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Reflection at arbitrary incidence from a parallel wire grid

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Summary

A solution is outlined for the problem of a plane wave, incident obliquely, with arbitrary polarization, on a planar grid. It is assumed that the wires composing the grid are of homogeneous material and that their diameter is small compared with the separation. The general result when specialized to parallel polarization agrees with published results.

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Abbreviations

a :

radius of the wires

σ :

conductivity of wires

ɛ 1 :

dielectric constant of wires

μ 1 :

permeability of wires

d :

spacing between adjacent wires

ɛ 0 :

dielectric constant of free space

μ 0 :

permeability of free space

ω :

angular frequency

Ep :

the electric field of the incident wave

A:

vector magnitude of electric field of incident wave

I 0 :

magnitude of the currents on the wires

Es :

the electric field of the scattered or reflected wave

E′ z :

the parallel electric field of the current in a single infinite wire

H (2)0 (u):

Hankel function of second type of order zero

ϑ, ψ 0 :

defines direction of incident wave (see fig. 1)

x, y, z :

Cartesian coordinate system for grid

ϱ, ψ, z :

polar coordinate system for single wire

I 0(u) andI 1(u):

Modified Bessel Functions of the first type

Z i :

internal impedance of the wire

j(z):

complex current in the wires

a, k, δ, ɛ :

arbitrary real and positive constants

F(d cosϑ /λ,ψ 0 :

correction factor defined in (22)

K 0 :

normal impedance of the incident, wave

Z g :

surface impedance of the wire grid

X g :

surface reactance of the wire grid

References

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  4. Groves, W. E., J. Appl. Phys.24 (1953) 845.

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  5. MacFarlane, G. G., Inst. Elect. Engrs.93 pt. III A, (1946) 1523.

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  6. Wait, J. R., Canad. J. Phys.32 (1954) 571.

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  7. Schelkunoff, S. A., Electromagnetic Waves, p. 264, D. van Nostrand Co. Inc., 1943.

  8. Jones, E. M. T. and S. B. Cohn, Surface Matching of Dielectric Lenses, Convention Record of the I.R.E., Pt. I, Session 37, pp. 46–53, 1954.

  9. Marcuvitz, N., Waveguide Handbook, p. 286, McGraw Hill Book Co. Inc., 1943.

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Author information

Authors and Affiliations

  1. Radio Physics Laboratory, Defence Research Board, Ottawa, Canada

    James R. Wait

Authors
  1. James R. Wait
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Additional information

Work carried out under D.R.B. Project No. D48-95-55-07.

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Wait, J.R. Reflection at arbitrary incidence from a parallel wire grid. Appl. Sci. Res. 4, 393–400 (1955). https://doi.org/10.1007/BF02316501

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  • DOI: https://doi.org/10.1007/BF02316501

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