Abstract

An analytical model is formulated for the extinction of light by particles in a cavity ringdown spectroscopy measurement. The electromagnetic field inside the cavity is assumed to be the lowest-order Gaussian beam, and the scattering by the particles is incorporated using van de Hulst’s approximation for the scattering by a sphere. This model includes both coherent scattering in the forward direction and strong scattering in the forward direction for electrically large particles. The model is used to estimate the amount of energy scattered by the particles that is coupled back into the incident beam. The consequences of this coupling for the measurement of the extinction cross section of spherical particles are examined.

© 2011 Optical Society of America

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  1. P. Zalicki and R. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
    [CrossRef]
  2. K. K. Lehmann and D. Romanini, “The superposition principle in cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
    [CrossRef]
  3. J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
    [CrossRef]
  4. G.Berden and R.Engeln, eds., Cavity Ring-Down Spectroscopy: Techniques and Applications (Wiley, 2009).
  5. S. Rudić, R. E. H. Miles, A. J. Orr-Ewing, and J. P. Reid, “Optical properties of micrometer size water droplets studied by cavity ringdown spectroscopy,” Appl. Opt. 46, 6142–6150(2007).
    [CrossRef] [PubMed]
  6. D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435–440 (2002).
    [CrossRef]
  7. G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge, 1997), pp. 240–250.
  8. A. E. Siegman, Lasers (University Science Books, 1986), pp. 663–674.
  9. P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998), pp. 9–38.
  10. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957), pp. 172–183.
  11. R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Dover, 2002), pp. 66–69.
  12. W. A. Farone and M. J. Robinson III, “The range of validity of the anomalous diffraction approximation to electromagnetic scattering by a sphere,” Appl. Opt. 7, 643–645(1968).
    [CrossRef] [PubMed]
  13. S. K. Sharma, “On the validity of the anomalous diffraction approximation,” J. Mod. Opt. 39, 2355–2361 (1992).
    [CrossRef]
  14. W. T. Grandy, Jr., Scattering of Waves from Large Spheres (Cambridge, 2000), pp. 115–118.
  15. G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge, 1997), p. 293.
  16. R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Dover, 2002), pp. 18–20.
  17. C. Mätzler, “MATLAB functions for Mie scattering and absorption,” Research report no. 2002-08 (University of Bern, 2002).
  18. A. E. Siegman, Lasers (University Science Books, 1986), pp. 646–648.
  19. P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998), pp. 59–68.
  20. A. Pettersson, E. R. Lovejoy, C. A. Brock, S. S. Brown, and A. R. Ravishankara, “Measurement of aerosol optical extinction at 532 nm with pulsed cavity ring down spectroscopy,” J. Aerosol Sci. 35, 995–1011 (2004).
    [CrossRef]
  21. T. J. A. Butler, J. L. Miller, and A. J. Orr-Ewing, “Cavity ring-down spectroscopy measurements of single aerosol particle extinction. I. The effect of position of a particle within the laser beam on extinction,” J. Chem. Phys. 126, 174302(2007).
    [CrossRef] [PubMed]
  22. T. J. A. Butler, D. Mellon, J. Kim, J. Litman, and A. J. Orr-Ewing, “Optical-feedback cavity ring-down spectroscopy measurements of extinction by aerosol particles,” J. Phys. Chem. A 113, 3963–3972 (2009).
    [CrossRef] [PubMed]
  23. N. Lang-Yona, Y. Rudich, E. Segre, E. Dinar, and A. Abo-Riziq, “Complex refractive indices of aerosols retrieved by continuous wave-cavity ring down aerosol spectrometer,” Anal. Chem. 81, 1762–1769 (2009).
    [CrossRef] [PubMed]
  24. R. E. H. Miles, S. Rudić, A. J. Orr-Ewing, and J. P. Reid, “Influence of uncertainties in the diameter and refractive index of calibration polystyrene beads on the retrieval of aerosol optical properties using cavity ring down spectroscopy,” J. Phys. Chem. A 114, 7077–7084 (2010).
    [CrossRef] [PubMed]
  25. D. Mellon, S. J. King, J. Kim, J. P. Reid, and A. J. Orr-Ewing, “Measurement of extinction by aerosol particles in the near-infrared using continuous wave cavity ring-down spectroscopy,” J. Phys. Chem. 115, 774–783 (2011).
    [CrossRef]

2011 (1)

D. Mellon, S. J. King, J. Kim, J. P. Reid, and A. J. Orr-Ewing, “Measurement of extinction by aerosol particles in the near-infrared using continuous wave cavity ring-down spectroscopy,” J. Phys. Chem. 115, 774–783 (2011).
[CrossRef]

2010 (1)

R. E. H. Miles, S. Rudić, A. J. Orr-Ewing, and J. P. Reid, “Influence of uncertainties in the diameter and refractive index of calibration polystyrene beads on the retrieval of aerosol optical properties using cavity ring down spectroscopy,” J. Phys. Chem. A 114, 7077–7084 (2010).
[CrossRef] [PubMed]

2009 (2)

T. J. A. Butler, D. Mellon, J. Kim, J. Litman, and A. J. Orr-Ewing, “Optical-feedback cavity ring-down spectroscopy measurements of extinction by aerosol particles,” J. Phys. Chem. A 113, 3963–3972 (2009).
[CrossRef] [PubMed]

N. Lang-Yona, Y. Rudich, E. Segre, E. Dinar, and A. Abo-Riziq, “Complex refractive indices of aerosols retrieved by continuous wave-cavity ring down aerosol spectrometer,” Anal. Chem. 81, 1762–1769 (2009).
[CrossRef] [PubMed]

2007 (2)

T. J. A. Butler, J. L. Miller, and A. J. Orr-Ewing, “Cavity ring-down spectroscopy measurements of single aerosol particle extinction. I. The effect of position of a particle within the laser beam on extinction,” J. Chem. Phys. 126, 174302(2007).
[CrossRef] [PubMed]

S. Rudić, R. E. H. Miles, A. J. Orr-Ewing, and J. P. Reid, “Optical properties of micrometer size water droplets studied by cavity ringdown spectroscopy,” Appl. Opt. 46, 6142–6150(2007).
[CrossRef] [PubMed]

2004 (1)

A. Pettersson, E. R. Lovejoy, C. A. Brock, S. S. Brown, and A. R. Ravishankara, “Measurement of aerosol optical extinction at 532 nm with pulsed cavity ring down spectroscopy,” J. Aerosol Sci. 35, 995–1011 (2004).
[CrossRef]

2002 (1)

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435–440 (2002).
[CrossRef]

1996 (2)

K. K. Lehmann and D. Romanini, “The superposition principle in cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

1995 (1)

P. Zalicki and R. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

1992 (1)

S. K. Sharma, “On the validity of the anomalous diffraction approximation,” J. Mod. Opt. 39, 2355–2361 (1992).
[CrossRef]

1968 (1)

Abo-Riziq, A.

N. Lang-Yona, Y. Rudich, E. Segre, E. Dinar, and A. Abo-Riziq, “Complex refractive indices of aerosols retrieved by continuous wave-cavity ring down aerosol spectrometer,” Anal. Chem. 81, 1762–1769 (2009).
[CrossRef] [PubMed]

Brock, C. A.

A. Pettersson, E. R. Lovejoy, C. A. Brock, S. S. Brown, and A. R. Ravishankara, “Measurement of aerosol optical extinction at 532 nm with pulsed cavity ring down spectroscopy,” J. Aerosol Sci. 35, 995–1011 (2004).
[CrossRef]

Brown, S. S.

A. Pettersson, E. R. Lovejoy, C. A. Brock, S. S. Brown, and A. R. Ravishankara, “Measurement of aerosol optical extinction at 532 nm with pulsed cavity ring down spectroscopy,” J. Aerosol Sci. 35, 995–1011 (2004).
[CrossRef]

Butler, T. J. A.

T. J. A. Butler, D. Mellon, J. Kim, J. Litman, and A. J. Orr-Ewing, “Optical-feedback cavity ring-down spectroscopy measurements of extinction by aerosol particles,” J. Phys. Chem. A 113, 3963–3972 (2009).
[CrossRef] [PubMed]

T. J. A. Butler, J. L. Miller, and A. J. Orr-Ewing, “Cavity ring-down spectroscopy measurements of single aerosol particle extinction. I. The effect of position of a particle within the laser beam on extinction,” J. Chem. Phys. 126, 174302(2007).
[CrossRef] [PubMed]

Dinar, E.

N. Lang-Yona, Y. Rudich, E. Segre, E. Dinar, and A. Abo-Riziq, “Complex refractive indices of aerosols retrieved by continuous wave-cavity ring down aerosol spectrometer,” Anal. Chem. 81, 1762–1769 (2009).
[CrossRef] [PubMed]

Farone, W. A.

Goldsmith, P. F.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998), pp. 9–38.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998), pp. 59–68.

Grandy, W. T.

W. T. Grandy, Jr., Scattering of Waves from Large Spheres (Cambridge, 2000), pp. 115–118.

Hahn, J. W.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435–440 (2002).
[CrossRef]

Hodges, J. T.

J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

Kim, B.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435–440 (2002).
[CrossRef]

Kim, J.

D. Mellon, S. J. King, J. Kim, J. P. Reid, and A. J. Orr-Ewing, “Measurement of extinction by aerosol particles in the near-infrared using continuous wave cavity ring-down spectroscopy,” J. Phys. Chem. 115, 774–783 (2011).
[CrossRef]

T. J. A. Butler, D. Mellon, J. Kim, J. Litman, and A. J. Orr-Ewing, “Optical-feedback cavity ring-down spectroscopy measurements of extinction by aerosol particles,” J. Phys. Chem. A 113, 3963–3972 (2009).
[CrossRef] [PubMed]

King, S. J.

D. Mellon, S. J. King, J. Kim, J. P. Reid, and A. J. Orr-Ewing, “Measurement of extinction by aerosol particles in the near-infrared using continuous wave cavity ring-down spectroscopy,” J. Phys. Chem. 115, 774–783 (2011).
[CrossRef]

Lang-Yona, N.

N. Lang-Yona, Y. Rudich, E. Segre, E. Dinar, and A. Abo-Riziq, “Complex refractive indices of aerosols retrieved by continuous wave-cavity ring down aerosol spectrometer,” Anal. Chem. 81, 1762–1769 (2009).
[CrossRef] [PubMed]

Lee, D.-H.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435–440 (2002).
[CrossRef]

Lee, J. Y.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435–440 (2002).
[CrossRef]

Lehmann, K. K.

K. K. Lehmann and D. Romanini, “The superposition principle in cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

Litman, J.

T. J. A. Butler, D. Mellon, J. Kim, J. Litman, and A. J. Orr-Ewing, “Optical-feedback cavity ring-down spectroscopy measurements of extinction by aerosol particles,” J. Phys. Chem. A 113, 3963–3972 (2009).
[CrossRef] [PubMed]

Looney, J. P.

J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

Lovejoy, E. R.

A. Pettersson, E. R. Lovejoy, C. A. Brock, S. S. Brown, and A. R. Ravishankara, “Measurement of aerosol optical extinction at 532 nm with pulsed cavity ring down spectroscopy,” J. Aerosol Sci. 35, 995–1011 (2004).
[CrossRef]

Mätzler, C.

C. Mätzler, “MATLAB functions for Mie scattering and absorption,” Research report no. 2002-08 (University of Bern, 2002).

Mellon, D.

D. Mellon, S. J. King, J. Kim, J. P. Reid, and A. J. Orr-Ewing, “Measurement of extinction by aerosol particles in the near-infrared using continuous wave cavity ring-down spectroscopy,” J. Phys. Chem. 115, 774–783 (2011).
[CrossRef]

T. J. A. Butler, D. Mellon, J. Kim, J. Litman, and A. J. Orr-Ewing, “Optical-feedback cavity ring-down spectroscopy measurements of extinction by aerosol particles,” J. Phys. Chem. A 113, 3963–3972 (2009).
[CrossRef] [PubMed]

Miles, R. E. H.

R. E. H. Miles, S. Rudić, A. J. Orr-Ewing, and J. P. Reid, “Influence of uncertainties in the diameter and refractive index of calibration polystyrene beads on the retrieval of aerosol optical properties using cavity ring down spectroscopy,” J. Phys. Chem. A 114, 7077–7084 (2010).
[CrossRef] [PubMed]

S. Rudić, R. E. H. Miles, A. J. Orr-Ewing, and J. P. Reid, “Optical properties of micrometer size water droplets studied by cavity ringdown spectroscopy,” Appl. Opt. 46, 6142–6150(2007).
[CrossRef] [PubMed]

Miller, J. L.

T. J. A. Butler, J. L. Miller, and A. J. Orr-Ewing, “Cavity ring-down spectroscopy measurements of single aerosol particle extinction. I. The effect of position of a particle within the laser beam on extinction,” J. Chem. Phys. 126, 174302(2007).
[CrossRef] [PubMed]

Newton, R. G.

R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Dover, 2002), pp. 66–69.

R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Dover, 2002), pp. 18–20.

Orr-Ewing, A. J.

D. Mellon, S. J. King, J. Kim, J. P. Reid, and A. J. Orr-Ewing, “Measurement of extinction by aerosol particles in the near-infrared using continuous wave cavity ring-down spectroscopy,” J. Phys. Chem. 115, 774–783 (2011).
[CrossRef]

R. E. H. Miles, S. Rudić, A. J. Orr-Ewing, and J. P. Reid, “Influence of uncertainties in the diameter and refractive index of calibration polystyrene beads on the retrieval of aerosol optical properties using cavity ring down spectroscopy,” J. Phys. Chem. A 114, 7077–7084 (2010).
[CrossRef] [PubMed]

T. J. A. Butler, D. Mellon, J. Kim, J. Litman, and A. J. Orr-Ewing, “Optical-feedback cavity ring-down spectroscopy measurements of extinction by aerosol particles,” J. Phys. Chem. A 113, 3963–3972 (2009).
[CrossRef] [PubMed]

T. J. A. Butler, J. L. Miller, and A. J. Orr-Ewing, “Cavity ring-down spectroscopy measurements of single aerosol particle extinction. I. The effect of position of a particle within the laser beam on extinction,” J. Chem. Phys. 126, 174302(2007).
[CrossRef] [PubMed]

S. Rudić, R. E. H. Miles, A. J. Orr-Ewing, and J. P. Reid, “Optical properties of micrometer size water droplets studied by cavity ringdown spectroscopy,” Appl. Opt. 46, 6142–6150(2007).
[CrossRef] [PubMed]

Pettersson, A.

A. Pettersson, E. R. Lovejoy, C. A. Brock, S. S. Brown, and A. R. Ravishankara, “Measurement of aerosol optical extinction at 532 nm with pulsed cavity ring down spectroscopy,” J. Aerosol Sci. 35, 995–1011 (2004).
[CrossRef]

Ravishankara, A. R.

A. Pettersson, E. R. Lovejoy, C. A. Brock, S. S. Brown, and A. R. Ravishankara, “Measurement of aerosol optical extinction at 532 nm with pulsed cavity ring down spectroscopy,” J. Aerosol Sci. 35, 995–1011 (2004).
[CrossRef]

Reid, J. P.

D. Mellon, S. J. King, J. Kim, J. P. Reid, and A. J. Orr-Ewing, “Measurement of extinction by aerosol particles in the near-infrared using continuous wave cavity ring-down spectroscopy,” J. Phys. Chem. 115, 774–783 (2011).
[CrossRef]

R. E. H. Miles, S. Rudić, A. J. Orr-Ewing, and J. P. Reid, “Influence of uncertainties in the diameter and refractive index of calibration polystyrene beads on the retrieval of aerosol optical properties using cavity ring down spectroscopy,” J. Phys. Chem. A 114, 7077–7084 (2010).
[CrossRef] [PubMed]

S. Rudić, R. E. H. Miles, A. J. Orr-Ewing, and J. P. Reid, “Optical properties of micrometer size water droplets studied by cavity ringdown spectroscopy,” Appl. Opt. 46, 6142–6150(2007).
[CrossRef] [PubMed]

Robinson, M. J.

Romanini, D.

K. K. Lehmann and D. Romanini, “The superposition principle in cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

Rudic, S.

R. E. H. Miles, S. Rudić, A. J. Orr-Ewing, and J. P. Reid, “Influence of uncertainties in the diameter and refractive index of calibration polystyrene beads on the retrieval of aerosol optical properties using cavity ring down spectroscopy,” J. Phys. Chem. A 114, 7077–7084 (2010).
[CrossRef] [PubMed]

S. Rudić, R. E. H. Miles, A. J. Orr-Ewing, and J. P. Reid, “Optical properties of micrometer size water droplets studied by cavity ringdown spectroscopy,” Appl. Opt. 46, 6142–6150(2007).
[CrossRef] [PubMed]

Rudich, Y.

N. Lang-Yona, Y. Rudich, E. Segre, E. Dinar, and A. Abo-Riziq, “Complex refractive indices of aerosols retrieved by continuous wave-cavity ring down aerosol spectrometer,” Anal. Chem. 81, 1762–1769 (2009).
[CrossRef] [PubMed]

Segre, E.

N. Lang-Yona, Y. Rudich, E. Segre, E. Dinar, and A. Abo-Riziq, “Complex refractive indices of aerosols retrieved by continuous wave-cavity ring down aerosol spectrometer,” Anal. Chem. 81, 1762–1769 (2009).
[CrossRef] [PubMed]

Sharma, S. K.

S. K. Sharma, “On the validity of the anomalous diffraction approximation,” J. Mod. Opt. 39, 2355–2361 (1992).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986), pp. 646–648.

A. E. Siegman, Lasers (University Science Books, 1986), pp. 663–674.

Smith, G. S.

G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge, 1997), pp. 240–250.

G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge, 1997), p. 293.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957), pp. 172–183.

van Zee, R. D.

J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

Yoo, Y. S.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435–440 (2002).
[CrossRef]

Yoon, Y.

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435–440 (2002).
[CrossRef]

Zalicki, P.

P. Zalicki and R. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

Zare, R.

P. Zalicki and R. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

Anal. Chem. (1)

N. Lang-Yona, Y. Rudich, E. Segre, E. Dinar, and A. Abo-Riziq, “Complex refractive indices of aerosols retrieved by continuous wave-cavity ring down aerosol spectrometer,” Anal. Chem. 81, 1762–1769 (2009).
[CrossRef] [PubMed]

Appl. Opt. (2)

Appl. Phys. B (1)

D.-H. Lee, Y. Yoon, B. Kim, J. Y. Lee, Y. S. Yoo, and J. W. Hahn, “Optimization of mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating,” Appl. Phys. B 74, 435–440 (2002).
[CrossRef]

J. Aerosol Sci. (1)

A. Pettersson, E. R. Lovejoy, C. A. Brock, S. S. Brown, and A. R. Ravishankara, “Measurement of aerosol optical extinction at 532 nm with pulsed cavity ring down spectroscopy,” J. Aerosol Sci. 35, 995–1011 (2004).
[CrossRef]

J. Chem. Phys. (4)

T. J. A. Butler, J. L. Miller, and A. J. Orr-Ewing, “Cavity ring-down spectroscopy measurements of single aerosol particle extinction. I. The effect of position of a particle within the laser beam on extinction,” J. Chem. Phys. 126, 174302(2007).
[CrossRef] [PubMed]

P. Zalicki and R. Zare, “Cavity ring-down spectroscopy for quantitative absorption measurements,” J. Chem. Phys. 102, 2708–2717 (1995).
[CrossRef]

K. K. Lehmann and D. Romanini, “The superposition principle in cavity ring-down spectroscopy,” J. Chem. Phys. 105, 10263–10277 (1996).
[CrossRef]

J. T. Hodges, J. P. Looney, and R. D. van Zee, “Response of a ring-down cavity to an arbitrary excitation,” J. Chem. Phys. 105, 10278–10288 (1996).
[CrossRef]

J. Mod. Opt. (1)

S. K. Sharma, “On the validity of the anomalous diffraction approximation,” J. Mod. Opt. 39, 2355–2361 (1992).
[CrossRef]

J. Phys. Chem. (1)

D. Mellon, S. J. King, J. Kim, J. P. Reid, and A. J. Orr-Ewing, “Measurement of extinction by aerosol particles in the near-infrared using continuous wave cavity ring-down spectroscopy,” J. Phys. Chem. 115, 774–783 (2011).
[CrossRef]

J. Phys. Chem. A (2)

T. J. A. Butler, D. Mellon, J. Kim, J. Litman, and A. J. Orr-Ewing, “Optical-feedback cavity ring-down spectroscopy measurements of extinction by aerosol particles,” J. Phys. Chem. A 113, 3963–3972 (2009).
[CrossRef] [PubMed]

R. E. H. Miles, S. Rudić, A. J. Orr-Ewing, and J. P. Reid, “Influence of uncertainties in the diameter and refractive index of calibration polystyrene beads on the retrieval of aerosol optical properties using cavity ring down spectroscopy,” J. Phys. Chem. A 114, 7077–7084 (2010).
[CrossRef] [PubMed]

Other (12)

W. T. Grandy, Jr., Scattering of Waves from Large Spheres (Cambridge, 2000), pp. 115–118.

G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge, 1997), p. 293.

R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Dover, 2002), pp. 18–20.

C. Mätzler, “MATLAB functions for Mie scattering and absorption,” Research report no. 2002-08 (University of Bern, 2002).

A. E. Siegman, Lasers (University Science Books, 1986), pp. 646–648.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998), pp. 59–68.

G.Berden and R.Engeln, eds., Cavity Ring-Down Spectroscopy: Techniques and Applications (Wiley, 2009).

G. S. Smith, An Introduction to Classical Electromagnetic Radiation (Cambridge, 1997), pp. 240–250.

A. E. Siegman, Lasers (University Science Books, 1986), pp. 663–674.

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam Quasioptical Propagation and Applications (IEEE, 1998), pp. 9–38.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957), pp. 172–183.

R. G. Newton, Scattering Theory of Waves and Particles, 2nd ed. (Dover, 2002), pp. 66–69.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram for the cavity and beam in a CRDS experiment. (a) Longitudinal cross section for the plane x = 0 . (b) Transverse cross section for the plane z = s j . Drawings are not to scale.

Fig. 2
Fig. 2

(a) Schematic drawing showing the scattering by particles in the beam. (b) Patterns for the scattered irradiance of spherical particles of different electrical size: a / λ = 0.01 , 1.0 ; n = 1.33 . Patterns are not to scale.

Fig. 3
Fig. 3

Diagram used in explaining van de Hulst’s approximation for the scattering from a sphere.

Fig. 4
Fig. 4

Extinction efficiency for the scattering of a plane wave by a sphere: (a) van de Hulst’s approximation (b) Mie theory.

Fig. 5
Fig. 5

Factor 4 | F | 2 / Q ext that occurs in the relative change in the extinction cross section. Results are shown for lossless and lossy spheres.

Fig. 6
Fig. 6

Schematic drawing showing the solid angles subtended by the beam for the scattered radiation from the spherical particle, Ω p , and the Gaussian beam, Ω G .

Equations (43)

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

f ( r , t ) = Re [ F ( r ) e i ω t ] .
E 00 i ( ρ , z ) = π 2 w 0 E 0 e 00 ( ρ , z ) e i k z ,
e 00 ( ρ , z ) = 2 π 1 W ( z ) e i ψ ( z ) e [ ρ / W ( z ) ] 2 e i k ρ 2 / 2 R ( z )
ϕ = 0 2 π ρ = 0 e 00 ( ρ , z ) e 00 * ( ρ , z ) ρ d ρ d ϕ = 1 ,
W ( z ) = w 0 [ 1 + γ 2 ( z ) ] 1 / 2 ,
R ( z ) = z [ 1 + γ 2 ( z ) ] ,
ψ ( z ) = arctan [ γ ( z ) ] ,
γ ( z ) = 2 k w 0 ( z w 0 ) .
I i ( ρ , z ) = 1 2 ζ | E 00 i ( ρ , z ) | 2 = I 0 i [ w 0 W ( z ) ] 2 e 2 [ ρ / W ( z ) ] 2 ,
I 0 i = 1 2 ζ | E 0 | 2 ,
P i = ϕ = 0 2 π ρ = 0 I i ( ρ , z ) ρ d ρ d ϕ = π w 0 2 2 I 0 i .
Δ P = σ ext I 0 i S ( w 0 , N ) ,
S ( w 0 , N ) = j = 1 N [ I i ( ρ j , z j ) I 0 i ] = j = 1 N [ w 0 W ( z j ) ] 2 e 2 [ ρ j / W ( z j ) ] 2 ,
A p = Δ P P i = 2 σ ext π w 0 2 S ( w 0 , N ) ,
τ p = t c A p = π w 0 2 t c 2 σ ext [ S ( w 0 , N ) ] 1 ,
S ( w 0 , N ) n p z = L / 2 L / 2 ϕ = 0 2 π ρ = 0 [ w 0 W ( z ) ] 2 e 2 [ ρ / W ( z ) ] 2 ρ d ρ d ϕ d z = n p π w 0 2 L 2 ,
Δ P = n p π w 0 2 L σ ext 2 I 0 i ,
A p = n p L σ ext .
Δ P = N e σ ext 2 I 0 i ,
A p = N e σ ext π w 0 2 .
e i k b ( n 1 ) = e i 2 k ( n 1 ) a 2 ρ 2 = e 2 k n a 2 ρ 2 e i 2 k ( n 1 ) a 2 ρ 2 .
E s ( ρ , s ) = E i ( s ) [ 1 U ( ρ a ) ] [ e i 2 k ( n 1 ) a 2 ρ 2 1 ] ,
E s r ( 0 , z ) = i k 2 π ( z s ) e i k ( z s ) ϕ = 0 2 π ρ = 0 E s ( ρ , s ) ρ d ρ d ϕ = i k ( z s ) e i k ( z s ) E i ( s ) ξ = 0 k a [ e i 2 ( n 1 ) ( k a ) 2 ξ 2 1 ] ξ d ξ .
E s r ( 0 , z ) = ( k a ) 2 E i ( s ) k ( z s ) e i k ( z s ) F ( k a , n ) ,
F ( k a , n ) = { [ cos ( δ ) 2 k a ( n 1 ) e 2 k a n cos [ 2 k a ( n 1 ) δ ] + cos 2 ( δ ) [ 2 k a ( n 1 ) ] 2 ( sin ( 2 δ ) + e 2 k a n sin { 2 [ k a ( n 1 ) δ ] } ) ] + i [ 1 2 cos ( δ ) 2 k a ( n 1 ) e 2 k a n sin [ 2 k a ( n 1 ) δ ] + cos 2 ( δ ) [ 2 k a ( n 1 ) ] 2 ( cos ( 2 δ ) e 2 k a n cos { 2 [ k a ( n 1 ) δ ] } ) ] } ,
δ = arctan ( n n 1 ) .
σ ext = 4 π k Im { ( z s ) [ E i ( s ) ] * E s r ( 0 , z ) | E i ( s ) | 2 e k ( z s ) } ,
σ ext = 4 π a 2 Im [ F ( k a , n ) ] = π a 2 [ 2 2 cos ( δ ) k a ( n 1 ) e 2 k a n sin [ 2 k a ( n 1 ) δ ] + cos 2 ( δ ) [ k a ( n 1 ) ] 2 ( cos ( 2 δ ) e 2 k a n cos { 2 [ k a ( n 1 ) δ ] } ) ] .
E j s ( ρ , ϕ , s j ) = E 00 i ( ρ j , s j ) [ 1 U ( ρ a ) ] [ e i 2 k ( n 1 ) a 2 ( ρ ) 2 1 ] .
E 00 , j s ( ρ , z ) = C j E 00 i ( ρ , z ) ,
ϕ = 0 2 π ρ = 0 E 00 , j s ( ρ , s j ) e 00 * ( ρ , s j ) ρ d ρ d ϕ = ϕ = 0 2 π ρ = 0 E j s ( ρ , ϕ , s j ) e 00 * ( ρ j , s j ) ρ d ρ d ϕ .
C j = 4 i [ a W ( s j ) ] 2 e 2 [ ρ j / W ( s j ) ] 2 F ( k a , n ) .
E 00 ( ρ , L / 2 ) = E 00 i ( ρ , L / 2 ) + j = 1 N E 00 , j s ( ρ , L / 2 ) = E 00 i ( ρ , L / 2 ) { 1 + 4 i ( a w 0 ) 2 F ( k a , n ) j = 1 N [ w 0 W ( s j ) ] 2 e 2 [ ρ j / W ( s j ) ] 2 } = E 00 i ( ρ , L / 2 ) [ 1 + 4 i ( a w 0 ) 2 F ( k a , n ) S ( w 0 , N ) ] .
I ( ρ , L / 2 ) = 1 2 ζ | E 00 ( ρ , L / 2 ) | 2 = I i ( ρ , L / 2 ) { 1 8 ( a w 0 ) 2 Im [ F ( k a , n ) ] S ( w 0 , N ) + 16 ( a w 0 ) 4 | F ( k a , n ) | 2 S 2 ( w 0 , N ) } ,
P = ϕ = 0 2 π ρ = 0 I ( ρ , L / 2 ) ρ d ρ d ϕ = P i { 1 8 ( a w 0 ) 2 Im [ F ( k a , n ) ] S ( w 0 , N ) + 16 ( a w 0 ) 4 | F ( k a , n ) | 2 S 2 ( w 0 , N ) } .
A p = Δ P P i = P i P P i = ( 2 π w 0 2 ) S ( w 0 , N ) [ σ ext 8 ( a w 0 ) 2 σ geom | F ( k a , n ) | 2 S ( w 0 , N ) ] ,
σ eff = σ ext + Δ σ ext ,
Δ σ ext = 8 ( a w 0 ) 4 σ geom | F ( k a , n ) | 2 S ( w 0 , N ) .
Δ σ ext σ ext = 2 ( a w 0 ) 2 S ( w 0 , N ) [ 4 | F ( k a , n ) | 2 Q ext ] .
A p = N e π w 0 2 [ σ ext 4 N e ( a w 0 ) 2 σ geom | F ( k a , n ) | 2 ] ,
Δ σ ext σ ext = ( a w 0 ) 2 N e [ 4 | F ( k a , n ) | 2 Q ext ( k a ) ] .
| Δ σ ext σ ext | < N e ( a w 0 ) 2 .
| Δ σ ext σ ext | = 1 Q ext ( 4 | F | 2 Q ext ) ( t c τ p ) 1 4 ( t c τ p ) .

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