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Diffraction by a double grating

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Abstract

The reflection and transmission of a plane electromagnetic wave by a double grating is investigated. The double grating consists of two mutually parallel, planar arrays of perfectly conducting strips of vanishing thickness. Two types of polarization are investigated, viz.E- and H-polarization. For both types, integral equations for the unknown current densities in the two strips belonging to a single period of the grating, are derived. Subsequently, these integral equations are solved numerically, whereupon the reflection and transmission factors for the different spectral orders are computed.

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Abbreviations

A n,B n :

amplitudes in the plane wave expansion of the scattered field in between the upper and the lower grating

D :

spatial period of the grating

E y :

electric field (E-polarization)

G :

Green's function

H y :

magnetic field (H-polarization)

h :

distance between upper and lower grating

i x, y, z :

unit vector in thex, y, z-direction, respectively

k :

wave number

l :

displacement of the lower grating with respect to the upper grating

l 1, 2 :

strip widths of the upper and lower grating, respectively

M 1, 2 :

strip of upper and lower grating, respectively

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{n} \) :

unit vector normal to a strip

R n :

reflection factor ofn-th spectral order

T n :

transmission factor ofn-th spectral order

U :

scalar wave function

α 0 :

k sin (θ 0)

γ 0 :

k cos (θ 0)

θ 0 :

angle between the negativez-axis and the direction of progagation of the incident wave

λ :

wavelength in free space

ω :

angular frequency

References

  1. Kodate, K., T. Kamiya andM. Kamiyama, Japanese J. of App. Physics,10, (1971), 1040.

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  2. Van den Berg, P. M., Appl. Sci. Res,24, (1971), 261.

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  3. Van den Berg, P. M. andO. J. Voorman, Appl. Sci. Res.26 (1972) 175.

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  4. Harrington, R. F., Field computation by moment methods, Macmillan New York.

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Authors and Affiliations

  1. Dept. of Electrical Engineering, Division of Electromagnetic Research, Delft University of Technology, Delft, The Netherlands

    H. Blok & G. Mur

Authors
  1. H. Blok
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  2. G. Mur
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Blok, H., Mur, G. Diffraction by a double grating. Appl. Sci. Res. 26, 389–397 (1972). https://doi.org/10.1007/BF01897866

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  • DOI: https://doi.org/10.1007/BF01897866

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