Abstract

Simple exponential functions that approach zero for reflection and shadow boundaries are considered to cancel the infinite values of diffraction coefficients at these regions. This method is applied to a wedge diffraction coefficient, and the resultant uniform coefficient is compared with the exact diffracted fields numerically.

© 2005 Optical Society of America

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References

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  1. J. B. Keller, J. Opt. Soc. Am. 52, 116 (1962).
    [CrossRef] [PubMed]
  2. D. A. McNamara, C. W.I. Pistorius, and J. A.G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction (Artech House, 1990).
  3. G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves (IEE Peter Peregrinus, 1976).
  4. D. S. Ahluwalia, R. M. Lewis, and J. Boersma, SIAM J. Appl. Math. 16, 783 (1968).
    [CrossRef]
  5. R. M. Lewis and J. Boersma, J. Math. Phys. 10, 2291 (1969).
    [CrossRef]
  6. R. G. Kouyoumjian and P. H. Pathak, Proc. IEEE 62, 1448 (1974).
    [CrossRef]
  7. S. W. Lee and G. A. Deschamps, IEEE Trans. Antennas Propag. 24, 25 (1976).
    [CrossRef]
  8. P. Ya. Ufimtsev, SIAM J. Appl. Math. 37, 459 (1979).
    [CrossRef]
  9. J. L. Volakis, IEEE Trans. Antennas Propag. 34, 172 (1986).
    [CrossRef]
  10. H. M. El-Sallabi and P. Vainikainen, Electron. Lett. 39, 10 (2003).
    [CrossRef]
  11. J. Boersma and S. W. Lee, IEEE Trans. Antennas Propag. 25, 171 (1977).
    [CrossRef]
  12. G. A. Deschamps, J. Boersma, and S. W. Lee, IEEE Trans. Antennas Propag. 32, 264 (1984).
    [CrossRef]
  13. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, 1991).

2003

H. M. El-Sallabi and P. Vainikainen, Electron. Lett. 39, 10 (2003).
[CrossRef]

1986

J. L. Volakis, IEEE Trans. Antennas Propag. 34, 172 (1986).
[CrossRef]

1984

G. A. Deschamps, J. Boersma, and S. W. Lee, IEEE Trans. Antennas Propag. 32, 264 (1984).
[CrossRef]

1979

P. Ya. Ufimtsev, SIAM J. Appl. Math. 37, 459 (1979).
[CrossRef]

1977

J. Boersma and S. W. Lee, IEEE Trans. Antennas Propag. 25, 171 (1977).
[CrossRef]

1976

S. W. Lee and G. A. Deschamps, IEEE Trans. Antennas Propag. 24, 25 (1976).
[CrossRef]

1974

R. G. Kouyoumjian and P. H. Pathak, Proc. IEEE 62, 1448 (1974).
[CrossRef]

1969

R. M. Lewis and J. Boersma, J. Math. Phys. 10, 2291 (1969).
[CrossRef]

1968

D. S. Ahluwalia, R. M. Lewis, and J. Boersma, SIAM J. Appl. Math. 16, 783 (1968).
[CrossRef]

1962

Ahluwalia, D. S.

D. S. Ahluwalia, R. M. Lewis, and J. Boersma, SIAM J. Appl. Math. 16, 783 (1968).
[CrossRef]

Boersma, J.

G. A. Deschamps, J. Boersma, and S. W. Lee, IEEE Trans. Antennas Propag. 32, 264 (1984).
[CrossRef]

J. Boersma and S. W. Lee, IEEE Trans. Antennas Propag. 25, 171 (1977).
[CrossRef]

R. M. Lewis and J. Boersma, J. Math. Phys. 10, 2291 (1969).
[CrossRef]

D. S. Ahluwalia, R. M. Lewis, and J. Boersma, SIAM J. Appl. Math. 16, 783 (1968).
[CrossRef]

Deschamps, G. A.

G. A. Deschamps, J. Boersma, and S. W. Lee, IEEE Trans. Antennas Propag. 32, 264 (1984).
[CrossRef]

S. W. Lee and G. A. Deschamps, IEEE Trans. Antennas Propag. 24, 25 (1976).
[CrossRef]

El-Sallabi, H. M.

H. M. El-Sallabi and P. Vainikainen, Electron. Lett. 39, 10 (2003).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, 1991).

James, G. L.

G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves (IEE Peter Peregrinus, 1976).

Keller, J. B.

Kouyoumjian, R. G.

R. G. Kouyoumjian and P. H. Pathak, Proc. IEEE 62, 1448 (1974).
[CrossRef]

Lee, S. W.

G. A. Deschamps, J. Boersma, and S. W. Lee, IEEE Trans. Antennas Propag. 32, 264 (1984).
[CrossRef]

J. Boersma and S. W. Lee, IEEE Trans. Antennas Propag. 25, 171 (1977).
[CrossRef]

S. W. Lee and G. A. Deschamps, IEEE Trans. Antennas Propag. 24, 25 (1976).
[CrossRef]

Lewis, R. M.

R. M. Lewis and J. Boersma, J. Math. Phys. 10, 2291 (1969).
[CrossRef]

D. S. Ahluwalia, R. M. Lewis, and J. Boersma, SIAM J. Appl. Math. 16, 783 (1968).
[CrossRef]

Malherbe, J. A.G.

D. A. McNamara, C. W.I. Pistorius, and J. A.G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction (Artech House, 1990).

McNamara, D. A.

D. A. McNamara, C. W.I. Pistorius, and J. A.G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction (Artech House, 1990).

Pathak, P. H.

R. G. Kouyoumjian and P. H. Pathak, Proc. IEEE 62, 1448 (1974).
[CrossRef]

Pistorius, C. W.I.

D. A. McNamara, C. W.I. Pistorius, and J. A.G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction (Artech House, 1990).

Ufimtsev, P. Ya.

P. Ya. Ufimtsev, SIAM J. Appl. Math. 37, 459 (1979).
[CrossRef]

Vainikainen, P.

H. M. El-Sallabi and P. Vainikainen, Electron. Lett. 39, 10 (2003).
[CrossRef]

Volakis, J. L.

J. L. Volakis, IEEE Trans. Antennas Propag. 34, 172 (1986).
[CrossRef]

Electron. Lett.

H. M. El-Sallabi and P. Vainikainen, Electron. Lett. 39, 10 (2003).
[CrossRef]

IEEE Trans. Antennas Propag.

J. Boersma and S. W. Lee, IEEE Trans. Antennas Propag. 25, 171 (1977).
[CrossRef]

G. A. Deschamps, J. Boersma, and S. W. Lee, IEEE Trans. Antennas Propag. 32, 264 (1984).
[CrossRef]

S. W. Lee and G. A. Deschamps, IEEE Trans. Antennas Propag. 24, 25 (1976).
[CrossRef]

J. L. Volakis, IEEE Trans. Antennas Propag. 34, 172 (1986).
[CrossRef]

J. Math. Phys.

R. M. Lewis and J. Boersma, J. Math. Phys. 10, 2291 (1969).
[CrossRef]

J. Opt. Soc. Am.

Proc. IEEE

R. G. Kouyoumjian and P. H. Pathak, Proc. IEEE 62, 1448 (1974).
[CrossRef]

SIAM J. Appl. Math.

D. S. Ahluwalia, R. M. Lewis, and J. Boersma, SIAM J. Appl. Math. 16, 783 (1968).
[CrossRef]

P. Ya. Ufimtsev, SIAM J. Appl. Math. 37, 459 (1979).
[CrossRef]

Other

D. A. McNamara, C. W.I. Pistorius, and J. A.G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction (Artech House, 1990).

G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves (IEE Peter Peregrinus, 1976).

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, 1991).

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Figures (3)

Fig. 1
Fig. 1

Perfectly conducting wedge geometry.

Fig. 2
Fig. 2

UTD and SUTD transition functions for the shadow boundary.

Fig. 3
Fig. 3

Diffracted fields for α = π 6 ( ϕ 0 = π 3 , ρ = 6 λ ) .

Equations (11)

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E d z = exp ( j k ρ ) k ρ exp ( j π 4 ) sin π n n 2 π ( 1 cos π n cos ϕ + ϕ 0 n 1 cos π n cos ϕ ϕ 0 n )
f ( ϕ , π ϕ 0 ) = A { 1 exp [ K ϕ ( π ϕ 0 ) ] }
E r [ ρ , ( π ϕ 0 ) ] + E d [ ρ , ( π ϕ 0 ) ] = E d [ ρ , + ( π ϕ 0 ) ] ,
E i [ ρ , ( π + ϕ 0 ) ] + E d [ ρ , ( π + ϕ 0 ) ] = E d [ ρ , + ( π + ϕ 0 ) ] ,
D e = exp ( j π 4 ) sin π n n 2 π [ f ( ϕ , π ϕ 0 ) cos π n cos ϕ + ϕ 0 n f ( ϕ , π + ϕ 0 ) cos π n cos ϕ ϕ 0 n ]
f ( ϕ , π ϕ 0 ) = p ( ϕ , π ϕ 0 ) { 1 exp [ π k ρ 2 ϕ ( π ϕ 0 ) ] }
lim x a d x a d x = 1 , lim x a + d x a d x = 1
f ( ϕ , π ϕ 0 ) = p ( ϕ , π ϕ 0 ) [ 1 exp ( 2 π k ρ cos ϕ ± ϕ 0 2 ) ] ,
E d z = exp ( j k ρ ) k ρ sin π n n 2 π [ f ( ϕ , π ϕ 0 ) cos π n cos ϕ + ϕ 0 n f ( ϕ , π + ϕ 0 ) cos π n cos ϕ ϕ 0 n ]
E d z = E t E i u [ ϕ + ( π + ϕ 0 ) ] + E r u [ ϕ + ( π ϕ 0 ) ] ,
E z = E i 4 π ψ m = 1 exp ( j ϑ m π 2 ) J ϑ m ( k ρ ) sin ϑ m ϕ sin ϑ m ϕ 0

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