3 sonuçlar
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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 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 Complex rays and applications(Işık University Press, 2025-12-01) Hasanoğlu, ElmanComplex rays are a fascinating aspect of modern diffraction theory, typically sought as complex solutions to the eikonal equation. Traditionally, these solutions are obtained by analytically continuing real rays into the complex domain. However, this approach demands the analyticity of initial data, significantly limiting its applicability to many practical problems. Additionally, unlike real rays, complex rays cannot be visualized in space, presenting another drawback. In this paper, we present an alternative interpretation of complex rays, as introduced in [1], and describe a novel approach to two model diffraction problems and Gaussian beams.
