Abstract

Localized beam models provide the most efficient and enlightening ways to evaluate beam shape coefficients of electromagnetic arbitrary shaped beams for use in light scattering theories. At the present time, they are valid in spherical and (circular and elliptical) cylindrical coordinates. A misuse of localized beam models in spherical coordinates recently appeared several times in the literature. We therefore present a warning to avoid the propagation of an incorrect use of localized beam models.

© 2012 Optical Society of America

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References

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  1. J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications; invited review paper,” J. Quant. Spectrosc. Radiat. Transfer 110, 800–807 (2009).
    [CrossRef]
  2. G. Gouesbet, “Generalized Lorenz–Mie theories, the third decade: a perspective; invited review paper,” J. Quant. Spectrosc. Radiat. Transfer 110, 1223–1238 (2009).
    [CrossRef]
  3. G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer-Verlag, 2011).
  4. G. Gouesbet, B. Maheu, and 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]
  5. G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
    [CrossRef]
  6. G. Gouesbet and L. Méès, “Generalized Lorenz–Mie theory for infinitely long elliptical cylinders,” J. Opt. Soc. Am. A 16, 1333–1341 (1999).
    [CrossRef]
  7. G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
    [CrossRef]
  8. G. Gouesbet, C. Letellier, K. F. Ren, and G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
    [CrossRef]
  9. G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
    [CrossRef]
  10. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
  11. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  12. J. A. Lock, “Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle,” J. Opt. Soc. Am. A 10, 693–706 (1993).
    [CrossRef]
  13. A. Doicu and T. Wriedt, “Computation of the beam shape coefficients in the generalized Lorenz–Mie theory by using the translational addition theorem for spherical vector wave functions,” Appl. Opt. 36, 2971–2978 (1997).
    [CrossRef]
  14. G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521, 2010.
    [CrossRef]
  15. T. J. Bromwich, “Electromagnetic waves,” Philos. Mag. 38, 143–164 (1919).
  16. F. E. Borgnis, “Elektromagnetische Eigenschwingungen dielektrischer Raüme,” Ann. Phys. 427, 359–384 (1939).
    [CrossRef]
  17. A. Angot, “Compléments de mathématiques à l’usage des ingénieurs de l’électrotechnique et des télé-communications,” Edtions de la Revue d’Optique (1952).
  18. G. Gouesbet, and G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. 13, 97–103 (1982).
    [CrossRef]
  19. G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
    [CrossRef]
  20. G. Gouesbet, G. Grehan, and B. Maheu, “On the generalized Lorenz–Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).
    [CrossRef]
  21. G. Gouesbet, G. Grehan, and B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7 (6), 998–1007 (1990).
    [CrossRef]
  22. G. Gouesbet, and 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]
  23. G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999).
    [CrossRef]
  24. G. Gouesbet, “Exact description of arbitrary shaped beams for use in light scattering theories,” J. Opt. Soc. Am. A 13, 2434–2440 (1996).
    [CrossRef]
  25. G. Gouesbet, J. A. Lock, J. J. Wang, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. V. Localized beam models,” Opt. Commun. 284, 411–417 (2011).
    [CrossRef]
  26. G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. I. General formulation,” Opt. Commun. 283, 3218–3225 (2010).
    [CrossRef]
  27. J. J. Wang, G. Gouesbet, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. II. Axisymmetric beams,” Opt. Commun. 283, 3226–3234(2010).
    [CrossRef]
  28. G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. III. Special values of Euler angles,” Opt. Commun. 283, 3235–3243 (2010).
    [CrossRef]
  29. G. Gouesbet, J. J. Wang, Y. P. Han, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. IV. Plane waves,” Opt. Commun. 283, 3244–3254 (2010).
    [CrossRef]

2011 (3)

G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, J. J. Wang, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. V. Localized beam models,” Opt. Commun. 284, 411–417 (2011).
[CrossRef]

2010 (5)

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. I. General formulation,” Opt. Commun. 283, 3218–3225 (2010).
[CrossRef]

J. J. Wang, G. Gouesbet, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. II. Axisymmetric beams,” Opt. Commun. 283, 3226–3234(2010).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. III. Special values of Euler angles,” Opt. Commun. 283, 3235–3243 (2010).
[CrossRef]

G. Gouesbet, J. J. Wang, Y. P. Han, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. IV. Plane waves,” Opt. Commun. 283, 3244–3254 (2010).
[CrossRef]

G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521, 2010.
[CrossRef]

2009 (2)

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications; invited review paper,” J. Quant. Spectrosc. Radiat. Transfer 110, 800–807 (2009).
[CrossRef]

G. Gouesbet, “Generalized Lorenz–Mie theories, the third decade: a perspective; invited review paper,” J. Quant. Spectrosc. Radiat. Transfer 110, 1223–1238 (2009).
[CrossRef]

1999 (2)

1997 (2)

1996 (3)

1994 (1)

1993 (1)

1990 (1)

1989 (1)

G. Gouesbet, G. Grehan, and B. Maheu, “On the generalized Lorenz–Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).
[CrossRef]

1988 (1)

1982 (1)

G. Gouesbet, and G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. 13, 97–103 (1982).
[CrossRef]

1939 (1)

F. E. Borgnis, “Elektromagnetische Eigenschwingungen dielektrischer Raüme,” Ann. Phys. 427, 359–384 (1939).
[CrossRef]

1919 (1)

T. J. Bromwich, “Electromagnetic waves,” Philos. Mag. 38, 143–164 (1919).

Angot, A.

A. Angot, “Compléments de mathématiques à l’usage des ingénieurs de l’électrotechnique et des télé-communications,” Edtions de la Revue d’Optique (1952).

Borgnis, F. E.

F. E. Borgnis, “Elektromagnetische Eigenschwingungen dielektrischer Raüme,” Ann. Phys. 427, 359–384 (1939).
[CrossRef]

Bromwich, T. J.

T. J. Bromwich, “Electromagnetic waves,” Philos. Mag. 38, 143–164 (1919).

Doicu, A.

Gouesbet, G.

G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, J. J. Wang, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. V. Localized beam models,” Opt. Commun. 284, 411–417 (2011).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. I. General formulation,” Opt. Commun. 283, 3218–3225 (2010).
[CrossRef]

J. J. Wang, G. Gouesbet, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. II. Axisymmetric beams,” Opt. Commun. 283, 3226–3234(2010).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. III. Special values of Euler angles,” Opt. Commun. 283, 3235–3243 (2010).
[CrossRef]

G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521, 2010.
[CrossRef]

G. Gouesbet, J. J. Wang, Y. P. Han, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. IV. Plane waves,” Opt. Commun. 283, 3244–3254 (2010).
[CrossRef]

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications; invited review paper,” J. Quant. Spectrosc. Radiat. Transfer 110, 800–807 (2009).
[CrossRef]

G. Gouesbet, “Generalized Lorenz–Mie theories, the third decade: a perspective; invited review paper,” J. Quant. Spectrosc. Radiat. Transfer 110, 1223–1238 (2009).
[CrossRef]

G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 16, 1641–1650 (1999).
[CrossRef]

G. Gouesbet and L. Méès, “Generalized Lorenz–Mie theory for infinitely long elliptical cylinders,” J. Opt. Soc. Am. A 16, 1333–1341 (1999).
[CrossRef]

G. Gouesbet, “Interaction between an infinite cylinder and an arbitrary shaped beam,” Appl. Opt. 36, 4292–4304 (1997).
[CrossRef]

G. Gouesbet, “Partial wave expansions and properties of axisymmetric light beams,” Appl. Opt. 35, 1543–1555 (1996).
[CrossRef]

G. Gouesbet, “Exact description of arbitrary shaped beams for use in light scattering theories,” J. Opt. Soc. Am. A 13, 2434–2440 (1996).
[CrossRef]

G. Gouesbet, C. Letellier, K. F. Ren, and G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
[CrossRef]

G. Gouesbet, and 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]

G. Gouesbet, G. Grehan, and B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7 (6), 998–1007 (1990).
[CrossRef]

G. Gouesbet, G. Grehan, and B. Maheu, “On the generalized Lorenz–Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).
[CrossRef]

G. Gouesbet, B. Maheu, and 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, and G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. 13, 97–103 (1982).
[CrossRef]

G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer-Verlag, 2011).

Grehan, G.

G. Gouesbet, G. Grehan, and B. Maheu, “A localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7 (6), 998–1007 (1990).
[CrossRef]

G. Gouesbet, G. Grehan, and B. Maheu, “On the generalized Lorenz–Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).
[CrossRef]

Gréhan, G.

G. Gouesbet, J. A. Lock, J. J. Wang, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. V. Localized beam models,” Opt. Commun. 284, 411–417 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

G. Gouesbet, J. J. Wang, Y. P. Han, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. IV. Plane waves,” Opt. Commun. 283, 3244–3254 (2010).
[CrossRef]

G. Gouesbet, C. Letellier, K. F. Ren, and G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
[CrossRef]

G. Gouesbet, B. Maheu, and 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, and G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. 13, 97–103 (1982).
[CrossRef]

G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer-Verlag, 2011).

Han, Y. P.

G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. III. Special values of Euler angles,” Opt. Commun. 283, 3235–3243 (2010).
[CrossRef]

J. J. Wang, G. Gouesbet, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. II. Axisymmetric beams,” Opt. Commun. 283, 3226–3234(2010).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. I. General formulation,” Opt. Commun. 283, 3218–3225 (2010).
[CrossRef]

G. Gouesbet, J. J. Wang, Y. P. Han, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. IV. Plane waves,” Opt. Commun. 283, 3244–3254 (2010).
[CrossRef]

Letellier, C.

Lock, J. A.

G. Gouesbet, J. A. Lock, J. J. Wang, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. V. Localized beam models,” Opt. Commun. 284, 411–417 (2011).
[CrossRef]

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications; invited review paper,” J. Quant. Spectrosc. Radiat. Transfer 110, 800–807 (2009).
[CrossRef]

G. Gouesbet, and 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]

J. A. Lock, “Contribution of high-order rainbows to the scattering of a Gaussian laser beam by a spherical particle,” J. Opt. Soc. Am. A 10, 693–706 (1993).
[CrossRef]

Maheu, B.

Méès, L.

Ren, K. F.

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

Wang, J. J.

G. Gouesbet, J. A. Lock, J. J. Wang, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. V. Localized beam models,” Opt. Commun. 284, 411–417 (2011).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. I. General formulation,” Opt. Commun. 283, 3218–3225 (2010).
[CrossRef]

J. J. Wang, G. Gouesbet, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. II. Axisymmetric beams,” Opt. Commun. 283, 3226–3234(2010).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. III. Special values of Euler angles,” Opt. Commun. 283, 3235–3243 (2010).
[CrossRef]

G. Gouesbet, J. J. Wang, Y. P. Han, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. IV. Plane waves,” Opt. Commun. 283, 3244–3254 (2010).
[CrossRef]

Wriedt, T.

Xu, F.

G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
[CrossRef]

Ann. Phys. (1)

F. E. Borgnis, “Elektromagnetische Eigenschwingungen dielektrischer Raüme,” Ann. Phys. 427, 359–384 (1939).
[CrossRef]

Appl. Opt. (4)

J. Opt. (1)

G. Gouesbet, and G. Gréhan, “Sur la généralisation de la théorie de Lorenz–Mie,” J. Opt. 13, 97–103 (1982).
[CrossRef]

J. Opt. (Paris) (1)

G. Gouesbet, G. Grehan, and B. Maheu, “On the generalized Lorenz–Mie theory: first attempt to design a localized approximation to the computation of the coefficients gnm,” J. Opt. (Paris) 20, 31–43 (1989).
[CrossRef]

J. Opt. Soc. Am. A (7)

J. Quant. Spectrosc. Radiat. Transfer (4)

G. Gouesbet, F. Xu, and Y. P. Han, “Expanded description of electromagnetic arbitrary shaped beams in spheroidal coordinates, for use in light scattering theories: a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 2249–2267 (2011).
[CrossRef]

J. A. Lock and G. Gouesbet, “Generalized Lorenz–Mie theory and applications; invited review paper,” J. Quant. Spectrosc. Radiat. Transfer 110, 800–807 (2009).
[CrossRef]

G. Gouesbet, “Generalized Lorenz–Mie theories, the third decade: a perspective; invited review paper,” J. Quant. Spectrosc. Radiat. Transfer 110, 1223–1238 (2009).
[CrossRef]

G. Gouesbet, J. A. Lock, and G. Gréhan, “Generalized Lorenz–Mie theories and description of electromagnetic arbitrary shaped beams: localized approximations and localized beam models, a review,” J. Quant. Spectrosc. Radiat. Transfer 112, 1–27 (2011).
[CrossRef]

Opt. Commun. (6)

G. Gouesbet, J. A. Lock, J. J. Wang, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. V. Localized beam models,” Opt. Commun. 284, 411–417 (2011).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. I. General formulation,” Opt. Commun. 283, 3218–3225 (2010).
[CrossRef]

J. J. Wang, G. Gouesbet, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. II. Axisymmetric beams,” Opt. Commun. 283, 3226–3234(2010).
[CrossRef]

G. Gouesbet, J. J. Wang, and Y. P. Han, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. III. Special values of Euler angles,” Opt. Commun. 283, 3235–3243 (2010).
[CrossRef]

G. Gouesbet, J. J. Wang, Y. P. Han, and G. Gréhan, “Transformations of spherical beam shape coefficients in generalized Lorenz–Mie theories through rotations of coordinate systems. IV. Plane waves,” Opt. Commun. 283, 3244–3254 (2010).
[CrossRef]

G. Gouesbet, “T-matrix formulation and generalized Lorenz–Mie theories in spherical coordinates,” Opt. Commun. 283, 517–521, 2010.
[CrossRef]

Philos. Mag. (1)

T. J. Bromwich, “Electromagnetic waves,” Philos. Mag. 38, 143–164 (1919).

Other (4)

A. Angot, “Compléments de mathématiques à l’usage des ingénieurs de l’électrotechnique et des télé-communications,” Edtions de la Revue d’Optique (1952).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

G. Gouesbet and G. Gréhan, Generalized Lorenz–Mie Theories (Springer-Verlag, 2011).

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Equations (28)

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2 U ( x 1 ) 2 μ ϵ 2 U ( t ) 2 + 1 e 2 e 3 ( x 2 e 3 e 2 U x 2 + x 3 e 2 e 3 U x 3 ) = 0 ,
k = ω μ ϵ .
2 U ( x 1 ) 2 + k 2 U + 1 e 2 e 3 ( x 2 e 3 e 2 U x 2 + x 3 e 2 e 3 U x 3 ) = 0.
x 1 = r x 2 = θ x 3 = φ }
e 1 = 1 e 2 = r e 3 = r sin θ } .
2 U r 2 + k 2 U + 1 r 2 sin θ θ sin θ U θ + 1 r 2 sin 2 θ 2 U φ 2 = 0.
U TM ( P ) = E 0 k n = 1 m = n + n c n pw g n , TM m ( P ) ψ n ( k r ) P n | m | ( cos θ ) exp ( i m φ ) ,
c n pw = 1 i k ( i ) n 2 n + 1 n ( n + 1 ) .
E r = 2 U TM r 2 + k 2 U TM .
E r ( P ) = E 0 n = 1 m = n + n c n pw g n , TM m ( P ) [ d 2 r ψ n ( 1 ) ( k r ) d r 2 + k 2 r ψ n ( 1 ) ( k r ) ] P n | m | ( cos θ ) exp ( i m φ ) ,
[ d 2 d r 2 + k 2 ] ( r ψ n ( 1 ) ( k r ) ) = n ( n + 1 ) r ψ n ( 1 ) ( k r ) .
E r ( P ) = E 0 n = 1 m = n + n c n pw g n , TM m ( P ) n ( n + 1 ) r ψ n ( 1 ) ( k r ) P n | m | ( cos θ ) exp ( i m φ ) .
0 2 π exp ( i ( m m ) φ ) d φ = 2 π δ m m ,
0 π P n | m | ( cos θ ) P l | m | ( cos θ ) sin θ d θ = 2 2 n + 1 ( n + | m | ) ! ( n | m | ) ! δ n l
g n , TM m ( P ) = 1 c n pw 2 n + 1 4 π n ( n + 1 ) ( n | m | ) ! ( n + | m | ) ! r ψ n ( 1 ) ( k r ) , 0 π 0 2 π E r ( P ) E 0 P n | m | ( cos θ ) exp ( i m φ ) sin θ d θ d φ ,
g n , TM m ( P ) = i n + 1 4 π ( n | m | ) ! ( n + | m | ) ! k r ψ n ( 1 ) ( k r ) , 0 π 0 2 π E r ( P ) E 0 P n | m | ( cos θ ) exp ( i m φ ) sin θ d θ d φ .
E r ( N ) = E r ( P ) * .
U TM ( N , V 1 ) = E 0 * k n = 1 m = n + n ( c n pw ) * g n , TM m ( N , V 1 ) ψ n ( k r ) P n | m | ( cos θ ) exp ( i m φ ) ,
U TM ( N , V 2 ) = E 0 * k n = 1 m = - n + n ( c n pw ) * g n , TM m ( N , V 2 ) ψ n ( k r ) P n | m | ( cos θ ) exp ( i m φ ) .
g n , TM m ( N , V 1 ) = ( i ) n + 1 4 π ( n | m | ) ! ( n + | m | ) ! k r ψ n ( 1 ) ( k r ) 0 π 0 2 π ( E r ( P ) E 0 ) * P n | m | ( cos θ ) exp ( i m φ ) sin θ d θ d φ ,
[ g n , TM m ( N , V 1 ) ] * = g n , TM m ( P )
g n , TM m ( N , V 2 ) = ( i ) n + 1 4 π ( n | m | ) ! ( n + | m | ) ! k r ψ n ( 1 ) ( k r ) 0 π 0 2 π ( E r ( P ) E 0 ) * P n | m | ( cos θ ) exp ( i m φ ) sin θ d θ d φ ,
[ g n , TM m ( N , V 2 ) ] * = g n , TM m ( P ) .
E r ( P ) = m = E r m ( P ) .
g n , TM m ( P ) ¯ = ( i L 1 / 2 ) | m | 1 E r m ( P , L 1 / 2 , π / 2 ) ,
L = ( n m ) ( n + m + 1 ) = ( n + 1 2 ) 2 ( m + 1 2 ) 2 .
E r ( N ) = E r ( P ) * = m = E r m ( N ) = m = E r m ( P ) * .
g n , TM m ( N ) ¯ = g n , TM m ( P ) ¯ * = ( i L 1 / 2 ) | m | 1 E r m ( N , L 1 / 2 , π / 2 ) .

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