Abstract

Diffraction of electromagnetic waves by a planar array of perfectly conducting strips is analyzed by a simple numerical technique based on mode expansion and point matching. Results are compared against other numerical results available in the literature to demonstrate the versatility and the accuracy of the proposed method. Further numerical results are presented which show the usefulness of these structures as shielding grids, reflectionless metallic supports, polarizers, and diffractors in obstructured communication links.

© 1978 Optical Society of America

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References

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  1. G. Baldwin and A. Heins, “On scattering of a plane wave by an infinite plane grating,” Math. Scand. 2, 103–118, (1954).
  2. Z. S. Agronovich, V. A. Marchenko, and V. P. Shestopalov, “The Diffraction of Electromagnetic Waves from Plane Metallic Lattices,” Soviet Phys.-Tech. Phys. 7, 277–286, (1962).
  3. A. I. Adonina and V. P. Shestopalov, “Diffraction of electromagnetic waves obliquely incident on a plane metallic grating with a dielectric layer,” Soviet Phys.-Tech. Phys. 8, 479–486, (1963).
  4. A. R. Neureuther and K. Zaki, “Numerical solutions of electromagnetic boundary value problems by means of the asymptotic anticipation method,” Radio Sci. 3, 1158–1163 (1968).
  5. H. A. Kalhor and A. Armand, “Scattering of Waves by Gratings of Conducting Cylinders,” Proc. IEE 122, 245–248 (1975).
  6. J. T. Mayhan and L. L. Tsai, “Reflection and Transmission Characteristic of thin Periodic Interfaces,” IEEE Trans. Antennas Propag. AP-24, 449–456, (1976).
    [CrossRef]

1976 (1)

J. T. Mayhan and L. L. Tsai, “Reflection and Transmission Characteristic of thin Periodic Interfaces,” IEEE Trans. Antennas Propag. AP-24, 449–456, (1976).
[CrossRef]

1975 (1)

H. A. Kalhor and A. Armand, “Scattering of Waves by Gratings of Conducting Cylinders,” Proc. IEE 122, 245–248 (1975).

1968 (1)

A. R. Neureuther and K. Zaki, “Numerical solutions of electromagnetic boundary value problems by means of the asymptotic anticipation method,” Radio Sci. 3, 1158–1163 (1968).

1963 (1)

A. I. Adonina and V. P. Shestopalov, “Diffraction of electromagnetic waves obliquely incident on a plane metallic grating with a dielectric layer,” Soviet Phys.-Tech. Phys. 8, 479–486, (1963).

1962 (1)

Z. S. Agronovich, V. A. Marchenko, and V. P. Shestopalov, “The Diffraction of Electromagnetic Waves from Plane Metallic Lattices,” Soviet Phys.-Tech. Phys. 7, 277–286, (1962).

1954 (1)

G. Baldwin and A. Heins, “On scattering of a plane wave by an infinite plane grating,” Math. Scand. 2, 103–118, (1954).

Adonina, A. I.

A. I. Adonina and V. P. Shestopalov, “Diffraction of electromagnetic waves obliquely incident on a plane metallic grating with a dielectric layer,” Soviet Phys.-Tech. Phys. 8, 479–486, (1963).

Agronovich, Z. S.

Z. S. Agronovich, V. A. Marchenko, and V. P. Shestopalov, “The Diffraction of Electromagnetic Waves from Plane Metallic Lattices,” Soviet Phys.-Tech. Phys. 7, 277–286, (1962).

Armand, A.

H. A. Kalhor and A. Armand, “Scattering of Waves by Gratings of Conducting Cylinders,” Proc. IEE 122, 245–248 (1975).

Baldwin, G.

G. Baldwin and A. Heins, “On scattering of a plane wave by an infinite plane grating,” Math. Scand. 2, 103–118, (1954).

Heins, A.

G. Baldwin and A. Heins, “On scattering of a plane wave by an infinite plane grating,” Math. Scand. 2, 103–118, (1954).

Kalhor, H. A.

H. A. Kalhor and A. Armand, “Scattering of Waves by Gratings of Conducting Cylinders,” Proc. IEE 122, 245–248 (1975).

Marchenko, V. A.

Z. S. Agronovich, V. A. Marchenko, and V. P. Shestopalov, “The Diffraction of Electromagnetic Waves from Plane Metallic Lattices,” Soviet Phys.-Tech. Phys. 7, 277–286, (1962).

Mayhan, J. T.

J. T. Mayhan and L. L. Tsai, “Reflection and Transmission Characteristic of thin Periodic Interfaces,” IEEE Trans. Antennas Propag. AP-24, 449–456, (1976).
[CrossRef]

Neureuther, A. R.

A. R. Neureuther and K. Zaki, “Numerical solutions of electromagnetic boundary value problems by means of the asymptotic anticipation method,” Radio Sci. 3, 1158–1163 (1968).

Shestopalov, V. P.

A. I. Adonina and V. P. Shestopalov, “Diffraction of electromagnetic waves obliquely incident on a plane metallic grating with a dielectric layer,” Soviet Phys.-Tech. Phys. 8, 479–486, (1963).

Z. S. Agronovich, V. A. Marchenko, and V. P. Shestopalov, “The Diffraction of Electromagnetic Waves from Plane Metallic Lattices,” Soviet Phys.-Tech. Phys. 7, 277–286, (1962).

Tsai, L. L.

J. T. Mayhan and L. L. Tsai, “Reflection and Transmission Characteristic of thin Periodic Interfaces,” IEEE Trans. Antennas Propag. AP-24, 449–456, (1976).
[CrossRef]

Zaki, K.

A. R. Neureuther and K. Zaki, “Numerical solutions of electromagnetic boundary value problems by means of the asymptotic anticipation method,” Radio Sci. 3, 1158–1163 (1968).

IEEE Trans. Antennas Propag. (1)

J. T. Mayhan and L. L. Tsai, “Reflection and Transmission Characteristic of thin Periodic Interfaces,” IEEE Trans. Antennas Propag. AP-24, 449–456, (1976).
[CrossRef]

Math. Scand. (1)

G. Baldwin and A. Heins, “On scattering of a plane wave by an infinite plane grating,” Math. Scand. 2, 103–118, (1954).

Proc. IEE (1)

H. A. Kalhor and A. Armand, “Scattering of Waves by Gratings of Conducting Cylinders,” Proc. IEE 122, 245–248 (1975).

Radio Sci. (1)

A. R. Neureuther and K. Zaki, “Numerical solutions of electromagnetic boundary value problems by means of the asymptotic anticipation method,” Radio Sci. 3, 1158–1163 (1968).

Soviet Phys.-Tech. Phys. (2)

Z. S. Agronovich, V. A. Marchenko, and V. P. Shestopalov, “The Diffraction of Electromagnetic Waves from Plane Metallic Lattices,” Soviet Phys.-Tech. Phys. 7, 277–286, (1962).

A. I. Adonina and V. P. Shestopalov, “Diffraction of electromagnetic waves obliquely incident on a plane metallic grating with a dielectric layer,” Soviet Phys.-Tech. Phys. 8, 479–486, (1963).

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Figures (7)

FIG. 1
FIG. 1

Arrangement of the planar array of strips and the incident wave.

FIG. 2
FIG. 2

Variation of the relative transmitted power of various orders with grating period at normal incidence for a self-complementary grating.

FIG. 3
FIG. 3

Variation of the amplitude of the transmitted wave of zero order against the grating period at an incidence angle of 45° for spacings specified by cos (πa/d) = 0.8, cos (πa/d) = 0, and cos (πa/d) = −0.8.

FIG. 4
FIG. 4

Variation of the relative transmitted power of various orders against the angle of incidence for a grating having parameters d = 1.6λ and a = 1.0λ in the E-polarized case.

FIG. 5
FIG. 5

Variation of the relative transmitted power of various orders against the angle of incidence for a grating with parameters d = 1.6λ and a = 1.0λ in the H-polarized case.

FIG. 6
FIG. 6

Variation of the relative transmitted power of various orders against the angle of incidence for a grating with parameters d = 1.6λ and a = 0.6λ in the E-polarized case.

FIG. 7
FIG. 7

Variation of the relative transmitted power of various orders against the angle of incidence for a grating with parameters d = 1.6λ and a = 0.6λ in the H-polarized case.

Equations (15)

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E ¯ i = ŷ E 0 exp ( - j β 0 x + j γ 0 z ) ,
E ¯ r = ŷ n = - N N A n exp ( - j β n x - j γ n z ) ,
β n = β 0 + 2 n π / d , γ n 2 = k 2 - β n 2 ,
E t = ŷ n = - N N B n exp ( - j β n x + j γ n z )
E 0 exp ( - j β 0 x ) + n = - N N A n exp ( - j β n x ) = n = - N N B n exp ( - j β n x )             0 < x a
E 0 exp ( - j β 0 x ) + n = - N N A n exp ( - j β n x ) = 0 , a < x d
n = - N N B n exp ( - j β n x ) = 0 , a < x d
j γ 0 exp ( - j β 0 x ) + n = - N N - j γ n A n exp ( - j β n x ) = n = - N N j γ n B n exp ( - j β n x ) , 0 < x a
H ¯ i = ŷ H 0 exp ( - j β 0 x + j γ 0 z ) .
H ¯ r = ŷ n = - N N A n exp ( - j β n x - j γ n z ) .
H ¯ t = ŷ n = - N N B n exp ( - j β n x + j γ n z )
H 0 exp ( - j β 0 x ) + n = - N N A n exp ( - j β n x ) = n = - N N B n exp ( - j β n x ) , 0 < x a .
j γ 0 H 0 exp ( - j β 0 x ) - n = - N N j γ n A n exp ( - j β n x ) = n = - N N j γ n B n exp ( - j β n x ) , 0 < x a
j γ 0 H 0 exp ( - j β 0 x ) - n = - N N j γ n A n exp ( - j β n x ) = 0 , a < x d
n = - N N j γ n B n exp ( - j β n x ) = 0 , a < x d