Abstract

A uniform diffracted field is obtained in terms of Fresnel functions with complex argument by subtracting the unit step function from the Fresnel integral. The method is applied to the problem of diffraction of inhomogeneous plane waves by a perfectly conducting half-plane and wedge. The results are plotted numerically and compared with results reported in the literature.

© 2007 Optical Society of America

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References

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  1. J. B. Keller and W. Streifer, "Complex rays with an application to Gaussian beams," J. Opt. Soc. Am. 61, 40-43 (1971).
    [CrossRef]
  2. S. Choudhary and L. B. Felsen, "Asymptotic theory for inhomogeneous waves," IEEE Trans. Antennas Propag. 21, 827-842 (1973).
    [CrossRef]
  3. W. D. Wang and G. A. Deschamps, "Application of complex ray tracing to scattering problems," Proc. IEEE 11, 1541-1551 (1974).
    [CrossRef]
  4. L. B. Felsen, "Evanescent waves," J. Opt. Soc. Am. 66, 751-760 (1976).
    [CrossRef]
  5. L. Ronchi, V. Russo, G. T. D. Francia, and C. Zaccagnini, "Scattering of evanescent waves by cylindrical structures," Opt. Acta 8, 281-299 (1961).
    [CrossRef]
  6. V. I. Shevernev, "Diffraction of an inhomogeneous plane wave by a half plane," Radiophys. Quantum Electron. 19, 1285-1291 (2005).
    [CrossRef]
  7. H. L. Bertoni, A. C. Green, and L. B. Felsen, "Shadowing an inhomogeneous plane wave by an edge," J. Opt. Soc. Am. 68, 983-989 (1978).
    [CrossRef]
  8. G. A. Deschamps, S. W. Lee, E. Gowan III, and T. Fontana, "Diffraction of an evanescent plane wave by a half plane," Wave Motion 1, 25-35 (1979).
    [CrossRef]
  9. R. G. Kouyoumjian, G. Manara, P. Nepa, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by a wedge," Radio Sci. 31, 1387-1397 (1996).
    [CrossRef]
  10. G. Manara, P. Nepa, R. G. Kouyoumjian, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by an impedance wedge in a lossy medium," IEEE Trans. Antennas Propag. 46, 1753-1755 (1998).
    [CrossRef]
  11. S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and R. H. Tew, "On the theory of complex rays," SIAM Rev. 41, 417-509 (1999).
    [CrossRef]
  12. S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and V. H. Saward, "Edge diffraction of complex rays," Wave Motion 33, 41-49 (2001).
    [CrossRef]
  13. Y. Z. Umul, "Modified theory of physical optics," Opt. Express 12, 4959-4972 (2004).
    [CrossRef] [PubMed]
  14. 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]
  15. Y. Z. Umul, "Modified theory of physical optics approach to wedge diffraction problems," Opt. Express 13, 216-224 (2005).
    [CrossRef] [PubMed]
  16. Y. Z. Umul, "Edge-dislocation waves in the diffraction process by an impedance half-plane," J. Opt. Soc. Am. A 24, 507-511 (2007).
    [CrossRef]

2007 (1)

2005 (2)

Y. Z. Umul, "Modified theory of physical optics approach to wedge diffraction problems," Opt. Express 13, 216-224 (2005).
[CrossRef] [PubMed]

V. I. Shevernev, "Diffraction of an inhomogeneous plane wave by a half plane," Radiophys. Quantum Electron. 19, 1285-1291 (2005).
[CrossRef]

2004 (1)

2001 (1)

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and V. H. Saward, "Edge diffraction of complex rays," Wave Motion 33, 41-49 (2001).
[CrossRef]

1999 (1)

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and R. H. Tew, "On the theory of complex rays," SIAM Rev. 41, 417-509 (1999).
[CrossRef]

1998 (1)

G. Manara, P. Nepa, R. G. Kouyoumjian, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by an impedance wedge in a lossy medium," IEEE Trans. Antennas Propag. 46, 1753-1755 (1998).
[CrossRef]

1996 (1)

R. G. Kouyoumjian, G. Manara, P. Nepa, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by a wedge," Radio Sci. 31, 1387-1397 (1996).
[CrossRef]

1979 (1)

G. A. Deschamps, S. W. Lee, E. Gowan III, and T. Fontana, "Diffraction of an evanescent plane wave by a half plane," Wave Motion 1, 25-35 (1979).
[CrossRef]

1978 (1)

1976 (1)

1974 (2)

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]

W. D. Wang and G. A. Deschamps, "Application of complex ray tracing to scattering problems," Proc. IEEE 11, 1541-1551 (1974).
[CrossRef]

1973 (1)

S. Choudhary and L. B. Felsen, "Asymptotic theory for inhomogeneous waves," IEEE Trans. Antennas Propag. 21, 827-842 (1973).
[CrossRef]

1971 (1)

1961 (1)

L. Ronchi, V. Russo, G. T. D. Francia, and C. Zaccagnini, "Scattering of evanescent waves by cylindrical structures," Opt. Acta 8, 281-299 (1961).
[CrossRef]

Bertoni, H. L.

Chapman, S. J.

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and V. H. Saward, "Edge diffraction of complex rays," Wave Motion 33, 41-49 (2001).
[CrossRef]

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and R. H. Tew, "On the theory of complex rays," SIAM Rev. 41, 417-509 (1999).
[CrossRef]

Choudhary, S.

S. Choudhary and L. B. Felsen, "Asymptotic theory for inhomogeneous waves," IEEE Trans. Antennas Propag. 21, 827-842 (1973).
[CrossRef]

Deschamps, G. A.

G. A. Deschamps, S. W. Lee, E. Gowan III, and T. Fontana, "Diffraction of an evanescent plane wave by a half plane," Wave Motion 1, 25-35 (1979).
[CrossRef]

W. D. Wang and G. A. Deschamps, "Application of complex ray tracing to scattering problems," Proc. IEEE 11, 1541-1551 (1974).
[CrossRef]

Felsen, L. B.

Fontana, T.

G. A. Deschamps, S. W. Lee, E. Gowan III, and T. Fontana, "Diffraction of an evanescent plane wave by a half plane," Wave Motion 1, 25-35 (1979).
[CrossRef]

Francia, G. T. D.

L. Ronchi, V. Russo, G. T. D. Francia, and C. Zaccagnini, "Scattering of evanescent waves by cylindrical structures," Opt. Acta 8, 281-299 (1961).
[CrossRef]

Gowan, E.

G. A. Deschamps, S. W. Lee, E. Gowan III, and T. Fontana, "Diffraction of an evanescent plane wave by a half plane," Wave Motion 1, 25-35 (1979).
[CrossRef]

Green, A. C.

Keller, J. B.

Kouyoumjian, R. G.

G. Manara, P. Nepa, R. G. Kouyoumjian, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by an impedance wedge in a lossy medium," IEEE Trans. Antennas Propag. 46, 1753-1755 (1998).
[CrossRef]

R. G. Kouyoumjian, G. Manara, P. Nepa, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by a wedge," Radio Sci. 31, 1387-1397 (1996).
[CrossRef]

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]

Lawry, J. M. H.

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and V. H. Saward, "Edge diffraction of complex rays," Wave Motion 33, 41-49 (2001).
[CrossRef]

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and R. H. Tew, "On the theory of complex rays," SIAM Rev. 41, 417-509 (1999).
[CrossRef]

Lee, S. W.

G. A. Deschamps, S. W. Lee, E. Gowan III, and T. Fontana, "Diffraction of an evanescent plane wave by a half plane," Wave Motion 1, 25-35 (1979).
[CrossRef]

Manara, G.

G. Manara, P. Nepa, R. G. Kouyoumjian, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by an impedance wedge in a lossy medium," IEEE Trans. Antennas Propag. 46, 1753-1755 (1998).
[CrossRef]

R. G. Kouyoumjian, G. Manara, P. Nepa, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by a wedge," Radio Sci. 31, 1387-1397 (1996).
[CrossRef]

Nepa, P.

G. Manara, P. Nepa, R. G. Kouyoumjian, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by an impedance wedge in a lossy medium," IEEE Trans. Antennas Propag. 46, 1753-1755 (1998).
[CrossRef]

R. G. Kouyoumjian, G. Manara, P. Nepa, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by a wedge," Radio Sci. 31, 1387-1397 (1996).
[CrossRef]

Ockendon, J. R.

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and V. H. Saward, "Edge diffraction of complex rays," Wave Motion 33, 41-49 (2001).
[CrossRef]

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and R. H. Tew, "On the theory of complex rays," SIAM Rev. 41, 417-509 (1999).
[CrossRef]

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]

Ronchi, L.

L. Ronchi, V. Russo, G. T. D. Francia, and C. Zaccagnini, "Scattering of evanescent waves by cylindrical structures," Opt. Acta 8, 281-299 (1961).
[CrossRef]

Russo, V.

L. Ronchi, V. Russo, G. T. D. Francia, and C. Zaccagnini, "Scattering of evanescent waves by cylindrical structures," Opt. Acta 8, 281-299 (1961).
[CrossRef]

Saward, V. H.

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and V. H. Saward, "Edge diffraction of complex rays," Wave Motion 33, 41-49 (2001).
[CrossRef]

Shevernev, V. I.

V. I. Shevernev, "Diffraction of an inhomogeneous plane wave by a half plane," Radiophys. Quantum Electron. 19, 1285-1291 (2005).
[CrossRef]

Streifer, W.

Taute, B. J. E.

G. Manara, P. Nepa, R. G. Kouyoumjian, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by an impedance wedge in a lossy medium," IEEE Trans. Antennas Propag. 46, 1753-1755 (1998).
[CrossRef]

R. G. Kouyoumjian, G. Manara, P. Nepa, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by a wedge," Radio Sci. 31, 1387-1397 (1996).
[CrossRef]

Tew, R. H.

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and R. H. Tew, "On the theory of complex rays," SIAM Rev. 41, 417-509 (1999).
[CrossRef]

Umul, Y. Z.

Wang, W. D.

W. D. Wang and G. A. Deschamps, "Application of complex ray tracing to scattering problems," Proc. IEEE 11, 1541-1551 (1974).
[CrossRef]

Zaccagnini, C.

L. Ronchi, V. Russo, G. T. D. Francia, and C. Zaccagnini, "Scattering of evanescent waves by cylindrical structures," Opt. Acta 8, 281-299 (1961).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

S. Choudhary and L. B. Felsen, "Asymptotic theory for inhomogeneous waves," IEEE Trans. Antennas Propag. 21, 827-842 (1973).
[CrossRef]

G. Manara, P. Nepa, R. G. Kouyoumjian, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by an impedance wedge in a lossy medium," IEEE Trans. Antennas Propag. 46, 1753-1755 (1998).
[CrossRef]

J. Opt. Soc. Am. (3)

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

Opt. Acta (1)

L. Ronchi, V. Russo, G. T. D. Francia, and C. Zaccagnini, "Scattering of evanescent waves by cylindrical structures," Opt. Acta 8, 281-299 (1961).
[CrossRef]

Opt. Express (2)

Proc. IEEE (2)

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]

W. D. Wang and G. A. Deschamps, "Application of complex ray tracing to scattering problems," Proc. IEEE 11, 1541-1551 (1974).
[CrossRef]

Radio Sci. (1)

R. G. Kouyoumjian, G. Manara, P. Nepa, and B. J. E. Taute, "The diffraction of an inhomogeneous plane wave by a wedge," Radio Sci. 31, 1387-1397 (1996).
[CrossRef]

Radiophys. Quantum Electron. (1)

V. I. Shevernev, "Diffraction of an inhomogeneous plane wave by a half plane," Radiophys. Quantum Electron. 19, 1285-1291 (2005).
[CrossRef]

SIAM Rev. (1)

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and R. H. Tew, "On the theory of complex rays," SIAM Rev. 41, 417-509 (1999).
[CrossRef]

Wave Motion (2)

S. J. Chapman, J. M. H. Lawry, J. R. Ockendon, and V. H. Saward, "Edge diffraction of complex rays," Wave Motion 33, 41-49 (2001).
[CrossRef]

G. A. Deschamps, S. W. Lee, E. Gowan III, and T. Fontana, "Diffraction of an evanescent plane wave by a half plane," Wave Motion 1, 25-35 (1979).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Geometry of the perfectly conducting wedge.

Fig. 2
Fig. 2

Error function for the total scattered fields for ϕ 02 = 3 ° .

Fig. 3
Fig. 3

Total diffracted field for ϕ 02 = 0 ° , 5 ° , 10 ° , 15 ° .

Fig. 4
Fig. 4

Total scattered field for ϕ 02 = 2 ° .

Equations (35)

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u s U ( x ) + F ̂ ( x )
F ̂ ( x ) = e j ( π 4 ) 2 π e j x 2 x .
u s U ( x ) + F ̂ ( x ) T ( x ) ,
T ( x ) = F [ x ] F ̂ ( x ) .
F [ z ] = e j ( π 4 ) π z e j t 2 d t ,
F [ x ] = U ( x ) + sgn ( x ) F [ x ]
sgn ( x ) = F ̂ ( x ) F ̂ ( x ) ,
D u = { F [ z ] 1 , x y < 0 F [ z ] , x y > 0 } ,
F [ z ] 1 = e j ( π 4 ) π x + y α e j t 2 d t .
D u = sgn ( x y ) F [ x y + sgn ( x y ) α ] ,
T ( z ) = F [ x y + sgn ( x y ) α ] F ̂ ( x y + sgn ( x y ) α )
T UTD ( x ) = 2 e j ( π 4 ) π x 2 e j x 2 F [ x 2 ] ,
D = x 2 x F [ x 2 ] ,
E s z = E i { e j k ρ cos ( ϕ ϕ 0 ) F [ ξ ] e j k ρ cos ( ϕ + ϕ 0 ) F [ ξ + ] }
ξ = 2 k ρ cos ϕ ϕ 0 2 .
F [ a + j b ] = U ( b a ) + sgn ( a b ) F [ a b + sgn ( a b ) α ] ,
E s z GO = E i { e j k ρ cos ( ϕ ϕ 0 ) U ( b a ) e j k ρ cos ( ϕ + ϕ 0 ) U ( b + a + ) } ,
E s z diff = E i diff E r diff ,
E i diff = sgn ( a b ) F [ a b + sgn ( a b ) 2 b e j ( π 4 ) ] e j k ρ cos ( ϕ ϕ 0 ) ,
E r diff = sgn ( a + b + ) F [ a + b + + sgn ( a + b + ) 2 b + e j ( π 4 ) ] e j k ρ cos ( ϕ + ϕ 0 ) ,
a = 2 k ρ cos ϕ ϕ 01 2 cosh ϕ 02 2 ,
b = ± 2 k ρ sin ϕ ϕ 01 2 sinh ϕ 02 2 .
D ̃ = [ D s 0 0 D h ] ,
D s = sgn ( a + b + ) F [ a + b + + sgn ( a + b + ) 2 b + e j ( π 4 ) ] sgn ( a b ) F [ a b + sgn ( a b ) 2 b e j ( π 4 ) ]
D s = sgn ( a + b + ) F [ a + b + + sgn ( a + b + ) 2 b + e j ( π 4 ) ] + sgn ( a b ) F [ a b + sgn ( a b ) 2 b e j ( π 4 ) ] .
E is = E i e j k ρ cos ( ϕ ϕ 0 ) { U ( ξ ) W n ( ϕ ϕ 0 ) sgn ( ξ ) F [ ξ ] } ,
E rs = E i e j k ρ cos ( ϕ + ϕ 0 ) { U ( ξ + ) W n ( ϕ + ϕ 0 ) sgn ( ξ + ) F [ ξ + ] } ,
W n ( θ ) = 2 sin π n cos θ 2 n ( cos π n cos θ n ) ;
E is GO = E i e j k ρ cos ( ϕ ϕ 0 ) U ( b a ) ,
E rs GO = E i e j k ρ cos ( ϕ + ϕ 0 ) U ( b + a + ) ,
E is diff = sgn ( a b ) F [ a b + sgn ( a b ) 2 b e j ( π 4 ) ] W n ( ϕ ϕ 0 ) e j k ρ cos ( ϕ ϕ 0 ) ,
E rs diff = sgn ( a + b + ) F [ a + b + + sgn ( a + b + ) 2 b + e j ( π 4 ) ] W n ( ϕ + ϕ 0 ) e j k ρ cos ( ϕ + ϕ 0 )
E st = E is GO + E rs GO + E is diff + E rs diff .
D ̃ = [ D s 0 0 D h ]
E st E i = 4 π ψ n = 1 e j ϑ n ( π 2 ) J ϑ n ( k ρ ) sin ϑ n ϕ 0 sin ϑ n ϕ

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