Abstract

Since diffraction is a scattering process in principle, light propagation through one aperture in a screen is discussed in the light-scattering theory. Through specific calculation, the expression of the electric field observed at an observation point is obtained and is used not only to explain why Kirchhoff’s diffraction theory is a good approximation when the screen is both opaque and sufficiently thin but also to demonstrate that the mathematical and physical problems faced by Kirchhoff’s theory are avoided in the light-scattering theory.

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References

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  1. J. D. Jackson, Classical Electrodynamics (Wiley, 1975).
  2. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, 1991).
  3. E. W. Marchand and E. Wolf, “Consistent formulation of Kirchhoff's diffraction theory,” J. Opt. Soc. Am. 56, 1712-1722 (1966).
    [CrossRef]
  4. S. Ganci, “A general scalar solution for the half-plane problem,” J. Mod. Opt. 42, 1707-1711 (1995).
    [CrossRef]
  5. Y. Z. Umul, “Young-Kirchhoff-Rubinowicz theory of diffraction in the light of Sommerfeld's solution,” J. Opt. Soc. Am. A 25, 2734-2742 (2008).
    [CrossRef]
  6. F. Kottler, “Diffraction at a black screen, Part I: Kirchhoff's theory,” in Progress in Optics, Vol. IV, E.Wolf, ed. (North-Holland, 1965), pp. 281-314.
    [CrossRef]
  7. F. Kottler, “Diffraction at a black screen, Part II: Electromagnetic theory,” in Progress in Optics, Vol. VI, E.Wolf, ed. (North-Holland, 1967), pp. 331-377.
    [CrossRef]
  8. S. Ganci, “Equivalence between two consistent formulations of Kirchhoff's diffraction theory,” J. Opt. Soc. Am. A 5, 1626-1628 (1988).
    [CrossRef]
  9. A. Roberts, “Electromagnetic theory of diffraction by a circular aperture in a thick, perfectly conducting screen,” J. Opt. Soc. Am. A 4, 1970-1983 (1987).
    [CrossRef]
  10. K.E.Oughstun, ed., Selected Papers on Scalar Wave Diffraction, Vol. MS51 of SPIE Milestone Series (SPIE Optical Engineering Press, 1992).
  11. W. Guo and S. Prasad, “Multiple scattering of light from a random slab: a density-fluctuation approach,” Opt. Commun. 212, 1-6 (2002).
    [CrossRef]
  12. W. Guo, “Multiple scattering of a plane scalar wave from a dielectric slab,” Am. J. Phys. 70, 1039-1043 (2002).
    [CrossRef]
  13. M. V. Klein and T. E. Furtak, Optics, 2nd ed. (Wiley, 1986).

2008 (1)

2002 (2)

W. Guo and S. Prasad, “Multiple scattering of light from a random slab: a density-fluctuation approach,” Opt. Commun. 212, 1-6 (2002).
[CrossRef]

W. Guo, “Multiple scattering of a plane scalar wave from a dielectric slab,” Am. J. Phys. 70, 1039-1043 (2002).
[CrossRef]

1995 (1)

S. Ganci, “A general scalar solution for the half-plane problem,” J. Mod. Opt. 42, 1707-1711 (1995).
[CrossRef]

1988 (1)

1987 (1)

1966 (1)

Furtak, T. E.

M. V. Klein and T. E. Furtak, Optics, 2nd ed. (Wiley, 1986).

Ganci, S.

Guo, W.

W. Guo, “Multiple scattering of a plane scalar wave from a dielectric slab,” Am. J. Phys. 70, 1039-1043 (2002).
[CrossRef]

W. Guo and S. Prasad, “Multiple scattering of light from a random slab: a density-fluctuation approach,” Opt. Commun. 212, 1-6 (2002).
[CrossRef]

Jackson, J. D.

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

Klein, M. V.

M. V. Klein and T. E. Furtak, Optics, 2nd ed. (Wiley, 1986).

Kottler, F.

F. Kottler, “Diffraction at a black screen, Part II: Electromagnetic theory,” in Progress in Optics, Vol. VI, E.Wolf, ed. (North-Holland, 1967), pp. 331-377.
[CrossRef]

F. Kottler, “Diffraction at a black screen, Part I: Kirchhoff's theory,” in Progress in Optics, Vol. IV, E.Wolf, ed. (North-Holland, 1965), pp. 281-314.
[CrossRef]

Marchand, E. W.

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, 1991).

Prasad, S.

W. Guo and S. Prasad, “Multiple scattering of light from a random slab: a density-fluctuation approach,” Opt. Commun. 212, 1-6 (2002).
[CrossRef]

Roberts, A.

Umul, Y. Z.

Wolf, E.

Am. J. Phys. (1)

W. Guo, “Multiple scattering of a plane scalar wave from a dielectric slab,” Am. J. Phys. 70, 1039-1043 (2002).
[CrossRef]

J. Mod. Opt. (1)

S. Ganci, “A general scalar solution for the half-plane problem,” J. Mod. Opt. 42, 1707-1711 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Commun. (1)

W. Guo and S. Prasad, “Multiple scattering of light from a random slab: a density-fluctuation approach,” Opt. Commun. 212, 1-6 (2002).
[CrossRef]

Other (6)

F. Kottler, “Diffraction at a black screen, Part I: Kirchhoff's theory,” in Progress in Optics, Vol. IV, E.Wolf, ed. (North-Holland, 1965), pp. 281-314.
[CrossRef]

F. Kottler, “Diffraction at a black screen, Part II: Electromagnetic theory,” in Progress in Optics, Vol. VI, E.Wolf, ed. (North-Holland, 1967), pp. 331-377.
[CrossRef]

K.E.Oughstun, ed., Selected Papers on Scalar Wave Diffraction, Vol. MS51 of SPIE Milestone Series (SPIE Optical Engineering Press, 1992).

M. V. Klein and T. E. Furtak, Optics, 2nd ed. (Wiley, 1986).

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

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, 1991).

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Equations (15)

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ψ ( r o ) = 1 4 π e i k R R n [ ψ inc + i k ( 1 + i k R ) R R ψ inc ] d a ,
ψ ( r o ) = k 2 π i e i k R R ( 1 + i k R ) n R R ψ inc d a .
ψ m ( r o ) = ψ inc ( r o ) + 4 π k 2 α n Ω G ( r o , r 1 ) ψ e ( r 1 ) d x 1 d y 1 d z 1 ,
ψ m ( r o ) = ψ inc ( r 0 ) + 4 π k 2 α n V G ( r o , r 1 ) ψ e ( r 1 ) d x 1 d y 1 d z 1 4 π k 2 α n Ω G ( r o , r 1 ) ψ e ( r 1 ) d x 1 d y 1 d z 1 .
ψ e ( r ) = ψ inc ( r ) + α ̃ V G ( r , r 1 ) ψ e ( r 1 ) d x 1 d y 1 d z 1 α ̃ Ω G ( r , r 1 ) ψ e ( r 1 ) d x 1 d y 1 d z 1 ,
ψ m = ψ inc + α ̃ G ̂ V ψ e α ̃ G ̂ Ω ψ e ,
ψ e = ψ inc + α ̃ G ̂ V ψ e α ̃ G ̂ Ω ψ e .
ψ e = ( 1 α ̃ G ̂ V ) 1 ψ inc α ̃ ( 1 α ̃ G ̂ V ) 1 G ̂ Ω ψ e ,
ψ e = ψ d α ̃ ( 1 α ̃ G ̂ V ) 1 G ̂ Ω ψ d + α ̃ 2 ( 1 α ̃ G ̂ V ) 1 G ̂ Ω ( 1 α ̃ G ̂ V ) 1 G ̂ Ω ψ d ,
ψ m = ψ inc + α ̃ G ̂ V ψ d α ̃ G ̂ Ω ψ d α ̃ 2 G ̂ V ( 1 α ̃ G ̂ V ) 1 G ̂ Ω ψ d + α ̃ 2 G ̂ Ω ( 1 α ̃ G ̂ V ) 1 G ̂ Ω ψ d + .
ψ m ( r o ) ψ t ( r o ) α ̃ Ω G ( r o , r 1 ) ψ d ( r 1 ) d x 1 d y 1 d z 1 ,
ψ d ( r ) = e i k r D 0 { [ k z ( θ ) + k cos θ ] e i k z ( θ ) z + [ k z ( θ ) k cos θ ] e 2 i k z ( θ ) d i k z ( θ ) z } ,
ψ t ( r ) = 2 D 0 k z ( θ ) e i [ k z ( θ ) k cos θ ] d e i k r .
ψ m ( r o ) ψ t ( r 0 ) α ̃ S d x 1 d y 1 ( A d A ( 1 ) d 2 2 + A ( 2 ) d 3 3 ! A ( 3 ) d 4 4 ! + ) ,
ψ m ( r o ) 2 α ̃ d D 0 k z ( θ ) e i k z ( θ ) d S G ( r o , r 1 ) e i k r 1 d x 1 d y 1 ,

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