Far-Field Pattern and Amplitude Matrix

Application of Stratton-Chu representation theorem to the vector fields E and Ee in the domain together with the boundary conditions eg - - eg = e, and hs + he = hi, yield 

Every radiating solution E, to the Maxwell equations has the asymptotic form 

Because Egoo also depends on the incident direction e, Egoo is known as the scattering amplitude from the direction e into the direction [229]. Using the Huygens principle and the asymptotic expressions 

To introduce the concepts of tensor scattering amplitude and amplitude matrix it is necessary to choose an orthonormal unit system for polarization description. In Sect. 1.2 we chose a global coordinate system and used the vertical and horizontal polarization unit vectors Ba and e,g, to describe the polarization state of the incident wave (Fig. 1.9a). For the scattered wave we can proceed analogously by considering the vertical and horizontal polarization unit vectors and eg. Essentially, (e/t, 6/3,60.) are the spherical unit vectors of fee, while er,eg,e ) are the spherical unit vectors of fcs in 

The tensor scattering amplitude or the scattering dyad is given by [169] 

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