Abstract

A new procedure for calculating the scattered fields from a perfectly conducting body is introduced. The method is defined by considering three assumptions. The reflection angle is taken as a function of integral variables, a new unit vector, dividing the angle between incident and reflected rays into two equal parts is evaluated and the perfectly conducting (PEC) surface is considered with the aperture part, together. This integral is named as Modified Theory of Physical Optics (MTPO) integral. The method is applied to the reflection and edge diffraction from a perfectly conducting half plane problem. The reflected, reflected diffracted, incident and incident diffracted fields are evaluated by stationary phase method and edge point technique, asymptotically. MTPO integral is compared with the exact solution and PO integral for the problem of scattering from a perfectly conducting half plane, numerically. It is observed that MTPO integral gives the total field that agrees with the exact solution and the result is more reliable than that of classical PO integral.

© 2004 Optical Society of America

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References

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  1. J. B. Keller, �??Geometrical theory of diffraction,�?? J. Opt. Soc. Of America 52, 116-130 (1962)
    [CrossRef]
  2. J. B. Keller, �??Diffraction by an aperture,�?? J. App. Physics 28, 426-444 (1957)
    [CrossRef]
  3. J. B. Keller, R. M. Lewis and B. D. Seckler, �??Diffraction by an aperture II,�?? J. App. Physics 28, 570-579 (1957)
    [CrossRef]
  4. G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves (IEE Peter Peregrinus Ltd., London, 1976)
  5. R. C. Hansen Ed., Geometric Theory of Diffraction (IEEE Press, New York, 1981)
  6. N. D. Taket and R. E. Burge, �??A physical optics version of geometrical theory diffraction,�?? IEEE Trans. Antennas and Propagat. 39, 719-731 (1991)
    [CrossRef]
  7. R. E. Burge, X. C. Yuan, B. D. Caroll, N. E. Fisher, T. J. Hall, G. A. Lester, N. D. Taket and C. J. Oliver, �??Microwave scattering from dielectric wedges with planar surfaces: A diffraction coefficient based on a physical optics version of GTD,�?? IEEE Trans. Antennas and Propagat., 47, 1515-1527 (1999).
    [CrossRef]
  8. T. B. A. Senior, �??Diffraction by a semi-infinite metallic sheet,�?? Proc. Roy. Soc. 213A, 436-458 (1952)
  9. G. D. Maliuzhinets, �??Excitation, reflection and emission of surface waves from a wedge with given face impedances,�?? Sov. Phys. Dokl. 3, 752-755 (1958)
  10. J. L. Volakis, �??A uniform geometrical theory of diffraction for an imperfectly conducting half-plane,�?? IEEE Trans. Antennas and Propagat. 34, 172-180 (1986)
    [CrossRef]
  11. S. Silver, "Microwave Antenna Theory and Design", (McGraw-Hill, New York, 1949)
  12. S. W. Lee, �??Comparison of uniform asymptotic theory and Ufimtsev�??s theory of electromagnetic edge diffraction,�?? IEEE Trans. Antennas and Propagat. 25, 162-170 (1977)
    [CrossRef]
  13. P. Ya. Ufimtsev, �??Method of edge waves in the Physical Theory of Diffraction,�?? Air Force System Command, Foreign Tech. Div. Document ID No. FTD-HC-23-259-71, (1971).
  14. A. Michaeli, �??Equivalent edge currents for arbitrary aspects of observation,�?? IEEE Trans. Antennas and Propagat. 23, 252-258 (1984)
    [CrossRef]
  15. F. E. Knott, �??The relationship between Mitzner�??s ILDC and Michaeli�??s equivalent currents,�?? IEEE Trans. Antennas and Propagat. 33, 112-114 (1985)
    [CrossRef]
  16. A. Michaeli, �??Incremental diffraction coefficients for the extended physical theory of diffraction,�?? IEEE Trans. Antennas and Propagat. 43, 732-734 (1995)
    [CrossRef]
  17. T. Griesser and C. A. Balanis, �??Backscatter analysis of dihedral corner reflectors using physical optics and physical theory of diffraction,�?? IEEE Trans. Antennas and Propagat. 35, 1137-1147 (1987)
    [CrossRef]
  18. M. Martinez-Burdalo, A. Martin and R. Villar, �??Uniform PO and PTD solution for calculating plane wave backscattering from a finite cylindrical shell of arbitrary cross section,�?? IEEE Trans. Antennas and Propagat. 41, 1336-1339 (1993)
    [CrossRef]
  19. T. Murasaki and M. Ando, �??Equivalent edge currents by the modified edge edge representation: physical optics components,�?? IEICE Trans. on Electronics E75-C, 617-626 (1992)
  20. K. Sakina, S. Cui and M. Ando, �??Mathematical investigation of modified edge representation,�?? presented at the 2000 IEEE AP-S URSI International Symposium, Salt Lake City-Utah, USA, 16-21 July 2000
  21. J. Goto, �??Interpretation of high frequency diffraction based upon PO,�?? M.S. thesis (Tokyo Institute of Technology, Tokyo, 2003), Chap. 3.
  22. Y. Z. Umul, E. Yengel, and A. Aydýn, �??Comparison of physical optics integral and exact solution for cylinder problem,�?? presented at Eleco�??2003 International Conference, Bursa, Turkey, 3-7 Dec. 2003, <a href="http://eleco.emo.org.tr/eleco2003/ELECO2003/bsession/B5-01.pdf">http://eleco.emo.org.tr/eleco2003/ELECO2003/bsession/B5-01.pdf</a>
  23. A. Sommerfeld, Optics (Academic Press, New York, 1954)
  24. L. B. Felsen and N. Marcuwitz, "Radiation and Scattering of Waves", (IEEE Press, New York, 1994)
    [CrossRef]
  25. W.L. Stutzman and G. A. Thiele, "Antenna Theory and Design", (John Wiley & Sons, New York, 1988)
  26. A. Ishimaru, "Electromagnetic Wave Propagation, Radiation and Scattering", (Prentice Hall, New Jersey, 1991).

. Opt. Soc. Of America (1)

J. B. Keller, �??Geometrical theory of diffraction,�?? J. Opt. Soc. Of America 52, 116-130 (1962)
[CrossRef]

IEEE Trans. Antennas and Propagat. (7)

N. D. Taket and R. E. Burge, �??A physical optics version of geometrical theory diffraction,�?? IEEE Trans. Antennas and Propagat. 39, 719-731 (1991)
[CrossRef]

A. Michaeli, �??Incremental diffraction coefficients for the extended physical theory of diffraction,�?? IEEE Trans. Antennas and Propagat. 43, 732-734 (1995)
[CrossRef]

T. Griesser and C. A. Balanis, �??Backscatter analysis of dihedral corner reflectors using physical optics and physical theory of diffraction,�?? IEEE Trans. Antennas and Propagat. 35, 1137-1147 (1987)
[CrossRef]

M. Martinez-Burdalo, A. Martin and R. Villar, �??Uniform PO and PTD solution for calculating plane wave backscattering from a finite cylindrical shell of arbitrary cross section,�?? IEEE Trans. Antennas and Propagat. 41, 1336-1339 (1993)
[CrossRef]

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

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

A. Michaeli, �??Equivalent edge currents for arbitrary aspects of observation,�?? IEEE Trans. Antennas and Propagat. 23, 252-258 (1984)
[CrossRef]

IEICE Trans. on Electronics (1)

T. Murasaki and M. Ando, �??Equivalent edge currents by the modified edge edge representation: physical optics components,�?? IEICE Trans. on Electronics E75-C, 617-626 (1992)

J. App. Physics (2)

J. B. Keller, �??Diffraction by an aperture,�?? J. App. Physics 28, 426-444 (1957)
[CrossRef]

J. B. Keller, R. M. Lewis and B. D. Seckler, �??Diffraction by an aperture II,�?? J. App. Physics 28, 570-579 (1957)
[CrossRef]

Proc. Roy. Soc. (1)

T. B. A. Senior, �??Diffraction by a semi-infinite metallic sheet,�?? Proc. Roy. Soc. 213A, 436-458 (1952)

Sov. Phys. Dokl. (1)

G. D. Maliuzhinets, �??Excitation, reflection and emission of surface waves from a wedge with given face impedances,�?? Sov. Phys. Dokl. 3, 752-755 (1958)

The relationship between Mitzner???s ILDC (1)

F. E. Knott, �??The relationship between Mitzner�??s ILDC and Michaeli�??s equivalent currents,�?? IEEE Trans. Antennas and Propagat. 33, 112-114 (1985)
[CrossRef]

Trans. Antennas and Propagat. (1)

R. E. Burge, X. C. Yuan, B. D. Caroll, N. E. Fisher, T. J. Hall, G. A. Lester, N. D. Taket and C. J. Oliver, �??Microwave scattering from dielectric wedges with planar surfaces: A diffraction coefficient based on a physical optics version of GTD,�?? IEEE Trans. Antennas and Propagat., 47, 1515-1527 (1999).
[CrossRef]

Other (11)

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

R. C. Hansen Ed., Geometric Theory of Diffraction (IEEE Press, New York, 1981)

K. Sakina, S. Cui and M. Ando, �??Mathematical investigation of modified edge representation,�?? presented at the 2000 IEEE AP-S URSI International Symposium, Salt Lake City-Utah, USA, 16-21 July 2000

J. Goto, �??Interpretation of high frequency diffraction based upon PO,�?? M.S. thesis (Tokyo Institute of Technology, Tokyo, 2003), Chap. 3.

Y. Z. Umul, E. Yengel, and A. Aydýn, �??Comparison of physical optics integral and exact solution for cylinder problem,�?? presented at Eleco�??2003 International Conference, Bursa, Turkey, 3-7 Dec. 2003, <a href="http://eleco.emo.org.tr/eleco2003/ELECO2003/bsession/B5-01.pdf">http://eleco.emo.org.tr/eleco2003/ELECO2003/bsession/B5-01.pdf</a>

A. Sommerfeld, Optics (Academic Press, New York, 1954)

L. B. Felsen and N. Marcuwitz, "Radiation and Scattering of Waves", (IEEE Press, New York, 1994)
[CrossRef]

W.L. Stutzman and G. A. Thiele, "Antenna Theory and Design", (John Wiley & Sons, New York, 1988)

A. Ishimaru, "Electromagnetic Wave Propagation, Radiation and Scattering", (Prentice Hall, New Jersey, 1991).

P. Ya. Ufimtsev, �??Method of edge waves in the Physical Theory of Diffraction,�?? Air Force System Command, Foreign Tech. Div. Document ID No. FTD-HC-23-259-71, (1971).

S. Silver, "Microwave Antenna Theory and Design", (McGraw-Hill, New York, 1949)

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Figures (7)

Fig. 1.
Fig. 1.

Scattered fields from a perfectly conducting surface and an aperture continuation

Fig. 2
Fig. 2

Reflection geometry from a perfectly conducting half plane

Fig. 3.
Fig. 3.

Transmission geometry for the modified theory of physical optics

Fig. 4.
Fig. 4.

Regions for scattered fields in a perfectly conducting half plane

Fig. 5.
Fig. 5.

Reflected and diffracted fields from perfectly conducting half plane (PO and exact solution)

Fig. 6.
Fig. 6.

Reflected and diffracted fields from perfectly conducting half plane [MTPO (β = ϕ 0) and exact solution]

Fig. 7.
Fig. 7.

Reflected and diffracted fields from perfectly conducting half plane (MTPO and exact solution)

Equations (66)

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J es = n 1 × H t | S 1
J es = n 2 × H i | S 2 , J ms = n 2 × E i | S 2
n 1 = cos ( u + α ) t + sin ( u + α ) n
n 2 = cos ( v + α ) t sin ( v + α ) n
E t = E is + E rs
E is = μ 0 4 π S 2 n 2 × H i | S 2 e jk R 2 R 2 dS ' + 1 4 π S 2 × ( n 2 × E i | S 2 e jk R 2 R 2 ) dS '
E rs = μ 0 4 π S 1 n 1 × H t | S 1 e jk R 1 R 1 dS '
H t = H is + H rs
H is = 1 4 π S 2 × ( n 2 × H i | S 2 e jk R 2 R 2 ) dS ' + ε 4 π S 2 n 2 × E i | S 2 e jk R 2 R 2 dS '
H rs = 1 4 π S 1 × ( n 1 × H t | S 1 e jk R 1 R 1 ) dS '
H i = E i Z 0 ( e x sin ϕ 0 e y cos ϕ 0 ) e jk ( x cos ϕ 0 + y sin ϕ 0 )
E r = e z E r e jk ( x cos β y sin β )
E r = E i e jkx ' ( cos ϕ 0 cos β )
J MTPO = E i Z 0 [ cos u cos ( u + β + ϕ 0 ) ] e jkx ' cos ϕ 0 e z
J PO = e z 2 E i Z 0 sin ϕ 0 e jkx ' cos ϕ 0
J MTPO = 2 E i Z 0 sin ( β + ϕ 0 2 ) e jkx ' cos ϕ 0 e z
E rs = e z jk E i 2 π x ' = 0 z ' = e jkx ' cos ϕ 0 e jk R 1 R 1 sin ( β + ϕ 0 2 ) dx ' dz '
R 1 = ( x x ' ) 2 + y 2 + ( z z ' ) 2 .
c e jkchα = π j H 0 ( 2 ) ( kR )
E rs = e z k E i 2 x ' = 0 e jkx ' cos ϕ 0 H 0 ( 2 ) ( kR ) sin ( β + ϕ 0 2 ) dx '
E ieq = e z E i e jk ( x cos ϕ 0 y sin ϕ 0 )
H ieq = E i Z 0 ( e x sin ϕ 0 + e y cos ϕ 0 ) e jk ( x cos ϕ 0 y sin ϕ 0 )
J MTPO = 2 E i Z 0 sin ( β + ϕ 0 2 ) e jkx ' cos ϕ 0 e z
E is e z k E i 2 π e j π 4 x ' = 0 e jkx ' cos ϕ 0 e jk R 1 k R 1 sin ϕ 0 + β 2 dx '
E s = E rs + E is
E rs e z k E i 2 π e j π 4 x ' = 0 e jkx ' cos ϕ 0 e jk R 1 k R 1 sin ( β + ϕ 0 2 ) dx '
E t e z k E i 2 π e j π 4 ( x ' = 0 e jkx ' cos ϕ 0 e jk R 1 k R 1 sin ϕ 0 + β 2 dx ' x ' = 0 e jkx ' cos ϕ 0 e jk R 1 k R 1 sin ( β + ϕ 0 2 ) dx ' )
g ( x ' ) = ρ cos γ + x ' ( cos β cos ϕ 0 )
g x ' = ρ sin γ dx ' x ' sin β dx ' + cos β cos ϕ 0
γ = π β ϕ
ρ sin γ dx ' = x ' sin β dx '
β s = ϕ 0
g x ' s = cos β s cos ϕ 0 = 0
2 g x ' 2 | s = sin 2 ϕ 0 l
l = R 1 | s = ρ cos γ s
g ( x ' ) l + 1 2 sin 2 ϕ 0 l ( x ' x ' s ) 2
f ( x ' s ) ± k E i 2 π e j π 4 sin ϕ 0 kl
E r , i ± k E i sin ϕ 0 2 π e j π 4 e jkl kl e jk sin 2 ϕ 0 l ( x ' x ' 2 ) dx '
e y 2 2 dy = 2 π .
E r E i e jkρ cos ( ϕ + ϕ 0 )
E i E i e jkρ cos ( ϕ ϕ 0 )
E d e z 1 jk f ( 0 ) g ' ( 0 ) e jkg ( 0 )
g ( 0 ) = ρ ,
g ' ( 0 ) = ( cos ϕ + cos ϕ 0 )
f ( 0 ) = k E i 2 2 π e j π 4 cos ( ϕ ϕ 0 2 )
E rd = e z E i 2 2 π e jkρ cos ( ϕ ϕ 0 2 ) cos ϕ + cos ϕ 0 e j π 4
D rd = e j π 4 2 2 π cos ( ϕ ϕ 0 2 ) cos ϕ + cos ϕ 0
g ( 0 ) = ρ ,
g ' ( 0 ) = ( cos ϕ + cos ϕ 0 )
f ( 0 ) = k E i 2 2 π e j π 4 cos ( ϕ + ϕ 0 2 )
E id = e z E i 2 2 π e jkρ cos ( ϕ + ϕ 0 2 ) cos ϕ + cos ϕ 0 e j π 4
D id = e j π 4 2 2 π cos ( ϕ + ϕ 0 2 ) cos ϕ + cos ϕ 0
D t = D id + D rd = e j π 4 2 π cos ( ϕ ϕ 0 2 ) cos ( ϕ + ϕ 0 2 ) cos ϕ + cos ϕ 0
E TPO E i e jk ( x cos ϕ 0 + y sin ϕ 0 ) k E i 2 sin ϕ 0 0 e jkx ' cos ϕ 0 H 0 ( 2 ) ( k R 1 ) dx '
E MTPO | β = ϕ 0 k E i 2 ( x ' = 0 e jkx ' cos ϕ 0 H 0 ( 2 ) ( k R 1 ) sin ϕ 0 dx ' 0 e jkx ' cos ϕ 0 H 0 ( 2 ) ( k R 1 ) sin ϕ 0 dx ' )
E TMTPO = 1 2 [ E i ( e jkρ cos ( ϕ ϕ 0 ) e jkρ cos ( ϕ + ϕ 0 ) ) u ( π ϕ ) + E TPO + E R ]
u ( π ϕ ) = { 1 , ϕ π 0 , ϕ π
E t = 2 E i m = 1 e jm π 4 J m 2 ( ) sin m 2 ϕ sin m 2 ϕ 0
E MTPO k E i 2 π e j π 4 ( x ' = 0 e jkx ' cos ϕ 0 e jk R 1 k R 1 sin ϕ 0 + β 2 dx ' x ' = 0 e jkx ' cos ϕ 0 e jk R 1 k R 1 sin ( β + ϕ 0 2 ) dx ' )
H i = e z H i e jk ( x cos ϕ 0 + y sin ϕ 0 )
E i = Z 0 H i ( sin ϕ 0 e x + cos ϕ 0 e y ) e jk ( x cos ϕ 0 + y sin ϕ 0 )
H r = e z H r e jk ( x cos β y sin β )
E r = Z 0 H r ( sin β e x + cos β e y ) e jk ( x cos β y sin β )
H r e jkx ' cos β = H i e jkx ' cos ϕ 0
J MTPO = 2 H i [ e x cos β ϕ 0 2 e y sin β ϕ 0 2 ] e jkx ' cos ϕ 0
J PO = e x 2 H i e jkx ' cos ϕ 0

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