Abstract

We investigate the feasibility of numerically calculating morphology-dependent resonance (MDR) peaks. To do so, one has to calculate the scattering intensities numerically and determine how difficult it is to numerically predict the position and the magnitude of the MDR peaks. However, at present, in practice it is impossible to calculate MDR peaks with a personal computer because so much computing time is required. Therefore the surface values of the Debye potential and its derivative for a homogeneous sphere are obtained from Mie’s analytical solution and then used in integral equations to give the scattering intensities at a specific position of infinity by numerical integrations. It is shown that if a sufficient number of surface elements are used, the MDR peaks are exactly calculated for a homogeneous sphere with refractive index of 1.5, 1.4, and 1.3 up to a size parameter of 20. One can conjecture the number of finite and boundary elements necessary to numerically compute accurate scattering intensities. It should be also noted that the number of surface elements necessary for exact integration shows peaks similar to MDR peaks with respect to the size parameter. Therefore one will need many more elements at the size parameter at which the MDR occurs.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962).
    [CrossRef]
  2. M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a high-temperature environment,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 269–286 (1993).
    [CrossRef]
  3. A. K. Ray, D. D. Bhanti, “Effect of optical resonances on photochemical reactions in microdroplets,” Appl. Opt. 36, 2663–2674 (1997).
    [CrossRef] [PubMed]
  4. S. C. Hill, H. L. Salaheen, K. A. Fuller, “Volume current method for modeling light scattering by inhomogeneously perturbed spheres,” J. Opt. Soc. Am. A 12, 905–915 (1995).
    [CrossRef]
  5. J. R. Brock, M. K. Choi, “Finite-element solution of the Maxwell equations for absorption and scattering of electromagnetic radiation by a coated sphere,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 287–293 (1993).
    [CrossRef]
  6. M. K. Choi, J. R. Brock, “Light scattering and absorption by a radially inhomogeneous sphere: application of a hybrid numerical method,” J. Opt. Soc. Am. B 14, 620–626 (1997).
    [CrossRef]
  7. M. K. Choi, “Numerical calculation of light scattering from a layered sphere by the boundary-element method,” J. Opt. Soc. Am. A 18, 577–583 (2001).
    [CrossRef]
  8. D. C. Taflin, E. J. Davis, “A study of aerosol chemical reactions by optical resonance spectroscopy,” J. Aerosol Sci. 21, 73–86 (1990).
    [CrossRef]
  9. E. J. Davis, M. F. Buehler, “Chemical reactions with single microparticles,” J. MRS Bull. 15, 26–33 (1990).
  10. J. L. Huckaby, A. K. Ray, “Layer formation on microdroplets: a study based on resonant light scattering,” Langmuir 11, 80–86 (1995).
    [CrossRef]
  11. A. K. Ray, R. Nandakumar, “Simultaneous determination of size and wavelength-dependent refractive indices of thin-layered droplets from optical resonances,” Appl. Opt. 34, 7759–7770 (1995).
    [CrossRef] [PubMed]
  12. P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 4.

2001 (1)

1997 (2)

1995 (3)

1990 (2)

D. C. Taflin, E. J. Davis, “A study of aerosol chemical reactions by optical resonance spectroscopy,” J. Aerosol Sci. 21, 73–86 (1990).
[CrossRef]

E. J. Davis, M. F. Buehler, “Chemical reactions with single microparticles,” J. MRS Bull. 15, 26–33 (1990).

1962 (1)

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962).
[CrossRef]

Barber, P. W.

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 4.

Bhanti, D. D.

Brock, J. R.

M. K. Choi, J. R. Brock, “Light scattering and absorption by a radially inhomogeneous sphere: application of a hybrid numerical method,” J. Opt. Soc. Am. B 14, 620–626 (1997).
[CrossRef]

J. R. Brock, M. K. Choi, “Finite-element solution of the Maxwell equations for absorption and scattering of electromagnetic radiation by a coated sphere,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 287–293 (1993).
[CrossRef]

Buehler, M. F.

E. J. Davis, M. F. Buehler, “Chemical reactions with single microparticles,” J. MRS Bull. 15, 26–33 (1990).

Choi, M. K.

M. K. Choi, “Numerical calculation of light scattering from a layered sphere by the boundary-element method,” J. Opt. Soc. Am. A 18, 577–583 (2001).
[CrossRef]

M. K. Choi, J. R. Brock, “Light scattering and absorption by a radially inhomogeneous sphere: application of a hybrid numerical method,” J. Opt. Soc. Am. B 14, 620–626 (1997).
[CrossRef]

J. R. Brock, M. K. Choi, “Finite-element solution of the Maxwell equations for absorption and scattering of electromagnetic radiation by a coated sphere,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 287–293 (1993).
[CrossRef]

Chowdhury, D. Q.

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a high-temperature environment,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 269–286 (1993).
[CrossRef]

Davis, E. J.

D. C. Taflin, E. J. Davis, “A study of aerosol chemical reactions by optical resonance spectroscopy,” J. Aerosol Sci. 21, 73–86 (1990).
[CrossRef]

E. J. Davis, M. F. Buehler, “Chemical reactions with single microparticles,” J. MRS Bull. 15, 26–33 (1990).

Fuller, K. A.

Hill, S. C.

S. C. Hill, H. L. Salaheen, K. A. Fuller, “Volume current method for modeling light scattering by inhomogeneously perturbed spheres,” J. Opt. Soc. Am. A 12, 905–915 (1995).
[CrossRef]

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a high-temperature environment,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 269–286 (1993).
[CrossRef]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 4.

Hirleman, E. D.

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a high-temperature environment,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 269–286 (1993).
[CrossRef]

Huckaby, J. L.

J. L. Huckaby, A. K. Ray, “Layer formation on microdroplets: a study based on resonant light scattering,” Langmuir 11, 80–86 (1995).
[CrossRef]

Nandakumar, R.

Ray, A. K.

Salaheen, H. L.

Saleheen, H. I.

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a high-temperature environment,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 269–286 (1993).
[CrossRef]

Schneider, M.

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a high-temperature environment,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 269–286 (1993).
[CrossRef]

Taflin, D. C.

D. C. Taflin, E. J. Davis, “A study of aerosol chemical reactions by optical resonance spectroscopy,” J. Aerosol Sci. 21, 73–86 (1990).
[CrossRef]

Wyatt, P. J.

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962).
[CrossRef]

Appl. Opt. (2)

J. Aerosol Sci. (1)

D. C. Taflin, E. J. Davis, “A study of aerosol chemical reactions by optical resonance spectroscopy,” J. Aerosol Sci. 21, 73–86 (1990).
[CrossRef]

J. MRS Bull. (1)

E. J. Davis, M. F. Buehler, “Chemical reactions with single microparticles,” J. MRS Bull. 15, 26–33 (1990).

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

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

Langmuir (1)

J. L. Huckaby, A. K. Ray, “Layer formation on microdroplets: a study based on resonant light scattering,” Langmuir 11, 80–86 (1995).
[CrossRef]

Phys. Rev. (1)

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962).
[CrossRef]

Other (3)

M. Schneider, E. D. Hirleman, H. I. Saleheen, D. Q. Chowdhury, S. C. Hill, “Light scattering by radially inhomogeneous fuel droplets in a high-temperature environment,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 269–286 (1993).
[CrossRef]

J. R. Brock, M. K. Choi, “Finite-element solution of the Maxwell equations for absorption and scattering of electromagnetic radiation by a coated sphere,” in Laser Applications in Combustion Diagnostics, C. Liou, ed., Proc. SPIE1862, 287–293 (1993).
[CrossRef]

P. W. Barber, S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990), Chap. 4.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Normalized differential scattering cross section at θ=90° as a function of size parameter for a sphere with refractive index of 1.5 for unpolarized light. Mie’s solutions and the scattering results from numerical integration agree, since only one curve is visible.

Fig. 2
Fig. 2

Minimum numbers of radial and θ-directional elements necessary to yield numerical results at θ=90° within 1% error as a function of size parameter for a sphere with refractive index of 1.5 for unpolarized light.

Fig. 3
Fig. 3

Comparison of the peaks of the minimum number of radial elements with MDR peaks at θ=90° as a function of size parameter for a sphere with refractive index of 1.5.

Fig. 4
Fig. 4

Comparison of the peaks of the minimum number of θ-directional elements with MDR peaks at θ=90° as a function of size parameter for a sphere with refractive index of 1.5.

Equations (18)

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

2E+k2E=0,
2H+k2H=iωddρE×er,
n×(EI-EII)=0,
n×(HI-HII)=0,
2uII-1ρddρρ(ρuII)+(kII)2uII=0,
2vII+(kII)2vII=0.
2uI+(kI)2uI=0,
2vI+(kI)2vI=0.
iωI(ρuI)ρ=r=iωII(ρuII)ρ=r,
ρ(ρuI)ρ=r=ρ(ρuII)ρ=r,
iωμI(ρvI)ρ=r=iωμII(ρvII)ρ=r,
ρ(ρvI)ρ=r=ρ(ρvII)ρ=r.
-4πuks=S1-uIgρ+guIρdS,
-4πvks=S1-vIgρ+gvIρdS,
g=exp(ikI|x-xk|)|x-xk|,
Eks=×[(ruks)×xk]+iωμ×(rvksxk),
EθsE0exp(ikρ)-ikρcos ϕS2(cos θ),
Eϕs-E0exp(ikρ)-ikρsin ϕS1(cos θ).

Metrics