Mathematical Physics
[Submitted on 7 Jul 2025
]
Title: On an analogy between the Wiener--Hopf formulations of discrete and continuous diffraction problems
Title: 离散和连续衍射问题维纳-霍普夫公式的类比
Abstract: This article is dedicated to unifying the framework used to derive the Wiener--Hopf equations arising from some discrete and continuous wave diffraction problems.The main tools are the discrete Green's identity and the appropriate notion of discrete normal derivative. The resulting formal analogy between the Wiener--Hopf equations allows one to effortlessly move between the discrete and continuous formulations. The validity of this novel analogy is illustrated through several famous two-dimensional canonical diffraction problems and extended to three-dimensional problems.
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