Abstract

The theory of scattering of arbitrary-shaped beams by an infinite cylinder with arbitrary location and arbitrary orientation is presented. The theory relies on the use of distributions that provide the most general framework, which allows the use of any description of the incident beam. Apart from this peculiarity, the theory relies on the use of scalar potentials, and the resulting framework is rather similar to that of the generalized Lorenz–Mie theory for spheres.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt.(Paris), 19, 59–67 (1988).
  3. G. Gouesbet, G. Gréhan, B. Maheu, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion MeasurementsN. Chigier, ed. (Hemisphere, Washington, D.C., 1991), pp. 339–384.
  4. G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
    [CrossRef]
  5. 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]
  6. K. F. Ren, G. Gréhan, G. Gouesbet, “Laser sheet scattering by spherical particles,” Part. Part. Syst. Charact. 10, 146–151 (1993).
    [CrossRef]
  7. G. Gréhan, K. F. Ren, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a particle sizing technique based on laser sheets,” Part. Part. Syst. Charact. 11, 101–106 (1994).
    [CrossRef]
  8. K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
    [CrossRef]
  9. K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
    [CrossRef]
  10. F. Corbin, G. Gréhan, G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Syst. Charact. 8, 222–228 (1991).
    [CrossRef]
  11. G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
    [CrossRef] [PubMed]
  12. G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt.(Paris) 26, 225–239 (1995).
  13. G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
    [CrossRef]
  14. L. W. Davis, “Theory of electromagnetic beams,” Phys. Rev. A 19, 1177–1179 (1979).
    [CrossRef]
  15. K. F. Ren, G. Gouesbet, G. Gréhan, “Scattering of a Gaussian beam by an infinite cylinder: numerical results in GLMT-framework,” presented at the Eighth InternationalSymposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 8–11 July 1996.
  16. G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
    [CrossRef]
  17. G. Gouesbet, G. Gréhan, “Interaction between a Gaussian beam and an infinite cylinder, using non-sigma-separable potentials,” J. Opt. Soc. Am. A 11, 3261–3273 (1994).
    [CrossRef]
  18. P. M. Morse, H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 5, Part I.
  19. G. Gouesbet, “The separability theorem revisited with applications to light scattering theory,” J. Opt. (Paris) 26, 123–135 (1995).
  20. E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. 37, 9705–9710 (1996).
    [CrossRef]
  21. G. Gouesbet, “General description of arbitrary shaped beams for introduction in light scattering theories,” in Recent Research Developments in Applied Optics, S. M. Krishnan, ed. (Research Signpost, Trivandrum, India, edited by the Scientific Information Guild, 1996).
  22. G. Gouesbet, “Exact description of arbitrary shaped beams for use in light scattering theories,” J. Opt. Soc. Am. A 13, 2434–2440 (1996).
    [CrossRef]
  23. J. F. Rice, The Approximation of Functions (Addison-Wesley, Reading Mass., 1969), Vols. 1 and 2.
  24. J. P. Barton, D. R. Alexander, “Fifth order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
    [CrossRef]
  25. 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]
  26. 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]
  27. G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
    [CrossRef] [PubMed]
  28. G. Gouesbet, “Higher-order description of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
    [CrossRef]
  29. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, London, 1969).
  30. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  31. 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]
  32. 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]
  33. N. G. Alexopoulos, P. K. Park, “Scattering of waves with normal amplitude distribution from cylinders,” IEEE Trans. Antennas Propag. AP-20, 216–217 (1972).
    [CrossRef]
  34. S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
    [CrossRef]
  35. S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
    [CrossRef]
  36. S. Kozaki, “Scattering of a Gaussian beam by an inhomogeneous dielectric cylinder,” J. Opt. Soc. Am. 72, 1470–1474 (1982).
    [CrossRef]
  37. T.-C. K. Rao, “Scattering by a radially inhomogeneous cylindrical dielectric shell due to an incident Gaussian beam,” Can. J. Phys. 67, 471–475 (1989).
    [CrossRef]
  38. E. Zimmermann, R. Dändliker, N. Souli, B. Krattiger, “Scattering of an off-axis Gaussian beam by a dielectric cylinder compared with a rigorous electromagnetic approach,” J. Opt. Soc. Am. A 12, 398–403 (1995).
    [CrossRef]
  39. L. Schwartz, Méthodes Mathématiques pour les Sciences Physiques (Hermann, Paris, 1965)
  40. F. Roddier, Distributions et Transformation de Fourier à l’Usage des Physiciens et des Ingénieurs (McGraw-Hill, Paris, 1982).
  41. E. Butkov, Mathematical Physics (Addison-Wesley, Reading, Mass., 1968).
  42. G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1968).

1997 (2)

1996 (4)

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

G. Gouesbet, “Higher-order description of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
[CrossRef]

E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. 37, 9705–9710 (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]

1995 (6)

E. Zimmermann, R. Dändliker, N. Souli, B. Krattiger, “Scattering of an off-axis Gaussian beam by a dielectric cylinder compared with a rigorous electromagnetic approach,” J. Opt. Soc. Am. A 12, 398–403 (1995).
[CrossRef]

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]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt.(Paris) 26, 225–239 (1995).

G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
[CrossRef]

G. Gouesbet, “The separability theorem revisited with applications to light scattering theory,” J. Opt. (Paris) 26, 123–135 (1995).

1994 (8)

G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, “Interaction between a Gaussian beam and an infinite cylinder, using non-sigma-separable potentials,” J. Opt. Soc. Am. A 11, 3261–3273 (1994).
[CrossRef]

G. Gréhan, K. F. Ren, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a particle sizing technique based on laser sheets,” Part. Part. Syst. Charact. 11, 101–106 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
[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]

1993 (1)

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

1991 (1)

F. Corbin, G. Gréhan, G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Syst. Charact. 8, 222–228 (1991).
[CrossRef]

1989 (2)

J. P. Barton, D. R. Alexander, “Fifth order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

T.-C. K. Rao, “Scattering by a radially inhomogeneous cylindrical dielectric shell due to an incident Gaussian beam,” Can. J. Phys. 67, 471–475 (1989).
[CrossRef]

1988 (2)

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]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt.(Paris), 19, 59–67 (1988).

1982 (3)

S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
[CrossRef]

S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
[CrossRef]

S. Kozaki, “Scattering of a Gaussian beam by an inhomogeneous dielectric cylinder,” J. Opt. Soc. Am. 72, 1470–1474 (1982).
[CrossRef]

1979 (1)

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

1972 (1)

N. G. Alexopoulos, P. K. Park, “Scattering of waves with normal amplitude distribution from cylinders,” IEEE Trans. Antennas Propag. AP-20, 216–217 (1972).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, “Fifth order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Alexopoulos, N. G.

N. G. Alexopoulos, P. K. Park, “Scattering of waves with normal amplitude distribution from cylinders,” IEEE Trans. Antennas Propag. AP-20, 216–217 (1972).
[CrossRef]

Arfken, G.

G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1968).

Barton, J. P.

J. P. Barton, D. R. Alexander, “Fifth order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

Bohren, C. F.

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

Butkov, E.

E. Butkov, Mathematical Physics (Addison-Wesley, Reading, Mass., 1968).

Corbin, F.

F. Corbin, G. Gréhan, G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Syst. Charact. 8, 222–228 (1991).
[CrossRef]

Dändliker, R.

Davis, L. W.

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

Durst, F.

G. Gréhan, K. F. Ren, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a particle sizing technique based on laser sheets,” Part. Part. Syst. Charact. 11, 101–106 (1994).
[CrossRef]

Feshback, H.

P. M. Morse, H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 5, Part I.

Gouesbet, G.

E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. 37, 9705–9710 (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, G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
[CrossRef] [PubMed]

G. Gouesbet, “Higher-order description of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
[CrossRef]

G. Gouesbet, “The separability theorem revisited with applications to light scattering theory,” J. Opt. (Paris) 26, 123–135 (1995).

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt.(Paris) 26, 225–239 (1995).

G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
[CrossRef]

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]

G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
[CrossRef]

G. Gréhan, K. F. Ren, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a particle sizing technique based on laser sheets,” Part. Part. Syst. Charact. 11, 101–106 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, “Interaction between a Gaussian beam and an infinite cylinder, using non-sigma-separable potentials,” J. Opt. Soc. Am. A 11, 3261–3273 (1994).
[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]

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

F. Corbin, G. Gréhan, G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Syst. Charact. 8, 222–228 (1991).
[CrossRef]

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]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt.(Paris), 19, 59–67 (1988).

G. Gouesbet, G. Gréhan, B. Maheu, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion MeasurementsN. Chigier, ed. (Hemisphere, Washington, D.C., 1991), pp. 339–384.

K. F. Ren, G. Gouesbet, G. Gréhan, “Scattering of a Gaussian beam by an infinite cylinder: numerical results in GLMT-framework,” presented at the Eighth InternationalSymposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 8–11 July 1996.

G. Gouesbet, “General description of arbitrary shaped beams for introduction in light scattering theories,” in Recent Research Developments in Applied Optics, S. M. Krishnan, ed. (Research Signpost, Trivandrum, India, edited by the Scientific Information Guild, 1996).

Gréhan, G.

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

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representations of laser beams for use in light-scattering calculations,” Appl. Opt. 34, 2133–2143 (1995).
[CrossRef] [PubMed]

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]

G. Gréhan, K. F. Ren, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a particle sizing technique based on laser sheets,” Part. Part. Syst. Charact. 11, 101–106 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, “Interaction between a Gaussian beam and an infinite cylinder, using non-sigma-separable potentials,” J. Opt. Soc. Am. A 11, 3261–3273 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
[CrossRef]

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

F. Corbin, G. Gréhan, G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Syst. Charact. 8, 222–228 (1991).
[CrossRef]

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt.(Paris), 19, 59–67 (1988).

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, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion MeasurementsN. Chigier, ed. (Hemisphere, Washington, D.C., 1991), pp. 339–384.

K. F. Ren, G. Gouesbet, G. Gréhan, “Scattering of a Gaussian beam by an infinite cylinder: numerical results in GLMT-framework,” presented at the Eighth InternationalSymposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 8–11 July 1996.

Huffman, D. R.

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

Kerker, M.

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

Kozaki, S.

S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
[CrossRef]

S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
[CrossRef]

S. Kozaki, “Scattering of a Gaussian beam by an inhomogeneous dielectric cylinder,” J. Opt. Soc. Am. 72, 1470–1474 (1982).
[CrossRef]

Krattiger, B.

Lenglart, E.

E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. 37, 9705–9710 (1996).
[CrossRef]

Letellier, C.

Lock, J. A.

Maheu, B.

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt.(Paris), 19, 59–67 (1988).

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, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion MeasurementsN. Chigier, ed. (Hemisphere, Washington, D.C., 1991), pp. 339–384.

Morse, P. M.

P. M. Morse, H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 5, Part I.

Naqwi, A.

G. Gréhan, K. F. Ren, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a particle sizing technique based on laser sheets,” Part. Part. Syst. Charact. 11, 101–106 (1994).
[CrossRef]

Onofri, F.

Park, P. K.

N. G. Alexopoulos, P. K. Park, “Scattering of waves with normal amplitude distribution from cylinders,” IEEE Trans. Antennas Propag. AP-20, 216–217 (1972).
[CrossRef]

Rao, T.-C. K.

T.-C. K. Rao, “Scattering by a radially inhomogeneous cylindrical dielectric shell due to an incident Gaussian beam,” Can. J. Phys. 67, 471–475 (1989).
[CrossRef]

Ren, K. F.

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

G. Gréhan, K. F. Ren, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a particle sizing technique based on laser sheets,” Part. Part. Syst. Charact. 11, 101–106 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
[CrossRef]

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

K. F. Ren, G. Gouesbet, G. Gréhan, “Scattering of a Gaussian beam by an infinite cylinder: numerical results in GLMT-framework,” presented at the Eighth InternationalSymposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 8–11 July 1996.

Rice, J. F.

J. F. Rice, The Approximation of Functions (Addison-Wesley, Reading Mass., 1969), Vols. 1 and 2.

Roddier, F.

F. Roddier, Distributions et Transformation de Fourier à l’Usage des Physiciens et des Ingénieurs (McGraw-Hill, Paris, 1982).

Schwartz, L.

L. Schwartz, Méthodes Mathématiques pour les Sciences Physiques (Hermann, Paris, 1965)

Souli, N.

Zimmermann, E.

Appl. Opt. (3)

Can. J. Phys. (1)

T.-C. K. Rao, “Scattering by a radially inhomogeneous cylindrical dielectric shell due to an incident Gaussian beam,” Can. J. Phys. 67, 471–475 (1989).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

N. G. Alexopoulos, P. K. Park, “Scattering of waves with normal amplitude distribution from cylinders,” IEEE Trans. Antennas Propag. AP-20, 216–217 (1972).
[CrossRef]

S. Kozaki, “A new expression for the scattering of a Gaussian beam by a conducting cylinder,” IEEE Trans. Antennas Propag. AP-30, 881–887 (1982).
[CrossRef]

J. Appl. Phys. (2)

S. Kozaki, “Scattering of a Gaussian beam by a homogeneous dielectric cylinder,” J. Appl. Phys. 53, 7195–7200 (1982).
[CrossRef]

J. P. Barton, D. R. Alexander, “Fifth order corrected electromagnetic field components for a fundamental Gaussian beam,” J. Appl. Phys. 66, 2800–2802 (1989).
[CrossRef]

J. Math. Phys. (1)

E. Lenglart, G. Gouesbet, “The separability theorem in terms of distributions with discussion of electromagnetic scattering theory,” J. Math. Phys. 37, 9705–9710 (1996).
[CrossRef]

J. Opt. (Paris) (3)

G. Gouesbet, “Higher-order description of Gaussian beams,” J. Opt. (Paris) 27, 35–50 (1996).
[CrossRef]

G. Gouesbet, “The separability theorem revisited with applications to light scattering theory,” J. Opt. (Paris) 26, 123–135 (1995).

K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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]

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]

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

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser sheet beam shape coefficients in generalized Lorenz–Mie theory by using a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

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, “Interaction between a Gaussian beam and an infinite cylinder, using non-sigma-separable potentials,” J. Opt. Soc. Am. A 11, 3261–3273 (1994).
[CrossRef]

E. Zimmermann, R. Dändliker, N. Souli, B. Krattiger, “Scattering of an off-axis Gaussian beam by a dielectric cylinder compared with a rigorous electromagnetic approach,” J. Opt. Soc. Am. A 12, 398–403 (1995).
[CrossRef]

J. Opt.(Paris) (2)

G. Gouesbet, “Interaction between Gaussian beams and infinite cylinders, by using the theory of distributions,” J. Opt.(Paris) 26, 225–239 (1995).

B. Maheu, G. Gouesbet, G. Gréhan, “A concise presentation of the generalized Lorenz-Mie theory for arbitrary location of the scatterer in an arbitrary incident profile,” J. Opt.(Paris), 19, 59–67 (1988).

Part. Part. Syst. Charact. (6)

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

G. Gréhan, K. F. Ren, G. Gouesbet, A. Naqwi, F. Durst, “Evaluation of a particle sizing technique based on laser sheets,” Part. Part. Syst. Charact. 11, 101–106 (1994).
[CrossRef]

G. Gouesbet, “Generalized Lorenz–Mie theory and applications,” Part. Part. Syst. Charact. 11, 22–34 (1994).
[CrossRef]

F. Corbin, G. Gréhan, G. Gouesbet, “Top-hat beam technique: improvements and application to bubble measurements,” Part. Part. Syst. Charact. 8, 222–228 (1991).
[CrossRef]

G. Gouesbet, “Scattering of a first-order Gaussian beam by an infinite cylinder with arbitrary location and arbitrary orientation,” Part. Part. Syst. Charact. 12, 242–256 (1995).
[CrossRef]

G. Gouesbet, G. Gréhan, “Interaction between shaped beams and an infinite cylinder including a discussion of Gaussian beams,” Part. Part. Syst. Charact. 11, 299–308 (1994).
[CrossRef]

Phys. Rev. A (1)

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

Other (11)

K. F. Ren, G. Gouesbet, G. Gréhan, “Scattering of a Gaussian beam by an infinite cylinder: numerical results in GLMT-framework,” presented at the Eighth InternationalSymposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 8–11 July 1996.

P. M. Morse, H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 5, Part I.

G. Gouesbet, G. Gréhan, B. Maheu, “Generalized Lorenz–Mie theory and applications to optical sizing,” in Combustion MeasurementsN. Chigier, ed. (Hemisphere, Washington, D.C., 1991), pp. 339–384.

J. F. Rice, The Approximation of Functions (Addison-Wesley, Reading Mass., 1969), Vols. 1 and 2.

G. Gouesbet, “General description of arbitrary shaped beams for introduction in light scattering theories,” in Recent Research Developments in Applied Optics, S. M. Krishnan, ed. (Research Signpost, Trivandrum, India, edited by the Scientific Information Guild, 1996).

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

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

L. Schwartz, Méthodes Mathématiques pour les Sciences Physiques (Hermann, Paris, 1965)

F. Roddier, Distributions et Transformation de Fourier à l’Usage des Physiciens et des Ingénieurs (McGraw-Hill, Paris, 1982).

E. Butkov, Mathematical Physics (Addison-Wesley, Reading, Mass., 1968).

G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1968).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Original and translated Cartesian coordinate systems. O p O = (U 0, V 0, W 0) with rescaled coordinates.

Fig. 2
Fig. 2

Rotated Cartesian coordinate system (OPxyz).

Fig. 3
Fig. 3

Cylindrical coordinates. The axis (Opz) is the cylinder axis.

Equations (156)

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

U, V, W=ku, kv, kw
Eu, Ev, Ew=E0 exp-iWp=0q=0l=0×Epqlu, Epqlv, EpqlwUpVqWl,
Hu, Hv, Hw=H0 exp-iWp=0q=0l=0×Hpqlu, Hpqlv, HpqlwUpVqWl,
q+1Epq+1lw-l+1Epql+1v+iEpqlv+Hpqlu=0,
l+1Epql+1u-p+1Ep+1qlw+iHpqlv-Epqlu=0,
p+1Ep+1qlv-q+1Epq+1lu+iHpqlw=0,
p+1Hp+1qlu+q+1Hpq+1lv+l+1Hpql+1w-iHpqlw=0,
q+1Hpq+1lw-l+1Hpql+1v+iHpqlv-Epqlu=0,
l+1Hpql+1u-p+1Hp+1qlw-iHpqlu+Epqlv=0,
p+1Hp+1qlv-q+1Hpq+1lu-iEpqlw=0,
p+1Ep+1qlu+q+1Epq+1lv+l+1Epql+1w-iEpqlw=0.
Eu, Hv=E0, H0exp-iW,
E000u=H000v=1.
OpO=U0, V0, W0.
Eu, Ev, Ew=E0 exp-iW-W0×p=0q=0l=0Epqlu, Epqlv, EpqlwU-U0p×V-V0qW-W0l,
Hu, Hv, Hw=H0 exp-iW-W0×p=0q=0l=0Hpqlu, Hpqlv, HpqlwU-U0p×V-V0qW-W0l.
Γ=Opz, -ei
ei=-Sex-Cez,
S=sin Γ, C=cos Γ.
Xx=XvC-XwS,
Xy=Xu,
Xz=-XvS-XwC,
Xρ=XxCφ+XySφ,
Xφ=-XxSφ+XyCφ,
Xz=Xz,
Sφ=sin φ, Cφ=cos φ.
U=RSφ,
V=RCCφ-SZ,
W=-RSCφ-CZ,
Z, R=kz, kρ.
Eρ=E0Ap=0q=0l=0CCφEpqlv-SCφEpqlw+SφEpqluApql,
Eφ=E0Ap=0q=0l=0SSφEpqlw-CSφEpqlv+CφEpqluApql,
Ez=E0Ap=0q=0l=0-SEpqlv-CEpqlwApql
Hρ=H0Ap=0q=0l=0CCφHpqlv-SCφHpqlw+SφHpqluApql,
Hφ=H0Ap=0q=0l=0SSφHpqlw-CSφHpqlv+CφHpqluApql,
Hz=H0Ap=0q=0l=0-SHpqlv-CHpqlwApql,
A=expiRSCφ+CZ+W0,
Apql=RSφ-U0pRCCφ-SZ-V0q×-RSCφ-CZ-W0l.
ds2=e12dz2+e22dρ2+e32dφ2,
e1=e2=1, e3=ρ,
e1=1, ze2e3=0.
2Uz2+k2U+1ρρ ρ Uρ+1ρ22Uφ2=0,
Ez, TM=2UTMz2+k2UTM,
Eρ, TM=2UTMzρ,
Eφ, TM=1ρ2UTMzφ,
Hz, TM=0,
Hρ, TM=iωρUTMφ,
Hφ, TM=-iω UTMρ,
Ez, TE=0,
Eρ, TE=-iωμρUTEφ,
Eφ, TE=iωμUTEρ,
Hz, TE=2UTEz2+k2UTE,
Hρ, TE=2UTEzρ,
Hφ, TE=1ρ2UTEzφ,
Gz, ρ, φ=JmrYmrHm1rHm2rexpimφexpikγz,
r=kρ1-γ21/2.
UTMi=E0k2m=-+-im expimφImTMγ, ×JmR1-γ21/2expiγZ,
UTEi=H0k2m=-+-im expimφImTEγ, ×JmR1-γ21/2expiγZ,
ImTMγ, 1-γ2JmR1-γ21/2expiγZ=12π-im02πEziE0exp-imφdφ,
ImTEγ, 1-γ2JmR1-γ21/2expiγZ=12π-im02πHziH0exp-imφdφ,
ImTMγ=n=0ImTMnδnγ-C,
Ar=-12π-im expiCZexpiW0p=0q=0l=0Epql×02π expiRSCφexp-imφRSφ-U0p×RCCφ-SZ-V0q-RSCφ-CZ-W0ldφ,
Epql=SEpqlv+CEpqlw.
RSφ-U0p=r=0pprRSφr-U0p-r,
RCCφ-SZ-V0q=s=0qt=0s-1q-tqsst×RSCφtSZs-tV0q-s,
-RSCφ-CZ-W0l=u=0lv=0u-1lluuv×RSCφvCZu-vW0l-u,
I=r=0ps=0qt=0su=0lv=0u-1p-r+q-t+lprqsstluuv×Rr+t+vZs-t+u-vCt+u-vSs-t+vU0p-rV0q-sW0l-uJrtcRS,
JrtvRS=02π expiRSCφexp-imφCφt+vSφrdφ.
I0=02π expiRSCφexp-imφdφ=2π-imJmRS,
I1=02π expiRSCφexp-imφSφdφ=-2πm-imJmRSRS,
Jrtv=2π-im1it+vw=0r/2r/2wJmt+v+2wRS,  r even,
Jrtv=-2πm-im1it+vw=0r-1/2r-1/2w×JmRSRSt+v+2w,  r odd.
JrtvRS=2π-im1it+vGrtvRS.
Ar=--1m expiCZexpiW0×p=0q=0l=0Epqlr=0ps=0qt=0su=0lv=0u×-1p-r+q-t+lit+vprqsstlu×uvRr+t+vZs-t+u-vCt+u-v×Ss-t+vU0p-rV0q-sW0l-uGrtvRS
s=0qt=0s=s=0qa=0s,
u=0lv=0uu=lb=0u,
Ar=-1m+1 expiCZexpiW0×p=0q=0l=0r=0ps=0qa=0su=0lb=0uApqlrsaubZa+b,
Apqlrsaub=-U0p-V0q-W0lEpql-RU0rprqs×ss-aiRs-aCs-aSaV0sluuu-b×-iRu-bCbSu-bW0uGr, s-a, u-bRS.
Ar=-1m+1 expiCZexpiW0j=0AjZj,
A0=p=0q=0l=0r=0ps=0qu=0lApqlrs0u0
A1=p=0q=0l=0r=0ps=1qu=0lApqlrs1u0+p=0q=0l=0r=0ps=0qu=1lApqlrs0u1.
Ar=-1m+1 expiCZexpiW0j=0NAjZj.
Al=n=0ImTMnδnγ-C, 1-γ2×JmR1-γ21/2expiγZ.
δnγ-C, fγ=-1nfγγ=Cn,
Al=n=0ImTMn-1n1-γ2×JmR1-γ21/2expiγZγ=Cn.
gγ=1-γ2JmR1-γ21/2
Al=expiCZn=0ImTMn-1nr=0nnriZrdn-rdγn-r gγγ=C,
Al=expiCZj=0NBjImTMj, , ImTMNZj,
BNImTMN=-1m+1 expiW0AN,
BN-1ImTMN-1, ImTMN=-1m+1×expiW0AN-1, ,
B0ImTM0, , ImTMN=-1m+1 expiW0A0.
Jmx=12Jm-1x-Jm+1x,
Jm-1x+Jm+1x=2mxJmx,
ImTEγ=n=0ImTEnδnγ-C.
ImTMγ=n=0NImTMnδnγ-C.
UTMi=E0k2m=-+-im expimφn=0NImTMn-1n×JmR1-γ21/2expiγZγ=Cn.
jmnR=dndγnJmR1-γ21/2γ=C,
n=0Nl=0n=l=0Nn=lN,
UTMi=E0k2 expiCZm=-+-im expimφ×l=0NZln=lNImTMn-1nnliljmn-lR.
UTEi=H0k2 expiCZm=-+-im expimφ×l=0NZln=lNImTEn-1nnliljmn-lR.
Ezi=k22UTMiZ2+UTMi,
Eρi=k22UTMiZR-iRE0H0UTEiφ,
Eφi=k21R2UTMiZφ+iE0H0UTEiR,
Hzi=k22UTEiZ2+UTEi,
Hρi=k2iRH0E0UTMiφ+2UTEiZR,
Hφi=k21iH0E0UTMiR+1R2UTEiZφ,
ωμ=kH0/E0E0/H0.
Xαi=X0 expiCZm=-+-im expimφl=0NXαmilRZl,
EzmilR=ImTMl-ilS2jm0R+ImTMl+1-ill+12Cjm0R-S2jm1R+n=l+2NImTMn-1nilS2nljmn-lR-2Cl+1nl+1jmn-l-1R-l+1l+2×nl+2jmn-l-2R,  l=0  N-2;
EzmiN-1R=2iCNImTMN-iNjm0R+S2n=N-1NImTMn-1nnN-1iN-1jmn-N+1R;
EzmiNR=S2ImTMN-iNjm0R;
Eρmil=i-ilCImTMldjm0RdR-imImTEljm0RR+n=l+1N-1niliCImTMnnldjmn-lRdR+l+1ImTMninl+1djmn-l-1RdR-iR imImTEnnljmn-lR,  l=0  N-1;
EρmiNR=-iNiCImTMNdjm0RdR-iR imImTENjm0R;
Eφmil=i-ilCimRImTMljm0R+ImTEldjm0RdR+n=l+1Ni-1nilCimRImTMnnljmn-lR+imR×l+1ImTMnnl+1jmn-l-1R+ImTEnnldjmn-lRdR,  l=0  N-1;
EφmiN=i-iNCimRImTMNjm0R+ImTENdjm0RdR;
Hρmil=i-ilimRImTMljm0R+CImTEldjm0RdR+n=l+1Ni-1nilimRImTMnnljmn-lR+CImTEnnldjmn-lRdR+l+1ImTEn×nl+1djmn-l-1RdR,  l=0  N-1;
HρmiN=i-iNimRImTMNjm0R+CImTENdjm0RdR;
Hφmil=i-il-ImTMldjm0RdR+CR imImTEljm0R+n=l+1Ni-1nil-ImTMnnldjmn-lRdR+CR imImTEnnljmn-lR+imRl+1ImTEn×nl+1jmn-l-1R, l=0  N-1;
HφmiN=i-iN-ImTMNdjm0RdR+CR imImTENjm0R.
UTMs=-E0k2m=-+-im expimφSmTMγ, HmR1-γ21/2expiγZ
UTEs=H0k2m=-+-im expimφSmTEγ, HmR1-γ21/2expiγZ,
SmTMγ=n=0NSmTMnδnγ-C,
SmTEγ=n=0NSmTEnδnγ-C.
UTMs=-E0k2m=-+-im expimφ×n=0NSmTMn-1nHmR1-γ21/2×expiγZγ=Cn,
UTEs=H0k2m=-+-im expimφ×n=0NSmTEn-1nHmR1-γ21/2×expiγZγ=Cn,
hmnR=dndγn HmR1-γ21/2γ=C,
UTMs=-E0k2 expiCZm=-+-im expimφl=0NZl×n=lNSmTMn-1nnlilhmn-lR,
UTEs=H0k2 expiCZm=-+-im expimφl=0NZl×n=lNSmTEn-1nnlilhmn-lR.
Xαs=X0 expiCZm=-+-im expimφl=0NXαmslRZl,
M=kc/k,
c=M2
μc=μ.
UTMc=E0k2Mm=-+-im expimφCmTMγ, JmMR1-γ21/2expiγZ,
UTEc=iH0k2m=-+-im expimφCmTEγ, JmMR1-γ21/2expiγZ,
CmTMγ=n=0NCmTMnδnγ-C,
CmTEγ=n=0NCmTEnδnγ-C.
j¯mnR=dndγnJmMR1-γ21/2γ=C;
UTMc=E0 expiCZMk2m=-+-im expimφl=0NZl×n=lNCmTMn-1nnlilj¯mn-lR,
UTEc=iH0 expiCZk2m=-+-im expimφl=0NZl×n=lNCmTEn-1nnlilj¯mn-lR.
Ezc=k22UTMcZ2+M2UTMc,
Eρc=k22UTMcZR-iRE0H0UTEcφ,
Eφc=k21R2UTMcZφ+iE0H0UTEcR,
Hzc=k22UTEcZ2+M2UTEc,
Hρc=k2iM2RH0E0UTMcφ+2UTEcZR,
Hφc=k21iM2H0E0UTMcR+1R2UTEcZφ.
Xαc=X0 expiCZm=-+-im expimφl=0NXαmclRZl.
EzmclR=CmTMlM-ilM2-C2jm0¯R+CmTMl+1M-il×l+12Cjm0¯R-M2jm1¯R+C2jm1¯R+n=l+2NCmTMnM-1nilM2-C2nlj¯mn-lR-2Cl+1nl+1j¯mn-l-1R-l+1l+2nl+2j¯mn-l-2R  l=0  N-2;
EzmCN-1R=2iCN CmTMNM-iNjm0¯R+M2-C2×n=N-1NCmTMnM-1nnN-1iN-1j¯mn-N+1R;
EzmCNR=M2-C2CmTMNM-iNjm0¯R.
Ezc-Ezs=Ezi, Eφc-Eφs=Eφi,
Hzc-Hzs=Hzi, Hφc-Hφs=Hφi;
Ezmcj-Ezmsj=Ezmij, Eφmcj-Eφmsj=Eφmij,
Hzmcj-Hzmsj=Hzmij, Hφmcj-Hφmsj=Hφmij,
UTMi=E0k2m=-+-im expimφ  ImTMγ×JmR1-γ21/2expiγZdγ,
 δxfxdx=f0,
δ, f=f0.

Metrics