Abstract

Uniform diffracted fields from impedance surfaces are investigated by the extended theory of boundary diffraction wave (ETBDW). The new vector potential of the ETBDW is constructed by considering the pseudoimpedance boundary condition. The method is applied to the diffraction problem from an impedance half-plane. It is shown that the total fields from an impedance half-plane reduce to the case of a perfectly electric or magnetic conducting and opaque half-plane for special values of surface impedance. The total and diffracted fields are compared numerically with the exact solution for the impedance half-plane and modified theory of physical optics (MTPO) solution for an impedance wedge. The numerical results show that the field expressions are in very good agreement with the exact and MTPO solutions.

© 2011 Optical Society of America

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  1. M. Born and E. Wolf, Principles of Optics (Cambridge University, 2003).
  2. G. A. Maggi, “Sulla propagazione libra e perturbata delle onde luminose in un mezzo Izotropo,” Ann. Mat. Pura. Appl. 16, 21–48 (1888).
    [CrossRef]
  3. A. Rubinowicz, “Die beugungswelle in der Kirchoffschen theorie der beugungsercheinungen,” Ann. Physik 358, 257–278(1917).
    [CrossRef]
  4. K. Miyamoto and E. Wolf, “Generalization of the Maggi–Rubinowicz theory of the boundary diffraction wave—part I,” J. Opt. Soc. Am. 52, 615–625 (1962).
    [CrossRef]
  5. K. Miyamoto and E. Wolf, “Generalization of the Maggi–Rubinowicz theory of the boundary diffraction wave—part II,” J. Opt. Soc. Am. 52, 626–637 (1962).
    [CrossRef]
  6. G. Otis, “Edge-on diffraction of a Gaussian laser beam by a semi-infinite plane,” Appl. Opt. 14, 1156–1160 (1975).
    [CrossRef] [PubMed]
  7. S. Ganci, “A general scalar solution for the half-plane problem,” J. Modern Opt. 42, 1707–1711 (1995).
    [CrossRef]
  8. S. Ganci, “Half-plane diffraction in a case of oblique incidence,” J. Modern Opt. 43, 2543–2551 (1996).
    [CrossRef]
  9. U. Yalçın, “The uniform diffracted fields from an opaque half plane: the theory of the boundary diffraction wave solution,” presented at 2. Engineering and Technology Symposium, Ankara, Turkey, 30 April–1 May 2009 (in national language), pp. 82–88.
  10. J. W. Y. Lit, “Boundary-diffraction waves due to a general point source and their applications to aperture systems,” J. Modern Opt. 19, 1007–1014 (1972).
    [CrossRef]
  11. S. Ganci, “Boundary diffraction wave theory for rectilinear apertures,” Eur. J. Phys. 18, 229–236 (1997).
    [CrossRef]
  12. S. Ganci, “Diffracted wavefield by an arbitrary aperture from Maggi–Rubinowicz transformation: Fraunhofer approximation,” Optik (Jena) 119, 41–45 (2008).
    [CrossRef]
  13. U. Yalçın, “Uniform scattered fields of the extended theory of boundary diffraction wave for PEC surfaces,” PIER M 7, 29–39 (2009).
    [CrossRef]
  14. U. Yalçın, “Scattering from perfectly magnetic conducting surfaces: the extended theory of boundary diffraction wave approach,” PIER M 7, 123–133 (2009).
    [CrossRef]
  15. Y. Z. Umul, “Modified theory of physical optics solution of impedance half plane problem,” IEEE Trans. Antennas Propagat. 54, 2048–2053 (2006).
    [CrossRef]
  16. S. W. Lee and G. A. Deschamps, “A uniform asymptotic theory of electromagnetic diffraction by a curved wedge,” IEEE Trans. Antennas Propagat. 24, 25–34 (1976).
    [CrossRef]
  17. S. W. Lee, “Comparison of uniform asymptotic theory and Ufimtsev’s theory of electromagnetic edge diffraction,” IEEE Trans. Antennas Propagat. 25, 162–170 (1977).
    [CrossRef]
  18. R. Tiberio, G. Pelosi, and G. Manara, “A uniform GTD formulation for the diffraction by a wedge with impedance faces,” IEEE Trans. Antennas Propagat. 33, 867–873(1985).
    [CrossRef]
  19. Y. Z. Umul, “Modified theory of the physical-optics approach to the impedance wedge problem,” Opt. Lett. 31, 401–403(2006).
    [CrossRef] [PubMed]
  20. J. L. Volakis, “A uniform geometrical theory of diffraction for an imperfectly conducting half-plane,” IEEE Trans. Antennas Propagat. 34, 172–180 (1986).
    [CrossRef]

2009 (2)

U. Yalçın, “Uniform scattered fields of the extended theory of boundary diffraction wave for PEC surfaces,” PIER M 7, 29–39 (2009).
[CrossRef]

U. Yalçın, “Scattering from perfectly magnetic conducting surfaces: the extended theory of boundary diffraction wave approach,” PIER M 7, 123–133 (2009).
[CrossRef]

2008 (1)

S. Ganci, “Diffracted wavefield by an arbitrary aperture from Maggi–Rubinowicz transformation: Fraunhofer approximation,” Optik (Jena) 119, 41–45 (2008).
[CrossRef]

2006 (2)

Y. Z. Umul, “Modified theory of physical optics solution of impedance half plane problem,” IEEE Trans. Antennas Propagat. 54, 2048–2053 (2006).
[CrossRef]

Y. Z. Umul, “Modified theory of the physical-optics approach to the impedance wedge problem,” Opt. Lett. 31, 401–403(2006).
[CrossRef] [PubMed]

1997 (1)

S. Ganci, “Boundary diffraction wave theory for rectilinear apertures,” Eur. J. Phys. 18, 229–236 (1997).
[CrossRef]

1996 (1)

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

1995 (1)

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

1986 (1)

J. L. Volakis, “A uniform geometrical theory of diffraction for an imperfectly conducting half-plane,” IEEE Trans. Antennas Propagat. 34, 172–180 (1986).
[CrossRef]

1985 (1)

R. Tiberio, G. Pelosi, and G. Manara, “A uniform GTD formulation for the diffraction by a wedge with impedance faces,” IEEE Trans. Antennas Propagat. 33, 867–873(1985).
[CrossRef]

1977 (1)

S. W. Lee, “Comparison of uniform asymptotic theory and Ufimtsev’s theory of electromagnetic edge diffraction,” IEEE Trans. Antennas Propagat. 25, 162–170 (1977).
[CrossRef]

1976 (1)

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

1975 (1)

1972 (1)

J. W. Y. Lit, “Boundary-diffraction waves due to a general point source and their applications to aperture systems,” J. Modern Opt. 19, 1007–1014 (1972).
[CrossRef]

1962 (2)

1917 (1)

A. Rubinowicz, “Die beugungswelle in der Kirchoffschen theorie der beugungsercheinungen,” Ann. Physik 358, 257–278(1917).
[CrossRef]

1888 (1)

G. A. Maggi, “Sulla propagazione libra e perturbata delle onde luminose in un mezzo Izotropo,” Ann. Mat. Pura. Appl. 16, 21–48 (1888).
[CrossRef]

Born, M.

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

Deschamps, G. A.

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

Ganci, S.

S. Ganci, “Diffracted wavefield by an arbitrary aperture from Maggi–Rubinowicz transformation: Fraunhofer approximation,” Optik (Jena) 119, 41–45 (2008).
[CrossRef]

S. Ganci, “Boundary diffraction wave theory for rectilinear apertures,” Eur. J. Phys. 18, 229–236 (1997).
[CrossRef]

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

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

Lee, S. W.

S. W. Lee, “Comparison of uniform asymptotic theory and Ufimtsev’s theory of electromagnetic edge diffraction,” IEEE Trans. Antennas Propagat. 25, 162–170 (1977).
[CrossRef]

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

Lit, J. W. Y.

J. W. Y. Lit, “Boundary-diffraction waves due to a general point source and their applications to aperture systems,” J. Modern Opt. 19, 1007–1014 (1972).
[CrossRef]

Maggi, G. A.

G. A. Maggi, “Sulla propagazione libra e perturbata delle onde luminose in un mezzo Izotropo,” Ann. Mat. Pura. Appl. 16, 21–48 (1888).
[CrossRef]

Manara, G.

R. Tiberio, G. Pelosi, and G. Manara, “A uniform GTD formulation for the diffraction by a wedge with impedance faces,” IEEE Trans. Antennas Propagat. 33, 867–873(1985).
[CrossRef]

Miyamoto, K.

Otis, G.

Pelosi, G.

R. Tiberio, G. Pelosi, and G. Manara, “A uniform GTD formulation for the diffraction by a wedge with impedance faces,” IEEE Trans. Antennas Propagat. 33, 867–873(1985).
[CrossRef]

Rubinowicz, A.

A. Rubinowicz, “Die beugungswelle in der Kirchoffschen theorie der beugungsercheinungen,” Ann. Physik 358, 257–278(1917).
[CrossRef]

Tiberio, R.

R. Tiberio, G. Pelosi, and G. Manara, “A uniform GTD formulation for the diffraction by a wedge with impedance faces,” IEEE Trans. Antennas Propagat. 33, 867–873(1985).
[CrossRef]

Umul, Y. Z.

Y. Z. Umul, “Modified theory of physical optics solution of impedance half plane problem,” IEEE Trans. Antennas Propagat. 54, 2048–2053 (2006).
[CrossRef]

Y. Z. Umul, “Modified theory of the physical-optics approach to the impedance wedge problem,” Opt. Lett. 31, 401–403(2006).
[CrossRef] [PubMed]

Volakis, J. L.

J. L. Volakis, “A uniform geometrical theory of diffraction for an imperfectly conducting half-plane,” IEEE Trans. Antennas Propagat. 34, 172–180 (1986).
[CrossRef]

Wolf, E.

Yalçin, U.

U. Yalçın, “Uniform scattered fields of the extended theory of boundary diffraction wave for PEC surfaces,” PIER M 7, 29–39 (2009).
[CrossRef]

U. Yalçın, “Scattering from perfectly magnetic conducting surfaces: the extended theory of boundary diffraction wave approach,” PIER M 7, 123–133 (2009).
[CrossRef]

U. Yalçın, “The uniform diffracted fields from an opaque half plane: the theory of the boundary diffraction wave solution,” presented at 2. Engineering and Technology Symposium, Ankara, Turkey, 30 April–1 May 2009 (in national language), pp. 82–88.

Ann. Mat. Pura. Appl. (1)

G. A. Maggi, “Sulla propagazione libra e perturbata delle onde luminose in un mezzo Izotropo,” Ann. Mat. Pura. Appl. 16, 21–48 (1888).
[CrossRef]

Ann. Physik (1)

A. Rubinowicz, “Die beugungswelle in der Kirchoffschen theorie der beugungsercheinungen,” Ann. Physik 358, 257–278(1917).
[CrossRef]

Appl. Opt. (1)

Eur. J. Phys. (1)

S. Ganci, “Boundary diffraction wave theory for rectilinear apertures,” Eur. J. Phys. 18, 229–236 (1997).
[CrossRef]

IEEE Trans. Antennas Propagat. (5)

Y. Z. Umul, “Modified theory of physical optics solution of impedance half plane problem,” IEEE Trans. Antennas Propagat. 54, 2048–2053 (2006).
[CrossRef]

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

S. W. Lee, “Comparison of uniform asymptotic theory and Ufimtsev’s theory of electromagnetic edge diffraction,” IEEE Trans. Antennas Propagat. 25, 162–170 (1977).
[CrossRef]

R. Tiberio, G. Pelosi, and G. Manara, “A uniform GTD formulation for the diffraction by a wedge with impedance faces,” IEEE Trans. Antennas Propagat. 33, 867–873(1985).
[CrossRef]

J. L. Volakis, “A uniform geometrical theory of diffraction for an imperfectly conducting half-plane,” IEEE Trans. Antennas Propagat. 34, 172–180 (1986).
[CrossRef]

J. Modern Opt. (3)

J. W. Y. Lit, “Boundary-diffraction waves due to a general point source and their applications to aperture systems,” J. Modern Opt. 19, 1007–1014 (1972).
[CrossRef]

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

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

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Optik (Jena) (1)

S. Ganci, “Diffracted wavefield by an arbitrary aperture from Maggi–Rubinowicz transformation: Fraunhofer approximation,” Optik (Jena) 119, 41–45 (2008).
[CrossRef]

PIER M (2)

U. Yalçın, “Uniform scattered fields of the extended theory of boundary diffraction wave for PEC surfaces,” PIER M 7, 29–39 (2009).
[CrossRef]

U. Yalçın, “Scattering from perfectly magnetic conducting surfaces: the extended theory of boundary diffraction wave approach,” PIER M 7, 123–133 (2009).
[CrossRef]

Other (2)

U. Yalçın, “The uniform diffracted fields from an opaque half plane: the theory of the boundary diffraction wave solution,” presented at 2. Engineering and Technology Symposium, Ankara, Turkey, 30 April–1 May 2009 (in national language), pp. 82–88.

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

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Figures (7)

Fig. 1
Fig. 1

Diffraction geometry of the ETBDW.

Fig. 2
Fig. 2

Geometry of the diffraction from a half-plane with surface impedance.

Fig. 3
Fig. 3

Geometry of the diffraction from a wedge with surface impedance faces.

Fig. 4
Fig. 4

Comparison of the ETBDW and the exact solution of the diffracted fields from the impedance half-plane.

Fig. 5
Fig. 5

The variation of the total fields for the impedance half-plane by the ETBDW and the exact solution.

Fig. 6
Fig. 6

Comparison of the ETBDW and MTPO solution diffracted fields from the impedance wedge.

Fig. 7
Fig. 7

Variation of the total fields for the impedance wedge by the ETBDW and MTPO solution.

Equations (40)

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U ( P ) = S [ × W ( Q , P ) ] n d S .
U ( P ) = U B ( P ) + U GO ( P ) .
U B ( P ) = Γ W ( Q , P ) l d l ,
W ( Q , P ) = u i 1 4 π e j k R R ( e R × e i 1 + e R e i e R × e r 1 + e R e r )
U GO ( P ) = i lim σ i 0 Γ i W ( Q i , P ) · l d l .
R ( ϕ 0 , θ ) = sin ϕ 0 sin θ sin ϕ 0 + sin θ
W ( Q , P ) = u i 1 4 π e j k R R { [ e R × e i 1 + e R e i ] + [ R ( ϕ 0 , θ ) ( e R × e r 1 + e R e r ) ] }
U i ( P ) = u i e j k i r ,
U r ( P ) = u i R ( ϕ 0 , θ ) e j k r r ,
e i = cos ϕ 0 e x sin ϕ 0 e y e r = cos ϕ 0 e x + sin ϕ 0 e y
U i ( P ) = u i e j k ρ cos ( ϕ ϕ 0 ) ,
U r ( P ) = u i R ( ϕ 0 , θ ) e j k ρ cos ( ϕ + ϕ 0 ) ,
e R = cos ϕ e x sin ϕ e y l = e z
( e R × e i ) l 1 + e R e i = sin ( ϕ ϕ 0 ) 1 + cos ( ϕ ϕ 0 ) = tan ( ϕ ϕ 0 2 ) ,
( e R × e r ) l 1 + e R e r = tan ( ϕ + ϕ 0 2 ) ,
W ( Q , P ) = u i 1 4 π e j k R R [ tan ( ϕ ϕ 0 2 ) + R ( ϕ 0 , θ ) tan ( ϕ + ϕ 0 2 ) ]
U B ( P ) = u i 1 4 π [ tan ( ϕ ϕ 0 2 ) + R ( ϕ 0 , θ ) tan ( ϕ + ϕ 0 2 ) ] Γ e j k R R d l .
U B ( P ) = u i 1 4 π [ tan ( ϕ ϕ 0 2 ) + R ( ϕ 0 , θ ) tan ( ϕ + ϕ 0 2 ) ] z = e j k R R d z .
c e j k ρ c h γ d γ = π j H 0 ( 2 ) ( k ρ )
U B ( P ) = u i 1 4 j [ tan ( ϕ ϕ 0 2 ) + R ( θ , ϕ 0 ) tan ( ϕ + ϕ 0 2 ) ] H 0 ( 2 ) ( k ρ ) .
H 0 ( 2 ) ( k υ ) 2 π e j [ k υ ( π / 4 ) ] k υ
U B ( P ) u i 2 2 π [ tan ( ϕ ϕ 0 2 ) + R ( θ , ϕ 0 ) tan ( ϕ + ϕ 0 2 ) ] e j k ρ j π / 4 k ρ
U B i ( P ) u i e j π / 4 2 π sin ( ϕ ϕ 0 2 ) e j 2 k ρ cos 2 ( ϕ ϕ 0 2 ) 2 k ρ cos ( ϕ ϕ 0 2 ) e j k ρ cos ( ϕ ϕ 0 )
U B i ( P ) u i F ( ξ i ) sin ( ϕ ϕ 0 2 ) e j k ρ cos ( ϕ ϕ 0 ) .
ξ i = 2 k ρ cos [ ( ϕ ϕ 0 ) / 2 ]
U B i ( P ) u i F ( | ξ i | ) sgn ( ξ i ) sin ( ϕ ϕ 0 2 ) e j k ρ cos ( ϕ ϕ 0 )
F ( ξ i ) = e j π 4 π ξ i e j t 2 d t .
U B r ( P ) u i F ( | ξ r | ) sgn ( ξ r ) R ( θ , ϕ 0 ) sin ( ϕ + ϕ 0 2 ) e j k ρ cos ( ϕ + ϕ 0 ) .
ξ r = 2 k ρ cos [ ( ϕ + ϕ 0 ) / 2 ]
U B ( P ) = u i [ F ( | ξ i | ) sgn ( ξ i ) sin ( ϕ ϕ 0 2 ) e j k ρ cos ( ϕ ϕ 0 ) + R ( θ , ϕ 0 ) F ( | ξ r | ) sgn ( ξ r ) sin ( ϕ + ϕ 0 2 ) e j k ρ cos ( ϕ + ϕ 0 ) ]
U B t ( imp ) = u i { e j k ρ cos ( ϕ ϕ 0 ) u ( ξ i ) + R ( θ , ϕ 0 ) e j k ρ cos ( ϕ + ϕ 0 ) u ( ξ r ) + [ F ( | ξ i | ) sgn ( ξ i ) sin ( ϕ ϕ 0 2 ) e j k ρ cos ( ϕ ϕ 0 ) + R ( θ , ϕ 0 ) F ( | ξ r | ) sgn ( ξ r ) sin ( ϕ + ϕ 0 2 ) e j k ρ cos ( ϕ + ϕ 0 ) ] }
U d i 1 ( P ) = u i 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 ) e j k ρ cos ( ϕ ϕ 0 ) ,
U d i 2 ( P ) = u i 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 ) e j k ρ cos [ ϕ ϕ 0 2 π ( n 1 ) ] .
U d r 1 ( P ) = u i 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 ) e j k ρ cos ( ϕ + ϕ 0 ) ,
U d r 2 ( P ) = u i 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 ) e j k ρ cos [ ϕ + ϕ 0 2 π ( n 1 ) ]
Γ 1 ( ϕ 0 , θ ) = cos [ ( ϕ ϕ 0 ) / 2 ] sin θ cos [ ( ϕ ϕ 0 ) / 2 ] + sin θ ,
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 .
U B t ( pec ) = u i { e j k ρ cos ( ϕ ϕ 0 ) u ( ξ i ) e j k ρ cos ( ϕ + ϕ 0 ) u ( ξ r ) + [ F ( | ξ i | ) sgn ( ξ i ) sin ( ϕ ϕ 0 2 ) e j k ρ cos ( ϕ ϕ 0 ) F ( | ξ r | ) sgn ( ξ r ) sin ( ϕ + ϕ 0 2 ) e j k ρ cos ( ϕ + ϕ 0 ) ] } .
U B t ( pmc ) = u i { e j k ρ cos ( ϕ ϕ 0 ) u ( ξ i ) + e j k ρ cos ( ϕ + ϕ 0 ) u ( ξ r ) + [ F ( | ξ i | ) sgn ( ξ i ) sin ( ϕ ϕ 0 2 ) e j k ρ cos ( ϕ ϕ 0 ) + F ( | ξ r | ) sgn ( ξ r ) sin ( ϕ + ϕ 0 2 ) e j k ρ cos ( ϕ + ϕ 0 ) ] } .
U B t ( opaque ) = u i { e j k ρ cos ( ϕ ϕ 0 ) u ( ξ i ) + [ F ( | ξ i | ) sgn ( ξ i ) sin ( ϕ ϕ 0 2 ) e j k ρ cos ( ϕ ϕ 0 ) ] }

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