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12 December 1984 Diffraction Of An Electromagnetic Wave By A New Type Of Crossed Grating
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A theoretical and experimental study of the diffraction of an electromagnetic wave by a plane metallic crossed grating of hemispherical cavities is presented here. The cavities with radius R are periodically hollowed along two perpendicular directions x'x and z'z; the periods are A and B respectively. This crossed grating is illuminated at arbitrary incidence by a linearly polarized harmonic plane wave with wavelength λ. To solve this problem theoretically we use a modal method. Within the cavities the field is expanded in terms of spherical wave functions and above the grating surface the total field is written as the sum of the incident field and of the diffracted one (which is expressed as a Rayleigh expansion). Two types of boundary conditions are then considered. Firstly, on the metallic surface the tangential components of the electric field cancel. Secondly, on the plane circular surface limiting the hemispherical cavity from the free-space the fields on both sides are matched. Thus, we obtain a set of algebraic equations which are then resolved by means of a least squares method. The numerical results concern the particular case of normal incidence which leads to simpler calculus. We show that the efficiency in the (0,0) order (noted ε(0,0)) is widely dependent on the ratio R/λ and with appropriate values of R/λ and A/λ very low values of ε(0,0) can be obtained. An experimental study is carried out in the microwave range (λ ≈ 8.6 mm) with two metallic crossed gratings having the same periods A E B = 13 mm and radii R1 = 4 mm and R2 = 6 mm. The experiments concern the variations of ε(0,0) versus the angle of incidence and the two cases of polarization (T.E. and T.M.) are investigated.
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Roger Deleuil and Elvino Toro "Diffraction Of An Electromagnetic Wave By A New Type Of Crossed Grating", Proc. SPIE 0503, Application, Theory, and Fabrication of Periodic Structures, DiffractionGratings, and Moire Phenomena II, (12 December 1984);

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