Abstract

A theory is developed for the scattering of a fundamental-mode laser beam by a homogeneous sphere located in the beam passage. The expression for the incident laser beam is obtained by using the complex-source-point method, and the light-field distributions inside and outside the sphere are given. The formulas for the energies scattered and absorbed by the sphere and for the radiation pressure exerted on the sphere are derived, and their qualitative features are discussed. Results of numerical calculation of the radiation pressure and their physical interpretations are presented. All the analytical formalism is generalized for immediate treatment of the scattering of higher-order Hermite–Gaussian-mode laser beams by a homogeneous sphere.

© 1983 Optical Society of America

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References

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  1. L. W. Casperson, C. Yeh, and W. F. Yeung, “Single particle scattering with focused laser beams,” Appl. Opt. 16, 1104–1107 (1977).
    [PubMed]
  2. G. Grehan and G. Gouesbet, “Optical levitation of a single particle to study the theory of the quasi-elastic scattering of light,” Appl. Opt. 19, 2485–2487 (1980);A. Ashkin and J. M. Dziedzic, “Observation of light scattering from nonspherical particles using optical levitation,” Appl. Opt. 19, 660–668 (1980).
    [Crossref] [PubMed]
  3. A. Ashkin and J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981);T. R. Lattieri, W. D. Jenkins, and D. A. Swyt, “Sizing of individual optically levitated evaporating droplets by measurement of resonances in the polarization ratio,” Appl. Opt. 20, 2799–2805 (1981).
    [Crossref] [PubMed]
  4. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
    [Crossref]
  5. J. S. Kim and S. S. Lee, “Radiation pressure on a dielectric sphere in a Gaussian laser beam,” Opt. Acta 29, 801–806 (1982).
    [Crossref]
  6. A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
    [Crossref]
  7. A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).
    [Crossref]
  8. A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).
    [Crossref]
  9. A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 23, 1351–1354 (1977).
    [Crossref]
  10. G. Roosen and C. Imbert, “Optical levitation by means of two horizontial laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976);G. Roosen, “A theoretical experimental study of the stable equilibrium position of spheres levitated by two horizontal laser beams,” Opt. Commun. 21, 189–194 (1977).
    [Crossref]
  11. G. Roosen and S. Slansky, “Influence of the beam divergence on the forces on a sphere by a laser beam and required condition for stable optical levitation,” Opt. Commun. 29, 341–346 (1979).
    [Crossref]
  12. A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980);G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260–1279 (1979).
    [Crossref] [PubMed]
  13. G. Mie, “Beitrage zur optik trüber Medien, speziell kolloidaller Metalösungen,” Ann. Phys. 25, 377–445 (1908);P. Debye, “Die Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57–136 (1909).
    [Crossref]
  14. H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
    [Crossref]
  15. L. W. Casperson and C. Yeh, “Rayleigh–Debye scattering with focused laser beams,” Appl. Opt. 17, 1637–1643 (1978);S. Colak, C. Yeh, and L. W. Casperson, “Scattering of focused beams by tenuous particles,” Appl. Opt. 18, 294–302 (1979).
    [Crossref] [PubMed]
  16. H. Chew, M. Kerker, and D. D. Cooke, “Electromagnetic scattering by a dielectric sphere in a diverging radiation field,” Phys. Rev. A 16, 320–323 (1977);“Light scattering in converging beams,” Opt. Lett. 1, 138–140 (1977).
    [Crossref] [PubMed]
  17. N. Morita, T. Tanaka, T. Yamasaki, and Y. Nakashini, “Scattering of beam wave by a spherical object,” IEEE Trans.Antennas Propag. AP-16, 724–727 (1968).
    [Crossref]
  18. W. C. Tsai and R. J. Pogorzelski, “Eigenfunction solution of the scattering of beam radiation fields by spherical object,” J. Opt. Soc. Am. 65, 1457–1463 (1975);W. G. Tam and R. Corriveau, “Scattering of electromagnetic beams by spherical objects,” J. Opt. Soc. Am. 68, 763–767 (1978).
    [Crossref]
  19. R. J. Pogorzelski and E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
    [Crossref]
  20. M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial optics,” Phys. Rev. A 11, 1365–1367 (1975).
    [Crossref]
  21. G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
    [Crossref]
  22. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [Crossref]
  23. J. S. Kim and S. S. Lee, “Radiation pressure on a dielectric sphere in focused laser beam,” presented at ICO-12, Graz, Austria, 1981.
  24. M. Couture and P. A. Belanger, “From Gaussian beam to complex-source-point wave,” Phys. Rev. A 24, 355–359 (1981).
    [Crossref]
  25. W. W. Hansen, “A new type of expansion in radiation problems,” Phys. Rev. 47, 139–143 (1935).To simplify the formulation, the VSWF’s in Eq. (6) are defined somewhat differently from those in the reference.
    [Crossref]
  26. G. N. Watson, Theory of Bessel Function (Cambridge U. Press, London, 1941), p. 366.
  27. P. Chylek, “Partial-wave resonances and the ripple structure in the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1976);P. Chylek, J. T. Kiehl, and M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978);“Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
    [Crossref] [PubMed]
  28. J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978);“Focusing and defocusing of neutral atomic beams using resonance-radiation pressure,” Appl. Phys. Lett. 36, 99–101 (1980).
    [Crossref]
  29. G. Roosen, B. F. de Saint Louvent, and S. Slansky, “Étude de la pression de radiation exercée sur une sphere creuse transparente par un faisceau cylindrique,” Opt. Comm. 24, 116–120 (1978);G. Roosen and C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
    [Crossref]
  30. S. Y. Shin and L. B. Felsen, “Gaussian beam modes by multipoles with complex source points,” J. Opt. Soc. Am. 67, 699–700 (1977).
    [Crossref]
  31. A. L. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
    [Crossref]
  32. G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1970), p. 560.

1982 (1)

J. S. Kim and S. S. Lee, “Radiation pressure on a dielectric sphere in a Gaussian laser beam,” Opt. Acta 29, 801–806 (1982).
[Crossref]

1981 (2)

1980 (2)

1979 (2)

G. Roosen and S. Slansky, “Influence of the beam divergence on the forces on a sphere by a laser beam and required condition for stable optical levitation,” Opt. Commun. 29, 341–346 (1979).
[Crossref]

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[Crossref]

1978 (3)

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978);“Focusing and defocusing of neutral atomic beams using resonance-radiation pressure,” Appl. Phys. Lett. 36, 99–101 (1980).
[Crossref]

G. Roosen, B. F. de Saint Louvent, and S. Slansky, “Étude de la pression de radiation exercée sur une sphere creuse transparente par un faisceau cylindrique,” Opt. Comm. 24, 116–120 (1978);G. Roosen and C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
[Crossref]

L. W. Casperson and C. Yeh, “Rayleigh–Debye scattering with focused laser beams,” Appl. Opt. 17, 1637–1643 (1978);S. Colak, C. Yeh, and L. W. Casperson, “Scattering of focused beams by tenuous particles,” Appl. Opt. 18, 294–302 (1979).
[Crossref] [PubMed]

1977 (5)

H. Chew, M. Kerker, and D. D. Cooke, “Electromagnetic scattering by a dielectric sphere in a diverging radiation field,” Phys. Rev. A 16, 320–323 (1977);“Light scattering in converging beams,” Opt. Lett. 1, 138–140 (1977).
[Crossref] [PubMed]

L. W. Casperson, C. Yeh, and W. F. Yeung, “Single particle scattering with focused laser beams,” Appl. Opt. 16, 1104–1107 (1977).
[PubMed]

A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 23, 1351–1354 (1977).
[Crossref]

S. Y. Shin and L. B. Felsen, “Gaussian beam modes by multipoles with complex source points,” J. Opt. Soc. Am. 67, 699–700 (1977).
[Crossref]

1976 (3)

R. J. Pogorzelski and E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[Crossref]

P. Chylek, “Partial-wave resonances and the ripple structure in the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1976);P. Chylek, J. T. Kiehl, and M. K. W. Ko, “Narrow resonance structure in the Mie scattering characteristics,” Appl. Opt. 17, 3019–3021 (1978);“Optical levitation and partial-wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
[Crossref] [PubMed]

G. Roosen and C. Imbert, “Optical levitation by means of two horizontial laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976);G. Roosen, “A theoretical experimental study of the stable equilibrium position of spheres levitated by two horizontal laser beams,” Opt. Commun. 21, 189–194 (1977).
[Crossref]

1975 (2)

1974 (1)

A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).
[Crossref]

1971 (2)

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
[Crossref]

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[Crossref]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[Crossref]

1968 (1)

N. Morita, T. Tanaka, T. Yamasaki, and Y. Nakashini, “Scattering of beam wave by a spherical object,” IEEE Trans.Antennas Propag. AP-16, 724–727 (1968).
[Crossref]

1966 (1)

H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[Crossref]

1951 (1)

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

1935 (1)

W. W. Hansen, “A new type of expansion in radiation problems,” Phys. Rev. 47, 139–143 (1935).To simplify the formulation, the VSWF’s in Eq. (6) are defined somewhat differently from those in the reference.
[Crossref]

1908 (1)

G. Mie, “Beitrage zur optik trüber Medien, speziell kolloidaller Metalösungen,” Ann. Phys. 25, 377–445 (1908);P. Debye, “Die Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57–136 (1909).
[Crossref]

Aden, A. L.

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

Arfken, G.

G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1970), p. 560.

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981);T. R. Lattieri, W. D. Jenkins, and D. A. Swyt, “Sizing of individual optically levitated evaporating droplets by measurement of resonances in the polarization ratio,” Appl. Opt. 20, 2799–2805 (1981).
[Crossref] [PubMed]

A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980);G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260–1279 (1979).
[Crossref] [PubMed]

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978);“Focusing and defocusing of neutral atomic beams using resonance-radiation pressure,” Appl. Phys. Lett. 36, 99–101 (1980).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 23, 1351–1354 (1977).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
[Crossref]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[Crossref]

Belanger, P. A.

M. Couture and P. A. Belanger, “From Gaussian beam to complex-source-point wave,” Phys. Rev. A 24, 355–359 (1981).
[Crossref]

Bjorkholm, J. E.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978);“Focusing and defocusing of neutral atomic beams using resonance-radiation pressure,” Appl. Phys. Lett. 36, 99–101 (1980).
[Crossref]

Casperson, L. W.

Chew, H.

H. Chew, M. Kerker, and D. D. Cooke, “Electromagnetic scattering by a dielectric sphere in a diverging radiation field,” Phys. Rev. A 16, 320–323 (1977);“Light scattering in converging beams,” Opt. Lett. 1, 138–140 (1977).
[Crossref] [PubMed]

Chylek, P.

Cooke, D. D.

H. Chew, M. Kerker, and D. D. Cooke, “Electromagnetic scattering by a dielectric sphere in a diverging radiation field,” Phys. Rev. A 16, 320–323 (1977);“Light scattering in converging beams,” Opt. Lett. 1, 138–140 (1977).
[Crossref] [PubMed]

Couture, M.

M. Couture and P. A. Belanger, “From Gaussian beam to complex-source-point wave,” Phys. Rev. A 24, 355–359 (1981).
[Crossref]

Davis, L. W.

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[Crossref]

de Saint Louvent, B. F.

G. Roosen, B. F. de Saint Louvent, and S. Slansky, “Étude de la pression de radiation exercée sur une sphere creuse transparente par un faisceau cylindrique,” Opt. Comm. 24, 116–120 (1978);G. Roosen and C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
[Crossref]

Deschamps, G. A.

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[Crossref]

Dziedzic, J. M.

A. Ashkin and J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981);T. R. Lattieri, W. D. Jenkins, and D. A. Swyt, “Sizing of individual optically levitated evaporating droplets by measurement of resonances in the polarization ratio,” Appl. Opt. 20, 2799–2805 (1981).
[Crossref] [PubMed]

A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 23, 1351–1354 (1977).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
[Crossref]

Felsen, L. B.

Freeman, R. R.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978);“Focusing and defocusing of neutral atomic beams using resonance-radiation pressure,” Appl. Phys. Lett. 36, 99–101 (1980).
[Crossref]

Gouesbet, G.

Grehan, G.

Hansen, W. W.

W. W. Hansen, “A new type of expansion in radiation problems,” Phys. Rev. 47, 139–143 (1935).To simplify the formulation, the VSWF’s in Eq. (6) are defined somewhat differently from those in the reference.
[Crossref]

Imbert, C.

G. Roosen and C. Imbert, “Optical levitation by means of two horizontial laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976);G. Roosen, “A theoretical experimental study of the stable equilibrium position of spheres levitated by two horizontal laser beams,” Opt. Commun. 21, 189–194 (1977).
[Crossref]

Kerker, M.

H. Chew, M. Kerker, and D. D. Cooke, “Electromagnetic scattering by a dielectric sphere in a diverging radiation field,” Phys. Rev. A 16, 320–323 (1977);“Light scattering in converging beams,” Opt. Lett. 1, 138–140 (1977).
[Crossref] [PubMed]

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

Kim, J. S.

J. S. Kim and S. S. Lee, “Radiation pressure on a dielectric sphere in a Gaussian laser beam,” Opt. Acta 29, 801–806 (1982).
[Crossref]

J. S. Kim and S. S. Lee, “Radiation pressure on a dielectric sphere in focused laser beam,” presented at ICO-12, Graz, Austria, 1981.

Kogelnik, H.

H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[Crossref]

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial optics,” Phys. Rev. A 11, 1365–1367 (1975).
[Crossref]

Lee, S. S.

J. S. Kim and S. S. Lee, “Radiation pressure on a dielectric sphere in a Gaussian laser beam,” Opt. Acta 29, 801–806 (1982).
[Crossref]

J. S. Kim and S. S. Lee, “Radiation pressure on a dielectric sphere in focused laser beam,” presented at ICO-12, Graz, Austria, 1981.

Li, T.

H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966).
[Crossref]

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial optics,” Phys. Rev. A 11, 1365–1367 (1975).
[Crossref]

Lun, E.

R. J. Pogorzelski and E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[Crossref]

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial optics,” Phys. Rev. A 11, 1365–1367 (1975).
[Crossref]

Mie, G.

G. Mie, “Beitrage zur optik trüber Medien, speziell kolloidaller Metalösungen,” Ann. Phys. 25, 377–445 (1908);P. Debye, “Die Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57–136 (1909).
[Crossref]

Morita, N.

N. Morita, T. Tanaka, T. Yamasaki, and Y. Nakashini, “Scattering of beam wave by a spherical object,” IEEE Trans.Antennas Propag. AP-16, 724–727 (1968).
[Crossref]

Nakashini, Y.

N. Morita, T. Tanaka, T. Yamasaki, and Y. Nakashini, “Scattering of beam wave by a spherical object,” IEEE Trans.Antennas Propag. AP-16, 724–727 (1968).
[Crossref]

Pearson, D. B.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978);“Focusing and defocusing of neutral atomic beams using resonance-radiation pressure,” Appl. Phys. Lett. 36, 99–101 (1980).
[Crossref]

Pogorzelski, R. J.

Roosen, G.

G. Roosen and S. Slansky, “Influence of the beam divergence on the forces on a sphere by a laser beam and required condition for stable optical levitation,” Opt. Commun. 29, 341–346 (1979).
[Crossref]

G. Roosen, B. F. de Saint Louvent, and S. Slansky, “Étude de la pression de radiation exercée sur une sphere creuse transparente par un faisceau cylindrique,” Opt. Comm. 24, 116–120 (1978);G. Roosen and C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
[Crossref]

G. Roosen and C. Imbert, “Optical levitation by means of two horizontial laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976);G. Roosen, “A theoretical experimental study of the stable equilibrium position of spheres levitated by two horizontal laser beams,” Opt. Commun. 21, 189–194 (1977).
[Crossref]

Shin, S. Y.

Slansky, S.

G. Roosen and S. Slansky, “Influence of the beam divergence on the forces on a sphere by a laser beam and required condition for stable optical levitation,” Opt. Commun. 29, 341–346 (1979).
[Crossref]

G. Roosen, B. F. de Saint Louvent, and S. Slansky, “Étude de la pression de radiation exercée sur une sphere creuse transparente par un faisceau cylindrique,” Opt. Comm. 24, 116–120 (1978);G. Roosen and C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
[Crossref]

Tanaka, T.

N. Morita, T. Tanaka, T. Yamasaki, and Y. Nakashini, “Scattering of beam wave by a spherical object,” IEEE Trans.Antennas Propag. AP-16, 724–727 (1968).
[Crossref]

Tsai, W. C.

Watson, G. N.

G. N. Watson, Theory of Bessel Function (Cambridge U. Press, London, 1941), p. 366.

Yamasaki, T.

N. Morita, T. Tanaka, T. Yamasaki, and Y. Nakashini, “Scattering of beam wave by a spherical object,” IEEE Trans.Antennas Propag. AP-16, 724–727 (1968).
[Crossref]

Yeh, C.

Yeung, W. F.

Ann. Phys. (1)

G. Mie, “Beitrage zur optik trüber Medien, speziell kolloidaller Metalösungen,” Ann. Phys. 25, 377–445 (1908);P. Debye, “Die Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. 30, 57–136 (1909).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (3)

A. Ashkin and J. M. Dziedzic, “Optical levitation by radiation pressure,” Appl. Phys. Lett. 19, 283–285 (1971).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Stability of optical levitation by radiation pressure,” Appl. Phys. Lett. 24, 586–588 (1974).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Feedback stabilization of optically levitated particles,” Appl. Phys. Lett. 30, 202–204 (1977).
[Crossref]

Electron. Lett. (1)

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[Crossref]

IEEE Trans.Antennas Propag. (1)

N. Morita, T. Tanaka, T. Yamasaki, and Y. Nakashini, “Scattering of beam wave by a spherical object,” IEEE Trans.Antennas Propag. AP-16, 724–727 (1968).
[Crossref]

J. Appl. Phys. (1)

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

J. Opt. Soc. Am. (3)

Opt. Acta (1)

J. S. Kim and S. S. Lee, “Radiation pressure on a dielectric sphere in a Gaussian laser beam,” Opt. Acta 29, 801–806 (1982).
[Crossref]

Opt. Comm. (1)

G. Roosen, B. F. de Saint Louvent, and S. Slansky, “Étude de la pression de radiation exercée sur une sphere creuse transparente par un faisceau cylindrique,” Opt. Comm. 24, 116–120 (1978);G. Roosen and C. Imbert, “The TEM01* mode laser beam—a powerful tool for optical levitation of various types of spheres,” Opt. Commun. 26, 432–436 (1978).
[Crossref]

Opt. Commun. (1)

G. Roosen and S. Slansky, “Influence of the beam divergence on the forces on a sphere by a laser beam and required condition for stable optical levitation,” Opt. Commun. 29, 341–346 (1979).
[Crossref]

Phys. Lett. (1)

G. Roosen and C. Imbert, “Optical levitation by means of two horizontial laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976);G. Roosen, “A theoretical experimental study of the stable equilibrium position of spheres levitated by two horizontal laser beams,” Opt. Commun. 21, 189–194 (1977).
[Crossref]

Phys. Rev. (1)

W. W. Hansen, “A new type of expansion in radiation problems,” Phys. Rev. 47, 139–143 (1935).To simplify the formulation, the VSWF’s in Eq. (6) are defined somewhat differently from those in the reference.
[Crossref]

Phys. Rev. A (4)

L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
[Crossref]

M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial optics,” Phys. Rev. A 11, 1365–1367 (1975).
[Crossref]

M. Couture and P. A. Belanger, “From Gaussian beam to complex-source-point wave,” Phys. Rev. A 24, 355–359 (1981).
[Crossref]

H. Chew, M. Kerker, and D. D. Cooke, “Electromagnetic scattering by a dielectric sphere in a diverging radiation field,” Phys. Rev. A 16, 320–323 (1977);“Light scattering in converging beams,” Opt. Lett. 1, 138–140 (1977).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978);“Focusing and defocusing of neutral atomic beams using resonance-radiation pressure,” Appl. Phys. Lett. 36, 99–101 (1980).
[Crossref]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[Crossref]

A. Ashkin and J. M. Dziedzic, “Observation of resonances in the radiation pressure on dielectric spheres,” Phys. Rev. Lett. 23, 1351–1354 (1977).
[Crossref]

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[Crossref]

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R. J. Pogorzelski and E. Lun, “On the expansion of cylindrical vector waves in terms of spherical vector waves,” Radio Sci. 11, 753–761 (1976).
[Crossref]

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A. Ashkin, “Applications of laser radiation pressure,” Science 210, 1081–1088 (1980);G. Roosen, “La lévitation optique de sphères,” Can. J. Phys. 57, 1260–1279 (1979).
[Crossref] [PubMed]

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J. S. Kim and S. S. Lee, “Radiation pressure on a dielectric sphere in focused laser beam,” presented at ICO-12, Graz, Austria, 1981.

G. N. Watson, Theory of Bessel Function (Cambridge U. Press, London, 1941), p. 366.

G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1970), p. 560.

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Figures (5)

Fig. 1
Fig. 1

Geometry of laser-beam scattering by a homogeneous sphere. (x0, y0, z0) are the beam-center coordinates, w0 is the radius of the beam waist, and a is the radius of the sphere.

Fig. 2
Fig. 2

(a) Variations of the three vector components FAX, FTR, and FTA of the radiation pressure of a Gaussian laser beam (λ = 5145 Å, w0 = 3λ, z0 = y0 = 0) acting on a sphere (n = 1.59, a = 3λ) across the beam waist. (b) Optical potential well for the sphere that is due to FTR.

Fig. 3
Fig. 3

(a) Variations of the three vector components FAX, FTR, and FTA of the radiation pressure of a Gaussian laser beam (λ = 5145 Å, w0 = 3λ, z0 = y0 = 0) acting on a sphere with refractive index less than one (n = 0.697, a = 3λ) across the beam waist. (b) Optical potential hill for the sphere that is due to FTR.

Fig. 4
Fig. 4

Variations of the components FAX and FTR of the radiation pressure of a Gaussian laser beam (λ = 5145 Å, w0 = 3λ, y0 = 0) on the spheres (n = 1.59, a = 3λ) at different axial positions. The dashed curves are for z0 = -5w0, the solid curves are for z0 = 0, and the dotted- dashed curves are for z0 = 5w0.

Fig. 5
Fig. 5

Variations of the components FAX and FTR of the radiation pressure of a Gaussian laser beam (λ = 5145 Å, w0 = 3λ, z0 = y0 = 0) on spheres of different radii (n = 1.59; a = 2λ, 3λ, 4λ). The dashed curves are for a = 2λ, the solid curves are for a = 3λ, and the dotted- dashed curves are for a = 4λ.

Equations (54)

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F = { F in = F t F out = F i + F s inside the sphere , outside the sphere
2 F out + k 2 F out = 0 , 2 F in + ( n k ) 2 F in = 0 .
E = x ̂ E 0 = i b z i b exp [ i k z + i k x 2 + y 2 2 ( z i b ) ] ,
A = x ̂ ψ 00 , ψ 00 = C e i k R i k R , R = [ ( x x 0 ) 2 + ( y y 0 ) 2 + ( z z 0 i b ) 2 ] 1 / 2 ,
E i = i k × × A , H i = × A .
E = x ̂ C i k z z 0 i b × exp [ i k ( z z 0 i b ) + i k ( x x 0 ) 2 + ( y y 0 ) 2 2 ( z z 0 i b ) ] ,
L l , m ( σ ) = f l , m ( σ ) , M l , m ( σ ) = × ( r f l , m ( σ ) ) ( σ = 0 , 1 , 2 ) , N l , m ( σ ) = 1 k × × ( r f l , m ( σ ) ) ,
f l , m ( σ ) = z l ( σ ) ( k r ) P l m ( cos θ ) e i m ϕ .
× M l , m ( σ ) = k N l , m ( σ ) , × N l , m ( σ ) = k M l , m ( σ ) .
ψ 00 = { C l = 0 m = l l H 00 ( 1 ) ( l , m ) f l , m ( 0 ) | r | < | r 0 e ± i Δ | C l = 0 m = l l H 00 ( 0 ) ( l , m ) f l , m ( 1 ) 0 θ π 2 , | r 0 | < | r ± i Δ | , C l = 0 m = l l H 00 ( 0 ) ( l , m ) f l , m ( 2 ) π 2 < θ π , | r 0 | < | r ± i Δ |
Δ = cos 1 x x 0 + y y 0 + z ( z 0 + i b ) r r 0
H 00 ( η ) ( l , m ) = ( 2 l + 1 ) ( l m ) ! ( l + m ) ! z l ( η ) ( k r 0 ) P l m ( cos θ 0 ) e i m ϕ 0 , r 0 = [ x 0 2 + y 0 2 + ( z 0 + i b ) 2 ] 1 / 2 , cos θ 0 = z 0 + i b r 0 , ϕ 0 = tan 1 y 0 x 0 .
A = C l , m [ α ( η ) ( l , m ) M l , m ( σ ) + β ( η ) ( l , m ) N l , m ( σ ) + γ ( η ) ( l , m ) L l , m ( σ ) ] ,
E i = i k C l , m [ α ( η ) ( l , m ) M l , m ( σ ) + β ( η ) ( l , m ) N l , m ( σ ) ] , H i = k C l , m [ β ( η ) ( l , m ) M l , m ( σ ) + α ( η ) ( l , m ) M l , m ( σ ) ] .
α ( η ) ( l , m ) = i 2 l ( l + 1 ) [ H 00 ( η ) ( l , m 1 ) + ( l m ) ( l + m + 1 ) H 00 ( η ) ( l , m + 1 ) ] , β ( η ) ( l , m ) = 1 2 l ( l + 1 ) { [ l + 1 2 l 1 H 00 ( η ) ( l 1 , m 1 ) ( l m 1 ) ( l m ) H 00 ( η ) ( l 1 , m + 1 ) ] l 2 l + 3 [ H 00 ( η ) ( l + 1 , m 1 ) ( l + m + 1 ) × ( l + m + 2 ) H 00 ( η ) ( l + 1 , m + 1 ) ] } .
E s = i k C l , m [ a l α ( l , m ) M l , m ( 1 ) + b l β ( l , m ) N l , m ( 1 ) ] , H s = k C l , m [ a l α ( l , m ) N l , m ( 1 ) + b l β ( l , m ) M l , m ( 1 ) ] , E t = i k C l , m [ c l α ( l , m ) M ¯ l , m ( 0 ) + d l β ( l , m ) N ¯ l , m ( 0 ) ] , H t = k C l , m [ c l α ( l , m ) N ¯ l , m ( 0 ) + d l β ( l , m ) M ¯ l , m ( 0 ) ] ,
a l = j l ( n ρ ) [ ρ j l ( ρ ) ] [ n ρ j l ( n ρ ) ] j l ( ρ ) j l ( n ρ ) [ ρ h l ( 1 ) ( ρ ) ] [ n ρ j l ( n ρ ) ] h l ( 1 ) ( ρ ) , b l = n 2 j l ( n ρ ) [ ρ j l ( ρ ) ] [ n ρ j l ( n ρ ) ] j l ( ρ ) n 2 j l ( n ρ ) [ ρ h l ( 1 ) ( ρ ) ] [ n ρ j l ( n ρ ) ] h l ( 1 ) ( ρ ) , c l = j l ( ρ ) [ ρ h l ( 1 ) ( ρ ) ] [ ρ j l ( ρ ) ] h l ( 1 ) ( ρ ) j l ( n ρ ) [ ρ h l ( 1 ) ( ρ ) ] [ n ρ j l ( n ρ ) ] h l ( 1 ) ( ρ ) , d l = n j l ( ρ ) [ ρ h l ( 1 ) ( ρ ) ] [ ρ j l ( ρ ) ] h l ( 1 ) ( ρ ) n 2 j l ( n ρ ) [ ρ h l ( 1 ) ( ρ ) ] [ n ρ j l ( n ρ ) ] h l ( 1 ) ( ρ ) ,
W ext = W sc + W ab .
S = υ 8 π E out × H out * = υ 8 π ( E i × H i * + E s × H s * + E i × H s * + E s × H s * ) ,
W sc = Re υ 8 π Γ d a ( E s × H s * ) ,
W ext = Re υ 8 π Γ da ( E i × H s * + E s × H i * ) .
W sc = υ | C | 2 2 l , m l ( l + 1 ) 2 l + 1 ( l + m ) ! ( l m ) ! × [ | a l α ( l , m ) | 2 + | b l β ( l , m ) | 2 ] , W ext = υ | C | 2 2 l , m l ( l + 1 ) 2 l + 1 ( l + m ) ! ( l m ) ! × Re [ a l | α ( l , m ) | 2 + b l | β ( l , m ) | 2 ] .
P = Re S υ .
F x + i F y = 1 8 π Γ d a ( E i × H s * + E s × H i * + E s × H s * ) sin θ e i ϕ , F z = 1 8 π Re Γ d a . ( E i × H s * + E s × H i * + E s × H s * ) cos θ .
F x + i F y = | C | 2 4 l , m 1 2 l + 1 ( l + m ) ! ( l m ) ! × { ( l m ) ( l + m + 1 ) [ M i c ( l ) α ( l , m ) β * ( l , m + 1 ) + M i c * ( l ) α * ( l , m + 1 ) β ( l , m ) ] i l ( l + 2 ) 2 l + 3 ( l + m + 1 ) × ( l + m + 2 ) [ M i a ( l ) α ( l , m ) α * ( l + 1 , m + 1 ) + M i b ( l ) β ( l , m ) β * ( l + 1 , m + 1 ) ] i l ( l + 2 ) 2 l + 3 × [ M i a * ( l ) α * ( l , m ) α ( l + 1 , m 1 ) + M i b * ( l ) β * ( l , m ) β * ( l + 1 , m 1 ) ] } , F z = | C | 2 2 Re l , m 1 2 l + 1 ( l + m ) ! ( l m ) ! × { m M i c ( l ) α ( l , m ) β * ( l , m ) i l ( l + 2 ) 2 l + 3 × [ ( l + m + 1 ) M i a ( l ) α ( l , m ) α * ( l + 1 , m ) + M i b ( l ) β ( l , m ) β * ( l + 1 , m ) ] } ,
M i a ( l ) = 2 a l a l + 1 * + a l + a l + 1 * , M i b ( l ) = 2 b l b l + 1 * + b l + b l + 1 * , M i c ( l ) = 2 a l b l * + a l + b l * .
α ( l , m ) | ( x 0 , y 0 , z 0 ) = ( 1 ) m 1 α ( l , m ) | ( x 0 , y 0 , z 0 ) , β ( l , m ) | ( x 0 , y 0 , z 0 ) = ( 1 ) m 1 β ( l , m ) | ( x 0 , y 0 , z 0 ) ,
W ext ( x 0 , y 0 , z 0 ) = W ext ( x 0 , y 0 , z 0 ) , W sc ( x 0 , y 0 , z 0 ) = W sc ( x 0 , y 0 , z 0 ) , F z ( x 0 , y 0 , z 0 ) = F z ( x 0 , y 0 , z 0 ) ,
{ F x + i F y } ( x 0 , y 0 , z 0 ) = { F x + i F y } ( x 0 , y 0 , z 0 ) .
α ( l , 1 ) = β ( l , 1 ) = C e k b k b 2 l + 1 2 l ( l + 1 ) i l 1 , α ( l , 1 ) = β ( l , 1 ) = C e k b k b 2 l + 1 2 i l 1 .
W sc = ( 2 l + 1 ) ( | a l | 2 + | b l | 2 ) , W ext = Re ( 2 l + 1 ) ( a l + b l ) , F z = 1 υ W ext Re 2 υ l [ 2 l + 1 l ( l + 1 ) a l b l * + l ( l + 2 ) ( l + 1 ) ( a l a l + 1 * + b l b l + 1 * ) ] , F x = F y = 0 ,
A = x ̂ C μ + ν x μ y ν ψ 00 .
H μ + 1 ν ( l , m ) = k 2 [ 1 2 l 1 [ H μ ν ( l 1 , m 1 ) + ( l m 1 ) ( l m ) H μ ν ( l 1 , m + 1 ) ] + 1 2 l + 3 [ H μ ν ( l + 1 , m 1 ) + ( l + m + 1 ) × ( l + m + 2 ) H μ ν ( l + 1 , m + 1 ) ] } , H μ ν + 1 ( l , m ) = i k 2 { 1 2 l 1 [ H μ ν ( l 1 , m 1 ) + ( l m 1 ) ( l m ) H μ ν ( l 1 , m + 1 ) + 1 2 l + 3 [ H μ ν ( l + 1 , m 1 ) + ( l + m + 1 ) × ( l + m + 2 ) H μ ν ( l + 1 , m + 1 ) ] } .
× A = × [ x ̂ C l , m H 00 ( η ) ( l , m ) f l , m ( σ ) ] = k C l , m [ α ( η ) ( l , m ) N l , m ( σ ) + β ( η ) ( l , m ) M l , m ( σ ) ] .
l , m [ α ( η ) ( l , m ) l ( l + 1 ) z l ( σ ) k r P l m e i m ϕ = l , m H 00 ( η ) ( l , m ) z l ( σ ) k r × ( P l m θ sin ϕ + im cos θ sin θ P l m cos ϕ ) e i m ϕ ,
i 2 l , m H 00 ( η ) ( l , m ) z l ( σ ) k r { e i ( m + 1 ) ϕ [ P l m θ m cos θ sin θ P l m ] e i ( m 1 ) ϕ [ P l m θ + m cos θ sin θ P l m ] } .
l , m α ( η ) ( l , m ) l ( l + 1 ) z l ( σ ) k r P l m e i m ϕ = i 2 l , m [ H 00 ( η ) ( l , m 1 ) + ( l m ) × ( l + m + 1 ) H 00 ( η ) ( l , m + 1 ) ] z l ( σ ) k r P l m e i m ϕ .
I 1 = 0 2 π d ϕ 0 π sin θ d θ × ( m P l m sin P l m θ + m P l m θ P l m sin θ ) exp [ i ( m m ) ϕ ] , I 2 = 0 2 π d ϕ 0 π sin θ d θ × ( m m P l m P l m sin 2 + P l m θ P l m θ ) exp [ i ( m m ) ϕ ] .
I 1 = 0 , I 2 = 4 π l ( l + 1 ) ( l + m ) ! 2 l + 1 ( l m ) ! δ m , m δ l , l ,
I 3 = 0 2 π d ϕ 0 π sin θ d θ ( m P l m sin θ P l m θ + m P l m θ P l m sin ) × cos θ exp [ i ( m m ) ϕ ] , I 4 = 0 2 π d ϕ 0 π sin θ d θ ( m m P l m P l m sin 2 θ + P l m θ P l m θ ) × cos θ exp [ i ( m m ) ϕ ] , I 5 = 0 2 π d ϕ 0 π sin θ d θ ( m P l m sin P l m θ + m P l m θ P l m sin θ ) × sin θ exp [ i ( m m + 1 ) ϕ ] , I 6 = 0 2 π d ϕ 0 π sin θ d θ ( m m P l m P l m sin 2 θ + P l m θ P l m θ ) × sin θ exp [ i ( m m + 1 ) ϕ ] .
I 3 = 4 π 2 l + 1 ( l + m ) ! ( l m ) ! m δ m , m δ l , l , I 4 = 4 π ( 2 l + 1 ) ( 2 l + 1 ) ( l + m ) ! ( l m ) ! δ m , m [ l ( l + 2 ) × ( l m + 1 ) δ l + 1 , l + ( l 1 ) ( l + 1 ) ( l + m ) δ l 1 , l ] , I 5 = 4 π 2 l + 1 ( l + m ) ! ( l m ) ! ( l m ) ( l + m + 1 ) δ m + 1 , m δ l , l I 6 = 4 π ( 2 l + 1 ) ( 2 l + 1 ) ( l + m ) ! ( l m ) ! δ m + 1 , m × [ ( l 1 ) ( l + 1 ) ( l + m ) ( l + m + 1 ) δ l , l 1 l ( l + 2 ) ( l m ) ( l m + 1 ) δ l , l + 1 ] .
ψ μ ν = C l , m H μ ν ( η ) ( l , m ) f l , m ( σ ) .
ψ μ + 1 ν = C l , m H μ + 1 ν ( η ) ( l , m ) f l , m ( σ ) = C l , m H μ ν ( η ) ( l , m ) x f l , m ( σ ) .
k 2 l , m H μ ν ( η ) ( l , m ) { exp [ i ( m + 1 ) ϕ ] [ z l ( σ ) ξ sin θ P l m + z l ( σ ) ξ ( cos θ P l m θ m sin θ P l m ) ] + exp [ i ( m 1 ) ϕ ] × [ z l ( σ ) ξ sin θ P l m + z l ( σ ) ξ ( cos θ P l m θ + m sin θ P l m ) ] } ,
k 2 { 1 2 l 1 [ H μ ν ( η ) ( l 1 , m 1 ) + ( l m 1 ) ( l m ) × H μ ν ( η ) ( l 1 , m + 1 ) ] + 1 2 l + 3 [ H μ ν ( η ) ( l + 1 , m 1 ) + ( l + m + 1 ) ( l + m + 2 ) H μ ν ( η ) ( l + 1 , m + 1 ) ] } .
( 2 l + 1 ) cos θ P l m = ( l + m ) P l 1 m + ( l m + 1 ) P l + 1 m ,
( 2 l + 1 ) sin θ P l m = ( l + m 1 ) ( l + m ) P l 1 m 1 ( l m + 1 ) ( l m + 2 ) P l + 1 m 1 = P l + 1 m + 1 P l 1 m + 1 ,
2 m sin θ P l m = cos θ [ ( l m + 1 ) ( l + m ) P l m 1 + P l m + 1 ] + 2 m sin θ P l m ,
2 P l m θ = ( l m + 1 ) ( l + m ) P l m 1 P l m + 1 ,
2 m cos θ sin θ P l m = ( l m + 1 ) ( l + m ) P l m 1 + P l m + 1 ,
( 2 l + 1 ) sin θ P l m θ = l ( l m + 1 ) P l + 1 m ( l + 1 ) ( l + m ) P l 1 m .
0 π sin θ d θ P l m P l m = 2 2 l + 1 ( l + m ) ! ( l m ) ! δ l , l .
( 2 l + 1 ) z l ( σ ) ξ = l z l 1 ( σ ) ( l + 1 ) z l + 1 ( σ ) ,
( 2 l + 1 ) z l ( σ ) ξ = z l 1 ( σ ) + z l + 1 ( σ ) , h l ( 1 ) ( ξ ) ( i ) l e i ξ i ξ , j l ( ξ ) 1 ξ sin ( ξ l π 2 ) .