Abstract

The size parameter spacing Δx between an1 and an+11 or between bn1 and bn+11 resonances have been derived to be Δx = x arctan [(mx/n)2 − 1]1/2/n[(mx/n)2 − 1]1/2. Comparison with numerical calculation of the position of resonances in Mie scattering suggests that the accuracy of the derived expression is near 1%.

© 1990 Optical Society of America

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References

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  1. A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
    [CrossRef]
  2. A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
    [CrossRef] [PubMed]
  3. 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]
  4. P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
    [CrossRef]
  5. P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
    [CrossRef] [PubMed]
  6. G. J. Rosasco, H. S. Bennett, “Internal field resonance structure: implications for optical absorption and scattering by microscopic particles,” J. Opt. Soc. Am. 68, 1242–1250 (1978).
    [CrossRef]
  7. H. S. Bennett, G. J. Rosasco, “Resonances in the efficiency factors for absorption: Mie scattering theory,” Appl. Opt. 17, 491–493 (1978).
    [CrossRef] [PubMed]
  8. P. Chýlek, V. Ramaswamy, A. Ashkin, J. M. Dziedzic, “Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data,” Appl. Opt. 22, 2302–2307 (1983).
    [CrossRef] [PubMed]
  9. P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant spectra of dielectric spheres,” J. Opt. Soc. Am. A 1, 62–67 (1984).
    [CrossRef]
  10. J. R. Probert-Jones, “Resonance component of backscatter by large dielectric spheres,” J. Opt. Soc. Am. A 1, 822–830 (1984).
    [CrossRef]
  11. R. Thurn, W. Kiefer, “Structural resonances observed in the Raman spectra of optically levitated liquid drops,” Appl. Opt. 24, 1515–1519 (1985).
    [CrossRef] [PubMed]
  12. S. C. Hill, C. K. Rushforth, R. E. Benner, P. R. Conwell, “Sizing dielectric spheres and cylinders by aligning measured and computed resonance locations: algorithm for multiple orders,” Appl. Opt. 24, 2380–2390 (1985).
    [CrossRef] [PubMed]
  13. B. A. Hunter, M. A. Box, B. Maier, “Resonance structure in weakly absorbing spheres,” J. Opt. Soc. Am. A 5, 1281–1286 (1988).
    [CrossRef]
  14. J. A. Lock, “Cooperative effects among partial waves in Mie scattering,” J. Opt. Soc. Am. A 5, 2032–2044 (1988).
    [CrossRef]
  15. R. G. Pinnick, A. Biswas, P. Chýlek, R. Armstrong, H. Latifi, E. Creegan, V. Srivastava, M. Jarzembski, G. Fernandez, “Stimulated Raman scattering in micrometer-sized droplets: time-resolved measurements,” Opt. Lett. 13, 494–496 (1988).
    [CrossRef] [PubMed]
  16. P. Chýlek, A. Biswas, M. Jarzembski, V. Srivastava, R. Pinnick, “Time delay of stimulated Raman scattering of micron-size droplets,” Appl. Phys. Lett. 52, 1642–1644 (1988).
    [CrossRef]
  17. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 17.
  18. P. Chýlek, “Large sphere limits of the Mie scattering functions,” J. Opt. Soc. Am. 63, 699–706 (1973).
    [CrossRef]
  19. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  20. D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).
  21. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  22. P. M. Morse, H. Freshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 5.3.

1988 (4)

1985 (2)

1984 (2)

1983 (1)

1981 (1)

1978 (4)

1977 (1)

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

1976 (1)

1973 (1)

Armstrong, R.

Ashkin, A.

Barber, P. W.

Benner, R. E.

Bennett, H. S.

Biswas, A.

Bohren, C. F.

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

Box, M. A.

Chýlek, P.

Conwell, P. R.

Creegan, E.

Deirmendjian, D.

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

Dziedzic, J. M.

Fernandez, G.

Freshbach, H.

P. M. Morse, H. Freshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 5.3.

Hill, S. C.

Huffman, D. R.

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

Hunter, B. A.

Jarzembski, M.

Kerker, M.

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

Kiefer, W.

Kiehl, J. T.

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
[CrossRef] [PubMed]

Ko, M. K. W.

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978).
[CrossRef] [PubMed]

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Latifi, H.

Lock, J. A.

Maier, B.

Morse, P. M.

P. M. Morse, H. Freshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 5.3.

Pinnick, R.

P. Chýlek, A. Biswas, M. Jarzembski, V. Srivastava, R. Pinnick, “Time delay of stimulated Raman scattering of micron-size droplets,” Appl. Phys. Lett. 52, 1642–1644 (1988).
[CrossRef]

Pinnick, R. G.

Probert-Jones, J. R.

Ramaswamy, V.

Rosasco, G. J.

Rushforth, C. K.

Srivastava, V.

Thurn, R.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 17.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

P. Chýlek, A. Biswas, M. Jarzembski, V. Srivastava, R. Pinnick, “Time delay of stimulated Raman scattering of micron-size droplets,” Appl. Phys. Lett. 52, 1642–1644 (1988).
[CrossRef]

J. Opt. Soc. Am. (3)

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

Opt. Lett. (1)

Phys. Rev. A (1)

P. Chýlek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[CrossRef]

Phys. Rev. Lett. (1)

A. Ashkin, J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 38, 1351–1354 (1977).
[CrossRef]

Other (5)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 17.

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

D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (Elsevier, New York, 1969).

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

P. M. Morse, H. Freshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 5.3.

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Figures (1)

Fig. 1
Fig. 1

Distance Δx in the size parameter x between the two resonances b n ( 1 ) and b n + 1 ( 1 ) or between a n ( 1 ) and a n + 1 ( 1 ) as a function of the refractive index m, the resonance number n, and the size parameter x. The spacing Δx(m, n, x) is given by Eq. (26) for |xn| ≫ 1/2 and by Eq. (27) for x/n ~ 1. The two upper curves show resonances in Qext and in radiation pressure Qpr; the lower curve shows resonances in the radiation pressure measurement of Ashkin1 and Dziedzic (from Ref. 4).

Tables (3)

Tables Icon

Table 1 Size Parameter x at Which the Indicated b n 1 or a n 1 Resonances Occura

Tables Icon

Table 2 Same as Table 1, Except for Resonances with the Size Parameter between 45 and 55

Tables Icon

Table 3 Same as Table 1, Except for the Size Parameter x around 200

Equations (32)

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Δ x = arctan m 2 1 m 2 1 ,
a n ( x , m ) = A n ( x , m ) A n ( x , m ) i C n ( x , m )
b n ( x , m ) = B n ( x , m ) B n ( x , m ) i D n ( x , m ) .
B n ( x , m ) = m J n 1 / 2 ( m x ) J n + 1 / 2 ( x ) J n + 1 / 2 ( m x ) J n 1 / 2 ( x ) ,
D n ( x , m ) = m J n 1 / 2 ( m x ) N n + 1 / 2 ( x ) J n + 1 / 2 ( m x ) N n 1 / 2 ( x ) ,
m J n 1 / 2 ( m x ) N n + 1 / 2 ( x ) J n + 1 / 2 ( m x ) J n 1 / 2 ( x ) = 0.
x n ( 1 ) < x n ( 2 ) < x n ( 3 ) < . < x n ( 1 ) < x n ( 1 + 1 ) < .
Δ x n ( 1 ) = x n + 1 ( 1 ) x n ( 1 ) .
x 1 ,
n 1 ,
x / n 1 ,
m x > n ,
N n + 1 / 2 ( x ) = 2 Γ ( 1 / 3 ) 6 1 / 3 3 π x 1 / 3 + 2 Γ ( 2 / 3 ) 6 2 / 3 3 π x 2 / 3 ( x n 1 / 2 ) ,
N n 1 / 2 ( x ) = 2 Γ ( 1 / 3 ) 6 1 / 3 3 π x 1 / 3 + 2 Γ ( 2 / 3 ) 6 2 / 3 3 π x 2 / 3 ( x n + 1 / 2 ) ,
J n 1 / 2 ( x ) = [ 2 π ( n 1 / 2 ) tan β ] 1 / 2 cos [ ( n 1 / 2 ) φ π / 4 ] ,
J n + 1 / 2 ( x ) = [ 2 π ( n + 1 / 2 ) tan β + ] 1 / 2 cos [ ( n + 1 / 2 ) φ + π / 4 ] ,
tan β ± = [ ( m x n ± 1 / 2 ) 2 1 ] 1 / 2
φ ± = [ ( m x n ± 1 / 2 ) 2 1 ] 1 / 2 arctan [ ( m x n + 1 / 2 ) 2 1 ] 1 / 2 .
( n + 1 / 2 ) tan β + ( n 1 / 2 ) tan β n [ ( m x n ) 2 1 ] 1 / 2
φ + = φ φ = [ ( m x n ) 2 1 ] 1 / 2 arctan [ ( m x n ) 2 1 ] 1 / 2 .
m cos [ ( n 1 / 2 ) φ π / 4 ] [ K ( x n 1 / 2 ) x 1 / 3 ] cos [ ( n + 1 / 2 ) φ π / 4 ] [ K ( x n + 1 / 2 ) x 1 / 3 ] = 0 ,
K = 6 1 / 3 Γ ( 2 / 3 ) Γ ( 1 / 3 ) 0.6.
| x n | 1 / 2 .
m cos [ ( n 1 / 2 ) φ π / 4 ] cos [ ( n + 1 / 2 ) φ π / 4 ] = 0 ,
φ = [ ( m x n ) 2 1 ] 1 / 2 arctan [ ( m x n ) 2 1 ] 1 / 2 .
F ( x , n ) = m cos [ ( n 1 / 2 ) φ π / 4 ] cos [ ( n + 1 / 2 ) φ π / 4 ] ,
δ F ( x , n ) = F x δ x + F n δ n .
δ F = 0 ,
δ x = δ n F / n F / x .
Δ x = F / n F / x .
Δ x x arctan [ ( m x / n ) 2 1 ] 1 / 2 n [ ( m x / n ) 2 1 ] 1 / 2 .
Δ x = arctan ( m 2 1 ) 1 / 2 ( m 2 1 ) 1 / 2 ,

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