Quadratic relationships for a strip small-period array

Abstract

A strip array with a period small with respect to the wavelength is considered. The far field of this array is described by the nonlocal equivalent boundary conditions. It is shown with the help of the active power theorem that a near field transferring the active power along metal strips exists in the strip. The relationships connecting the far field on the strip surface with the active power of the near field are derived. It is demonstrated with the help of the Lorentz lemma that the near field has a nonzero quadratic shape and the relationships connecting it with the far field are obtained. A method of determination of the far field components on the array surface that are normal to the array plane is proposed. This method allows one to take into account the finite values of the quadratic forms.