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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.Yayın On the theory of single aspheric lenses(Institute of Electrical and Electronics Engineers Inc., 2024) Hasanoğlu, ElmanAspheric lenses play a pivotal role in a myriad of applications, including antenna theory, communication systems, sophisticated optical systems etc. These lenses, unlike their spherical counterparts, possess an infinite number of free parameters and by utilizing these parameters it is possible to achieve optical and antenna systems with very high and sophisticated performances. However, the lack of a rigorous mathematical theory essentially limits possibility to utilize their full potential in the related fields. In our days, the design process relies heavily on elementary mathematical principles and empirical methods [1-2]. Even a single thick aspheric lens lacks a comprehensive mathematical theory. In this paper a new mathematical approach to the theory of single lenses is proposed. Surprisingly, even in this seemingly straightforward case, the serious mathematical theory of a single aspherical lens relies on rather nontrivial mathematical principles as partial differential equations, differential geometry, Riemann geometry.
