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E - Bibliothèque et Archives Canada

E - Bibliothèque et Archives Canada

Consider the two

Consider the two dimensional scatterer (finite wiâth strip or cylinder of any shape) with a primeter C, illurninated by a TMz unifm plane wave (it could be also a alindrical wave). Sinœ the incident elednc field has only a z component whkh is independent of z variations (W dimensional). the scattered field and henœ the surface cumnts densiües are assumed to have only 2 components independent of z variations. This means that current on the surtace of the scatterer is comqmwd of infinite cunent line sources in the z diredion. The field radiated by an infinite line source is [2][11]: Where 1 is the current of the Iine source, and p is the distance from the line source to the observation point. Similady, the scattered field a a certain point due to the surface current of a 2-0 scatterer illuminateci by a TMz wave is: Where JZ is the current density on the surfa- of the scatterer at a distanœ p' (from a specified origin point) p is the vector from the origin to the observation point. C is the primeter of the 2-0 scatterer. To enforce the boundary conditions, the total tangential electric field must vanish on the surface of the scatterer, thus

where, fZ&) is the incident field on point rn on the surfaœ of the scatterer ,and Sm is the vector from the origin to point m. Equation (2.17) is the desired hivo-dimensional elednc field integral equation to be solved for the cunent density JZ over the surface of the scatterer. The solution can be accomplished by using the moment mhod. b) TEz Polarization: Sinœ the incident electric field has x and y components with no z variations. the scattered Celd is assumecl also to have the same characteristics. This is actually what makes this example less straight fornard aien the TMz caw. To denve the EFlE for the TG case a speafic example of a sûip of finite width (aligned with the x axis) illurninated by a TEz type wave will be used. Even though this example seems to be specific. its solution is considerd a building block for more cornplex scatterer geometries as it will be seen later. Using vedor ptentials (2) the x and y components of the scattered elecbic field can be written as: w = the width of the strip (O sr sw) Jx = Cunent density on the surface of the strip x' = position of source current on the stnp

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