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Yayın A new theory of complex rays(Oxford Univ Press, 2004-12) Hasanoğlu, ElmanA new approach to the theory of complex rays is presented. It is shown that the three-dimensional Minkowski space, the variant of the well known four-dimensional space-time Minkowski space of the special theory of relativity, is more appropriate for describing both real and complex rays than the usual Euclidean space. It turns out that in this space complex rays, as real ones, may have quite definite directions and magnitudes. This allows us to understand the geometrical meaning of the complex magnitudes such as complex distances and complex angles, intensively discussed over the last several decades. From this point of view a new interpretation of the Gaussian beams and reflection laws is presented.Yayın Two reflector non symmetric shaped antenna systems(IEEE, 2000) Hasanoğlu, ElmanTwo reflector antenna systems with non symmetric reflecting surfaces under GO approximation are investigated. It is shown, that the problem of forming desired far field pattern leades to solving the system of partial differential equations with respect to mapping functions between wave fronts. One of these equations is non linear and expresses energy conversation law. It is shown that this equation can be solved separetly in the class of non smooth functions which has a discontinuty of first kind along a given curve.
