Abstract

Edge-dislocation waves, created in the diffraction of plane waves by an impedance half-plane, are examined by the method of modified theory of physical optics. The integrals, obtained by a related technique, are decomposed according to their boundaries and evaluated by using uniform asymptotic methods. The results are plotted and are investigated numerically.

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References

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  1. A. Sommerfeld, Optics (Academic, 1954).
  2. A. Rubinowicz, "Thomas Young and theory of diffraction," Nature (London) 180, 160-162 (1957).
    [CrossRef]
  3. J. B. Keller, "Geometrical theory of diffraction," J. Opt. Soc. Am. 52, 116-130 (1962).
    [CrossRef] [PubMed]
  4. R. G. Kouyoumjian and P. B. Pathak, "A uniform geometrical theory of diffraction for an edge in a perfectly conducting screen," Proc. IEEE 62, 1448-1461 (1974).
    [CrossRef]
  5. S. W. Lee and G. A. Deschamps, "A uniform asymptotic theory of electromagnetic diffraction by a curved wedge," IEEE Trans. Antennas Propag. 24, 25-34 (1976).
    [CrossRef]
  6. A. I. Khizhnyak, S. P. Anokhov, R. A. Lymarenko, 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]
  7. Y. Z. Umul, "Modified theory of physical optics solution of impedance half plane problem," IEEE Trans. Antennas Propag. 54, 2048-2053 (2006).
    [CrossRef]
  8. Y. Z. Umul, "Modified theory of physical optics," Opt. Express 12, 4959-4972 (2004).
    [CrossRef] [PubMed]

2006 (1)

Y. Z. Umul, "Modified theory of physical optics solution of impedance half plane problem," IEEE Trans. Antennas Propag. 54, 2048-2053 (2006).
[CrossRef]

2004 (1)

2000 (1)

1976 (1)

S. W. Lee and G. A. Deschamps, "A uniform asymptotic theory of electromagnetic diffraction by a curved wedge," IEEE Trans. Antennas Propag. 24, 25-34 (1976).
[CrossRef]

1974 (1)

R. G. Kouyoumjian and P. B. 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 theory of diffraction," Nature (London) 180, 160-162 (1957).
[CrossRef]

Anokhov, S. P.

Deschamps, G. A.

S. W. Lee and G. A. Deschamps, "A uniform asymptotic theory of electromagnetic diffraction by a curved wedge," IEEE Trans. Antennas Propag. 24, 25-34 (1976).
[CrossRef]

Keller, J. B.

Khizhnyak, A. I.

Kouyoumjian, R. G.

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

Lee, S. W.

S. W. Lee and G. A. Deschamps, "A uniform asymptotic theory of electromagnetic diffraction by a curved wedge," IEEE Trans. Antennas Propag. 24, 25-34 (1976).
[CrossRef]

Lymarenko, R. A.

Pathak, P. B.

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

Rubinowicz, A.

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

Sommerfeld, A.

A. Sommerfeld, Optics (Academic, 1954).

Soskin, M. S.

Umul, Y. Z.

Y. Z. Umul, "Modified theory of physical optics solution of impedance half plane problem," IEEE Trans. Antennas Propag. 54, 2048-2053 (2006).
[CrossRef]

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

Vasnetsov, M. V.

IEEE Trans. Antennas Propag. (2)

S. W. Lee and G. A. Deschamps, "A uniform asymptotic theory of electromagnetic diffraction by a curved wedge," IEEE Trans. Antennas Propag. 24, 25-34 (1976).
[CrossRef]

Y. Z. Umul, "Modified theory of physical optics solution of impedance half plane problem," IEEE Trans. Antennas Propag. 54, 2048-2053 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nature (London) (1)

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

Opt. Express (1)

Proc. IEEE (1)

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

Other (1)

A. Sommerfeld, Optics (Academic, 1954).

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Figures (7)

Fig. 1
Fig. 1

Geometry of a half-plane with impedance boundary conditions.

Fig. 2
Fig. 2

EDW and its subfields for reflected scattered waves.

Fig. 3
Fig. 3

EDW and its subfields for incident scattered waves.

Fig. 4
Fig. 4

Alternative decomposition of EDW and its subfields for reflected scattered waves.

Fig. 5
Fig. 5

Alternative decomposition of EDW and its subfields for incident scattered waves.

Fig. 6
Fig. 6

Reflected scattered field and its subcomponents in terms of EDW.

Fig. 7
Fig. 7

Incident scattered field and its subcomponents in terms of EDW.

Equations (41)

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E s = e z E i [ e j k ρ cos ( ϕ ϕ 0 ) + k e j ( π 4 ) 2 π 0 Γ ( β , ϕ 0 , Z ) f ( β , ϕ 0 ) e j k x cos ϕ 0 e j k R k R d x ] ,
Γ ( β , ϕ 0 , Z ) = Z sin [ ( β + ϕ 0 ) 2 ] Z 0 Z sin [ ( β + ϕ 0 ) 2 ] + Z 0 ,
f ( β , ϕ 0 ) = sin β + ϕ 0 2 sin β ϕ 0 2 ,
E s = E r s + E i s ,
E r s = k E i e j ( π 4 ) 2 π 0 Γ ( β , ϕ 0 , Z ) sin β + ϕ 0 2 e j k x cos ϕ 0 e j k R k R d x ,
E i s = k E i e j ( π 4 ) 2 π 0 Γ ( β , ϕ 0 , Z ) sin β ϕ 0 2 e j k x cos ϕ 0 e j k R k R d x
E r s = k E i e j ( π 4 ) 2 π [ 0 x s Γ ( β , ϕ 0 , Z ) sin β + ϕ 0 2 e j k x cos ϕ 0 e j k R k R d x + x s Γ ( β , ϕ 0 , Z ) sin β + ϕ 0 2 e j k x cos ϕ 0 e j k R k R d x ]
I 1 = k E i e j ( π 4 ) 2 π 0 x s Γ ( β , ϕ 0 , Z ) p ( x ) sin β + ϕ 0 2 p ( x ) e j k x cos ϕ 0 e j k R k R d x ,
G ( x ) = k E i e j ( π 4 ) 2 π Γ ( β , ϕ 0 , Z ) R p ( x ) sin β + ϕ 0 2 .
I 1 = 0 x s [ G ( x ) G ( 0 ) ] p ( x ) e j k ( x cos ϕ 0 R ) d x + G ( 0 ) 0 x s p ( x ) e j k ( x cos ϕ 0 R ) d x
t 2 = k [ g ( x s ) g ( x ) ]
g ( x ) = x cos ϕ 0 R .
I 12 = G ( 0 ) e j k ρ cos ( ϕ + ϕ 0 ) 0 t e Ω ( t ) e j t 2 d t
g ( x ) = ρ cos ( ϕ + ϕ 0 ) .
Ω ( t ) = 2 k p ( x ) t g ( x ) ,
p ( x ) = k 2 g ( x ) g ( x s ) g ( x ) = k 2 R sin β + ϕ 0 2
G ( x ) = E i e j ( π 4 ) π Γ ( β , ϕ 0 , Z )
I 12 = E i Γ ( π ϕ , ϕ 0 , Z ) e j k ρ cos ( ϕ + ϕ 0 ) e j ( π 4 ) π 0 t e e j t 2 d t ,
I 11 = 0 [ G ( x ) G ( 0 ) ] p ( x ) e j k g ( x ) d x x s [ G ( x ) G ( 0 ) ] p ( x ) e j k g ( x ) d x
0 f ( α ) e j k g ( α ) d α e j ( π 4 ) 2 π f ( α s ) k g ( α s ) U ( t a ) e j k g ( α s ) ,
α s f ( α ) e j k g ( α ) d α e j ( π 4 ) π 2 f ( α s ) k g ( α s ) e j k g ( α s ) ,
p ( x s ) = k g ( x s ) j 2 .
I 12 E i [ Γ ( β s , ϕ 0 , Z ) Γ ( π ϕ , ϕ 0 , Z ) ] e j k ρ cos ( ϕ + ϕ 0 ) [ U ( t e ) 1 2 ]
E r s EDW E i e j k ρ cos ( ϕ + ϕ 0 ) { [ Γ ( β s , ϕ 0 , Z ) Γ ( π ϕ , ϕ 0 , Z ) ] [ U ( t e ) 1 2 ] Γ ( π ϕ , ϕ 0 , Z ) e j ( π 4 ) π 0 t e e j t 2 d t } .
E r s 2 ( E i 2 ) e j k ρ cos ( ϕ + ϕ 0 ) Γ ( β s , ϕ 0 , Z ) .
Γ ( β s , ϕ 0 , Z ) = sin ϕ 0 sin θ sin ϕ 0 + sin θ ,
Γ ( π ϕ , ϕ 0 , Z ) = cos [ ( ϕ ϕ 0 ) 2 ] sin θ cos [ ( ϕ ϕ 0 ) 2 ] + sin θ ,
E i s 2 ( E i 2 ) e j k ρ cos ( ϕ ϕ 0 ) ,
E i s EDW E i e j k ρ cos ( ϕ ϕ 0 ) { [ 1 + Γ ( π ϕ , ϕ 0 , Z ) ] [ U ( t e ) 1 2 ] + Γ ( π ϕ , ϕ 0 , Z ) e j ( π 4 ) π 0 t e e j t 2 d t }
E r s EDW = E r s 11 + E r s 12 ,
E r s 11 E i e j k ρ cos ( ϕ + ϕ 0 ) [ Γ ( β s , ϕ 0 , Z ) Γ ( π ϕ , ϕ 0 , Z ) ] [ U ( t e ) 1 2 ] ,
E r s 12 = E i e j k ρ cos ( ϕ + ϕ 0 ) Γ ( π ϕ , ϕ 0 , Z ) e j ( π 4 ) π 0 t e e j t 2 d t ,
E i s EDW = E i s 11 + E i s 12 ,
E i s 11 E i e j k ρ cos ( ϕ ϕ 0 ) [ 1 + Γ ( π ϕ , ϕ 0 , Z ) ] [ U ( t e ) 1 2 ] ,
E i s 12 = E i e j k ρ cos ( ϕ ϕ 0 ) Γ ( π ϕ , ϕ 0 , Z ) e j ( π 4 ) π 0 t e e j t 2 d t ,
E r s EDW = E r s 21 + E r s 22 ,
E r s 21 E i e j k ρ cos ( ϕ + ϕ 0 ) Γ ( β s , ϕ 0 , Z ) [ U ( t e ) 1 2 ] ,
E r s 22 E i e j k ρ cos ( ϕ + ϕ 0 ) Γ ( π ϕ , ϕ 0 , Z ) [ U ( t e ) 1 2 + e j ( π 4 ) π 0 t e e j t 2 d t ] ,
E i s EDW = E i s 21 + E i s 22 ,
E i s 21 E i e j k ρ cos ( ϕ ϕ 0 ) [ U ( t e ) 1 2 ] ,
E i s 22 E i e j k ρ cos ( ϕ ϕ 0 ) Γ ( π ϕ , ϕ 0 , Z ) [ U ( t e ) 1 2 + e j ( π 4 ) π 0 t e j t 2 d t ] ,

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