Abstract

The problem of a wedge with equal face impedances is examined with a modified theory of physical optics. The surface integral is constructed by use of the impedance boundary condition. The aperture equivalent current is estimated from the behavior of the reflected diffracted field. The integrals obtained are evaluated asymptotically and compared with the exact solution numerically.

© 2006 Optical Society of America

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References

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  1. G. D. Maliuzhinets, Sov. Phys. Dokl. 3, 752 (1958).
  2. W. E. Williams, Proc. R. Soc. London Ser. A 252, 376 (1959).
    [Crossref]
  3. T. B. A. Senior, Commun. Pure Appl. Math. 12, 337 (1959).
    [Crossref]
  4. R. Tiberio, G. Pelosi, and G. Manara, IEEE Trans. Antennas Propag. 33, 867 (1985).
    [Crossref]
  5. A N. Norris and A. V. Osipov, Wave Motion 30, 69 (1999).
    [Crossref]
  6. H. M. El-Sallabi, I. T. Rekanos, and P. Vainikainen, IEEE Antennas Wireless Propag. Lett. 1, 165 (2002).
    [Crossref]
  7. Y. Z. Umul, Opt. Express 12, 4959 (2004).
    [Crossref] [PubMed]
  8. Y. Z. Umul, Opt. Express 13, 216 (2005).
    [Crossref] [PubMed]
  9. M. Oodo, T. Murasaki and M. Ando, in Antennas and Propagation Society International Symposium, 1993 (Institute of Electrical and Electronics Engineers, 1993), Vol. 3, p. 1730.
  10. E. Yazgan, Int. J. Electron. 66, 283 (1989).
    [Crossref]

2005 (1)

2004 (1)

2002 (1)

H. M. El-Sallabi, I. T. Rekanos, and P. Vainikainen, IEEE Antennas Wireless Propag. Lett. 1, 165 (2002).
[Crossref]

1999 (1)

A N. Norris and A. V. Osipov, Wave Motion 30, 69 (1999).
[Crossref]

1989 (1)

E. Yazgan, Int. J. Electron. 66, 283 (1989).
[Crossref]

1985 (1)

R. Tiberio, G. Pelosi, and G. Manara, IEEE Trans. Antennas Propag. 33, 867 (1985).
[Crossref]

1959 (2)

W. E. Williams, Proc. R. Soc. London Ser. A 252, 376 (1959).
[Crossref]

T. B. A. Senior, Commun. Pure Appl. Math. 12, 337 (1959).
[Crossref]

1958 (1)

G. D. Maliuzhinets, Sov. Phys. Dokl. 3, 752 (1958).

Ando, M.

M. Oodo, T. Murasaki and M. Ando, in Antennas and Propagation Society International Symposium, 1993 (Institute of Electrical and Electronics Engineers, 1993), Vol. 3, p. 1730.

El-Sallabi, H. M.

H. M. El-Sallabi, I. T. Rekanos, and P. Vainikainen, IEEE Antennas Wireless Propag. Lett. 1, 165 (2002).
[Crossref]

Maliuzhinets, G. D.

G. D. Maliuzhinets, Sov. Phys. Dokl. 3, 752 (1958).

Manara, G.

R. Tiberio, G. Pelosi, and G. Manara, IEEE Trans. Antennas Propag. 33, 867 (1985).
[Crossref]

Murasaki, T.

M. Oodo, T. Murasaki and M. Ando, in Antennas and Propagation Society International Symposium, 1993 (Institute of Electrical and Electronics Engineers, 1993), Vol. 3, p. 1730.

Norris, A N.

A N. Norris and A. V. Osipov, Wave Motion 30, 69 (1999).
[Crossref]

Oodo, M.

M. Oodo, T. Murasaki and M. Ando, in Antennas and Propagation Society International Symposium, 1993 (Institute of Electrical and Electronics Engineers, 1993), Vol. 3, p. 1730.

Osipov, A. V.

A N. Norris and A. V. Osipov, Wave Motion 30, 69 (1999).
[Crossref]

Pelosi, G.

R. Tiberio, G. Pelosi, and G. Manara, IEEE Trans. Antennas Propag. 33, 867 (1985).
[Crossref]

Rekanos, I. T.

H. M. El-Sallabi, I. T. Rekanos, and P. Vainikainen, IEEE Antennas Wireless Propag. Lett. 1, 165 (2002).
[Crossref]

Senior, T. B.

T. B. A. Senior, Commun. Pure Appl. Math. 12, 337 (1959).
[Crossref]

Tiberio, R.

R. Tiberio, G. Pelosi, and G. Manara, IEEE Trans. Antennas Propag. 33, 867 (1985).
[Crossref]

Umul, Y. Z.

Vainikainen, P.

H. M. El-Sallabi, I. T. Rekanos, and P. Vainikainen, IEEE Antennas Wireless Propag. Lett. 1, 165 (2002).
[Crossref]

Williams, W. E.

W. E. Williams, Proc. R. Soc. London Ser. A 252, 376 (1959).
[Crossref]

Yazgan, E.

E. Yazgan, Int. J. Electron. 66, 283 (1989).
[Crossref]

Commun. Pure Appl. Math. (1)

T. B. A. Senior, Commun. Pure Appl. Math. 12, 337 (1959).
[Crossref]

IEEE Antennas Wireless Propag. Lett. (1)

H. M. El-Sallabi, I. T. Rekanos, and P. Vainikainen, IEEE Antennas Wireless Propag. Lett. 1, 165 (2002).
[Crossref]

IEEE Trans. Antennas Propag. (1)

R. Tiberio, G. Pelosi, and G. Manara, IEEE Trans. Antennas Propag. 33, 867 (1985).
[Crossref]

Int. J. Electron. (1)

E. Yazgan, Int. J. Electron. 66, 283 (1989).
[Crossref]

Opt. Express (2)

Proc. R. Soc. London Ser. A (1)

W. E. Williams, Proc. R. Soc. London Ser. A 252, 376 (1959).
[Crossref]

Sov. Phys. Dokl. (1)

G. D. Maliuzhinets, Sov. Phys. Dokl. 3, 752 (1958).

Wave Motion (1)

A N. Norris and A. V. Osipov, Wave Motion 30, 69 (1999).
[Crossref]

Other (1)

M. Oodo, T. Murasaki and M. Ando, in Antennas and Propagation Society International Symposium, 1993 (Institute of Electrical and Electronics Engineers, 1993), Vol. 3, p. 1730.

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Figures (3)

Fig. 1
Fig. 1

Geometry of the impedance wedge.

Fig. 2
Fig. 2

(Color online) Total scattered fields from an impedance wedge.

Fig. 3
Fig. 3

(Color online) Comparison of the total diffracted fields from an impedance wedge.

Equations (14)

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E S = e z k E i 2 π sin ( π n ) n exp ( j ( π 4 ) ) 0 cos ϕ 0 cos β cos ( π n ) cos [ ( π β + ϕ 0 ) n ] E r exp ( j k x cos β ) exp ( j k R ) k R d x ,
E A = e z k E i 2 π sin ( π n ) n exp ( j ( π 4 ) ) 0 cos ϕ 0 cos β cos ( π n ) cos [ ( π β ϕ 0 ) n ] E r exp ( j k x cos β ) exp ( j k R ) k R d x ,
E r exp ( j k x cos β ) = E i exp ( j k x cos ϕ 0 ) cos u sin θ cos u + sin θ
E i = e z E i { exp [ j k ρ cos ( ϕ ϕ 0 ) ] u ( π ϕ + ϕ 0 ) + sin ϕ 0 sin θ sin ϕ 0 + sin θ exp [ j k ρ cos ( ϕ + ϕ 0 ) ] u ( π ϕ ϕ 0 ) }
E d = e z sin ( π n ) n 2 π exp ( j ( π 4 ) ) exp ( j k ρ ) k ρ { 1 cos ( π n ) cos [ ( ϕ + ϕ 0 ) n ] 1 cos ( π n ) cos [ ( ϕ ϕ 0 ) n ] } Γ ( ϕ 0 , θ ) ,
Γ ( ϕ 0 , θ ) = cos [ ( ϕ ϕ 0 ) 2 ] sin θ cos [ ( ϕ ϕ 0 ) 2 ] + sin θ
E d i u = e z 2 sin ( π n ) n cos [ ( ϕ ϕ 0 ) 2 ] cos ( π n ) cos [ ( ϕ ϕ 0 ) n ] Γ ( ϕ 0 , θ ) F ( ξ i ) sgn ( ξ i ) exp [ j k ρ cos ( ϕ ϕ 0 ) ] ,
E d r u = e z 2 sin ( π n ) n cos [ ( ϕ + ϕ 0 ) 2 ] cos ( π n ) cos [ ( ϕ + ϕ 0 ) n ] Γ ( ϕ 0 , θ ) F ( ξ r ) sgn ( ξ r ) exp [ j k ρ cos ( ϕ + ϕ 0 ) ]
E d i 1 = e z cos [ ( ϕ ϕ 0 ) 2 ] n tan [ ( π ϕ + ϕ 0 ) 2 n ] Γ 1 ( ϕ 0 , θ ) F ( ξ i 1 ) sgn ( ξ i 1 ) exp [ j k ρ cos ( ϕ ϕ 0 ) ] ,
E d i 2 = e z cos [ ( ϕ ϕ 0 ) 2 ] n tan [ ( π + ϕ ϕ 0 ) 2 n ] Γ 2 ( ϕ 0 , θ ) F ( ξ i 2 ) sgn ( ξ i 2 ) exp { j k ρ cos [ ϕ ϕ 0 2 π ( n 1 ) ] } .
Γ 2 ( ϕ 0 , θ ) = cos { [ ϕ ϕ 0 2 π ( n 1 ) ] 2 } sin θ cos { [ ϕ ϕ 0 2 π ( n 1 ) ] 2 } + sin θ .
sin ( π n ) cos ( π n ) cos [ ( ϕ ϕ 0 ) n ] = 1 2 { cot g [ ( π ϕ + ϕ 0 ) 2 n ] + cot g [ ( π + ϕ ϕ 0 ) 2 n ] } ,
E d r 1 = e z cos [ ( ϕ + ϕ 0 ) 2 ] n tan [ ( π ϕ ϕ 0 ) 2 n ] Γ 1 ( ϕ 0 , θ ) F ( ξ r 1 ) sgn ( ξ r 1 ) exp [ j k ρ cos ( ϕ + ϕ 0 ) ] ,
E d r 2 = e z cos [ ( ϕ + ϕ 0 ) 2 ] n tan [ ( π + ϕ + ϕ 0 ) 2 n ] Γ 2 ( ϕ 0 , θ ) F ( ξ r 2 ) sgn ( ξ r 2 ) exp { j k ρ cos [ ϕ + ϕ 0 2 π ( n 1 ) ] }

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