Abstract

An alternative interpretation of the phenomenon of edge diffraction is proposed according to a new separation of the Fresnel function. The subfields are investigated in the problem of diffraction of a plane wave by a perfectly conducting half-plane, and the results are compared numerically with other interpretations.

© 2008 Optical Society of America

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References

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  1. R. Cecchini and G. Pelosi, "Diffraction: The first recorded observation," IEEE Antennas Propag. Mag. 32, 27-30 (1990).
    [CrossRef]
  2. G. Pelosi, S. Selleri, and P. Ya. Ufimtsev, "Newton's observations of diffracted rays," IEEE Antennas Propag. Mag. 40, 7-14 (1998).
    [CrossRef]
  3. A. Rubinowicz, "Thomas Young and the theory of diffraction," Nature 180, 160-162 (1957).
    [CrossRef]
  4. G. A. Maggi, "Sulla propagazione libra e perturbata delle onde limunose in un mezzo isotropo," Ann. Mat. 16, 21-48 (1888).
  5. A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen," Ann. Phys. 53, 257-278 (1917).
    [CrossRef]
  6. A. Rubinowicz, "Zur Kirchhoffschen Beugungstheorie," Ann. Phys. 73, 339-364 (1924).
    [CrossRef]
  7. P. Ya. Ufimtsev, "Rubinowicz and the modern theory of diffracted rays," Electromagnetics 15, 547-565 (1995).
    [CrossRef]
  8. A. Sommerfeld, "Matematische Theorie der Diffraction," Math. Ann. 47, 317-374 (1896).
    [CrossRef]
  9. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 2003).
  10. J. B. Keller, "Geometrical theory of diffraction," J. Opt. Soc. Am. 52, 116-130 (1962).
    [CrossRef] [PubMed]
  11. P. Ya. Ufimtsev, "Elementary edge waves and the physical theory of diffraction," Electromagnetics 11, 125-160 (1991).
    [CrossRef]
  12. A. I. Khizhnyak, S. P. Anokhov, R. A. Lyramenko, M. S. Soskin, and M. V. Vasnetsov, "Structure of an edge-dislocation wave originating in plane wave diffraction by a half-plane," J. Opt. Soc. Am. A 17, 2199-2207 (2000).
    [CrossRef]
  13. P. V. Polyanskii and G. V. Bogatiryova, "EDW-edge diffraction wave, edge dislocation wave, or whether tertio est datur? (On the bicentenary of Thomas Young's wave diffraction theory)," Proc. SPIE 4607, 109-124 (2002).
    [CrossRef]
  14. S. Ganci, "An experiment on the physical reality of edge-diffracted waves," Am. J. Phys. 57, 370-373 (1989).
    [CrossRef]
  15. R. G. Kouyoumjian and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting screen," Proc. IEEE 62, 1448-1461 (1974).
    [CrossRef]
  16. Y. Z. Umul, "Edge-dislocation waves in the diffraction process by an impedance half-plane," J. Opt. Soc. Am. A 24, 507-511 (2007).
    [CrossRef]
  17. Y. Z. Umul, "Modified theory of physical optics," Opt. Express 12, 4959-4972 (2004).
    [CrossRef] [PubMed]
  18. Z. L. Horvath, J. Klebniczki, G. Kurdi, and A. P. Kovacs, "Experimental investigation of the boundary wave pulse," Opt. Commun. 239, 243-250 (2004).
    [CrossRef]
  19. R. Kumar, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, "Direct visualization of Young's boundary diffraction wave," Opt. Commun. 276, 54-57 (2007).
    [CrossRef]
  20. R. Kumar, "Structure of boundary diffraction wave revisited," Appl. Phys. B: Photophys. Laser Chem. DOI:10.1007/s00340-007-2897-y (to be published).

2007 (2)

Y. Z. Umul, "Edge-dislocation waves in the diffraction process by an impedance half-plane," J. Opt. Soc. Am. A 24, 507-511 (2007).
[CrossRef]

R. Kumar, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, "Direct visualization of Young's boundary diffraction wave," Opt. Commun. 276, 54-57 (2007).
[CrossRef]

2004 (2)

Y. Z. Umul, "Modified theory of physical optics," Opt. Express 12, 4959-4972 (2004).
[CrossRef] [PubMed]

Z. L. Horvath, J. Klebniczki, G. Kurdi, and A. P. Kovacs, "Experimental investigation of the boundary wave pulse," Opt. Commun. 239, 243-250 (2004).
[CrossRef]

2002 (1)

P. V. Polyanskii and G. V. Bogatiryova, "EDW-edge diffraction wave, edge dislocation wave, or whether tertio est datur? (On the bicentenary of Thomas Young's wave diffraction theory)," Proc. SPIE 4607, 109-124 (2002).
[CrossRef]

2000 (1)

1998 (1)

G. Pelosi, S. Selleri, and P. Ya. Ufimtsev, "Newton's observations of diffracted rays," IEEE Antennas Propag. Mag. 40, 7-14 (1998).
[CrossRef]

1995 (1)

P. Ya. Ufimtsev, "Rubinowicz and the modern theory of diffracted rays," Electromagnetics 15, 547-565 (1995).
[CrossRef]

1991 (1)

P. Ya. Ufimtsev, "Elementary edge waves and the physical theory of diffraction," Electromagnetics 11, 125-160 (1991).
[CrossRef]

1990 (1)

R. Cecchini and G. Pelosi, "Diffraction: The first recorded observation," IEEE Antennas Propag. Mag. 32, 27-30 (1990).
[CrossRef]

1989 (1)

S. Ganci, "An experiment on the physical reality of edge-diffracted waves," Am. J. Phys. 57, 370-373 (1989).
[CrossRef]

1974 (1)

R. G. Kouyoumjian and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting screen," Proc. IEEE 62, 1448-1461 (1974).
[CrossRef]

1962 (1)

1957 (1)

A. Rubinowicz, "Thomas Young and the theory of diffraction," Nature 180, 160-162 (1957).
[CrossRef]

1924 (1)

A. Rubinowicz, "Zur Kirchhoffschen Beugungstheorie," Ann. Phys. 73, 339-364 (1924).
[CrossRef]

1917 (1)

A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen," Ann. Phys. 53, 257-278 (1917).
[CrossRef]

1896 (1)

A. Sommerfeld, "Matematische Theorie der Diffraction," Math. Ann. 47, 317-374 (1896).
[CrossRef]

1888 (1)

G. A. Maggi, "Sulla propagazione libra e perturbata delle onde limunose in un mezzo isotropo," Ann. Mat. 16, 21-48 (1888).

Am. J. Phys. (1)

S. Ganci, "An experiment on the physical reality of edge-diffracted waves," Am. J. Phys. 57, 370-373 (1989).
[CrossRef]

Ann. Mat. (1)

G. A. Maggi, "Sulla propagazione libra e perturbata delle onde limunose in un mezzo isotropo," Ann. Mat. 16, 21-48 (1888).

Ann. Phys. (2)

A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen," Ann. Phys. 53, 257-278 (1917).
[CrossRef]

A. Rubinowicz, "Zur Kirchhoffschen Beugungstheorie," Ann. Phys. 73, 339-364 (1924).
[CrossRef]

Electromagnetics (2)

P. Ya. Ufimtsev, "Rubinowicz and the modern theory of diffracted rays," Electromagnetics 15, 547-565 (1995).
[CrossRef]

P. Ya. Ufimtsev, "Elementary edge waves and the physical theory of diffraction," Electromagnetics 11, 125-160 (1991).
[CrossRef]

IEEE Antennas Propag. Mag. (2)

R. Cecchini and G. Pelosi, "Diffraction: The first recorded observation," IEEE Antennas Propag. Mag. 32, 27-30 (1990).
[CrossRef]

G. Pelosi, S. Selleri, and P. Ya. Ufimtsev, "Newton's observations of diffracted rays," IEEE Antennas Propag. Mag. 40, 7-14 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Math. Ann. (1)

A. Sommerfeld, "Matematische Theorie der Diffraction," Math. Ann. 47, 317-374 (1896).
[CrossRef]

Nature (1)

A. Rubinowicz, "Thomas Young and the theory of diffraction," Nature 180, 160-162 (1957).
[CrossRef]

Opt. Commun. (2)

Z. L. Horvath, J. Klebniczki, G. Kurdi, and A. P. Kovacs, "Experimental investigation of the boundary wave pulse," Opt. Commun. 239, 243-250 (2004).
[CrossRef]

R. Kumar, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, "Direct visualization of Young's boundary diffraction wave," Opt. Commun. 276, 54-57 (2007).
[CrossRef]

Opt. Express (1)

Proc. IEEE (1)

R. G. Kouyoumjian and P. H. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting screen," Proc. IEEE 62, 1448-1461 (1974).
[CrossRef]

Proc. SPIE (1)

P. V. Polyanskii and G. V. Bogatiryova, "EDW-edge diffraction wave, edge dislocation wave, or whether tertio est datur? (On the bicentenary of Thomas Young's wave diffraction theory)," Proc. SPIE 4607, 109-124 (2002).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 2003).

R. Kumar, "Structure of boundary diffraction wave revisited," Appl. Phys. B: Photophys. Laser Chem. DOI:10.1007/s00340-007-2897-y (to be published).

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Figures (10)

Fig. 1
Fig. 1

Edge-diffracted wave.

Fig. 2
Fig. 2

Fields scattered by an edge discontinuity.

Fig. 3
Fig. 3

Total field with the edge-dislocation wave.

Fig. 4
Fig. 4

Field representations of the third interpretation.

Fig. 5
Fig. 5

Geometry of the edge-diffraction problem.

Fig. 6
Fig. 6

Plot of the total fields.

Fig. 7
Fig. 7

Comparison of the edge-dislocation wave and the quasi-aperture field.

Fig. 8
Fig. 8

Comparison of Eqs. (22, 23).

Fig. 9
Fig. 9

Comparison of the PO and the rigorous fields.

Fig. 10
Fig. 10

Stationary phase geometry of the half-plane problem.

Equations (27)

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F [ x ] = exp ( j π 4 ) π x exp ( j t 2 ) d t ,
F [ x ] = U ( x ) + sign ( x ) F [ x ]
F [ x ] = F [ 0 ] exp ( j π 4 ) π 0 x exp ( j t 2 ) d t
u d = F [ x ] ,
u s = u t u d .
u s = exp ( j π 4 ) π x exp ( j t 2 ) d t exp ( j π 4 ) π x exp ( j t 2 ) d t ,
u s = exp ( j π 4 ) π x x exp ( j t 2 ) d t .
u s = { 1 2 F [ x ] } U ( x ) .
u i = u 0 exp [ j k ρ cos ( ϕ ϕ 0 ) ] .
u t = u t 1 + u t 2 .
u t 1 = u o exp [ j k ρ cos ( ϕ ϕ 0 ) ] F [ ξ 1 ] ,
u t 2 = u o exp [ j k ρ cos ( ϕ + ϕ 0 ) ] F [ ξ 2 ] .
u t 1 = u s 1 + u d 1 ,
u t 2 = u s 2 + u d 2
u s 1 = u o exp [ j k ρ cos ( ϕ ϕ 0 ) ] U ( ξ 1 ) ( 1 2 F [ ξ 1 ] ) ,
u s 2 = u o exp [ j k ρ cos ( ϕ + ϕ 0 ) ] U ( ξ 2 ) ( 1 2 F [ ξ 2 ] ) .
u d 1 = u o exp [ j k ρ cos ( ϕ ϕ 0 ) ] F [ ξ 1 ] ,
u d 2 = u o exp [ j k ρ cos ( ϕ + ϕ 0 ) ] F [ ξ 2 ] .
u s = 2 { F [ x ] F [ 0 ] } U ( x ) ,
u s = 2 u edw U ( x )
u s = exp ( j π 4 ) π [ x 0 exp ( j t 2 ) d t + 0 x exp ( j t 2 ) d t ] .
u s = exp ( j π 4 ) π [ 0 x exp ( j t 2 ) d t + 0 x exp ( j t 2 ) d t ] ,
u s = 2 U ( x ) exp ( j π 4 ) π 0 x exp ( j t 2 ) d t .
u = k u 0 e j π 4 2 π 0 x s sin β + ϕ 0 2 e j k x cos ϕ 0 e j k R k R d x
u = u 0 e j k ρ cos ( ϕ + ϕ 0 ) e j π 4 π 0 ξ 2 e j t 2 d t ,
x s = ρ sin ( ϕ + ϕ 0 ) sin ϕ 0 .
u = 2 U ( ξ 2 ) k u 0 e j π 4 2 π 0 x s sin β + ϕ 0 2 e j k x cos ϕ 0 e j k R k R d x

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