Abstract

A uniform line integral representation is derived for edge-diffracted fields by using the modified theory of physical optics and uniform asymptotic evaluation methods. The method is applied to the problem of diffraction of plane waves by a semi-infinite edge, which creates tip-diffracted fields with edge-diffracted waves. The uniform diffracted fields are plotted and examined numerically.

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References

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  1. N. Morton, "Thomas Young and the theory of diffraction," Phys. Educ. 14, 450-453 (1979).
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2007 (2)

2005 (1)

2004 (1)

1996 (1)

S. Ganci, "Half-plane diffraction in a case of oblique incidence," J. Mod. Opt. 43, 2543-2551 (1996).
[CrossRef]

1995 (3)

P. M. Johansen and O. Breinbjerg, "An exact line integral representation of the physical optics scattered field: the case of a perfectly conducting polyhedral structure illuminated by electric Hertzian dipoles," IEEE Antennas Propag. Mag. 43, 689-696 (1995).
[CrossRef]

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

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

1993 (1)

1985 (2)

1984 (1)

A. Michaeli, "Equivalent edge currents for arbitrary aspects of observation," IEEE Antennas Propag. Mag. 32, 252-258 (1984).
[CrossRef]

1979 (1)

N. Morton, "Thomas Young and the theory of diffraction," Phys. Educ. 14, 450-453 (1979).
[CrossRef]

1962 (5)

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. 4, 339-364 (1924).
[CrossRef]

1917 (1)

A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie der Beugungsercheinungen," Ann. Phys. 4, 257-278 (1917).
[CrossRef]

1888 (1)

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

Ansbro, A. P.

Arnold, J. M.

Asvestas, J. S.

Breinbjerg, O.

P. M. Johansen and O. Breinbjerg, "An exact line integral representation of the physical optics scattered field: the case of a perfectly conducting polyhedral structure illuminated by electric Hertzian dipoles," IEEE Antennas Propag. Mag. 43, 689-696 (1995).
[CrossRef]

Ganci, S.

S. Ganci, "Half-plane diffraction in a case of oblique incidence," J. Mod. Opt. 43, 2543-2551 (1996).
[CrossRef]

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

Johansen, P. M.

P. M. Johansen and O. Breinbjerg, "An exact line integral representation of the physical optics scattered field: the case of a perfectly conducting polyhedral structure illuminated by electric Hertzian dipoles," IEEE Antennas Propag. Mag. 43, 689-696 (1995).
[CrossRef]

Keller, J. B.

Maggi, G. A.

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

Michaeli, A.

A. Michaeli, "Equivalent edge currents for arbitrary aspects of observation," IEEE Antennas Propag. Mag. 32, 252-258 (1984).
[CrossRef]

Miyamoto, K.

Morton, N.

N. Morton, "Thomas Young and the theory of diffraction," Phys. Educ. 14, 450-453 (1979).
[CrossRef]

Rubinowicz, A.

A. Rubinowicz, "Simple derivation of the Miyamoto-Wolf formula for the vector potential associated with a solution of the Helmholtz equation," J. Opt. Soc. Am. 52, 717 (1962).
[CrossRef]

A. Rubinowicz, "Geometric derivation of the Miyamoto-Wolf formula for the vector potential associated with a solution of the Helmholtz equation," J. Opt. Soc. Am. 52, 717-718 (1962).
[CrossRef]

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

A. Rubinowicz, "Zur Kirchhoffschen Beugungstheorie," Ann. Phys. 4, 339-364 (1924).
[CrossRef]

A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie der Beugungsercheinungen," Ann. Phys. 4, 257-278 (1917).
[CrossRef]

Umul, Y. Z.

Wolf, E.

Ya. Ufimtsev, P.

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

Ann. Mat. (1)

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

Ann. Phys. (2)

A. Rubinowicz, "Die Beugungswelle in der Kirchhoffschen Theorie der Beugungsercheinungen," Ann. Phys. 4, 257-278 (1917).
[CrossRef]

A. Rubinowicz, "Zur Kirchhoffschen Beugungstheorie," Ann. Phys. 4, 339-364 (1924).
[CrossRef]

Electromagnetics (1)

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

IEEE Antennas Propag. Mag. (2)

P. M. Johansen and O. Breinbjerg, "An exact line integral representation of the physical optics scattered field: the case of a perfectly conducting polyhedral structure illuminated by electric Hertzian dipoles," IEEE Antennas Propag. Mag. 43, 689-696 (1995).
[CrossRef]

A. Michaeli, "Equivalent edge currents for arbitrary aspects of observation," IEEE Antennas Propag. Mag. 32, 252-258 (1984).
[CrossRef]

J. Mod. Opt. (2)

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

S. Ganci, "Half-plane diffraction in a case of oblique incidence," J. Mod. Opt. 43, 2543-2551 (1996).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (5)

Nature (1)

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

Opt. Express (2)

Phys. Educ. (1)

N. Morton, "Thomas Young and the theory of diffraction," Phys. Educ. 14, 450-453 (1979).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Geometry of the PEC half-plane problem.

Fig. 2
Fig. 2

Geometry of the edge-diffracted rays.

Fig. 3
Fig. 3

Edge-diffracted field at the ( x , y ) plane.

Fig. 4
Fig. 4

Edge-diffracted field for various values of ϕ.

Fig. 5
Fig. 5

Edge- and tip-diffracted fields.

Equations (39)

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u ( P ) = u i ( P ) + j k 2 π S u i ( Q ) ( sin β ϕ 0 2 sin β + ϕ 0 2 ) e j k R R d S
u ( P ) = u i s ( P ) + u r s ( P ) ,
u i s ( P ) = u i ( P ) + j k 2 π S u i ( Q ) sin β ϕ 0 2 e j k R R d S ,
u r s ( P ) = j k 2 π S u i ( Q ) sin β + ϕ 0 2 e j k R R d S ,
u i s ( P ) = u 0 e j k ρ cos ( ϕ ϕ 0 ) + j k u 0 2 π S e j k x cos ϕ 0 sin β ϕ 0 2 e j k R R d x d z ,
u r s ( P ) = j k u 0 2 π S e j k x cos ϕ 0 sin β + ϕ 0 2 e j k R R d x d z .
u s = C α e f ( α , l ) exp [ j k g ( α , l ) ] d α d l .
I = α e f ( α ) exp [ j k g ( α ) ] d α .
I = exp [ j k g ( α s ) ] f ( α s ) h ( α s ) U ( t e ) + exp [ j k g ( α s ) ] f ( α e ) h ( α e ) sign ( t e ) F [ t e ] ,
F [ x ] = e j ( π 4 ) π x e j t 2 d t .
h ( α ) = k g ( α ) 2 t ,
f ( α ) = u i 1 ( Q ) R sin β ϕ 0 2
g ( α ) = R u i 2 ( Q ) .
u e ( P ) = C exp [ j k g ( α s , l ) ] f ( α e , l ) h ( α e , l ) s i g n ( t e ) F [ t e ] d l
g ( x , z ) = x cos ϕ 0 R ,
g ( x s , z ) = x cos ϕ 0 R s sin 2 ϕ 0
t e = 2 k R e sin β e ϕ 0 2 ,
β e = cos 1 ( x R e )
f ( 0 , z ) h ( 0 , z ) = e j ( π 4 ) k u o 2 π R e .
u r e = u 0 e j ( π 4 ) e j k x cos ϕ 0 k 2 π z = e j k R s sin 2 ϕ 0 R e sign ( t e ) F [ t e ] d z
sign ( x ) F [ x ] = e j x 2 I ( x ) ,
I ( x ) = e j ( π 4 ) 2 π x n = 1 Γ ( n + 1 2 ) ( j x 2 ) n .
u r e = u 0 e j ( π 4 ) e j k x cos ϕ 0 k 2 π z = e j k R s sin 2 ϕ 0 R e e j t e 2 I ( t e ) d z
u r e = u 0 e j ( π 4 ) k 2 π z = e j k R e R e I ( t e ) d z .
u r e = u 0 e j k ρ I ( t e z = z ) ,
t e z = z = 2 k ρ cos ϕ + ϕ 0 2 .
k ρ = 2 k ρ cos 2 ϕ + ϕ 0 2 k ρ cos ( ϕ + ϕ 0 ) ,
u r e = u 0 e j k ρ cos ( ϕ + ϕ 0 ) sign ( ξ r ) F [ ξ r ]
ξ r = 2 k ρ cos ϕ + ϕ 0 2 .
u e ( P ) = C exp [ j k g ( α s , l ) j t e 2 ] f ( α e , l ) h ( α e , l ) I ( t e ) d l ,
u e ( P ) = C exp [ j k g ( α e , l ) ] f ( α e , l ) h ( α e , l ) I ( t e ) d l
t e 2 = k g ( α s , l ) k g ( α e , l )
u r e = u 0 e j ( π 4 ) k 2 π z = 0 e j k R e R e I ( t e ) d z
q ( z ) = k ( R e ρ ) ,
h ( z = z ) = k 2 ρ
u t d = u e d + u t d ,
u e d = u 0 e j k ρ cos ( ϕ + ϕ 0 ) sign ( ξ r ) F [ ξ r ] U ( q e ) ,
u t d = u 0 e j k ρ cos ( ϕ + ϕ 0 ) exp [ j 2 k ( ρ cos 2 ϕ + ϕ 0 2 r sin 2 β t ϕ 0 2 ) ] 2 1 + sin θ sign ( t t ) F [ t t ] sign ( q e ) F [ q e ] .
β t = cos 1 ( sin θ cos ϕ ) .

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