Modified theory of physical optics approach to wedge diffraction problems

Yusuf Z. Umul

doi:10.1364/OPEX.13.000216

Modified theory of physical optics approach to wedge diffraction problems

Yusuf Z. Umul

Optics Express
Vol. 13,
Issue 1,
pp. 216-224
(2005)
•doi: 10.1364/OPEX.13.000216

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

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Abstract

The problem of diffraction from a perfectly conducting wedge is examined with the modified theory of physical optics (MTPO). The exact wedge diffraction coefficient is compared with the asymptotic edge waves of MTPO integral and related surface currents are evaluated. The scattered electric fields are expressed by using these current components. The total, incident and reflected diffracted fields are compared with the exact series solution of the wedge problem, numerically.

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References

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Publication

J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116–130 (1962).
[Crossref] [PubMed]
D. A. McNamara, C. W. I. Pistorius, and J. A. G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction (Artech House, Norwood, 1990).
G. L. James, Geometrical Theory of Diffraction for Electromagnetic Waves (IEE Peter Peregrinus Ltd., London, 1976).
A. Sommerfeld, Optics (Academic Press, New York, 1954).
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]
S. Lee and G. A. Deschamps, “A uniform asymptotic theory of electromagnetic diffraction by a curved wedge,” IEEE Trans. Antennas and Propagat. 24, 25–34 (1976).
[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]
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]
W.L. Stutzman and G. A. Thiele, Antenna Theory and Design (John Wiley & Sons, New York, 1988).
S. Y. Kim, J. W. Ra, and S. Y. Shin, “Diffraction by an arbitrary-angled dielectric wedge: Part I — Physical optics approximation,” IEEE Trans. Antennas and Propagat. 39, 1272–1281 (1991).
[Crossref]
S. Y. Kim, J. W. Ra, and S. Y. Shin, “Diffraction by an arbitrary-angled dielectric wedge: Part II — Correction to physical optics solution,” IEEE Trans. Antennas and Propagat. 39, 1282–1292 (1991).
[Crossref]
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]
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]
A. I. Papadopoulos and D. P. Chrissoulidis, “Electric-dipole radiation over a wedge with imperfectly conductive faces: a first-order physical-optics solution,” IEEE Trans. Antennas and Propagat. 47, 1649–1657 (1999).
[Crossref]
A. I. Papadopoulos and D. P. Chrissoulidis, “A corrected physical-optics solution to 3-d wedge diffraction,” Electromagnetics 20, 79–98 (2000).
[Crossref]
Y. Z. Umul, “Modified theory of physical optics,” Opt. Express 12, 4959–4972 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4959
[Crossref] [PubMed]
A. Ishimaru, Electromagnetic Wave Propagation, Radiation and Scattering (Prentice Hall, New Jersey, 1991).
A. K. Bhattacharyya, High-Frequency Electromagnetic Techniques (John Wiley & Sons, New York, 1995).

2004 (1)

Y. Z. Umul, “Modified theory of physical optics,” Opt. Express 12, 4959–4972 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4959
[Crossref] [PubMed]

2000 (1)

A. I. Papadopoulos and D. P. Chrissoulidis, “A corrected physical-optics solution to 3-d wedge diffraction,” Electromagnetics 20, 79–98 (2000).
[Crossref]

1999 (2)

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]

A. I. Papadopoulos and D. P. Chrissoulidis, “Electric-dipole radiation over a wedge with imperfectly conductive faces: a first-order physical-optics solution,” IEEE Trans. Antennas and Propagat. 47, 1649–1657 (1999).
[Crossref]

1991 (3)

S. Y. Kim, J. W. Ra, and S. Y. Shin, “Diffraction by an arbitrary-angled dielectric wedge: Part I — Physical optics approximation,” IEEE Trans. Antennas and Propagat. 39, 1272–1281 (1991).
[Crossref]

S. Y. Kim, J. W. Ra, and S. Y. Shin, “Diffraction by an arbitrary-angled dielectric wedge: Part II — Correction to physical optics solution,” IEEE Trans. Antennas and Propagat. 39, 1282–1292 (1991).
[Crossref]

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]

1987 (1)

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]

1977 (1)

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]

1976 (1)

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

1974 (1)

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]

1962 (1)

J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116–130 (1962).
[Crossref] [PubMed]

Balanis, C. A.

Bhattacharyya, A. K.

A. K. Bhattacharyya, High-Frequency Electromagnetic Techniques (John Wiley & Sons, New York, 1995).

Burge, R. E.

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]

Caroll, B. D.

Chrissoulidis, D. P.

A. I. Papadopoulos and D. P. Chrissoulidis, “A corrected physical-optics solution to 3-d wedge diffraction,” Electromagnetics 20, 79–98 (2000).
[Crossref]

Deschamps, G. A.

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

Fisher, N. E.

Griesser, T.

Hall, T. J.

Ishimaru, A.

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

James, G. L.

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

Keller, J. B.

J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116–130 (1962).
[Crossref] [PubMed]

Kim, S. Y.

Kouyoumjian, R. G.

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]

Lee, S.

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

Lee, S. W.

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]

Lester, G. A.

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, Norwood, 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, Norwood, 1990).

Oliver, C. J.

Papadopoulos, A. I.

A. I. Papadopoulos and D. P. Chrissoulidis, “A corrected physical-optics solution to 3-d wedge diffraction,” Electromagnetics 20, 79–98 (2000).
[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]

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, Norwood, 1990).

Ra, J. W.

Shin, S. Y.

Sommerfeld, A.

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

Stutzman, W.L.

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

Taket, N. D.

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]

Thiele, G. A.

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

Umul, Y. Z.

Y. Z. Umul, “Modified theory of physical optics,” Opt. Express 12, 4959–4972 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4959
[Crossref] [PubMed]

Yuan, X. C.

Electromagnetics (1)

A. I. Papadopoulos and D. P. Chrissoulidis, “A corrected physical-optics solution to 3-d wedge diffraction,” Electromagnetics 20, 79–98 (2000).
[Crossref]

IEEE Trans. Antennas and Propagat. (8)

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]

S. Lee and G. A. Deschamps, “A uniform asymptotic theory of electromagnetic diffraction by a curved wedge,” IEEE Trans. Antennas and 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 and Propagat. 25, 162–170 (1977).
[Crossref]

J. Opt. Soc. Am. (1)

J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116–130 (1962).
[Crossref] [PubMed]

Opt. Express (1)

Y. Z. Umul, “Modified theory of physical optics,” Opt. Express 12, 4959–4972 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4959
[Crossref] [PubMed]

Proc. IEEE (1)

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]

Other (6)

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

A. K. Bhattacharyya, High-Frequency Electromagnetic Techniques (John Wiley & Sons, New York, 1995).

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

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

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

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

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Fig. 1.

Perfectly conducting wedge geometry

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Fig. 2.

Incident diffracted fields at the perfectly conducting wedge (MTPO and exact solution)

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Fig. 3.

Reflected diffracted fields at the perfectly conducting wedge (MTPO and exact solution)

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Fig. 4.

Total diffracted fields at the perfectly conducting wedge (MTPO and exact solution)

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Fig. 5.

Reciprocity check of the total diffracted MTPO integral

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Fig. 6.

Total scattered fields from a perfectly conducting wedge (MTPO and exact solution)

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Equations (19)

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D_{w} = D_{wi} - D_{wr}

D_{wi} = \frac{A (n)}{\cos (\frac{π}{n}) - \cos (\frac{ϕ - ϕ_{0}}{n})}

D_{wr} = \frac{B (n)}{\cos (\frac{π}{n}) - \cos (\frac{ϕ + ϕ_{0}}{n})}

{\vec{E}}_{t} \approx {\vec{e}}_{z} \frac{{kE}_{i}}{\sqrt{2 π}} e^{j \frac{π}{4}} (\int_{x' = - \infty}^{0} e^{jkx' \cos ϕ_{0}} \frac{e^{- jk R_{1}}}{\sqrt{{kR}_{1}}} I_{1} (ϕ_{0}, β_{1}) dx' - \int_{x' = 0}^{\infty} e^{jkx' \cos ϕ_{0}} \frac{e^{- jk R_{2}}}{\sqrt{{kR}_{2}}} I_{2} (ϕ_{0}, β_{2}) dx')

{\vec{J}}_{S} = \frac{{2 E}_{i}}{Z_{0}} I_{2} (ϕ_{0}, β_{2}) e^{jkx' \cos ϕ_{0}} {\vec{e}}_{z}

{\vec{J}}_{A} = - \frac{{2 E}_{i}}{Z_{0}} I_{1} (ϕ_{0}, β_{1}) e^{jkx' \cos ϕ_{0}} {\vec{e}}_{z}

{\vec{E}}_{wd} = {\vec{e}}_{z} \frac{E_{i}}{\sqrt{2 π}} e^{- j \frac{π}{4}} \frac{[I_{1} (ϕ_{0}, ϕ - π) + I_{2} (ϕ_{0}, π - ϕ)]}{\cos ϕ + \cos ϕ_{0}} \frac{e^{- j k ρ}}{\sqrt{k ρ}}

E_{dz} = \frac{E_{i}}{\sqrt{2 π}} e^{- j \frac{π}{4}} (D_{wi} - D_{wr}) \frac{e^{- j k ρ}}{\sqrt{k ρ}}

I_{1} (ϕ_{0}, ϕ - π) = \frac{A (n) (\cos ϕ + \cos ϕ_{0})}{\cos \frac{π}{n} - \cos \frac{ϕ - ϕ_{0}}{n}}, I_{2} (ϕ_{0}, π - ϕ) = - \frac{B (n) (\cos ϕ + \cos ϕ_{0})}{\cos \frac{π}{n} - \cos \frac{ϕ - ϕ_{0}}{n}}

I_{1} (ϕ_{0}, β_{1}) = \frac{A (n) (\cos ϕ_{0} - \cos β_{1})}{\cos \frac{π}{n} - \cos \frac{π + β_{1} - ϕ_{0}}{n}}, I_{2} (ϕ_{0}, β_{2}) = - \frac{B (n) (\cos ϕ_{0} + \cos β_{2})}{\cos \frac{π}{n} - \cos \frac{π - β_{2} - ϕ_{0}}{n}}

E_{tz} = E_{iz} + E_{rz}

E_{iz} = \frac{k E_{i} A (n)}{\sqrt{2 π}} e^{j \frac{π}{4}} \int_{- \infty}^{0} \frac{\cos ϕ_{0} - \cos β_{1}}{\cos \frac{π}{n} - \cos \frac{π + β_{1} - ϕ_{0}}{n}} e^{j k x' \cos ϕ_{0}} \frac{e^{- jkR}}{\sqrt{kR}} dx'

E_{rz} = \frac{k E_{i} B (n)}{\sqrt{2 π}} e^{j \frac{π}{4}} \int_{0}^{\infty} \frac{\cos ϕ_{0} - \cos β_{2}}{\cos \frac{π}{n} - \cos \frac{π - β_{2} + ϕ_{0}}{n}} e^{j k x' \cos ϕ_{0}} \frac{e^{- jkR}}{\sqrt{kR}} dx'

β_{s} = \mp ϕ_{0}

f ({x'}_{s}) \approx \frac{k E_{i} Q (n)}{\sqrt{2 π}} e^{j \frac{π}{4}} lim_{β \to ϕ_{0}} \frac{\cos ϕ_{0} - \cos β}{\cos \frac{π}{n} - \cos \frac{π \mp (β - ϕ_{0})}{n}}

\mp \frac{E_{i} Q (n)}{\frac{1}{n} \sin \frac{π}{n}} e^{j k ρ \cos (ϕ \pm ϕ_{0})} = \mp E_{i} e^{j k ρ \cos (ϕ \pm ϕ_{0})}

E_{rz} = \frac{k E_{i} \sin (\frac{π}{n})}{n \sqrt{2 π}} e^{j \frac{π}{4}} \int_{0}^{\infty} \frac{\cos ϕ_{0} - \cos β_{2}}{\cos \frac{π}{n} - \cos \frac{π - β_{2} + ϕ_{0}}{n}} e^{j k x' \cos ϕ_{0}} \frac{e^{- jkR}}{\sqrt{kR}} dx'

E_{iz} = \frac{k E_{i} \sin (\frac{π}{n})}{n \sqrt{2 π}} e^{j \frac{π}{4}} \int_{- \infty}^{0} \frac{\cos ϕ_{0} - \cos β_{1}}{\cos \frac{π}{n} - \cos \frac{π - β_{1} + ϕ_{0}}{n}} e^{j k x' \cos ϕ_{0}} \frac{e^{- jkR}}{\sqrt{kR}} dx'

E_{z} = \frac{E_{i} 4 π}{ψ} \sum_{m = 1}^{\infty} e^{j ϑ_{m} \frac{π}{2}} J_{ϑ_{m}} (k ρ) \sin ϑ_{m} ϕ \sin ϑ_{m} ϕ_{0}

Abstract

References

2004 (1)

2000 (1)

1999 (2)

1991 (3)

1987 (1)

1977 (1)

1976 (1)

1974 (1)

1962 (1)

Balanis, C. A.

Bhattacharyya, A. K.

Burge, R. E.

Caroll, B. D.

Chrissoulidis, D. P.

Deschamps, G. A.

Fisher, N. E.

Griesser, T.

Hall, T. J.

Ishimaru, A.

James, G. L.

Keller, J. B.

Kim, S. Y.

Kouyoumjian, R. G.

Lee, S.

Lee, S. W.

Lester, G. A.

Malherbe, J. A. G.

McNamara, D. A.

Oliver, C. J.

Papadopoulos, A. I.

Pathak, P. B.

Pistorius, C. W. I.

Ra, J. W.

Shin, S. Y.

Sommerfeld, A.

Stutzman, W.L.

Taket, N. D.

Thiele, G. A.

Umul, Y. Z.

Yuan, X. C.

Electromagnetics (1)

IEEE Trans. Antennas and Propagat. (8)

J. Opt. Soc. Am. (1)

Opt. Express (1)

Proc. IEEE (1)

Other (6)

Cited By

Figures (6)

Equations (19)

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