Abstract

This study concerns the diffraction problem relevant to a plane wave normally incident with respect to a 90° wedge. A penetrable material with finite conductivity forms the structure. A high-frequency solution is here obtained by adopting a physical optics approximation for the equivalent electric and magnetic surface currents involved in the radiation integrals used to represent the fields scattered in the inner region of the wedge and the surrounding space. Uniform asymptotic evaluations of such integrals lead to closed form expressions for the diffraction coefficient in terms of the transition function of the uniform theory of diffraction and the Fresnel coefficients for the reflection and transmission mechanisms. No limitation exists on the loss tangent of the medium. Comparisons with numerical tools assess the effectiveness of the proposed solutions for the field diffracted in the inner and outer regions.

© 2013 Optical Society of America

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References

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  1. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116–130 (1962).
    [CrossRef]
  2. R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proc. IEEE 62, 1448–1461 (1974).
    [CrossRef]
  3. R. J. Luebbers, “Finite conductivity uniform GTD versus knife edge diffraction in prediction of propagation path loss,” IEEE Trans. Antennas Propag. 32, 70–76 (1984).
    [CrossRef]
  4. R. Tiberio, G. Pelosi, and G. Manara, “A uniform GTD formulation for diffraction by a wedge with impedance faces,” IEEE Trans. Antennas Propag. 33, 867–873 (1985).
    [CrossRef]
  5. R. G. Rojas, “Electromagnetic diffraction of an obliquely incident plane wave field by a wedge with impedance faces,” IEEE Trans. Antennas Propag. 36, 956–970 (1988).
    [CrossRef]
  6. G. Gennarelli and G. Riccio, “A UAPO-based model for propagation prediction in microcellular environments,” Prog. Electromagn. Res. B 17, 101–116 (2009).
    [CrossRef]
  7. S. Berntsen, “Diffraction of an electric polarized wave by a dielectric wedge,” SIAM J. Appl. Math. 43, 186–211 (1983).
    [CrossRef]
  8. A. D. Rawlins, “Diffraction by, or diffusion into, a penetrable wedge,” Proc. R. Soc. London Ser. A 455, 2655–2686 (1999).
    [CrossRef]
  9. E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
    [CrossRef]
  10. J. F. Rouviere, N. Douchin, and P. F. Combes, “Diffraction by lossy dielectric wedges using both heuristic UTD formulations and FDTD,” IEEE Trans. Antennas Propag. 47, 1702–1708 (1999).
    [CrossRef]
  11. P. Bernardi, R. Cicchetti, and O. Testa, “A three-dimensional UTD heuristic diffraction coefficient for complex penetrable wedges,” IEEE Trans. Antennas Propag. 50, 217–224 (2002).
    [CrossRef]
  12. 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 Propag. 39, 1272–1281 (1991).
    [CrossRef]
  13. C. H. Seo and J. W. Ra, “Plane wave scattering by a lossy dielectric wedge,” Microw. Opt. Technol. Lett. 25, 360–363 (2000).
    [CrossRef]
  14. M. A. Salem, A. H. Kamel, and A. V. Osipov, “Electromagnetic fields in presence of an infinite dielectric wedge,” Proc. R. Soc. London Ser. A 462, 2503–2522 (2006).
    [CrossRef]
  15. G. Gennarelli and G. Riccio, “A uniform asymptotic solution for diffraction by a right-angled dielectric wedge,” IEEE Trans. Antennas Propag. 59, 898–903 (2011).
    [CrossRef]
  16. G. Gennarelli and G. Riccio, “Plane-wave diffraction by an obtuse-angled dielectric wedge,” J. Opt. Soc. Am. A 28, 627–632 (2011).
    [CrossRef]
  17. V. Daniele and G. Lombardi, “The Wiener–Hopf solution of the isotropic penetrable wedge problem: diffraction and total field,” IEEE Trans. Antennas Propag. 59, 3797–3818 (2011).
    [CrossRef]
  18. F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).
  19. G. L. James, Geometrical Theory of Diffraction (Peter Peregrinus, 1986).
  20. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).
  21. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, 2000).
  22. S. D. Gedney, “An anisotropic perfectly matched layer absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
    [CrossRef]
  23. G. Gennarelli and G. Riccio, “Time domain diffraction by a right-angled penetrable wedge,” IEEE Trans. Antennas Propag. 60, 2829–2833 (2012).
    [CrossRef]
  24. G. Gennarelli and G. Riccio, “Obtuse-angled penetrable wedges: a time domain solution for the diffraction coefficients,” J. Electromagn. Waves Appl. 27, 2020–2028 (2013).
    [CrossRef]

2013 (1)

G. Gennarelli and G. Riccio, “Obtuse-angled penetrable wedges: a time domain solution for the diffraction coefficients,” J. Electromagn. Waves Appl. 27, 2020–2028 (2013).
[CrossRef]

2012 (1)

G. Gennarelli and G. Riccio, “Time domain diffraction by a right-angled penetrable wedge,” IEEE Trans. Antennas Propag. 60, 2829–2833 (2012).
[CrossRef]

2011 (3)

G. Gennarelli and G. Riccio, “A uniform asymptotic solution for diffraction by a right-angled dielectric wedge,” IEEE Trans. Antennas Propag. 59, 898–903 (2011).
[CrossRef]

G. Gennarelli and G. Riccio, “Plane-wave diffraction by an obtuse-angled dielectric wedge,” J. Opt. Soc. Am. A 28, 627–632 (2011).
[CrossRef]

V. Daniele and G. Lombardi, “The Wiener–Hopf solution of the isotropic penetrable wedge problem: diffraction and total field,” IEEE Trans. Antennas Propag. 59, 3797–3818 (2011).
[CrossRef]

2009 (1)

G. Gennarelli and G. Riccio, “A UAPO-based model for propagation prediction in microcellular environments,” Prog. Electromagn. Res. B 17, 101–116 (2009).
[CrossRef]

2006 (1)

M. A. Salem, A. H. Kamel, and A. V. Osipov, “Electromagnetic fields in presence of an infinite dielectric wedge,” Proc. R. Soc. London Ser. A 462, 2503–2522 (2006).
[CrossRef]

2002 (1)

P. Bernardi, R. Cicchetti, and O. Testa, “A three-dimensional UTD heuristic diffraction coefficient for complex penetrable wedges,” IEEE Trans. Antennas Propag. 50, 217–224 (2002).
[CrossRef]

2000 (1)

C. H. Seo and J. W. Ra, “Plane wave scattering by a lossy dielectric wedge,” Microw. Opt. Technol. Lett. 25, 360–363 (2000).
[CrossRef]

1999 (3)

A. D. Rawlins, “Diffraction by, or diffusion into, a penetrable wedge,” Proc. R. Soc. London Ser. A 455, 2655–2686 (1999).
[CrossRef]

E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
[CrossRef]

J. F. Rouviere, N. Douchin, and P. F. Combes, “Diffraction by lossy dielectric wedges using both heuristic UTD formulations and FDTD,” IEEE Trans. Antennas Propag. 47, 1702–1708 (1999).
[CrossRef]

1996 (1)

S. D. Gedney, “An anisotropic perfectly matched layer absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

1991 (1)

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 Propag. 39, 1272–1281 (1991).
[CrossRef]

1988 (1)

R. G. Rojas, “Electromagnetic diffraction of an obliquely incident plane wave field by a wedge with impedance faces,” IEEE Trans. Antennas Propag. 36, 956–970 (1988).
[CrossRef]

1985 (1)

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

1984 (1)

R. J. Luebbers, “Finite conductivity uniform GTD versus knife edge diffraction in prediction of propagation path loss,” IEEE Trans. Antennas Propag. 32, 70–76 (1984).
[CrossRef]

1983 (1)

S. Berntsen, “Diffraction of an electric polarized wave by a dielectric wedge,” SIAM J. Appl. Math. 43, 186–211 (1983).
[CrossRef]

1974 (1)

R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proc. IEEE 62, 1448–1461 (1974).
[CrossRef]

1962 (1)

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Bernardi, P.

P. Bernardi, R. Cicchetti, and O. Testa, “A three-dimensional UTD heuristic diffraction coefficient for complex penetrable wedges,” IEEE Trans. Antennas Propag. 50, 217–224 (2002).
[CrossRef]

Berntsen, S.

S. Berntsen, “Diffraction of an electric polarized wave by a dielectric wedge,” SIAM J. Appl. Math. 43, 186–211 (1983).
[CrossRef]

Boisvert, R. F.

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Burge, E.

E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
[CrossRef]

Carroll, B. D.

E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
[CrossRef]

Cicchetti, R.

P. Bernardi, R. Cicchetti, and O. Testa, “A three-dimensional UTD heuristic diffraction coefficient for complex penetrable wedges,” IEEE Trans. Antennas Propag. 50, 217–224 (2002).
[CrossRef]

Clark, C. W.

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Combes, P. F.

J. F. Rouviere, N. Douchin, and P. F. Combes, “Diffraction by lossy dielectric wedges using both heuristic UTD formulations and FDTD,” IEEE Trans. Antennas Propag. 47, 1702–1708 (1999).
[CrossRef]

Daniele, V.

V. Daniele and G. Lombardi, “The Wiener–Hopf solution of the isotropic penetrable wedge problem: diffraction and total field,” IEEE Trans. Antennas Propag. 59, 3797–3818 (2011).
[CrossRef]

Douchin, N.

J. F. Rouviere, N. Douchin, and P. F. Combes, “Diffraction by lossy dielectric wedges using both heuristic UTD formulations and FDTD,” IEEE Trans. Antennas Propag. 47, 1702–1708 (1999).
[CrossRef]

Fisher, N. E.

E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
[CrossRef]

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

Gennarelli, G.

G. Gennarelli and G. Riccio, “Obtuse-angled penetrable wedges: a time domain solution for the diffraction coefficients,” J. Electromagn. Waves Appl. 27, 2020–2028 (2013).
[CrossRef]

G. Gennarelli and G. Riccio, “Time domain diffraction by a right-angled penetrable wedge,” IEEE Trans. Antennas Propag. 60, 2829–2833 (2012).
[CrossRef]

G. Gennarelli and G. Riccio, “Plane-wave diffraction by an obtuse-angled dielectric wedge,” J. Opt. Soc. Am. A 28, 627–632 (2011).
[CrossRef]

G. Gennarelli and G. Riccio, “A uniform asymptotic solution for diffraction by a right-angled dielectric wedge,” IEEE Trans. Antennas Propag. 59, 898–903 (2011).
[CrossRef]

G. Gennarelli and G. Riccio, “A UAPO-based model for propagation prediction in microcellular environments,” Prog. Electromagn. Res. B 17, 101–116 (2009).
[CrossRef]

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, 2000).

Hall, T. J.

E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
[CrossRef]

James, G. L.

G. L. James, Geometrical Theory of Diffraction (Peter Peregrinus, 1986).

Kamel, A. H.

M. A. Salem, A. H. Kamel, and A. V. Osipov, “Electromagnetic fields in presence of an infinite dielectric wedge,” Proc. R. Soc. London Ser. A 462, 2503–2522 (2006).
[CrossRef]

Keller, J. B.

Kim, S. Y.

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 Propag. 39, 1272–1281 (1991).
[CrossRef]

Kouyoumjian, R. G.

R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proc. IEEE 62, 1448–1461 (1974).
[CrossRef]

Lester, G. A.

E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
[CrossRef]

Lombardi, G.

V. Daniele and G. Lombardi, “The Wiener–Hopf solution of the isotropic penetrable wedge problem: diffraction and total field,” IEEE Trans. Antennas Propag. 59, 3797–3818 (2011).
[CrossRef]

Lozier, D. W.

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Luebbers, R. J.

R. J. Luebbers, “Finite conductivity uniform GTD versus knife edge diffraction in prediction of propagation path loss,” IEEE Trans. Antennas Propag. 32, 70–76 (1984).
[CrossRef]

Manara, G.

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

Oliver, C. J.

E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
[CrossRef]

Olver, F. W. J.

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

Osipov, A. V.

M. A. Salem, A. H. Kamel, and A. V. Osipov, “Electromagnetic fields in presence of an infinite dielectric wedge,” Proc. R. Soc. London Ser. A 462, 2503–2522 (2006).
[CrossRef]

Pathak, P. H.

R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proc. IEEE 62, 1448–1461 (1974).
[CrossRef]

Pelosi, G.

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

Ra, J. W.

C. H. Seo and J. W. Ra, “Plane wave scattering by a lossy dielectric wedge,” Microw. Opt. Technol. Lett. 25, 360–363 (2000).
[CrossRef]

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 Propag. 39, 1272–1281 (1991).
[CrossRef]

Rawlins, A. D.

A. D. Rawlins, “Diffraction by, or diffusion into, a penetrable wedge,” Proc. R. Soc. London Ser. A 455, 2655–2686 (1999).
[CrossRef]

Riccio, G.

G. Gennarelli and G. Riccio, “Obtuse-angled penetrable wedges: a time domain solution for the diffraction coefficients,” J. Electromagn. Waves Appl. 27, 2020–2028 (2013).
[CrossRef]

G. Gennarelli and G. Riccio, “Time domain diffraction by a right-angled penetrable wedge,” IEEE Trans. Antennas Propag. 60, 2829–2833 (2012).
[CrossRef]

G. Gennarelli and G. Riccio, “Plane-wave diffraction by an obtuse-angled dielectric wedge,” J. Opt. Soc. Am. A 28, 627–632 (2011).
[CrossRef]

G. Gennarelli and G. Riccio, “A uniform asymptotic solution for diffraction by a right-angled dielectric wedge,” IEEE Trans. Antennas Propag. 59, 898–903 (2011).
[CrossRef]

G. Gennarelli and G. Riccio, “A UAPO-based model for propagation prediction in microcellular environments,” Prog. Electromagn. Res. B 17, 101–116 (2009).
[CrossRef]

Rojas, R. G.

R. G. Rojas, “Electromagnetic diffraction of an obliquely incident plane wave field by a wedge with impedance faces,” IEEE Trans. Antennas Propag. 36, 956–970 (1988).
[CrossRef]

Rouviere, J. F.

J. F. Rouviere, N. Douchin, and P. F. Combes, “Diffraction by lossy dielectric wedges using both heuristic UTD formulations and FDTD,” IEEE Trans. Antennas Propag. 47, 1702–1708 (1999).
[CrossRef]

Salem, M. A.

M. A. Salem, A. H. Kamel, and A. V. Osipov, “Electromagnetic fields in presence of an infinite dielectric wedge,” Proc. R. Soc. London Ser. A 462, 2503–2522 (2006).
[CrossRef]

Seo, C. H.

C. H. Seo and J. W. Ra, “Plane wave scattering by a lossy dielectric wedge,” Microw. Opt. Technol. Lett. 25, 360–363 (2000).
[CrossRef]

Shin, S. Y.

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 Propag. 39, 1272–1281 (1991).
[CrossRef]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, 2000).

Taket, N. D.

E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
[CrossRef]

Testa, O.

P. Bernardi, R. Cicchetti, and O. Testa, “A three-dimensional UTD heuristic diffraction coefficient for complex penetrable wedges,” IEEE Trans. Antennas Propag. 50, 217–224 (2002).
[CrossRef]

Tiberio, R.

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

Yuan, X.-C.

E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
[CrossRef]

IEEE Trans. Antennas Propag. (11)

R. J. Luebbers, “Finite conductivity uniform GTD versus knife edge diffraction in prediction of propagation path loss,” IEEE Trans. Antennas Propag. 32, 70–76 (1984).
[CrossRef]

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

R. G. Rojas, “Electromagnetic diffraction of an obliquely incident plane wave field by a wedge with impedance faces,” IEEE Trans. Antennas Propag. 36, 956–970 (1988).
[CrossRef]

E. Burge, X.-C. Yuan, B. D. Carroll, 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 Propag. 47, 1515–1527 (1999).
[CrossRef]

J. F. Rouviere, N. Douchin, and P. F. Combes, “Diffraction by lossy dielectric wedges using both heuristic UTD formulations and FDTD,” IEEE Trans. Antennas Propag. 47, 1702–1708 (1999).
[CrossRef]

P. Bernardi, R. Cicchetti, and O. Testa, “A three-dimensional UTD heuristic diffraction coefficient for complex penetrable wedges,” IEEE Trans. Antennas Propag. 50, 217–224 (2002).
[CrossRef]

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 Propag. 39, 1272–1281 (1991).
[CrossRef]

G. Gennarelli and G. Riccio, “A uniform asymptotic solution for diffraction by a right-angled dielectric wedge,” IEEE Trans. Antennas Propag. 59, 898–903 (2011).
[CrossRef]

V. Daniele and G. Lombardi, “The Wiener–Hopf solution of the isotropic penetrable wedge problem: diffraction and total field,” IEEE Trans. Antennas Propag. 59, 3797–3818 (2011).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996).
[CrossRef]

G. Gennarelli and G. Riccio, “Time domain diffraction by a right-angled penetrable wedge,” IEEE Trans. Antennas Propag. 60, 2829–2833 (2012).
[CrossRef]

J. Electromagn. Waves Appl. (1)

G. Gennarelli and G. Riccio, “Obtuse-angled penetrable wedges: a time domain solution for the diffraction coefficients,” J. Electromagn. Waves Appl. 27, 2020–2028 (2013).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Microw. Opt. Technol. Lett. (1)

C. H. Seo and J. W. Ra, “Plane wave scattering by a lossy dielectric wedge,” Microw. Opt. Technol. Lett. 25, 360–363 (2000).
[CrossRef]

Proc. IEEE (1)

R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proc. IEEE 62, 1448–1461 (1974).
[CrossRef]

Proc. R. Soc. London Ser. A (2)

M. A. Salem, A. H. Kamel, and A. V. Osipov, “Electromagnetic fields in presence of an infinite dielectric wedge,” Proc. R. Soc. London Ser. A 462, 2503–2522 (2006).
[CrossRef]

A. D. Rawlins, “Diffraction by, or diffusion into, a penetrable wedge,” Proc. R. Soc. London Ser. A 455, 2655–2686 (1999).
[CrossRef]

Prog. Electromagn. Res. B (1)

G. Gennarelli and G. Riccio, “A UAPO-based model for propagation prediction in microcellular environments,” Prog. Electromagn. Res. B 17, 101–116 (2009).
[CrossRef]

SIAM J. Appl. Math. (1)

S. Berntsen, “Diffraction of an electric polarized wave by a dielectric wedge,” SIAM J. Appl. Math. 43, 186–211 (1983).
[CrossRef]

Other (4)

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions (Cambridge University, 2010).

G. L. James, Geometrical Theory of Diffraction (Peter Peregrinus, 1986).

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method (Artech House, 2000).

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Figures (8)

Fig. 1.
Fig. 1.

Geometry of the problem.

Fig. 2.
Fig. 2.

GO and UAPO diffracted field contributions. Test case data: εr=5, tanδ=0.05, ϕ=150°, and ρ=5λ0.

Fig. 3.
Fig. 3.

Total field. Test case data: εr=5, tanδ=0.05, ϕ=150°, and ρ=5λ0.

Fig. 4.
Fig. 4.

UAPO diffracted fields. Test case data: εr=5, tanδ=0, ϕ=150°, and ρ=5λ0.

Fig. 5.
Fig. 5.

Test case data: εr=2, tanδ=0.01, ϕ=150°, and ρ=5λ0.

Fig. 6.
Fig. 6.

Test case data: εr=2, tanδ=0.1, ϕ=150°, and ρ=5λ0.

Fig. 7.
Fig. 7.

Test case data: εr=10, tanδ=0.01, ϕ=150°, and ρ=5λ0.

Fig. 8.
Fig. 8.

Test case data: εr=10, tanδ=0.1, ϕ=150°, and ρ=5λ0.

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

EsjkS0Sπ/2[(uRuR)(ζJs)+Jms×uR]G(r,r)dS,
Esjk[(usus)(ζJs0*)+Jms0*×us]S0ejφ0G(r,r)dS0+jk[(usus)(ζJsπ/2*)+Jmsπ/2*×us]Sπ/2ejφπ/2G(r,r)dSπ/2=E0s+Eπ/2s=[A0I0+Aπ/2Iπ/2]uz.
Ed=(A0I0d+Aπ/2Iπ/2d)uz=(D0+Dπ/2)E0iejkρρuz,
(A0)out=[(1R0)sinϕ(1+R0)sinϕ]E0i,
(I0)out=k040+ejk0xcosϕH0(2)(k0d)dx,
H0(2)(k0d)k0d12πk0dejπ/4ejk0d,
(I0)outk022πejπ/40+ejk0(xcosϕd)k0ddx.
(I0d)out=ejπ/422πk0Ft(k0ρ2(cosϕ+cosϕsinϕ)2)cosϕ+cosϕejk0ρρ,
(Aπ/2)out=[(1Rπ/2)cosϕ(1+Rπ/2)cosϕ]E0i,
(Iπ/2d)out=ejπ/422πk0Ft(k0ρ2(cos(3π/2ϕ)+cos(3π/2ϕ)sin(3π/2ϕ))2)cos(3π/2ϕ)+cos(3π/2ϕ)ejk0ρρ.
β̲=βe(sinψt^+cosψn^),
α̲=αen^,
βe={(k0sinθi)2+C2(αdsinγ+βdcosγ)2}1/2,
αe=C(αdcosγβdsinγ).
Cejγ={1(k0sinθi)2/kd2}1/2
βdαd=k0{εr2[(1+tan2δ)1/2±1]}1/2.
ζd(Js0*)in=E0iT0kdejk0xcosϕ(βe0cosψ0jαe0)uz,
(Jms0*)in=E0iT0ejk0xcosϕux
(A0)in=E0iT0[1kd(βe0cosψ0jαe0)sinϕ],
(I0d)in=(kd/k0)ejπ/422πkdFt(βdρ2((βd/k0)cosϕ+cosϕ(βd/k0)2cos2ϕ)2)(βd/k0)cosϕ+cosϕejkdρρ.
ζd(Jsπ/2*)in=E0iTπ/2kdejk0ysinϕ(βeπ/2cosψπ/2jαeπ/2)uz,
(Jmsπ/2*)in=E0iTπ/2ejk0ysinϕuy.
(Aπ/2)in=E0iTπ/2[1kd(βeπ/2cosψπ/2jαeπ/2)+cosϕ],
(Iπ/2d)in=(kd/k0)ejπ/422πkdFt(βdρ2((βd/k0)sinϕ+sinϕ(βd/k0)2sin2ϕ)2)(βd/k0)sinϕ+sinϕejkdρρ.

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