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Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media

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Abstract

The diffraction pattern due to a plane H-polarized electromagnetic wave is investigated, when this wave is incident upon an infinitely long slit of finite width in an opaque screen of non-vanishing thickness. The screen is located between the plane boundaries of two media with different electromagnetic properties. A Green's function formulation of the problem is employed, leading to a system of four coupled integral equations in which the field distributions in the slit occur as unknowns. Numerical results are presented for the field just below the screen as well as for the far field pattern.

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Abbreviations

E :

electric field vector

G I, II, III :

Green's function in Regions I, II, III respectively

H :

magnetic field vector

i:

imaginary unit

k 1, 2, 3 :

wave number in Regions I, II, III respectively

n :

unit vector in the direction of the normal to the screen

t :

time

U i :

incident magnetic field

U 1, 2, 3 :

total magnetic field in Regions I, II, III respectively

U r :

reflected magnetic field that would be present in the absence of a slit in the screen

U d :

deviation from U i +U r due to the presence of the slit

ν :

unit vector in the direction of the outward normal to the contour to which Green's theorem is applied

x, y, z :

Cartesian coordinates

α i :

sin (θ i)

γi :

cos(θ i)

δ :

Dirac delta distribution

ε 1, 2, 3 :

permittivity of the medium in Regions I, II, III respectively

θ i :

angle of incidence

μ 1, 2, 3 :

permeability of the medium in Regions I, II, III respectively

ω :

angular frequency

x, z, n, v :

partial derivative with respect to x, z, n, ν

References

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Neerhoff, F.L., Mur, G. Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media. Appl. Sci. Res. 28, 73–88 (1973). https://doi.org/10.1007/BF00413058

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Keywords

  • Plane Boundary
  • Electromagnetic Property
  • Field Pattern
  • Finite Width
  • Plane Electromagnetic Wave