Abstract

An original computational method for solving the two-dimensional problem of the scattering of an axisymmetric laser beam by an arbitrary-shaped inhomogeneous body of revolution is presented. This method relies on a domain decomposition of the scattering zone into concentric spherical radially homogeneous subdomains and on an expansion of the angular dependence of the fields on the Legendre functions. Numerical results for the fields obtained for various scatterer geometries are presented and analyzed.

© 2005 Optical Society of America

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References

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  1. F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 775–824 (2003).
    [CrossRef]
  2. W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, 1990).
  3. A. Khebir, J. D’Angelo, “A new finite element formulation for RF scattering by complex bodies of revolution,” IEEE Trans. Antennas Propag. 41, 534–541 (1993).
    [CrossRef]
  4. M. G. Andreasen, “Scattering from bodies of revolution,” IEEE Trans. Antennas Propag. AP-13, 303–310 (1964).
  5. M. A. Morgan, K. K. Mei, “Coupled azimuthal potential for electromagnetic field problems in inhomogeneous axially symmetric media,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
    [CrossRef]
  6. M. A. Morgan, S.-K. Chang, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-25, 413–417 (1984).
  7. L. N. Medgyesi-Mitschang, J. M. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797–806 (1984).
    [CrossRef]
  8. J. M. Tranquilla, H. M. Al-Rizzo, “Electromagnetic scattering from dielectic-coated axisymmetric objects using the generalized point-matching technique (GPMT),” IEEE Trans. Antennas Propag. 43, 63–71 (1995).
    [CrossRef]
  9. D. W. Prather, S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A 16, 1131–1142 (1999).
    [CrossRef]
  10. D. W. Prather, S. Shi, “Electromagnetic analysis of axially symmetric diffractive lens with the method of moments,” J. Opt. Soc. Am. A 17, 729–739 (2000).
    [CrossRef]
  11. G. Mie, “Beitzrâge zur optik truber Medien, speziell kolloidaler Metalolsungen,” Ann. Phys. 25, 377–452 (1908).
    [CrossRef]
  12. P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys., 30, 57–136 (1909).
    [CrossRef]
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).
  14. L. D. Landau, E. M. Lifshitz, L. A. Pitaevskii, Electrodynamics of Continuous Media (Butterworth Heinemann, 1984).
  15. A. L. Alden, M. Kerker, “Scattering of electromagnetic waves from two concenctric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
    [CrossRef]
  16. R. Bhandari, “Scattering coefficients for a multilayered sphere: analytical expressions and algorithms,” Appl. Opt. 24, 1960–1967 (1985).
    [CrossRef]
  17. L. Kai, P. Massoli, “Scattering of electromagnetic-plane waves by radially inhomogeneous spheres: a finely stratified sphere model,” Appl. Opt. 33, 501–511 (1994).
    [CrossRef] [PubMed]
  18. B. R. Johnson, “Light scattering by a multilayer sphere,” Appl. Opt. 35, 3286–3296 (1996).
    [CrossRef] [PubMed]
  19. B. R. Johnson, “Exact theory of electromagnetic scattering by a heteregenous multilayer sphere in the infinite-layer limit: effective-media approach,” J. Opt. Soc. Am. A 16, 845–852 (1999).
    [CrossRef]
  20. T. A. Wriedt, “A review of elastic light scattering theories,” Part. Part. Syst. Charact. 15, 67–74 (1998).
    [CrossRef]
  21. P. E. Bisbing, “Electromagnetic scattering by an exponenttially inhomogeneous plasma sphere,” IEEE Trans. Antennas Propag. AP-14, 219–224 (1966).
    [CrossRef]
  22. P. J. Wyatt, “Scattering of electromagnetic plane waves from inhomogeneous spherically symmetric objects,” Phys. Rev. 127, 1837–1843 (1962).
    [CrossRef]
  23. J. R. Wait, “Electromagnetic scattering from radially inhomogeneous spheres,” Appl. Sci. Res., Sect. A 10, 441–450 (1963).
    [CrossRef]
  24. J. D. Jackson, Classical Electrodynamics (Wiley, 1975).
  25. P.-M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).
  26. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986).
    [CrossRef]
  27. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  28. M. G. Moharam, D. A. Pommet, E. B. Grann, T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
    [CrossRef]
  29. A. Taflove, Computationnal Electrodynamics (Artech House, 1995).
  30. S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [CrossRef]
  31. T. Van, A. Wood, “A time-domain finite element method for Helmholtz equations,” J. Comput. Phys. 183, 486–507 (2002).
    [CrossRef]
  32. J.-P. Bérenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
    [CrossRef]
  33. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitraly located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  34. K. F. Ren, G. Gréhan, G. Gouesbet, “Laser sheet scattering by sphericals particles,” Part. Part. Syst. Charact. 10, 146–151 (1993).
    [CrossRef]
  35. K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam coeffcients in generalized Lorenz–Mie theory by using a localized approximations,” J. Opt. Soc. Am. A 11, 2072–2079 (1992).
    [CrossRef]
  36. G. Gouesbet, “Exact description of arbitrary-shaped beams for use in light scattering theories,” J. Opt. Soc. Am. A 13, 2434–2079 (1996).
    [CrossRef]
  37. F. Onofri, G. Gréhan, G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
    [CrossRef] [PubMed]
  38. Z. S. Wu, L. X. Guo, K. F. Ren, G. Gouesbet, G. Gréhan, “Improved algorithm for electromagnetic scattering of plane waves and shaped beams by multilayered spheres,” Appl. Opt. 36, 5188–5198 (1997).
    [CrossRef] [PubMed]
  39. Z. S. Wu, Y. P. Wang, “Electromagnetic scattering for multilayered sphere: recursive algorithms,” Radio Sci. 26, 1393–1401 (1991).
    [CrossRef]
  40. H. R Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D Palik, ed. (Academic, 1985), pp. 749–763.
    [CrossRef]
  41. D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminium,” in Handbook of Optical Constants of Solids, E. D Palik, ed. (Academic, 1985), pp. 369–406.
    [CrossRef]

2003 (1)

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 775–824 (2003).
[CrossRef]

2002 (1)

T. Van, A. Wood, “A time-domain finite element method for Helmholtz equations,” J. Comput. Phys. 183, 486–507 (2002).
[CrossRef]

2000 (1)

1999 (2)

1998 (1)

T. A. Wriedt, “A review of elastic light scattering theories,” Part. Part. Syst. Charact. 15, 67–74 (1998).
[CrossRef]

1997 (1)

1996 (3)

1995 (4)

1994 (1)

1993 (2)

A. Khebir, J. D’Angelo, “A new finite element formulation for RF scattering by complex bodies of revolution,” IEEE Trans. Antennas Propag. 41, 534–541 (1993).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Laser sheet scattering by sphericals particles,” Part. Part. Syst. Charact. 10, 146–151 (1993).
[CrossRef]

1992 (1)

1991 (1)

Z. S. Wu, Y. P. Wang, “Electromagnetic scattering for multilayered sphere: recursive algorithms,” Radio Sci. 26, 1393–1401 (1991).
[CrossRef]

1988 (1)

1986 (1)

1985 (1)

1984 (2)

M. A. Morgan, S.-K. Chang, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-25, 413–417 (1984).

L. N. Medgyesi-Mitschang, J. M. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797–806 (1984).
[CrossRef]

1979 (1)

M. A. Morgan, K. K. Mei, “Coupled azimuthal potential for electromagnetic field problems in inhomogeneous axially symmetric media,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

1966 (2)

P. E. Bisbing, “Electromagnetic scattering by an exponenttially inhomogeneous plasma sphere,” IEEE Trans. Antennas Propag. AP-14, 219–224 (1966).
[CrossRef]

S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

1964 (1)

M. G. Andreasen, “Scattering from bodies of revolution,” IEEE Trans. Antennas Propag. AP-13, 303–310 (1964).

1963 (1)

J. R. Wait, “Electromagnetic scattering from radially inhomogeneous spheres,” Appl. Sci. Res., Sect. A 10, 441–450 (1963).
[CrossRef]

1962 (1)

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

1951 (1)

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

1909 (1)

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys., 30, 57–136 (1909).
[CrossRef]

1908 (1)

G. Mie, “Beitzrâge zur optik truber Medien, speziell kolloidaler Metalolsungen,” Ann. Phys. 25, 377–452 (1908).
[CrossRef]

Alden, A. L.

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

Al-Rizzo, H. M.

J. M. Tranquilla, H. M. Al-Rizzo, “Electromagnetic scattering from dielectic-coated axisymmetric objects using the generalized point-matching technique (GPMT),” IEEE Trans. Antennas Propag. 43, 63–71 (1995).
[CrossRef]

Andreasen, M. G.

M. G. Andreasen, “Scattering from bodies of revolution,” IEEE Trans. Antennas Propag. AP-13, 303–310 (1964).

Bérenger, J.-P.

J.-P. Bérenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

Bhandari, R.

Bisbing, P. E.

P. E. Bisbing, “Electromagnetic scattering by an exponenttially inhomogeneous plasma sphere,” IEEE Trans. Antennas Propag. AP-14, 219–224 (1966).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).

Chang, S.-K.

M. A. Morgan, S.-K. Chang, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-25, 413–417 (1984).

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, 1990).

D’Angelo, J.

A. Khebir, J. D’Angelo, “A new finite element formulation for RF scattering by complex bodies of revolution,” IEEE Trans. Antennas Propag. 41, 534–541 (1993).
[CrossRef]

Debye, P.

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys., 30, 57–136 (1909).
[CrossRef]

Feshbach, H.

P.-M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).

Gaylord, T. K.

Gouesbet, G.

Grann, E. B.

Gréhan, G.

Guo, L. X.

Inokuti, M.

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminium,” in Handbook of Optical Constants of Solids, E. D Palik, ed. (Academic, 1985), pp. 369–406.
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1975).

Johnson, B. R.

Kahnert, F. M.

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 775–824 (2003).
[CrossRef]

Kai, L.

Kerker, M.

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

Khebir, A.

A. Khebir, J. D’Angelo, “A new finite element formulation for RF scattering by complex bodies of revolution,” IEEE Trans. Antennas Propag. 41, 534–541 (1993).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, L. A. Pitaevskii, Electrodynamics of Continuous Media (Butterworth Heinemann, 1984).

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, L. A. Pitaevskii, Electrodynamics of Continuous Media (Butterworth Heinemann, 1984).

Maheu, B.

Massoli, P.

Medgyesi-Mitschang, L. N.

L. N. Medgyesi-Mitschang, J. M. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797–806 (1984).
[CrossRef]

Mei, K. K.

M. A. Morgan, S.-K. Chang, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-25, 413–417 (1984).

M. A. Morgan, K. K. Mei, “Coupled azimuthal potential for electromagnetic field problems in inhomogeneous axially symmetric media,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

Mie, G.

G. Mie, “Beitzrâge zur optik truber Medien, speziell kolloidaler Metalolsungen,” Ann. Phys. 25, 377–452 (1908).
[CrossRef]

Moharam, M. G.

Morgan, M. A.

M. A. Morgan, S.-K. Chang, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-25, 413–417 (1984).

M. A. Morgan, K. K. Mei, “Coupled azimuthal potential for electromagnetic field problems in inhomogeneous axially symmetric media,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

Morse, P.-M.

P.-M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).

Onofri, F.

Philipp, H. R

H. R Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D Palik, ed. (Academic, 1985), pp. 749–763.
[CrossRef]

Pitaevskii, L. A.

L. D. Landau, E. M. Lifshitz, L. A. Pitaevskii, Electrodynamics of Continuous Media (Butterworth Heinemann, 1984).

Pommet, D. A.

Prather, D. W.

Putnam, J. M.

L. N. Medgyesi-Mitschang, J. M. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797–806 (1984).
[CrossRef]

Ren, K. F.

Shi, S.

Shiles, E.

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminium,” in Handbook of Optical Constants of Solids, E. D Palik, ed. (Academic, 1985), pp. 369–406.
[CrossRef]

Smith, D. Y.

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminium,” in Handbook of Optical Constants of Solids, E. D Palik, ed. (Academic, 1985), pp. 369–406.
[CrossRef]

Taflove, A.

A. Taflove, Computationnal Electrodynamics (Artech House, 1995).

Tranquilla, J. M.

J. M. Tranquilla, H. M. Al-Rizzo, “Electromagnetic scattering from dielectic-coated axisymmetric objects using the generalized point-matching technique (GPMT),” IEEE Trans. Antennas Propag. 43, 63–71 (1995).
[CrossRef]

Van, T.

T. Van, A. Wood, “A time-domain finite element method for Helmholtz equations,” J. Comput. Phys. 183, 486–507 (2002).
[CrossRef]

Wait, J. R.

J. R. Wait, “Electromagnetic scattering from radially inhomogeneous spheres,” Appl. Sci. Res., Sect. A 10, 441–450 (1963).
[CrossRef]

Wang, Y. P.

Z. S. Wu, Y. P. Wang, “Electromagnetic scattering for multilayered sphere: recursive algorithms,” Radio Sci. 26, 1393–1401 (1991).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).

Wood, A.

T. Van, A. Wood, “A time-domain finite element method for Helmholtz equations,” J. Comput. Phys. 183, 486–507 (2002).
[CrossRef]

Wriedt, T. A.

T. A. Wriedt, “A review of elastic light scattering theories,” Part. Part. Syst. Charact. 15, 67–74 (1998).
[CrossRef]

Wu, Z. S.

Wyatt, P. J.

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

Yee, S. K.

S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

Ann. Phys. (2)

G. Mie, “Beitzrâge zur optik truber Medien, speziell kolloidaler Metalolsungen,” Ann. Phys. 25, 377–452 (1908).
[CrossRef]

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys., 30, 57–136 (1909).
[CrossRef]

Appl. Opt. (5)

Appl. Sci. Res., Sect. A (1)

J. R. Wait, “Electromagnetic scattering from radially inhomogeneous spheres,” Appl. Sci. Res., Sect. A 10, 441–450 (1963).
[CrossRef]

IEEE Trans. Antennas Propag. (8)

A. Khebir, J. D’Angelo, “A new finite element formulation for RF scattering by complex bodies of revolution,” IEEE Trans. Antennas Propag. 41, 534–541 (1993).
[CrossRef]

M. G. Andreasen, “Scattering from bodies of revolution,” IEEE Trans. Antennas Propag. AP-13, 303–310 (1964).

M. A. Morgan, K. K. Mei, “Coupled azimuthal potential for electromagnetic field problems in inhomogeneous axially symmetric media,” IEEE Trans. Antennas Propag. AP-27, 202–214 (1979).
[CrossRef]

M. A. Morgan, S.-K. Chang, K. K. Mei, “Finite-element computation of scattering by inhomogeneous penetrable bodies of revolution,” IEEE Trans. Antennas Propag. AP-25, 413–417 (1984).

L. N. Medgyesi-Mitschang, J. M. Putnam, “Electromagnetic scattering from axially inhomogeneous bodies of revolution,” IEEE Trans. Antennas Propag. AP-32, 797–806 (1984).
[CrossRef]

J. M. Tranquilla, H. M. Al-Rizzo, “Electromagnetic scattering from dielectic-coated axisymmetric objects using the generalized point-matching technique (GPMT),” IEEE Trans. Antennas Propag. 43, 63–71 (1995).
[CrossRef]

P. E. Bisbing, “Electromagnetic scattering by an exponenttially inhomogeneous plasma sphere,” IEEE Trans. Antennas Propag. AP-14, 219–224 (1966).
[CrossRef]

S. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

J. Appl. Phys. (1)

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

J. Comput. Phys. (2)

T. Van, A. Wood, “A time-domain finite element method for Helmholtz equations,” J. Comput. Phys. 183, 486–507 (2002).
[CrossRef]

J.-P. Bérenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996).
[CrossRef]

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

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam coeffcients in generalized Lorenz–Mie theory by using a localized approximations,” J. Opt. Soc. Am. A 11, 2072–2079 (1992).
[CrossRef]

B. R. Johnson, “Exact theory of electromagnetic scattering by a heteregenous multilayer sphere in the infinite-layer limit: effective-media approach,” J. Opt. Soc. Am. A 16, 845–852 (1999).
[CrossRef]

D. W. Prather, S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A 16, 1131–1142 (1999).
[CrossRef]

M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986).
[CrossRef]

G. Gouesbet, “Exact description of arbitrary-shaped beams for use in light scattering theories,” J. Opt. Soc. Am. A 13, 2434–2079 (1996).
[CrossRef]

M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
[CrossRef]

M. G. Moharam, D. A. Pommet, E. B. Grann, T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
[CrossRef]

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

D. W. Prather, S. Shi, “Electromagnetic analysis of axially symmetric diffractive lens with the method of moments,” J. Opt. Soc. Am. A 17, 729–739 (2000).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf. (1)

F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 775–824 (2003).
[CrossRef]

Part. Part. Syst. Charact. (2)

T. A. Wriedt, “A review of elastic light scattering theories,” Part. Part. Syst. Charact. 15, 67–74 (1998).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Laser sheet scattering by sphericals particles,” Part. Part. Syst. Charact. 10, 146–151 (1993).
[CrossRef]

Phys. Rev. (1)

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

Radio Sci. (1)

Z. S. Wu, Y. P. Wang, “Electromagnetic scattering for multilayered sphere: recursive algorithms,” Radio Sci. 26, 1393–1401 (1991).
[CrossRef]

Other (8)

H. R Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D Palik, ed. (Academic, 1985), pp. 749–763.
[CrossRef]

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminium,” in Handbook of Optical Constants of Solids, E. D Palik, ed. (Academic, 1985), pp. 369–406.
[CrossRef]

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, 1990).

J. D. Jackson, Classical Electrodynamics (Wiley, 1975).

P.-M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953).

A. Taflove, Computationnal Electrodynamics (Artech House, 1995).

M. Born, E. Wolf, Principles of Optics (Pergamon, 1980).

L. D. Landau, E. M. Lifshitz, L. A. Pitaevskii, Electrodynamics of Continuous Media (Butterworth Heinemann, 1984).

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Figures (11)

Fig. 1
Fig. 1

Geometrical arrangement.

Fig. 2
Fig. 2

Example of body of revolution for which the theory applys.

Fig. 3
Fig. 3

Laser beam intensity in the vicinity of the focus point. The peak power is 1 GW cm 2 ; the wavelength is 0.351 μ m .

Fig. 4
Fig. 4

Onionlike computation domain. Within each shell, the complex dielectric constant is assumed to be independent of the radius.

Fig. 5
Fig. 5

Glass sphere of radius 2 μ m illuminated by a 0.351 μ m laser with the intensity represented in Fig. 3; n = 1.5 , κ = 0 .

Fig. 6
Fig. 6

Aluminium sphere of radius 0.2 μ m illuminated by a 0.351 μ m laser with the intensity represented in Fig. 3.

Fig. 7
Fig. 7

(a) Intensity map of the incident laser beam; the wavelength is 0.351 μ m . (b) The electric field strength E in megavolts per meter in the vicinity of an aluminium hemispheric obstacle with its center located at z = 0 , r = 0 ; the radius is 1.2 μ m and width is 0.3 μ m . (c) Magnetic field strength in tesla, same parameters as in (b).

Fig. 8
Fig. 8

Same as Fig. 7 but for a smaller obstacle. The radius is 0.5 μ m , and the thickness is 0.3 μ m .

Fig. 9
Fig. 9

Electric field strength E in megavolts per meter in the vicinity of a conical crater in a block of silica at 800 K illuminated by a CO 2 laser beam whose intensity is represented Fig. 8. The refractive index is n = 2 and the extinction coefficients κ = 0.0687 .

Fig. 10
Fig. 10

Aluminium mirror illuminated by a laser beam whose intensity is represented in Fig. 3. (a) Magnetic field obtained by our method; (b) magnetic field calculated by a 2-D FDM. The value of the magnetic field at the edge of the box in (a) has been used as the Dirichlet boundary conditions in the computations.

Fig. 11
Fig. 11

Magnetic field in the the focusing zone without any absorbing structure. (a) Incident magnetic field given by the expansion over the associated Legendre functions. (b) Magnetic field calculated by a 2-D FDM. The Value of the magnetic field at the edge of the box in (a) has been used as the Dirichlet boundary conditions in the computations.

Equations (141)

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E ( x , t ) = R ( E exp [ i ( ω t π 2 ) ] ) = E 1 cos ( ω t ) + E 2 sin ( ω t ) ,
k ̃ 2 = i μ 0 ω σ ̃ + ω 2 ϵ r c 2 = k 0 2 ( ϵ r i σ ̃ ω ϵ 0 ) ,
E = 0 ,
B = 0 ,
× E = i ω B ,
× B = i k 0 2 ω E ,
E l , m ( M ) = l , m [ A l , m 1 h l 1 ( k r ) + A l , m 2 h l 2 ( k r ) ] L Y l m ( θ , φ ) ,
B l , m ( M ) = i ω × E l , m ( M )
B l , m ( E ) = l , m [ A l , m 1 h l 1 ( k r ) + A l , m 2 h l 2 ( k r ) ] L Y l m ( θ , φ ) ,
E l , m ( E ) = i ω k 2 × B l , m ( E ) ,
L = 1 i r × .
L r Y l m = 0 ,
L θ Y l m ( θ , ϕ ) = m Y l m ( θ , ϕ ) ,
L φ Y l m = i m cos θ Y l m ( θ , ϕ ) + i sin θ e i φ [ l ( l + 1 ) m ( m + 1 ) ] 1 2 Y l m + 1 ( θ , ϕ ) .
B φ ( r , θ ) = l = 0 + [ A l 1 h l 1 ( k 0 r ) + A l 2 h l 2 ( k 0 r ) ] P l 1 ( θ ) ,
h l 1 ( x ) ( i ) l e i x i x , h l 2 ( x ) i l e i x i x
h l 1 ( x ) = j l ( x ) + i n l ( x )
B φ = l = 0 + α l i 2 [ h l 1 ( k 0 r ) + h l 2 ( k 0 r ) ] P l 1 = l = 0 + α l i j l ( k 0 r ) P l 1 ,
B φ [ exp ( i k 0 r ) 2 i k 0 r exp ( i k 0 r ) 2 i k 0 r ] l = 0 + α l i ( i ) l P l 1 ( θ ) .
D ( θ ) = l α l i ( i ) l P l 1 ( θ ) ,
α l i = 2 l + 1 2 l ( l + 1 ) i l + 1 0 π D ( θ ) P l 1 ( θ ) sin θ d θ .
B φ i = l = 0 + α l i j l ( k 0 r ) P l 1 ( θ ) ,
E θ i = i ω k 0 2 r l = 0 + α l i [ r j l ( k 0 r ) ] r P l 1 ( θ ) ,
E r i = i ω k 0 2 r l = 0 + α l i j l ( k 0 r ) [ P l 1 ( θ ) + P l 1 ( θ ) tan θ ] ,
D ( θ ) = K θ exp ( θ θ 0 ) 2 ,
r B φ c ( r , θ ) = l = 0 α l c ψ l ( k c r ) P l 1 ( θ ) ,
r E θ c ( r , θ ) = i ω k c l = 0 α l c ψ l ( k c r ) P l 1 ( θ ) ,
r B φ ( 1 ) ( r , θ ) = l = 1 [ α l ( 1 ) ψ l ( k 1 r ) + β l ( 1 ) ζ l 1 ( k 1 r ) ] P l 1 ( θ ) ,
r E θ ( 1 ) ( r , θ ) = i ω k 1 l = 1 [ α l ( 1 ) ψ l ( k 1 r ) + β l ( 1 ) ζ l 1 ( k 1 r ) ] P l 1 ( θ ) .
α l ( 1 ) α l c ψ l ( k 1 r 1 ) + β l ( 1 ) α l c ζ l 1 ( k 1 r 1 ) = ψ l ( k c r 1 ) t 1 , l ( 1 ) ,
α l ( 1 ) α l c ψ l ( k 1 r 1 ) + β l ( 1 ) α l c ζ l 1 ( k 1 r 1 ) = k 1 k c ψ l ( k c r 1 ) t 2 , l ( 1 ) ,
α l ( 1 ) α l c = ζ l 1 ( k 1 r 1 ) t 2 , l ( 1 ) ζ l 1 ( k 1 r 1 ) t 1 , l ( 1 ) ,
β l ( 1 ) α l c = ψ l ( k 1 r 1 ) t 1 , l ( 1 ) ψ l ( k 1 r 1 ) t 2 , l ( 1 ) ,
ζ l 1 ( x ) ψ l ( x ) ψ l ( x ) ζ l 1 ( x ) = 1 .
r B φ ( 2 ) ( r , θ ) = l = 1 [ α l ( 2 ) ψ l ( k 2 r ) + β l ( 2 ) ζ l 1 ( k 2 r ) ] P l 1 ( θ ) ,
r E θ ( 2 ) ( r , θ ) = i ω k 2 l = 1 [ α l ( 2 ) ψ l ( k 2 r ) + β l ( 2 ) ζ l 1 ( k 2 r ) ] P l 1 ( θ ) .
α l ( 2 ) α l c ψ l ( k 2 r 2 ) + β l ( 2 ) α l c ζ l 1 ( k 2 r 2 ) = α l ( 1 ) α l c ψ l ( k 1 r 2 ) + β l ( 1 ) α l c ζ l 1 ( k 1 r 2 ) t 1 , l ( 2 ) ,
α l ( 2 ) α l c ψ l ( k 2 r 2 ) + β l ( 2 ) α l c ζ l 1 ( k 2 r 2 ) = k 2 k 1 [ α l ( 1 ) α l c ψ l ( k 1 r 2 )
+ β l ( 1 ) α l c ζ l 1 ( k 1 r 2 ) ] t 2 , l ( 2 ) ,
α l ( 2 ) α l c = ζ l 1 ( k 2 r 2 ) t 2 , l ( 2 ) ζ l 1 ( k 2 r 2 ) t 1 , l ( 2 ) ,
β l ( 2 ) α l c = ψ l ( k 2 r 2 ) t 1 , l ( 2 ) ψ l ( k 2 r 2 ) t 2 , l ( 2 ) .
α l ( j ) α l c = ζ l 1 ( k j r j ) t 2 , l ( j ) ζ l 1 ( k j r j ) t 1 , l ( j ) ,
β l ( j ) α l c = ψ l ( k j r j ) t 1 , l ( j ) ψ l ( k j r j ) t 2 , l ( j ) ,
t 1 , l ( j ) α l ( j 1 ) α l c ψ l ( k j 1 r j ) + β l ( j 1 ) α l c ζ l 1 ( k j 1 r j ) ,
t 2 , l ( j ) k j k j 1 [ α l ( j 1 ) α l c ψ l ( k j 1 r j ) + β l ( j 1 ) α l c ζ l 1 ( k j 1 r j ) ] .
r B φ e = l = 1 + [ α l s ζ l 1 ( k e r ) + α l i ψ l ( k e r ) ] P l 1 ,
r E θ e = i ω k e l = 1 + [ α l s ζ l 1 ( k e r ) + α l i ψ l ( k e r ) ] P l 1 ,
α l s α l c ζ l 1 ( k e r N s ) + α l i α l c ψ l ( k e r N s ) = α l ( N s 1 ) α l c ψ l ( k N s 1 r N s ) + β l ( N s 1 ) α l c ζ l 1 ( k N s 1 r N s ) t 1 , l ( N s ) ,
α l s α l c ζ l 1 ( k e r N s ) + α l i α l c ψ l ( k e r N s ) = k e k N s 1 [ α l ( N s 1 ) α l c ψ l ( k N s 1 r N s ) + β l ( N s 1 ) α l c ζ l 1 ( k N s 1 r N s ) ] t 2 , l ( N s ) .
α l c = α l i t 2 , l ( N s ) ζ l 1 ( k e r N s ) t 1 , l ( N s ) ζ l 1 ( k e r N s ) ,
α l s = α l i t 1 , l ( N s ) ψ l ( k e r N s ) t 2 , l ( N s ) ψ n ( k e r N s ) t 2 , l ( N s ) ζ l 1 ( k e r N s ) t 1 , l ( N s ) ζ l 1 ( k e r N s ) .
P abs = S N Π ( x , t ) d s = r N 2 Π r ( r N , θ ) d 2 Ω .
Π r ( r N , θ ) = 1 4 μ 0 [ E θ e ( r N , θ ) B φ e * ( r N , θ ) + c . c ] ,
P abs = π ω k e μ 0 l = 1 + 2 l ( l + 1 ) 2 l + 1 [ I ( α l s α l i * ) α l s 2 ] ,
P abs = J E d V = 1 2 R ( σ ) E 2 d V .
r B φ in = l α l i 2 ζ l 2 ( k e r ) P l 1 ,
r E θ in = i ω k e l α l i 2 ζ l 2 ( k e r ) P l 1 .
Π r in = 1 4 μ 0 ( E θ in B φ * in + c . c . ) .
P in = π ω 4 k e μ 0 l = 1 + 2 l ( l + 1 ) 2 l + 1 α l i 2 .
B φ out = l = 1 ( α l s + α l i 2 ) ζ l 1 ( k e r ) P l 1 ,
E θ out = i ω k e l = 1 ( α l s + α l i 2 ) ζ l 1 ( k e r ) P l 1 .
Π r out = 1 4 μ 0 E θ out B φ * out + c . c . ,
P out = π ω k e μ 0 l = 1 + 2 l ( l + 1 ) 2 l + 1 α l s + i α l i 2 2 .
P in = P out + P abs .
× E = i ω B ,
× B = i k ̃ 2 ω E ,
Δ B + 1 k 2 k 2 × × B + k 2 B = 0 ,
2 r 2 r B φ + F r r B φ r + 1 r 2 2 r B φ θ 2 + 1 r 2 r B φ θ ( F θ + cot θ ) + ( r B φ ) ( k 2 + F θ r 2 tan θ 1 r 2 sin 2 θ ) = 0 .
F r ( r , θ ) = k 2 ( r , θ ) r 1 k 2 ( r , θ ) ,
F θ ( r , θ ) = k 2 ( r , θ ) θ 1 k 2 ( r , θ ) .
1 r 2 r 2 r B φ + 1 r 2 2 r B φ θ 2 + 1 r 2 r B φ θ [ F i ( θ ) + cot θ ] + ( r B φ ) [ k i 2 ( θ ) + F i ( θ ) r 2 tan θ 1 r 2 sin 2 θ ] = 0 , r i r r i + 1 ,
r B φ ( i ) ( r , θ ) = n = 1 + f n ( i ) ( r ) P n 1 ( θ ) ,
f n ( i ) ( r ) n ( n + 1 ) r 2 f n ( i ) ( r ) + m = 1 + [ B n m ( i ) + A n m ( i ) r 2 ] f m ( i ) ( r ) = 0 ,
r i r r i + 1 ,
A n m ( i ) = 2 n + 1 2 n 0 π F i ( θ ) P n 1 ( θ ) P m 0 ( θ ) sin θ d θ ,
B n m ( i ) = 2 n + 1 2 n ( n + 1 ) 0 π k i 2 ( θ ) P n 1 ( θ ) P m 1 ( θ ) sin θ d θ .
r B φ ( i ) ( r , θ ) = n = 1 N l f n ( i ) ( r ) P n 1 ( θ ) ,
r E θ ( i ) ( r , θ ) = i ω k i 2 ( θ ) n = 1 N l f n ( i ) ( r ) P n 1 ( θ ) n = 1 N l g n ( i ) ( r ) P n 1 ( θ ) ,
B φ ( i ) ( r i ) = B φ ( i 1 ) ( r i ) f n ( i ) ( r i ) = f n ( i 1 ) ( r i ) ,
E θ ( i ) ( r i ) = E θ ( i 1 ) ( r i ) g n ( i ) ( r i ) = g n ( i 1 ) ( r i ) .
f n ( i ) ( r ) = i ω m = 1 N l B n m ( i ) g m ( i ) ( r ) ,
g n ( i ) ( r ) = i ω m = 1 N l C n m ( i ) f m ( i ) ( r ) ,
C n m ( i ) = 2 n + 1 2 n ( n + 1 ) 0 π k i 2 ( θ ) P n 1 ( θ ) P m 1 ( θ ) sin θ d θ .
f n ( i ) ( r i ) = m = 1 N l p = 1 N l [ B n m ( i ) C m p ( i 1 ) ] f p ( i 1 ) ( r i ) .
m = 1 N l B n m ( i ) C m p ( i ) = δ n p .
F ( i ) ( r ) = ( f 1 ( i ) ( r ) f N l ( i ) ( r ) ) , G ( i ) ( r ) = ( g 1 ( i ) ( r ) g N l ( i ) ( r ) ) ,
F ( i ) ( r ) = i ω B ( i ) G ( i ) ( r ) ,
G ( i ) ( r ) = i ω C ( i ) F ( i ) ( r ) ,
B ( i ) C ( i ) = I ,
F ( i ) ( r i ) = F ( i 1 ) ( r i ) ,
F ( i ) ( r i ) = J ( i ) F ( i 1 ) ( r i ) ,
J n m ( i ) = 2 n + 1 2 n ( n + 1 ) 0 π k i 2 ( θ ) k i 1 2 ( θ ) P n 1 ( θ ) P m 1 ( θ ) sin θ d θ .
r B φ c ( r , θ ) = n = 1 N l a n c ψ n ( k c r ) P n 1 ( θ ) ,
r E θ c ( r , θ ) = i ω k c n = 1 N l a n c ψ n ( k c r ) P n 1 ( θ ) ,
P ( r ) = ( a 1 c ψ 1 ( k c r ) a N l c ψ N l ( k c r ) ) ,
P ( r ) = i ω k c ( a 1 c ψ 1 ( k c r ) a N l c ψ N l ( k c r ) ) .
Ξ n m ( r ) = i ω k c ψ m ψ m ( k c r ) δ n m ,
F ( 1 ) ( r 1 ) = P ( r 1 ) ,
G ( 1 ) ( r 1 ) = C ( 1 ) F ( 1 ) ( r 1 ) = P ( r 1 ) .
F ( 1 ) ( r 1 ) = B ( 1 ) P ( r 1 ) .
F ( 1 ) ( r 1 ) = D F ( 1 ) ( r 1 ) ,
D = B ( 1 ) Ξ ( r 1 ) .
F ( i ) N r 2 F ( i ) + [ B ( i ) + A ( i ) r 2 ] F ( i ) = 0 ,
F ( i ) ( r i ) = F ( i 1 ) ( r i ) ,
F ( i ) ( r i ) = J ( i 1 ) F ( i ) ( r i ) ,
F ( 1 ) ( r 1 ) = P ( r 1 ) ,
F ( 1 ) ( r 1 ) = D F ( 1 ) ( r 1 ) ,
F ( 1 ) ( r 1 ) = ( f 1 ( 1 ) ( r 1 ) f N l ( 1 ) ( r 1 ) ) = f 1 ( 1 ) ( r 1 ) ( 1 0 0 ) + + f N l ( 1 ) ( r 1 ) ( 0 0 1 ) .
F ( 1 ) ( r 1 ) = D F ( 1 ) ( r 1 ) = f 1 ( 1 ) ( r 1 ) ( D 11 D 12 D 1 N l ) + + f N l ( 1 ) ( r 1 ) ( D N l 1 D N l 2 D N l N l ) .
Φ n ( 1 ) ( r ) = ( ϕ n 1 ( 1 ) ( r ) ϕ n N l ( 1 ) ( r ) ) ,
F ( 1 ) ( r ) = α 1 Φ 1 ( 1 ) ( r ) + + α N l Φ N l ( 1 ) ( r ) ,
Φ l ( 2 ) ( r 2 ) = Φ l ( 1 ) ( r 2 ) ,
Φ l ( 2 ) ( r 2 ) = J ( 2 ) Φ l ( 1 ) ( r 2 ) ,
F = α 1 Φ 1 ( r ) + + α N l Φ N l ( r ) ,
r B φ ( r , θ ) = n = 1 N l f n ( r ) P n 1 ( θ ) = n = 1 N l [ m = 1 N l α m ϕ m n ( r ) ] P n 1 ( θ ) ,
Γ n ( i ) ( r ) = i ω C ( i ) Φ n ( i ) ( r ) .
G ( r ) = α 1 Γ 1 ( r ) + + α N l Γ N l ( r ) .
r E θ ( r , θ ) = n = 1 N l g n ( r ) P n 1 ( θ ) = n = 1 N l [ m = 1 N l α m γ m n ( r ) ] P n 1 ( θ ) ,
r B φ ( r , θ ) = n = 1 N l f n ( r ) P n 1 ( θ ) = n = 1 N l [ m = 1 N l α m ϕ m n ( r ) ] P n 1 ( θ ) ,
r E θ ( r , θ ) = n = 1 N l g n ( r ) P n 1 ( θ ) = n = 1 N [ m = 1 N l α m γ m n ( r ) ] P n 1 ( θ ) ,
r B φ e ( r , θ ) = n = 1 N l [ α n s ζ n 1 ( k e r ) + α n i ψ n ( k e r ) ] P n 1 ( θ ) ,
r E θ e ( r , θ ) = i ω k e n = 1 N l [ α n s ζ n 1 ( k e r ) + α n i ψ n ( k e r ) ] P n 1 ( θ ) .
m = 1 N l α m ϕ m n ( r N s ) α n s ζ n 1 ( k e r N s ) = α n i ψ n ( k e r N s ) ,
k e i ω m = 1 N l α m γ m n ( r N s ) α n s ζ n 1 ( k e r N s ) = α n i ψ n ( k e r N s ) .
m = 1 N l [ k e i ω ζ n 1 ( k e r N s ) γ m n ( r N s ) ζ n 1 ( k e r N s ) ϕ m n ( r N s ) ] α m = α n i
ψ l ( x ) = x j l ( x ) = x ( π 2 x ) 1 2 J l + 1 2 ( x ) ,
χ l ( x ) = x n l ( x ) = x ( π 2 x ) 1 2 N l + 1 2 ( x ) ,
ζ l ( 1 ) ( x ) = x h l ( 1 ) ( x ) = x ( π 2 x ) 1 2 H l + 1 2 ( 1 ) ( x ) ,
ζ l ( 2 ) ( x ) = x h l ( 2 ) ( x ) = x ( π 2 x ) 1 2 H l + 1 2 ( 2 ) ( x ) .
H l ( 1 , 2 ) = J l ± i N l ( x ) ,
h l ( 1 , 2 ) = j l ± i n l ( x ) ,
ζ l ( 1 , 2 ) = ψ l i χ l ( x ) .
ψ l ( x ) sin ( x l π 2 ) ,
χ l ( x ) cos ( x l π 2 ) ,
ζ l ( 1 , 2 ) ( x ) ( i ) l + 1 e ± i x .
ψ l ( x ) x l + 1 ( 2 l + 1 ) ! ! + ,
n l ( x ) ( 2 l 1 ) ! ! x l + ,
0 π P l 1 ( θ ) P l 1 ( θ ) sin θ d θ = 2 l ( l + 1 ) 2 l + 1 δ l l .
( θ 2 + cot θ θ 1 sin 2 θ ) P n 1 ( θ ) = n ( n + 1 ) P n 1 ( θ ) .
Y l m ( θ , φ ) = [ 2 l + 1 4 π ( 1 m ) ! ( l + m ) ! ] 1 2 P l m ( cos θ ) e i m φ .
d P n 1 ( θ ) d θ + P n 1 ( θ ) tan θ = n ( n + 1 ) P n 0 ( θ ) n ( n + 1 ) P n ( θ ) .

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