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arXiv · 2608.00753

Functional Ordinary Differential Equations and the Design of Dichromatic Lenses

Mohammad Tarek Al Masri·Stéphane Najjar·Ahmad Sabra·Maya Said·Muna Sattouf
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Abstract

This paper establishes an existence and uniqueness theorem for a class of functional ordinary differential equations under assumptions weaker than those found in the literature. We then consider the problem of designing a lens that refracts rays of two distinct frequencies emitted from a point source into a common collimated beam. We derive a system of functional ordinary differential equations whose solvability characterizes the existence of such lenses. Using the existence theorem, we prove that such a lens exists in two dimensions. We then extend the corresponding result to three dimensions.

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Mohammad Tarek Al Masri, Stéphane Najjar, Ahmad Sabra, Maya Said, Muna Sattouf. 2026-08-01. Functional Ordinary Differential Equations and the Design of Dichromatic Lenses. https://arxiv.org/abs/2608.00753

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