Abstract

The excitation efficiency of a morphology-dependent resonance (MDR) by an incident beam is defined as the fraction of the beam power channeled into the MDR. The efficiency is calculated for a focused Gaussian beam of arbitrary width incident on either a spherical particle or a cylindrical fiber located at an arbitrary position in the plane of the beam waist. In each case a simple formula for the efficiency is derived by use of the localized approximation for the beam-shape coefficients in the partial-wave expansion of the beam. The physical interpretation of the efficiency formulas is also discussed.

© 1998 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 208–209.
  2. H. M. Nussenzveig, “Tunneling effects in diffractive scattering and resonances,” Comments At. Mol. Phys. 4, 175–187 (1989).
  3. L. G. Guimaraes, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
    [CrossRef]
  4. B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993).
    [CrossRef]
  5. P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant spectra of dielectric spheres,” J. Opt. Soc. Am. A 1, 62–67 (1984).
    [CrossRef]
  6. P. Chylek, J. D. Pendleton, R. G. Pinnick, “Internal and near-surface scattered field of a spherical particle at resonant conditions,” Appl. Opt. 24, 3940–3942 (1985).
    [CrossRef] [PubMed]
  7. P. Chylek, “Partial-wave resonances and the ripple structure in the Mie normalized extinction cross section,” J. Opt. Soc. Am. 66, 285–287 (1976).
    [CrossRef]
  8. A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
    [CrossRef] [PubMed]
  9. T. Baer, “Continuous-wave laser oscillation in a Nd:YAG sphere,” Opt. Lett. 12, 392–394 (1987).
    [CrossRef] [PubMed]
  10. J.-Z. Zhang, D. H. Leach, R. K. Chang, “Photon lifetime within a droplet: temporal determination of elastic and stimulated Raman scattering,” Opt. Lett. 13, 270–272 (1988).
    [CrossRef] [PubMed]
  11. B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
    [CrossRef]
  12. J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
    [CrossRef]
  13. E. E. M. Khaled, S. C. Hill, P. W. Barber, D. Q. Chowdhury, “Near-resonance excitation of dielectric spheres with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
    [CrossRef] [PubMed]
  14. E. E. M. Khaled, S. C. Hill, P. W. Barber, “Internal electric energy in a spherical particle illuminated with a plane wave or off-axis Gaussian beam,” Appl. Opt. 33, 524–532 (1994).
    [CrossRef] [PubMed]
  15. J. A. Lock, “Improved Gaussian beam-scattering algorithm,” Appl. Opt. 34, 559–570 (1995).
    [CrossRef] [PubMed]
  16. G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
    [CrossRef]
  17. J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz–Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
    [CrossRef]
  18. G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
    [CrossRef]
  19. A. Serpenguzel, S. Arnold, G. Griffel, J. A. Lock, “Enhanced coupling to microsphere resonances with optical fibers,” J. Opt. Soc. Am. B 14, 790–795 (1997).
    [CrossRef]
  20. Equation (63) of Ref. 15 giving the optimal beam position for sphere MDR’s, is also valid for cylinder MDR’s since the calculation leading to Eq. (1.1) of C. C. Lam, P. T. Leung, K. Young, “Explicit asymptotic formulas for the positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992), on which the result of Ref. 15 is based, is valid for Bessel functions of both integer order (cylinders) and half-integer order (spheres).
    [CrossRef]
  21. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  22. A. Gray, G. B. Mathews, A Treatise on Bessel Functions and Their Applications to Physics (Dover, New York, 1966), p. 36.
  23. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 718, Eq. (6.633.4).
  24. H. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  25. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 378, Eqs. (9.8.1)–(9.8.4) along with the recursion relation of Eq. (9.6.26).
  26. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 375, Eq. (9.6.10).
  27. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 377, Eq. (9.7.1).
  28. P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical levitation and partial wave resonances,” Phys. Rev. A 18, 2229–2233 (1978).
    [CrossRef]
  29. P. M. Aker, P. A. Moortgat, J.-X. Zhang, “Morphology-dependent stimulated Raman scattering imaging. 1. Theoretical aspects,” J. Chem. Phys. 105, 7268–7275 (1996).
    [CrossRef]
  30. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 194–204.
  31. J. A. Lock, “Morphology-dependent resonances of an infinitely long circular cylinder illuminated by a diagonally incident plane wave or a focused Gaussian beam,” J. Opt. Soc. Am. A 14, 653–661 (1997).
    [CrossRef]
  32. L. G. Guimaraes, J. P. Rodrigues, F. de Mendonca, “Analysis of the resonant scattering of light by cylinders at oblique incidence,” Appl. Opt. 36, 8010–8019 (1997).
    [CrossRef]
  33. J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder,” J. Opt. Soc. Am. A 14, 640–652 (1997).
    [CrossRef]
  34. Another localized approximation for the beam-shape coefficients for scattering by a cylinder is described in K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in the framework of generalized Lorenz–Mie theory: formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
    [CrossRef]
  35. 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.
  36. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 307, Eq. (3.323.3).
  37. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 375, Eq. (9.6.9); p. 378, Eq. (9.7.2).
  38. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 307, Eq. (3.326).
  39. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 98–99, Figs. 4.1 and 4.2.
  40. The situation is described clearly in M. Kerker, P. J. McNulty, M. Sculley, H. Chew, D. D. Cooke, “Raman and fluorescent scattering by molecules embedded in small particles: numerical results for incoherent optical processes,” J. Opt. Soc. Am. 68, 1676–1686 (1978).
    [CrossRef]
  41. J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Reading, Mass., 1980), pp. 36–57.
  42. G. Roll, G. Schweiger, “Resonance shift of obliquely illuminated dielectric cylinders,” Appl. Opt. 37, 5628–5630 (1998).
    [CrossRef]
  43. H.-B. Lin, J. D. Eversole, A. J. Campillo, J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. (to published).

1998 (1)

1997 (5)

1996 (1)

P. M. Aker, P. A. Moortgat, J.-X. Zhang, “Morphology-dependent stimulated Raman scattering imaging. 1. Theoretical aspects,” J. Chem. Phys. 105, 7268–7275 (1996).
[CrossRef]

1995 (1)

1994 (3)

1993 (1)

1992 (3)

1990 (1)

1989 (3)

B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

H. M. Nussenzveig, “Tunneling effects in diffractive scattering and resonances,” Comments At. Mol. Phys. 4, 175–187 (1989).

1988 (2)

1987 (1)

1985 (1)

1984 (1)

1981 (1)

1978 (2)

1976 (1)

1966 (1)

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 377, Eq. (9.7.1).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 378, Eqs. (9.8.1)–(9.8.4) along with the recursion relation of Eq. (9.6.26).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 375, Eq. (9.6.10).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 375, Eq. (9.6.9); p. 378, Eq. (9.7.2).

Aker, P. M.

P. M. Aker, P. A. Moortgat, J.-X. Zhang, “Morphology-dependent stimulated Raman scattering imaging. 1. Theoretical aspects,” J. Chem. Phys. 105, 7268–7275 (1996).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Arnold, S.

Ashkin, A.

Baer, T.

Barber, P. W.

Barton, J. P.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

H.-B. Lin, J. D. Eversole, A. J. Campillo, J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. (to published).

Benner, R. E.

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.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 194–204.

Campillo, A. J.

H.-B. Lin, J. D. Eversole, A. J. Campillo, J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. (to published).

Chang, R. K.

Chew, H.

Chowdhury, D. Q.

Chylek, P.

Conwell, P. R.

Cooke, D. D.

de Mendonca, F.

Dziedzic, J. M.

Eversole, J. D.

H.-B. Lin, J. D. Eversole, A. J. Campillo, J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. (to published).

Gouesbet, G.

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 307, Eq. (3.326).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 307, Eq. (3.323.3).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 718, Eq. (6.633.4).

Gray, A.

A. Gray, G. B. Mathews, A Treatise on Bessel Functions and Their Applications to Physics (Dover, New York, 1966), p. 36.

Gréhan, G.

Griffel, G.

Guimaraes, L. G.

L. G. Guimaraes, J. P. Rodrigues, F. de Mendonca, “Analysis of the resonant scattering of light by cylinders at oblique incidence,” Appl. Opt. 36, 8010–8019 (1997).
[CrossRef]

L. G. Guimaraes, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

Hill, S. C.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 194–204.

Johnson, B. R.

Kerker, M.

Khaled, E. E. M.

Kiehl, J. T.

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

Ko, M. K. W.

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

Kogelnik, H.

Lam, C. C.

Leach, D. H.

Leung, P. T.

Li, T.

Lin, H.-B.

H.-B. Lin, J. D. Eversole, A. J. Campillo, J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. (to published).

Lock, J. A.

Maheu, B.

Mathews, G. B.

A. Gray, G. B. Mathews, A Treatise on Bessel Functions and Their Applications to Physics (Dover, New York, 1966), p. 36.

McNulty, P. J.

Moortgat, P. A.

P. M. Aker, P. A. Moortgat, J.-X. Zhang, “Morphology-dependent stimulated Raman scattering imaging. 1. Theoretical aspects,” J. Chem. Phys. 105, 7268–7275 (1996).
[CrossRef]

Nussenzveig, H. M.

L. G. Guimaraes, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

H. M. Nussenzveig, “Tunneling effects in diffractive scattering and resonances,” Comments At. Mol. Phys. 4, 175–187 (1989).

Pendleton, J. D.

Pinnick, R. G.

Ren, K. F.

Rodrigues, J. P.

Roll, G.

Rushforth, C. K.

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 718, Eq. (6.633.4).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 307, Eq. (3.323.3).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 307, Eq. (3.326).

Sakurai, J. J.

J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Reading, Mass., 1980), pp. 36–57.

Schaub, S. A.

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

Schweiger, G.

Sculley, M.

Serpenguzel, A.

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 375, Eq. (9.6.10).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 375, Eq. (9.6.9); p. 378, Eq. (9.7.2).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 378, Eqs. (9.8.1)–(9.8.4) along with the recursion relation of Eq. (9.6.26).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 377, Eq. (9.7.1).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 208–209.

Young, K.

Zhang, J.-X.

P. M. Aker, P. A. Moortgat, J.-X. Zhang, “Morphology-dependent stimulated Raman scattering imaging. 1. Theoretical aspects,” J. Chem. Phys. 105, 7268–7275 (1996).
[CrossRef]

Zhang, J.-Z.

Appl. Opt. (8)

Comments At. Mol. Phys. (1)

H. M. Nussenzveig, “Tunneling effects in diffractive scattering and resonances,” Comments At. Mol. Phys. 4, 175–187 (1989).

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
[CrossRef]

J. Chem. Phys. (1)

P. M. Aker, P. A. Moortgat, J.-X. Zhang, “Morphology-dependent stimulated Raman scattering imaging. 1. Theoretical aspects,” J. Chem. Phys. 105, 7268–7275 (1996).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (9)

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz–Mie theory. I. On-axis beams,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
[CrossRef]

G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
[CrossRef]

P. R. Conwell, P. W. Barber, C. K. Rushforth, “Resonant spectra of dielectric spheres,” J. Opt. Soc. Am. A 1, 62–67 (1984).
[CrossRef]

J. A. Lock, “Scattering of a diagonally incident focused Gaussian beam by an infinitely long homogeneous circular cylinder,” J. Opt. Soc. Am. A 14, 640–652 (1997).
[CrossRef]

J. A. Lock, “Morphology-dependent resonances of an infinitely long circular cylinder illuminated by a diagonally incident plane wave or a focused Gaussian beam,” J. Opt. Soc. Am. A 14, 653–661 (1997).
[CrossRef]

Another localized approximation for the beam-shape coefficients for scattering by a cylinder is described in K. F. Ren, G. Gréhan, G. Gouesbet, “Scattering of a Gaussian beam by an infinite cylinder in the framework of generalized Lorenz–Mie theory: formulation and numerical results,” J. Opt. Soc. Am. A 14, 3014–3025 (1997).
[CrossRef]

B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993).
[CrossRef]

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

Opt. Commun. (2)

L. G. Guimaraes, H. M. Nussenzveig, “Theory of Mie resonances and ripple fluctuations,” Opt. Commun. 89, 363–369 (1992).
[CrossRef]

B. Maheu, G. Gréhan, G. Gouesbet, “Ray localization in Gaussian beams,” Opt. Commun. 70, 259–262 (1989).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

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

Other (14)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 208–209.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 378, Eqs. (9.8.1)–(9.8.4) along with the recursion relation of Eq. (9.6.26).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 375, Eq. (9.6.10).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 377, Eq. (9.7.1).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983), pp. 194–204.

A. Gray, G. B. Mathews, A Treatise on Bessel Functions and Their Applications to Physics (Dover, New York, 1966), p. 36.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 718, Eq. (6.633.4).

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.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 307, Eq. (3.323.3).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), p. 375, Eq. (9.6.9); p. 378, Eq. (9.7.2).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p. 307, Eq. (3.326).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969), pp. 98–99, Figs. 4.1 and 4.2.

J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Reading, Mass., 1980), pp. 36–57.

H.-B. Lin, J. D. Eversole, A. J. Campillo, J. P. Barton, “Excitation localization principle for spherical microcavities,” Opt. Lett. (to published).

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Figures (3)

Fig. 1
Fig. 1

Focused Gaussian beam with the center of its focal waist at (x0, y0, 0) incident on a spherical particle of radius a whose center is at the origin of coordinates.

Fig. 2
Fig. 2

Dependence of (a) the resonant size parameter and (b) the incident beam’s angular spectrum of plane waves on the angle η that a plane-wave component makes with the normal to the cylinder axis. The MDR linewidth is 2Γ, the laser beam linewidth is 2γ, and the beam’s angular spectrum extends to η2s.

Fig. 3
Fig. 3

(a) Focused Gaussian beam with the center of its focal waist at (0, y0, 0) normally incident on a cylindrical fiber of radius a whose axis coincides with the z axis. (b) Detector a distance r from the fiber in the far zone and concentric with the fiber axis.

Equations (55)

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

Pbeam=E022μ0cπ4k2l=1 2l+1l(l+1) m=-ll (l+|m|)!(l-|m|)!×(|Al,m|2+|Bl,m|2),
Pscatt=E022μ0cπk2l=1 2l+1l(l+1) m=-ll (l+|m|)!(l-|m|)!×(|Al,m|2|al|2+|Bl,m|2|bl|2),
LTE=Pscatt, LTE/Pbeam,
LTM=Pscatt, LTM/Pbeam,
Pscatt, LTE=E022μ0cπk2 2L+1L(L+1)×m=-LL (L+|m|)!(L-|m|)!|BL,m|2,
Pscatt, LTM=E022μ0cπk2 2L+1L(L+1)×m=-LL (L+|m|)!(L-|m|)!|AL,m|2.
Al,0=2il(l+1)(l+12)cos ϕ0×exp-ρ02w02+s2(l+12)2I1(Q),
Al,±m=[-i exp(iϕ0)/(l+12)]|m|-1×exp-ρ02w02+s2(l+12)2×[I|m|-1(Q)+exp(i2ϕ0)I|m|+1(Q)];
Bl,0=2il(l+1)(l+12)sin ϕ0×exp-ρ02w02+s2(l+12)2I1(Q),
Bl,±m=±1i[-i exp(iϕ0)/(l+12)]|m|-1×exp-ρ02w02+s2(l+12)2×[I|m|-1(Q)-exp(±2iϕ0)I|m|+1(Q)],
x0=ρ0 cos ϕ0,
y0=ρ0 sin ϕ0,
z0=0,
s=1/kw0,
Q=2s(l+12)ρ0/w0.
(l+|m|)!(l-|m|)!(l+12)|2m|,
IP(2x)=n=-In(x)Ip-n(x)
m (L+|m|)!(L-|m|)!|AL,m|22(L+12)2 exp-2ρ02w02+s2(L+12)2×I0(2Q)+cos 2ϕ0I2(2Q),
m (L+|m|)!(L-|m|)!|BL,m|22(L+12)2 exp-2ρ02w02+s2(L+12)2×[I0(2Q)-cos 2ϕ0 I2(2Q)].
PbeamE022μ0c2πk2exp(-2ρ02/w02)l=1(l+12)×I0[4s(l+12)ρ0/w0]exp[-2s2(l+12)2].
PbeamE022μ0c2πk2exp(-2ρ02/w02)0ldl×I0(4slρ0/w0)exp(-2s2l2)=E022μ0cπ w022,
LTE=8(L+12)s2 exp-2ρ02w02+s2(L+12)2×[I0(2Q)-cos 2ϕ0I2(2Q)],
LTM=8(L+12)s2 exp-2ρ02w02+s2(L+12)2×[I0(2Q)+cos 2ϕ0I2(2Q)].
LTELTM8(L+12)s2 exp[-2s2(L+12)2]×[1+O(Q2)].
2s2(L+12)2=1,
W0=λL/(2)1/2π(2)1/2 na
(L)max4e-1/L0.234 λ/na.
LTE4s2(L+12)(πQ)1/2×exp-2ρ0w0-s(L+12)21-cos 2ϕ0+116Q(1+15 cos 2ϕ0)+O1Q2,
LTM4s2(L+12)(πQ)1/2×exp-2ρ0w0-s(L+12)2(1+cos 2ϕ0)+116Q(1-15 cos 2ϕ0)+O1Q2.
ρ0/w0=s(L+12).
LTELTM2π3/2 λw00.508 λw0.
2γ=xΔλbeam/λ
xres(η)xres(0)+Kη2,
PbeamTE=E022μ0c2πk2rΔz cos5 ηl=-| Al(η)|2,
PbeamTM=E022μ0c2πk2rΔz cos5 ηl=-|Bl(η)|2.
Al(η)=(2sπ 1/2 cos2 η)-1 exp(-sin2 η /4s2)×exp[-s2(l/cos η+ky0)2],
Bl(η)=0.
Pbeam=E022μ0cπw022,
PscattTE=E022μ0c8πk2rΔz cos5 ηl=-|Al(η)|2×[|al(η)|2+|ql(η)|2],
PscattTM=E022μ0c8πk2rΔ z cos5 ηl=-|Bl(η)|2×[|bl(η)|2+|ql(η)|2].
LTELTM2π1/24kw0exp-2s2(L±ky0)2.
(L)max2π3/2λw0
ky0=±L.
ky0=±L/cos η.
|aL(η)|2|bL(η)|2exp{-[x-xres(η)]2/Γ2},
|qL(η)|20,
PLscattE022μ0c(2w02)- cos ηdη×exp-2s2L21cos η-12×exp(-sin2 η/2s2)×exp{-[x-xres(0)-Kη 2]2/Γ2}.
PLscattE022μ0c(2w02)-dη×exp(-η2/2s2)exp-s2L22+K2Γ2η4,
PLscattE022μ0c(2w02)2sΩ1/2 exp(Ω)K1/4(Ω),
Ω=(s2L2+2K2/Γ2)-1(2s)-4.
2K2/Γ2s2L2.
Γ/K2s2,
PLscattE022μ0c(2w02)-dη exp(-Kη4/Γ2)=E022μ0c(w02)ΓK1/2Γ14,
LTE=LTM=2π ΓK1/2Γ(1/4),
LTE=LTM=2π (Γ2+γ2)1/4K1/2 Γ(Γ2+γ2)1/2Γ14

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