride droplets at low relative humidity using aerosol optical tweezers and an electrodynamic balance,” J. Phys. Chem. A 114, 1806–1815 (2010).
[CrossRef]

2009 (1)

2008 (2)

T. Ioppolo, M. Kozhevnikov, V. Stepaniuk, M. V. Otügen, and V. Sheverev, “Micro-optical force sensor concept based on whispering gallery mode resonators,” Appl. Opt. 47, 3009–3014 (2008).
[CrossRef]

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

2007 (1)

2006 (2)

L. Mitchem, J. Buajarern, R. J. Hopkins, A. D. Ward, R. J. J. Gilham, R. L. Johnston, and J. P. Reid, “Spectroscopy of growing and evaporating water droplets: exploring the variation in equilibrium droplet size with relative humidity,” J. Phys. Chem. A 110, 8116–8125 (2006).
[CrossRef]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes–Part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2006).
[CrossRef]

2005 (1)

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

2004 (1)

R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: Principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474–487 (2004).
[CrossRef]

2003 (1)

1999 (1)

X. Zheng and D. Carroll, “Exact resonant condition for dielectric spheres,” J. Opt. A 1, 168–172 (1999).
[CrossRef]

1998 (1)

S. L. Clegg, P. Brimblecombe, and A. S. Wexler, “Thermodynamic model of the system H+-NH4+-Na+-SO42−-NO3−-Cl−-H2O at 298.15 K,” J. Phys. Chem. A 102, 2155–2171 (1998).
[CrossRef]

1996 (1)

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383, 802–804 (1996).
[CrossRef]

1993 (2)

1992 (2)

1990 (3)

R. C. Millard and G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep Sea Res. Part A 37, 1909–1926 (1990).
[CrossRef]

G. Bernardo-Gil, M. Esquivel, and A. Ribeiro, “Densities and refractive indices of pure organic acids as a function of temperature,” J. Chem. Eng. Data 35, 202–204 (1990).
[CrossRef]

P. Chýlek, “Resonance structure of Mie scattering: distance between resonances,” J. Opt. Soc. Am. A 7, 1609–1613 (1990).
[CrossRef]

1988 (1)

1985 (3)

1984 (2)

1980 (1)

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

1976 (1)

1973 (1)

1968 (1)

1939 (1)

R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys. 10, 391–398 (1939).
[CrossRef]

1909 (1)

P. Debye, “Der lichtdruck auf kugeln von beliebigem material,” Ann. Phys. 335, 57–136 (1909).
[CrossRef]

Arnold, S.

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

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]

Barber, P. W.

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

Bawendi, M. G.

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383, 802–804 (1996).
[CrossRef]

Benner, R.

Benner, R. E.

P. R. Conwell, C. K. Rushforth, R. E. Benner, and S. C. Hill, “Efficient automated algorithm for the sizing of dielectric microspheres using the resonance spectrum,” J. Opt. Soc. Am. A 1, 1181–1187 (1984).
[CrossRef]

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

Bernardo-Gil, G.

G. Bernardo-Gil, M. Esquivel, and A. Ribeiro, “Densities and refractive indices of pure organic acids as a function of temperature,” J. Chem. Eng. Data 35, 202–204 (1990).
[CrossRef]

Bohren, C.

C. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Science Paperback, 1998), pp. 100–101.

Bones, D. L.

D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger, “Comparing the mechanism of water condensation and evaporation in glassy aerosol,” Proc. Natl. Acad. Sci. USA 109, 11613–11618 (2012).
[CrossRef]

H.-J. Tong, J. P. Reid, D. L. Bones, B. P. Luo, and U. K. Krieger, “Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature,” Atmos. Chem. Phys. 11, 4739–4754 (2011).
[CrossRef]

Box, M.

Brimblecombe, P.

S. L. Clegg, P. Brimblecombe, and A. S. Wexler, “Thermodynamic model of the system H+-NH4+-Na+-SO42−-NO3−-Cl−-H2O at 298.15 K,” J. Phys. Chem. A 102, 2155–2171 (1998).
[CrossRef]

Brus, L. E.

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383, 802–804 (1996).
[CrossRef]

Buajarern, J.

L. Mitchem, J. Buajarern, R. J. Hopkins, A. D. Ward, R. J. J. Gilham, R. L. Johnston, and J. P. Reid, “Spectroscopy of growing and evaporating water droplets: exploring the variation in equilibrium droplet size with relative humidity,” J. Phys. Chem. A 110, 8116–8125 (2006).
[CrossRef]

Burnham, D. R.

R. E. H. Miles, J. S. Walker, D. R. Burnham, and J. P. Reid, “Retrieval of the complex refractive index of aerosol droplets from optical tweezers measurements,” Phys. Chem. Chem. Phys. 14, 3037–3047 (2012).
[CrossRef]

Butler, J. R.

G. Hargreaves, N.-O. A. Kwamena, Y. H. Zhang, J. R. Butler, S. Rushworth, S. L. Clegg, and J. P. Reid, “Measurements of the equilibrium size of supersaturated aqueous sodium chloride droplets at low relative humidity using aerosol optical tweezers and an electrodynamic balance,” J. Phys. Chem. A 114, 1806–1815 (2010).
[CrossRef]

Campillo, A. J.

Carroll, D.

X. Zheng and D. Carroll, “Exact resonant condition for dielectric spheres,” J. Opt. A 1, 168–172 (1999).
[CrossRef]

Chang, R. K.

J. B. Snow, S. X. Qian, and R. K. Chang, “Stimulated Raman scattering from individual water and ethanol droplets at morphology-dependent resonances,” Opt. Lett. 10, 37–39 (1985).
[CrossRef]

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

Chang, S.-H.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Chýlek, P.

Clegg, S. L.

G. Hargreaves, N.-O. A. Kwamena, Y. H. Zhang, J. R. Butler, S. Rushworth, S. L. Clegg, and J. P. Reid, “Measurements of the equilibrium size of supersaturated aqueous sodium chloride droplets at low relative humidity using aerosol optical tweezers and an electrodynamic balance,” J. Phys. Chem. A 114, 1806–1815 (2010).
[CrossRef]

S. L. Clegg, P. Brimblecombe, and A. S. Wexler, “Thermodynamic model of the system H+-NH4+-Na+-SO42−-NO3−-Cl−-H2O at 298.15 K,” J. Phys. Chem. A 102, 2155–2171 (1998).
[CrossRef]

Conwell, P.

Conwell, P. R.

Dabbousi, B. O.

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383, 802–804 (1996).
[CrossRef]

Daimon, M.

Debye, P.

P. Debye, “Der lichtdruck auf kugeln von beliebigem material,” Ann. Phys. 335, 57–136 (1909).
[CrossRef]

Dennis-Smither, B. J.

B. J. Dennis-Smither, K. L. Hanford, N.-O. A. Kwamena, R. E. H. Miles, and J. P. Reid, “Phase, morphology, and hygroscopicity of mixed oleic acid/sodium chloride/water aerosol particles before and after ozonolysis,” J. Phys. Chem. A 116, 6159–6168 (2012).
[CrossRef]

B. J. Dennis-Smither, R. E. H. Miles, and J. P. Reid, “Oxidative aging of mixed oleic acid/sodium chloride aerosol particles,” J. Geophys. Res. 117, D20204 (2012).
[CrossRef]

Esquivel, M.

G. Bernardo-Gil, M. Esquivel, and A. Ribeiro, “Densities and refractive indices of pure organic acids as a function of temperature,” J. Chem. Eng. Data 35, 202–204 (1990).
[CrossRef]

Eversole, J. D.

Fuchs, R.

Gilham, R. J. J.

L. Mitchem, J. Buajarern, R. J. Hopkins, A. D. Ward, R. J. J. Gilham, R. L. Johnston, and J. P. Reid, “Spectroscopy of growing and evaporating water droplets: exploring the variation in equilibrium droplet size with relative humidity,” J. Phys. Chem. A 110, 8116–8125 (2006).
[CrossRef]

Hanford, K. L.

B. J. Dennis-Smither, K. L. Hanford, N.-O. A. Kwamena, R. E. H. Miles, and J. P. Reid, “Phase, morphology, and hygroscopicity of mixed oleic acid/sodium chloride/water aerosol particles before and after ozonolysis,” J. Phys. Chem. A 116, 6159–6168 (2012).
[CrossRef]

Hargreaves, G.

G. Hargreaves, N.-O. A. Kwamena, Y. H. Zhang, J. R. Butler, S. Rushworth, S. L. Clegg, and J. P. Reid, “Measurements of the equilibrium size of supersaturated aqueous sodium chloride droplets at low relative humidity using aerosol optical tweezers and an electrodynamic balance,” J. Phys. Chem. A 114, 1806–1815 (2010).
[CrossRef]

Harris, T. D.

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383, 802–804 (1996).
[CrossRef]

Hill, S.

Hill, S. C.

Holler, S.

Hopkins, R. J.

L. Mitchem, J. Buajarern, R. J. Hopkins, A. D. Ward, R. J. J. Gilham, R. L. Johnston, and J. P. Reid, “Spectroscopy of growing and evaporating water droplets: exploring the variation in equilibrium droplet size with relative humidity,” J. Phys. Chem. A 110, 8116–8125 (2006).
[CrossRef]

Huffman, D. R.

C. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Science Paperback, 1998), pp. 100–101.

Hunter, B.

Huston, A. L.

Ilchenko, V. S.

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes–Part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2006).
[CrossRef]

Ioppolo, T.

Johnston, R. L.

L. Mitchem, J. Buajarern, R. J. Hopkins, A. D. Ward, R. J. J. Gilham, R. L. Johnston, and J. P. Reid, “Spectroscopy of growing and evaporating water droplets: exploring the variation in equilibrium droplet size with relative humidity,” J. Phys. Chem. A 110, 8116–8125 (2006).
[CrossRef]

Khoshsima, M.

Kiefer, W.

Kliewer, K.

Kozhevnikov, M.

Krieger, U. K.

U. K. Krieger, C. Marcolli, and J. P. Reid, “Exploring the complexity of aerosol particle properties and processes using single particle techniques,” Chem. Soc. Rev. 41, 6631–6662 (2012).
[CrossRef]

D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger, “Comparing the mechanism of water condensation and evaporation in glassy aerosol,” Proc. Natl. Acad. Sci. USA 109, 11613–11618 (2012).
[CrossRef]

H.-J. Tong, J. P. Reid, D. L. Bones, B. P. Luo, and U. K. Krieger, “Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature,” Atmos. Chem. Phys. 11, 4739–4754 (2011).
[CrossRef]

A. A. Zardini and U. K. Krieger, “Evaporation kinetics of a non-spherical, levitated aerosol particle using optical resonance spectroscopy for precision sizing,” Opt. Express 17, 4659–4669 (2009).
[CrossRef]

Kwamena, N.-O. A.

B. J. Dennis-Smither, K. L. Hanford, N.-O. A. Kwamena, R. E. H. Miles, and J. P. Reid, “Phase, morphology, and hygroscopicity of mixed oleic acid/sodium chloride/water aerosol particles before and after ozonolysis,” J. Phys. Chem. A 116, 6159–6168 (2012).
[CrossRef]

G. Hargreaves, N.-O. A. Kwamena, Y. H. Zhang, J. R. Butler, S. Rushworth, S. L. Clegg, and J. P. Reid, “Measurements of the equilibrium size of supersaturated aqueous sodium chloride droplets at low relative humidity using aerosol optical tweezers and an electrodynamic balance,” J. Phys. Chem. A 114, 1806–1815 (2010).
[CrossRef]

Lam, C.

Leung, P.

Leung, P. T.

Lienhard, D. M.

D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger, “Comparing the mechanism of water condensation and evaporation in glassy aerosol,” Proc. Natl. Acad. Sci. USA 109, 11613–11618 (2012).
[CrossRef]

Lin, H. B.

Liu, S. Y.

Luo, B. P.

H.-J. Tong, J. P. Reid, D. L. Bones, B. P. Luo, and U. K. Krieger, “Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature,” Atmos. Chem. Phys. 11, 4739–4754 (2011).
[CrossRef]

Macklin, J. J.

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383, 802–804 (1996).
[CrossRef]

Maier, B.

Marcolli, C.

U. K. Krieger, C. Marcolli, and J. P. Reid, “Exploring the complexity of aerosol particle properties and processes using single particle techniques,” Chem. Soc. Rev. 41, 6631–6662 (2012).
[CrossRef]

Masumura, A.

Matsko, A. B.

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes–Part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2006).
[CrossRef]

Miles, R. E. H.

B. J. Dennis-Smither, K. L. Hanford, N.-O. A. Kwamena, R. E. H. Miles, and J. P. Reid, “Phase, morphology, and hygroscopicity of mixed oleic acid/sodium chloride/water aerosol particles before and after ozonolysis,” J. Phys. Chem. A 116, 6159–6168 (2012).
[CrossRef]

R. E. H. Miles, J. S. Walker, D. R. Burnham, and J. P. Reid, “Retrieval of the complex refractive index of aerosol droplets from optical tweezers measurements,” Phys. Chem. Chem. Phys. 14, 3037–3047 (2012).
[CrossRef]

B. J. Dennis-Smither, R. E. H. Miles, and J. P. Reid, “Oxidative aging of mixed oleic acid/sodium chloride aerosol particles,” J. Geophys. Res. 117, D20204 (2012).
[CrossRef]

Millard, R. C.

R. C. Millard and G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep Sea Res. Part A 37, 1909–1926 (1990).
[CrossRef]

Mitchem, L.

L. Mitchem, J. Buajarern, R. J. Hopkins, A. D. Ward, R. J. J. Gilham, R. L. Johnston, and J. P. Reid, “Spectroscopy of growing and evaporating water droplets: exploring the variation in equilibrium droplet size with relative humidity,” J. Phys. Chem. A 110, 8116–8125 (2006).
[CrossRef]

Nirmal, M.

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383, 802–804 (1996).
[CrossRef]

Otügen, M. V.

Owen, J. F.

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

Probert-Jones, J.

Qian, S. X.

Reid, J. P.

U. K. Krieger, C. Marcolli, and J. P. Reid, “Exploring the complexity of aerosol particle properties and processes using single particle techniques,” Chem. Soc. Rev. 41, 6631–6662 (2012).
[CrossRef]

D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger, “Comparing the mechanism of water condensation and evaporation in glassy aerosol,” Proc. Natl. Acad. Sci. USA 109, 11613–11618 (2012).
[CrossRef]

R. E. H. Miles, J. S. Walker, D. R. Burnham, and J. P. Reid, “Retrieval of the complex refractive index of aerosol droplets from optical tweezers measurements,” Phys. Chem. Chem. Phys. 14, 3037–3047 (2012).
[CrossRef]

B. J. Dennis-Smither, K. L. Hanford, N.-O. A. Kwamena, R. E. H. Miles, and J. P. Reid, “Phase, morphology, and hygroscopicity of mixed oleic acid/sodium chloride/water aerosol particles before and after ozonolysis,” J. Phys. Chem. A 116, 6159–6168 (2012).
[CrossRef]

B. J. Dennis-Smither, R. E. H. Miles, and J. P. Reid, “Oxidative aging of mixed oleic acid/sodium chloride aerosol particles,” J. Geophys. Res. 117, D20204 (2012).
[CrossRef]

H.-J. Tong, J. P. Reid, D. L. Bones, B. P. Luo, and U. K. Krieger, “Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature,” Atmos. Chem. Phys. 11, 4739–4754 (2011).
[CrossRef]

G. Hargreaves, N.-O. A. Kwamena, Y. H. Zhang, J. R. Butler, S. Rushworth, S. L. Clegg, and J. P. Reid, “Measurements of the equilibrium size of supersaturated aqueous sodium chloride droplets at low relative humidity using aerosol optical tweezers and an electrodynamic balance,” J. Phys. Chem. A 114, 1806–1815 (2010).
[CrossRef]

L. Mitchem, J. Buajarern, R. J. Hopkins, A. D. Ward, R. J. J. Gilham, R. L. Johnston, and J. P. Reid, “Spectroscopy of growing and evaporating water droplets: exploring the variation in equilibrium droplet size with relative humidity,” J. Phys. Chem. A 110, 8116–8125 (2006).
[CrossRef]

R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: Principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474–487 (2004).
[CrossRef]

Ribeiro, A.

G. Bernardo-Gil, M. Esquivel, and A. Ribeiro, “Densities and refractive indices of pure organic acids as a function of temperature,” J. Chem. Eng. Data 35, 202–204 (1990).
[CrossRef]

Richtmyer, R. D.

R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys. 10, 391–398 (1939).
[CrossRef]

Rushforth, C.

Rushforth, C. K.

Rushworth, S.

G. Hargreaves, N.-O. A. Kwamena, Y. H. Zhang, J. R. Butler, S. Rushworth, S. L. Clegg, and J. P. Reid, “Measurements of the equilibrium size of supersaturated aqueous sodium chloride droplets at low relative humidity using aerosol optical tweezers and an electrodynamic balance,” J. Phys. Chem. A 114, 1806–1815 (2010).
[CrossRef]

Sayer, R. M.

R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: Principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474–487 (2004).
[CrossRef]

Schatz, G. C.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Schiller, S.

Seaver, G.

R. C. Millard and G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep Sea Res. Part A 37, 1909–1926 (1990).
[CrossRef]

Sherry, L. J.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Sheverev, V.

Snow, J. B.

Stepaniuk, V.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), pp. 556–557.

Symes, R.

R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: Principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474–487 (2004).
[CrossRef]

Teraoka, I.

Thurn, R.

Tong, H.-J.

H.-J. Tong, J. P. Reid, D. L. Bones, B. P. Luo, and U. K. Krieger, “Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature,” Atmos. Chem. Phys. 11, 4739–4754 (2011).
[CrossRef]

Trautman, J. K.

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383, 802–804 (1996).
[CrossRef]

Van Duyne, R. P.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Vollmer, F.

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

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]

Walker, J. S.

R. E. H. Miles, J. S. Walker, D. R. Burnham, and J. P. Reid, “Retrieval of the complex refractive index of aerosol droplets from optical tweezers measurements,” Phys. Chem. Chem. Phys. 14, 3037–3047 (2012).
[CrossRef]

Ward, A. D.

L. Mitchem, J. Buajarern, R. J. Hopkins, A. D. Ward, R. J. J. Gilham, R. L. Johnston, and J. P. Reid, “Spectroscopy of growing and evaporating water droplets: exploring the variation in equilibrium droplet size with relative humidity,” J. Phys. Chem. A 110, 8116–8125 (2006).
[CrossRef]

Wexler, A. S.

S. L. Clegg, P. Brimblecombe, and A. S. Wexler, “Thermodynamic model of the system H+-NH4+-Na+-SO42−-NO3−-Cl−-H2O at 298.15 K,” J. Phys. Chem. A 102, 2155–2171 (1998).
[CrossRef]

Wiley, B. J.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Xia, Y.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Young, K.

Zardini, A. A.

Zhang, Y. H.

G. Hargreaves, N.-O. A. Kwamena, Y. H. Zhang, J. R. Butler, S. Rushworth, S. L. Clegg, and J. P. Reid, “Measurements of the equilibrium size of supersaturated aqueous sodium chloride droplets at low relative humidity using aerosol optical tweezers and an electrodynamic balance,” J. Phys. Chem. A 114, 1806–1815 (2010).
[CrossRef]

Zheng, X.

X. Zheng and D. Carroll, “Exact resonant condition for dielectric spheres,” J. Opt. A 1, 168–172 (1999).
[CrossRef]

Ann. Phys. (1)

P. Debye, “Der lichtdruck auf kugeln von beliebigem material,” Ann. Phys. 335, 57–136 (1909).
[CrossRef]

Appl. Opt. (5)

Atmos. Chem. Phys. (1)

H.-J. Tong, J. P. Reid, D. L. Bones, B. P. Luo, and U. K. Krieger, “Measurements of the timescales for the mass transfer of water in glassy aerosol at low relative humidity and ambient temperature,” Atmos. Chem. Phys. 11, 4739–4754 (2011).
[CrossRef]

Chem. Soc. Rev. (1)

U. K. Krieger, C. Marcolli, and J. P. Reid, “Exploring the complexity of aerosol particle properties and processes using single particle techniques,” Chem. Soc. Rev. 41, 6631–6662 (2012).
[CrossRef]

Deep Sea Res. Part A (1)

R. C. Millard and G. Seaver, “An index of refraction algorithm for seawater over temperature, pressure, salinity, density, and wavelength,” Deep Sea Res. Part A 37, 1909–1926 (1990).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes–Part II: applications,” IEEE J. Sel. Top. Quantum Electron. 12, 15–32 (2006).
[CrossRef]

J. Appl. Phys. (1)

R. D. Richtmyer, “Dielectric resonators,” J. Appl. Phys. 10, 391–398 (1939).
[CrossRef]

J. Chem. Eng. Data (1)

G. Bernardo-Gil, M. Esquivel, and A. Ribeiro, “Densities and refractive indices of pure organic acids as a function of temperature,” J. Chem. Eng. Data 35, 202–204 (1990).
[CrossRef]

J. Geophys. Res. (1)

B. J. Dennis-Smither, R. E. H. Miles, and J. P. Reid, “Oxidative aging of mixed oleic acid/sodium chloride aerosol particles,” J. Geophys. Res. 117, D20204 (2012).
[CrossRef]

J. Opt. A (1)

X. Zheng and D. Carroll, “Exact resonant condition for dielectric spheres,” J. Opt. A 1, 168–172 (1999).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (4)

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

J. Phys. Chem. A (4)

L. Mitchem, J. Buajarern, R. J. Hopkins, A. D. Ward, R. J. J. Gilham, R. L. Johnston, and J. P. Reid, “Spectroscopy of growing and evaporating water droplets: exploring the variation in equilibrium droplet size with relative humidity,” J. Phys. Chem. A 110, 8116–8125 (2006).
[CrossRef]

S. L. Clegg, P. Brimblecombe, and A. S. Wexler, “Thermodynamic model of the system H+-NH4+-Na+-SO42−-NO3−-Cl−-H2O at 298.15 K,” J. Phys. Chem. A 102, 2155–2171 (1998).
[CrossRef]

G. Hargreaves, N.-O. A. Kwamena, Y. H. Zhang, J. R. Butler, S. Rushworth, S. L. Clegg, and J. P. Reid, “Measurements of the equilibrium size of supersaturated aqueous sodium chloride droplets at low relative humidity using aerosol optical tweezers and an electrodynamic balance,” J. Phys. Chem. A 114, 1806–1815 (2010).
[CrossRef]

B. J. Dennis-Smither, K. L. Hanford, N.-O. A. Kwamena, R. E. H. Miles, and J. P. Reid, “Phase, morphology, and hygroscopicity of mixed oleic acid/sodium chloride/water aerosol particles before and after ozonolysis,” J. Phys. Chem. A 116, 6159–6168 (2012).
[CrossRef]

Nano Lett. (1)

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005).

Nat. Methods (1)

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

Nature (1)

M. Nirmal, B. O. Dabbousi, M. G. Bawendi, J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, “Fluorescence intermittency in single cadmium selenide nanocrystals,” Nature 383, 802–804 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Chem. Chem. Phys. (2)

R. Symes, R. M. Sayer, and J. P. Reid, “Cavity enhanced droplet spectroscopy: Principles, perspectives and prospects,” Phys. Chem. Chem. Phys. 6, 474–487 (2004).
[CrossRef]

R. E. H. Miles, J. S. Walker, D. R. Burnham, and J. P. Reid, “Retrieval of the complex refractive index of aerosol droplets from optical tweezers measurements,” Phys. Chem. Chem. Phys. 14, 3037–3047 (2012).
[CrossRef]

Phys. Rev. Lett. (1)

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

Proc. Natl. Acad. Sci. USA (1)

D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger, “Comparing the mechanism of water condensation and evaporation in glassy aerosol,” Proc. Natl. Acad. Sci. USA 109, 11613–11618 (2012).
[CrossRef]

Other (2)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941), pp. 556–557.

C. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Science Paperback, 1998), pp. 100–101.

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Figures (7)

Fig. 1.
Fig. 1.

Real part of the index of refraction of water with a linear fit. Data points were taken from [40].

Fig. 2.
Fig. 2.

Comparison of mode spacing for a sphere with a=4000nm with no dispersion to cases where the refractive index (a) increases linearly with ν and (b) decreases linearly with ν. In both cases, m=m0. Only first-order modes with TE polarization are shown.

Fig. 3.
Fig. 3.

Set of simulated first-order modes generated using a=4000nm and m=1.35+5×106(ν15503.88). When these modes were fitted without dispersion, the resulting a and m that provided the best fit were 4279 nm and 1.3369, respectively.

Fig. 4.
Fig. 4.

Best fits for mode sets that contain dispersion without accounting for dispersion. Best fits for (a) the radius without dispersion a and (b) the refractive index without dispersion m. The parameters used to generate the simulated mode set were a=5000nm and m0=1.30 while m1 was varied as indicated on the abscissa of (a) and (b).

Fig. 5.
Fig. 5.

Pictorial representation of the search discussed in Section 3.C for the case of a particle with a refractive index that is described by Eq. 13 and where m1>106cm.

Fig. 6.
Fig. 6.

WGM peak positions from CERS spectra for an aqueous sodium chloride droplet held at RH=72%.

Fig. 7.
Fig. 7.

Time-dependent changes to a, m0, and m1 during the oxidative aging of an oleic acid/NaCl particle. Points with errors that are well above the median have been removed.

Tables (3)

Tables Icon

Table 1. Size Parameters x at Which Resonances Occur in a Homogeneous Sphere with m=1.33 for Both TE and TM Polarizations Across the First 10 Orders of Mode Numbers n=25, 50, and 75a

Tables Icon

Table 2. Size Parameters x at Which Resonances Occur in a Homogeneous Sphere with m=1.33 for Both TE and TM Polarizations of Mode Numbers n=25, 50, and 75a

Tables Icon

Table 3. Uncertainties Determined by Fitting a Set of Simulated Modes Using the Algorithm from Section 3.Ca

Equations (18)

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

an=pnpn+iqn,
bn=rnrn+isn,
pn=jn(z)[mzjn(mz)]m2jn(mz)[xjn(z)],
qn=yn(z)[mzjn(mz)]m2jn(mz)[xyn(z)],
rn=jn(z)[mzjn(mx)]jn(mz)[zjn(z)],
sn=yn(z)[mzjn(mz)]jn(mz)[zyn(z)],
mpjn(mx)jn(mx)=yn(x)yn(x)+1px,
mpjn(mz)jn(mz)=hn(1)(z)hn(1)(z)+1pz,
x<n+12,
f(z)=mpjn(mz)jn(mz)hn(1)(z)hn(1)(z)1pz=0
zs+1=zsf(zs)f(zs)s=0,1,2,.
mxn,l,t=η+αl(η2)1/3+k=0ck(αl,m,t)ηk/3,
m=m0+m1(νν0),
sj(a,m)=|xje(a)xn,l,t(m)|
E(a,m)=1Jj=1J(sj(a,m)2πa)2.
sj(a,m0,m1)=|xje(a)xj,n,l,t(m0,m1)|
xj,n,l,t(m0,m1)=xn,l,t(m0)+m1qn,l,t(m0)(νjeν0).
E(a,m0,m1)=1Jj=1J(sj(a,m0,m1)2πa)2.

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