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Yayın On complex solutions of the eikonal equation(IEEE, 2007) Hasanoğlu, ElmanIn this paper a new approach of complex rays in an inhomogeneous medium is presented. Complex rays are complex solutions of the eikonal equation, the main equation of the geometical optics. It is shown that solving the eikonal equation by using the characteristic method naturally leads to the pseudoriemann and Minkowski geometries. In framework of these geometries complex rays , like the real ones, can be drawn in real space and they may have caustics, and caustics also can be drawn in real space.Yayın On the realization of optical mappings and transformation of amplitudes by means of an aspherical "thick" lens(Gustav Fischer Verlag, 2000) Hasanoğlu, Elman; Polat, Burak DenizThe constraints for the realization of a given optical mapping by means of an aspherical ''thick" lens are investigated by using the laws of geometrical optics. The analysis yields us a partial differential equation which the optical mapping functions must satisfy as a necessary and sufficient condition. It is shown that thick lenses, which convert plane waves to plane waves, can be considered as a pure amplitude element, An interesting feature of this equation is that it does not involve the lens profiles. The problem of realization is later discussed for some special mappings and graphical illustrations of the aspherical lens profiles for a linear mapping are 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.Yayın Complex and real rays in three dimensional Minkowski space(IEEE, 2002) Hasanoğlu, ElmanA new approach to the theory of complex rays is proposed. It is shown that the Minkowski space is more appropriate for describing these rays than the usual, Euclidian spaces. Some illustrative examples are represented.Yayın Beam tracing theory in Minkowski space(IEEE, 2011) Hasanoğlu, ElmanThis paper provides a novel approach to beam theory in homogeneous lossless mediun. The main idea is to interpret the classic eikonal equation in three dimensional Minkowski space.
