Abstract

A uniform heuristic high-frequency solution is obtained for plane-wave scattering from edges in periodic planar surfaces. The case of a wedge with periodic impedance boundary conditions on its faces and that of a truncated strip grating are analyzed. Numerical results are presented and compared with reference solutions to validate the heuristic expressions proposed.

© 1996 Optical Society of America

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References

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  1. G. Pelosi, G. Manara, J. M. L. Bernard, A. Freni, “Diffraction by a planar junction of a perfectly conducting and a periodically loaded impedance surface,”IEEE Trans. Antennas Propag. 41, 1516–1522 (1993).
    [CrossRef]
  2. R. G. Kouyoumjian, 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. W. D. Burnside, K. W. Burgener, “High frequency scattering by thin lossless dielectric slab,”IEEE Trans. Antennas Propag. 31, 104–110 (1983).
    [CrossRef]
  4. R. J. Luebbers, “A heuristic UTD slope diffraction coefficient for rough lossy wedge,”IEEE Trans. Antennas Propag. 37, 206–211 (1989).
    [CrossRef]
  5. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
    [CrossRef]
  6. R. G. Kouyoumjian, G. Manara, P. Nepa, B. J. E. Taute, “The diffraction of an inhomogeneous plane wave by a wedge,” Radio Sci. (to be published).
  7. G. D. Maliuzhinets, “Excitation, reflection and emission of surface waves from a wedge with given face impedances,” Sov. Phys. Dokl. 3, 752–755 (1958).
  8. G. Manara, R. Tiberio, G. Pelosi, P. H. Pathak, “High-frequency scattering from a wedge with impedance faces illuminated by a line source. Part II. Surface waves,”IEEE Trans. Antennas Propag. 41, 877–883 (1993).
    [CrossRef]
  9. H. A. Kalhor, “Electromagnetic scattering by a dielectric slab loaded with a periodic array of strips over a ground plane,”IEEE Trans. Antennas Propag. 36, 147–151 (1988).
    [CrossRef]
  10. T. Delort, D. Maystre, “Finite-element method for gratings,” J. Opt. Soc. Am. A 10, 2592–2601 (1993).
    [CrossRef]
  11. R. Cecchini, R. Coccioli, G. Pelosi, “Periodic3: a software package for the analysis of artificially anisotropic surfaces,” IEEE Antennas Propag. Mag. 37, 83–86 (1995).
    [CrossRef]
  12. L. Carin, L. B. Felsen, “Time harmonic and transient scattering by finite periodic flat strip array: hybrid (ray)–(Floquet mode)–(MoM) algorithm,”IEEE Trans. Antennas Propag. 41, 412–421 (1993).
    [CrossRef]
  13. G. Pelosi, G. Manara, A. Monorchio, R. Coccioli, “A perturbative approach to the scattering from a perfectly conducting wedge with a crack or gap in one of its faces,” Microwave Opt. Technol. Lett. 7, 667–670 (1994).
    [CrossRef]

1995 (1)

R. Cecchini, R. Coccioli, G. Pelosi, “Periodic3: a software package for the analysis of artificially anisotropic surfaces,” IEEE Antennas Propag. Mag. 37, 83–86 (1995).
[CrossRef]

1994 (1)

G. Pelosi, G. Manara, A. Monorchio, R. Coccioli, “A perturbative approach to the scattering from a perfectly conducting wedge with a crack or gap in one of its faces,” Microwave Opt. Technol. Lett. 7, 667–670 (1994).
[CrossRef]

1993 (4)

L. Carin, L. B. Felsen, “Time harmonic and transient scattering by finite periodic flat strip array: hybrid (ray)–(Floquet mode)–(MoM) algorithm,”IEEE Trans. Antennas Propag. 41, 412–421 (1993).
[CrossRef]

G. Pelosi, G. Manara, J. M. L. Bernard, A. Freni, “Diffraction by a planar junction of a perfectly conducting and a periodically loaded impedance surface,”IEEE Trans. Antennas Propag. 41, 1516–1522 (1993).
[CrossRef]

G. Manara, R. Tiberio, G. Pelosi, P. H. Pathak, “High-frequency scattering from a wedge with impedance faces illuminated by a line source. Part II. Surface waves,”IEEE Trans. Antennas Propag. 41, 877–883 (1993).
[CrossRef]

T. Delort, D. Maystre, “Finite-element method for gratings,” J. Opt. Soc. Am. A 10, 2592–2601 (1993).
[CrossRef]

1989 (1)

R. J. Luebbers, “A heuristic UTD slope diffraction coefficient for rough lossy wedge,”IEEE Trans. Antennas Propag. 37, 206–211 (1989).
[CrossRef]

1988 (1)

H. A. Kalhor, “Electromagnetic scattering by a dielectric slab loaded with a periodic array of strips over a ground plane,”IEEE Trans. Antennas Propag. 36, 147–151 (1988).
[CrossRef]

1983 (1)

W. D. Burnside, K. W. Burgener, “High frequency scattering by thin lossless dielectric slab,”IEEE Trans. Antennas Propag. 31, 104–110 (1983).
[CrossRef]

1974 (1)

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

1958 (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).

Bernard, J. M. L.

G. Pelosi, G. Manara, J. M. L. Bernard, A. Freni, “Diffraction by a planar junction of a perfectly conducting and a periodically loaded impedance surface,”IEEE Trans. Antennas Propag. 41, 1516–1522 (1993).
[CrossRef]

Burgener, K. W.

W. D. Burnside, K. W. Burgener, “High frequency scattering by thin lossless dielectric slab,”IEEE Trans. Antennas Propag. 31, 104–110 (1983).
[CrossRef]

Burnside, W. D.

W. D. Burnside, K. W. Burgener, “High frequency scattering by thin lossless dielectric slab,”IEEE Trans. Antennas Propag. 31, 104–110 (1983).
[CrossRef]

Carin, L.

L. Carin, L. B. Felsen, “Time harmonic and transient scattering by finite periodic flat strip array: hybrid (ray)–(Floquet mode)–(MoM) algorithm,”IEEE Trans. Antennas Propag. 41, 412–421 (1993).
[CrossRef]

Cecchini, R.

R. Cecchini, R. Coccioli, G. Pelosi, “Periodic3: a software package for the analysis of artificially anisotropic surfaces,” IEEE Antennas Propag. Mag. 37, 83–86 (1995).
[CrossRef]

Coccioli, R.

R. Cecchini, R. Coccioli, G. Pelosi, “Periodic3: a software package for the analysis of artificially anisotropic surfaces,” IEEE Antennas Propag. Mag. 37, 83–86 (1995).
[CrossRef]

G. Pelosi, G. Manara, A. Monorchio, R. Coccioli, “A perturbative approach to the scattering from a perfectly conducting wedge with a crack or gap in one of its faces,” Microwave Opt. Technol. Lett. 7, 667–670 (1994).
[CrossRef]

Delort, T.

Felsen, L. B.

L. Carin, L. B. Felsen, “Time harmonic and transient scattering by finite periodic flat strip array: hybrid (ray)–(Floquet mode)–(MoM) algorithm,”IEEE Trans. Antennas Propag. 41, 412–421 (1993).
[CrossRef]

Freni, A.

G. Pelosi, G. Manara, J. M. L. Bernard, A. Freni, “Diffraction by a planar junction of a perfectly conducting and a periodically loaded impedance surface,”IEEE Trans. Antennas Propag. 41, 1516–1522 (1993).
[CrossRef]

Kalhor, H. A.

H. A. Kalhor, “Electromagnetic scattering by a dielectric slab loaded with a periodic array of strips over a ground plane,”IEEE Trans. Antennas Propag. 36, 147–151 (1988).
[CrossRef]

Kouyoumjian, R. G.

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

R. G. Kouyoumjian, G. Manara, P. Nepa, B. J. E. Taute, “The diffraction of an inhomogeneous plane wave by a wedge,” Radio Sci. (to be published).

Luebbers, R. J.

R. J. Luebbers, “A heuristic UTD slope diffraction coefficient for rough lossy wedge,”IEEE Trans. Antennas Propag. 37, 206–211 (1989).
[CrossRef]

Maliuzhinets, G. D.

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

Manara, G.

G. Pelosi, G. Manara, A. Monorchio, R. Coccioli, “A perturbative approach to the scattering from a perfectly conducting wedge with a crack or gap in one of its faces,” Microwave Opt. Technol. Lett. 7, 667–670 (1994).
[CrossRef]

G. Manara, R. Tiberio, G. Pelosi, P. H. Pathak, “High-frequency scattering from a wedge with impedance faces illuminated by a line source. Part II. Surface waves,”IEEE Trans. Antennas Propag. 41, 877–883 (1993).
[CrossRef]

G. Pelosi, G. Manara, J. M. L. Bernard, A. Freni, “Diffraction by a planar junction of a perfectly conducting and a periodically loaded impedance surface,”IEEE Trans. Antennas Propag. 41, 1516–1522 (1993).
[CrossRef]

R. G. Kouyoumjian, G. Manara, P. Nepa, B. J. E. Taute, “The diffraction of an inhomogeneous plane wave by a wedge,” Radio Sci. (to be published).

Maystre, D.

Monorchio, A.

G. Pelosi, G. Manara, A. Monorchio, R. Coccioli, “A perturbative approach to the scattering from a perfectly conducting wedge with a crack or gap in one of its faces,” Microwave Opt. Technol. Lett. 7, 667–670 (1994).
[CrossRef]

Nepa, P.

R. G. Kouyoumjian, G. Manara, P. Nepa, B. J. E. Taute, “The diffraction of an inhomogeneous plane wave by a wedge,” Radio Sci. (to be published).

Pathak, P. H.

G. Manara, R. Tiberio, G. Pelosi, P. H. Pathak, “High-frequency scattering from a wedge with impedance faces illuminated by a line source. Part II. Surface waves,”IEEE Trans. Antennas Propag. 41, 877–883 (1993).
[CrossRef]

R. G. Kouyoumjian, 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. Cecchini, R. Coccioli, G. Pelosi, “Periodic3: a software package for the analysis of artificially anisotropic surfaces,” IEEE Antennas Propag. Mag. 37, 83–86 (1995).
[CrossRef]

G. Pelosi, G. Manara, A. Monorchio, R. Coccioli, “A perturbative approach to the scattering from a perfectly conducting wedge with a crack or gap in one of its faces,” Microwave Opt. Technol. Lett. 7, 667–670 (1994).
[CrossRef]

G. Pelosi, G. Manara, J. M. L. Bernard, A. Freni, “Diffraction by a planar junction of a perfectly conducting and a periodically loaded impedance surface,”IEEE Trans. Antennas Propag. 41, 1516–1522 (1993).
[CrossRef]

G. Manara, R. Tiberio, G. Pelosi, P. H. Pathak, “High-frequency scattering from a wedge with impedance faces illuminated by a line source. Part II. Surface waves,”IEEE Trans. Antennas Propag. 41, 877–883 (1993).
[CrossRef]

Petit, R.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

Taute, B. J. E.

R. G. Kouyoumjian, G. Manara, P. Nepa, B. J. E. Taute, “The diffraction of an inhomogeneous plane wave by a wedge,” Radio Sci. (to be published).

Tiberio, R.

G. Manara, R. Tiberio, G. Pelosi, P. H. Pathak, “High-frequency scattering from a wedge with impedance faces illuminated by a line source. Part II. Surface waves,”IEEE Trans. Antennas Propag. 41, 877–883 (1993).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

R. Cecchini, R. Coccioli, G. Pelosi, “Periodic3: a software package for the analysis of artificially anisotropic surfaces,” IEEE Antennas Propag. Mag. 37, 83–86 (1995).
[CrossRef]

IEEE Trans. Antennas Propag. (6)

L. Carin, L. B. Felsen, “Time harmonic and transient scattering by finite periodic flat strip array: hybrid (ray)–(Floquet mode)–(MoM) algorithm,”IEEE Trans. Antennas Propag. 41, 412–421 (1993).
[CrossRef]

W. D. Burnside, K. W. Burgener, “High frequency scattering by thin lossless dielectric slab,”IEEE Trans. Antennas Propag. 31, 104–110 (1983).
[CrossRef]

R. J. Luebbers, “A heuristic UTD slope diffraction coefficient for rough lossy wedge,”IEEE Trans. Antennas Propag. 37, 206–211 (1989).
[CrossRef]

G. Pelosi, G. Manara, J. M. L. Bernard, A. Freni, “Diffraction by a planar junction of a perfectly conducting and a periodically loaded impedance surface,”IEEE Trans. Antennas Propag. 41, 1516–1522 (1993).
[CrossRef]

G. Manara, R. Tiberio, G. Pelosi, P. H. Pathak, “High-frequency scattering from a wedge with impedance faces illuminated by a line source. Part II. Surface waves,”IEEE Trans. Antennas Propag. 41, 877–883 (1993).
[CrossRef]

H. A. Kalhor, “Electromagnetic scattering by a dielectric slab loaded with a periodic array of strips over a ground plane,”IEEE Trans. Antennas Propag. 36, 147–151 (1988).
[CrossRef]

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

Microwave Opt. Technol. Lett. (1)

G. Pelosi, G. Manara, A. Monorchio, R. Coccioli, “A perturbative approach to the scattering from a perfectly conducting wedge with a crack or gap in one of its faces,” Microwave Opt. Technol. Lett. 7, 667–670 (1994).
[CrossRef]

Proc. IEEE (1)

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

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).

Other (2)

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

R. G. Kouyoumjian, G. Manara, P. Nepa, B. J. E. Taute, “The diffraction of an inhomogeneous plane wave by a wedge,” Radio Sci. (to be published).

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Figures (6)

Fig. 1
Fig. 1

Geometry for the scattering at the edge of a wedge with periodic impedance BC’s. The face ϕ = is perfectly conducting.

Fig. 2
Fig. 2

Integration contours on the complex a plane.

Fig. 3
Fig. 3

Amplitude of the magnetic field scattered by a planar junction between a periodically loaded and a perfectly conducting surface (TM case): heuristic solution (M = 15, solid curve); perturbative solution (dashed curve). The electrical and the geometrical parameters are n = 1, a = 0.2λ, b = λ, = 10, ϕ = 45°, Z0/ζ0 = 0.5; p.e.c., perfect electric conductor.

Fig. 4
Fig. 4

(a) Real and (b) imaginary parts of the magnetic field scattered by a perfectly conducting wedge (n = 1.5) with an impedance strip (Z0/ζ0 = −j0.5) on its ϕ = 0 face (TM case): heuristic solution (M =50, solid curve); perturbative solution (dashed curve). The geometrical parameters are a = 0.1λ, b = 15λ, ρ = 5λ, ϕ = 135°, d = 0.5λ. The incident magnetic field has a unit amplitude and a zero phase at the edge.

Fig. 5
Fig. 5

Amplitude of the field scattered from an array of five strips of width λ and spacing 2λ/3 (a = 2λ/3, b = 5λ/3), plotted as a function of the observation angle at a distance 33.33λ from the array center: heuristic solution (M = 10, solid curve); exact solution (diamonds, moment-method results from Ref. 13). The angle of incidence is ϕ = 45°; (a) TM-polarization case, (b) TE-polarization case. The incident plane wave has a unit-amplitude (a) magnetic or (b) electric field.

Fig. 6
Fig. 6

Amplitude of the total (thin curve) and scattered (thick curve) electric fields in the presence of an array of five strips of width λ and spacing 2λ/3 (a = 2λ/3, b = 5λ/3), plotted as a function of the observation angle (0° ≤ ϕ ≤ 360°) at a distance of 33.33λ from the array center (TE-polarization case, M = 15). The angle of incidence is ϕ = 45°. The incident plane wave has a unit-amplitude electric field.

Equations (22)

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Z 0 ( ρ + l b ) = Z 0 ( ρ ) ,
Z 0 ( ρ ) = Z 0 , 0 ρ a ,
Z 0 ( ρ ) = 0 , a ρ b .
[ 1 ρ ϕ j k sin θ TM , TE ( ρ ) ] u ( ρ , ϕ ) = 0 ,
1 ρ u ( ρ , ϕ ) ϕ = 0
u ( ρ , ϕ ) = 0
sin θ TM ( ρ ) = Z 0 ( ρ ) ζ 0 , sin θ TE ( ρ ) = ζ 0 Z 0 ( ρ ) ,
u ( ρ , ϕ ) = 1 2 π j γ f ( α + ϕ n π / 2 ) exp ( j k ρ cos α ) d α ,
u r ( ρ , ϕ ) = Res [ f ( α + ϕ n π / 2 ) exp ( j k ρ cos α ) ; α = ϕ + ϕ ] = Γ ( Z 0 , ϕ ) exp [ ( j k ρ cos ( ϕ + ϕ ) ] × U [ π ( ϕ + ϕ ) ] .
u plane ( ρ , ϕ ) = u i ( ρ , ϕ ) + m = Res [ f ( α + ϕ n π / 2 ) × exp ( j k ρ cos α ; ) α = α m + ϕ ] = u i ( ρ , ϕ ) + m = + A m × exp [ j k ρ cos ( α m + ϕ ) ] × U { π ( α m + ϕ ) + g d [ ( α m + ϕ ) ] } ,
cos α m = cos ϕ + m λ b ,
u d ( ρ , ϕ ) = D ( ϕ , ϕ ; ρ ) u i ( Q ) exp ( j k ρ ) ρ ,
D ( ϕ , ϕ ; ρ ) = d i , 0 ( ϕ , ϕ ; ρ ) + d i , n ( ϕ , ϕ ; ρ ) + m = M + M d m r , 0 ( α m , ϕ ; ρ ) + d r , n ( ϕ , ϕ ; ρ ) ,
d i , 0 ( ϕ , ϕ ; ρ ) = exp ( j π / 4 ) 2 n 2 π k cot ( π β 2 n ) F [ k ρ a ( β ) ] ,
d i , n ( ϕ , ϕ ; ρ ) = exp ( j π / 4 ) 2 n 2 π k cot ( π + β 2 n ) F [ k ρ a + ( β ) ] ,
d m r , 0 ( α m , ϕ ; ρ ) = exp ( j π / 4 ) 2 n 2 π k cot ( π β m + 2 n ) × F [ k ρ a ( β m + ) ] A m ,
d r , n ( ϕ , ϕ ; ρ ) = exp ( j π / 4 ) 2 n 2 π k cot ( π + β + 2 n ) F [ k ρ a + ( β + ) ] .
a = 2 cos 2 ( 2 n π N β 2 ) ,
D ( ϕ , ϕ ; ρ ) = d i ( ϕ , ϕ ; ρ ) + m = M + M [ d m r ( α m , ϕ ; ρ ) + d m t ( α m , ϕ ; ρ ) ] .
d i ( ϕ , ϕ ; ρ ) = exp ( j π / 4 ) 2 2 π k F [ k ρ a ( ϕ ϕ ) ] cos ( ϕ ϕ 2 ) ,
d m r ( α m , ϕ ; ρ ) = exp ( j π / 4 ) 2 2 π k F [ k ρ a ( ϕ + α m ) ] cos ( ϕ + α m 2 ) A m ,
d m t ( α m , ϕ ; ρ ) = exp ( j π / 4 ) 2 2 π k F [ k ρ a ( ϕ α m ) ] cos ( ϕ α m 2 ) B m .

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