Abstract

Resonant frequencies and quality-factor (Q’s) of the morphology-dependent resonances of radially inhomogeneous spherical particles are computed with a Runge–Kutta method. In one type of inhomogeneity the refractive index of the sphere decreases smoothly from a core value of 1.5 to a value of 1.0(0.1)1.4 at the surface. The fraction of the radius over which the refractive index rolls off varies from 0.01 to 0.25. As the refractive index near the surface is decreased, the resonant frequencies shift to higher values and the Q’s decrease. Numerical results for modes with Q’s in the range of 500–1016 show that, when the change in refractive index occurs in only the outer few percent of the droplet radius, the change in the Q is less than 20%. Calculated resonant frequencies and Q’s simulating a refractive index that increases near the surface are also shown.

© 1991 Optical Society of America

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References

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    [Crossref] [PubMed]
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1990 (1)

W. P. Acker, A. Serpengüzel, R. K. Chang, S. C. Hill, “Stimulated Raman scattering of fuel droplets: chemical concentration and size determination,” Appl. Phys. B 51, 9–16 (1990).
[Crossref]

1989 (2)

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[Crossref] [PubMed]

W. P. Acker, D. H. Leach, R. K. Chang, “Third-order optical sum-frequency generation in micrometer-sized droplets,” Opt. Lett. 14, 402–404 (1989).
[Crossref] [PubMed]

1988 (2)

1987 (1)

1986 (2)

1985 (4)

1984 (1)

1983 (1)

1981 (1)

1962 (1)

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962);errata, Phys. Rev. 134, AB1 (1964).
[Crossref]

1951 (1)

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[Crossref]

Acker, W. P.

W. P. Acker, A. Serpengüzel, R. K. Chang, S. C. Hill, “Stimulated Raman scattering of fuel droplets: chemical concentration and size determination,” Appl. Phys. B 51, 9–16 (1990).
[Crossref]

W. P. Acker, D. H. Leach, R. K. Chang, “Third-order optical sum-frequency generation in micrometer-sized droplets,” Opt. Lett. 14, 402–404 (1989).
[Crossref] [PubMed]

Ackerman, T. P.

Aden, A. L.

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[Crossref]

Armstrong, R. L.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[Crossref] [PubMed]

Arnold, S.

Ashkin, A.

Barber, P. W.

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

Benner, R. E.

S. C. Hill, R. E. Benner, C. K. Rushforth, P. R. Conwell, “Sizing dielectric spheres and cylinders by aligning measured and computed structural resonance locations: algorithm for niultipole order,” Appl. Opt. 24, 2380–2390 (1985).
[Crossref] [PubMed]

S. C. Hill, R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated With Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.

Biswas, A.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[Crossref] [PubMed]

Bohren, C. F.

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

Campillo, A. J.

Chang, R. K.

Ching, S. C.

Chylek, P.

Conwell, P. R.

Dziedzic, J. M.

Eversole, J. D.

Hightower, R. L.

Hill, S. C.

W. P. Acker, A. Serpengüzel, R. K. Chang, S. C. Hill, “Stimulated Raman scattering of fuel droplets: chemical concentration and size determination,” Appl. Phys. B 51, 9–16 (1990).
[Crossref]

S. C. Hill, R. E. Benner, C. K. Rushforth, P. R. Conwell, “Sizing dielectric spheres and cylinders by aligning measured and computed structural resonance locations: algorithm for niultipole order,” Appl. Opt. 24, 2380–2390 (1985).
[Crossref] [PubMed]

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

S. C. Hill, R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated With Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.

Houston, A. L.

Huffman, D. R.

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

Justus, B. L.

Kerker, M.

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[Crossref]

M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Lai, H. M.

S. C. Ching, H. M. Lai, K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am. B 4, 1995–2003 (1987).
[Crossref]

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “The effect of perturbation on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. A (to be published).

Lam, C. C.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “The effect of perturbation on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. A (to be published).

Latifi, H.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[Crossref] [PubMed]

Leach, D. H.

Leung, P. T.

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “The effect of perturbation on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. A (to be published).

Lin, H. B.

Long, M. B.

Murphy, E. K.

Pinnick, R. G.

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[Crossref] [PubMed]

Qian, S. X.

Ramaswamy, V.

Richardson, C. B.

Rushforth, C. K.

Sageer, G.

Serpengüzel, A.

W. P. Acker, A. Serpengüzel, R. K. Chang, S. C. Hill, “Stimulated Raman scattering of fuel droplets: chemical concentration and size determination,” Appl. Phys. B 51, 9–16 (1990).
[Crossref]

Snow, J. B.

Snow, J. R.

Toon, O. B.

Tzeng, H. M.

Wall, K. F.

Wyatt, P. J.

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962);errata, Phys. Rev. 134, AB1 (1964).
[Crossref]

Young, K.

S. C. Ching, H. M. Lai, K. Young, “Dielectric microspheres as optical cavities: thermal spectrum and density of states,” J. Opt. Soc. Am. B 4, 1995–2003 (1987).
[Crossref]

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “The effect of perturbation on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. A (to be published).

Appl. Opt. (5)

Appl. Phys. B (1)

W. P. Acker, A. Serpengüzel, R. K. Chang, S. C. Hill, “Stimulated Raman scattering of fuel droplets: chemical concentration and size determination,” Appl. Phys. B 51, 9–16 (1990).
[Crossref]

J. Appl. Phys. (1)

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[Crossref]

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

Opt. Lett. (7)

Phys. Rev. (1)

P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962);errata, Phys. Rev. 134, AB1 (1964).
[Crossref]

Phys. Rev. A (1)

A. Biswas, H. Latifi, R. L. Armstrong, R. G. Pinnick, “Double-resonance stimulated Raman scattering from optically levitated glycerol droplets,” Phys. Rev. A 40, 7413–7416 (1989).
[Crossref] [PubMed]

Other (5)

H. M. Lai, C. C. Lam, P. T. Leung, K. Young, “The effect of perturbation on the widths of narrow morphology-dependent resonances in Mie scattering,” J. Opt. Soc. Am. A (to be published).

M. Kerker, Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

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

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

S. C. Hill, R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated With Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.

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Figures (5)

Fig. 1
Fig. 1

Radial dependence of the refractive index simulating (a) a smooth roll-off and (b) a refractive index with higher value near the surface. The quantity aΔ is equal to ar0 (Δ = 1 − r0/a).

Fig. 2
Fig. 2

Resonance location of a60,1, in terms of size parameter (2πa/λ) versus Δ. Five curves are shown for five different values of boundary refractive index mb. The core refractive index mi is 1.5.

Fig. 3
Fig. 3

Q versus Δ for the same parameters as in Fig. 2. The arrows at (a) and (b) define the cases illustrated in Fig. 4.

Fig. 4
Fig. 4

Radial functions Wn(r) for (a) Δ = 0.13 [arrow (a) in Fig. 3] and (b) Δ = 0.25 [arrow (b) in Fig. 3] versus the normalized radial distance r/a, where a is the sphere radius. The core refractive index mi is 1.5.

Fig. 5
Fig. 5

(a) Resonant frequencies and (b) corresponding Q’s for the radial refractive-index profile shown in Fig. 1(b) as a function of the maximum change in refractive index Δm that varies from 0.0 to 0.003. The core refractive index mi is 1.5.

Equations (9)

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W n ( r ) 2 k 1 ( r ) k 1 ( r ) W n ( r ) + [ k 1 2 ( r ) n ( n + 1 ) r 2 ] W n ( r ) = 0 ,
G n ( r ) + [ k 1 2 ( r ) n ( n + 1 ) r 2 ] G n ( r ) = 0 .
W n ( ρ ) 2 m ( ρ ) m ( ρ ) W n ( ρ ) + [ m 2 ( ρ ) n ( n + 1 ) ρ 2 ] W n ( ρ ) = 0 ,
G n ( ρ ) + [ m 2 ( ρ ) n ( n + 1 ) ρ 2 ] G n ( ρ ) = 0 ,
a n ( x ) = ψ n ( x ) W n ( 1 ) ( x ) m 2 ( x ) ψ n ( x ) W n ( 1 ) ( x ) ζ n ( x ) W n ( 1 ) ( x ) m 2 ( x ) ζ n ( x ) W n ( 1 ) ( x ) ,
b n ( x ) = ψ n ( x ) G n ( 1 ) ( x ) ψ n ( x ) G n ( 1 ) ( x ) ζ n ( x ) G n ( 1 ) ( x ) ζ n ( x ) G n ( 1 ) ( x ) ,
m ( r ) = m b ( m i m b ) cos 2 [ π ( r r 0 ) 2 ( a r 0 ) ]
m ( r ) = m i + m 2 j n 2 ( m i ρ ) ,
Δ = 1 r 0 / a .

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