A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914810842578944 |
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| author | Shanin, Andrey V. Assier, Raphael C. Korolkov, Andrey I. Makarov, Oleg I. |
| author_facet | Shanin, Andrey V. Assier, Raphael C. Korolkov, Andrey I. Makarov, Oleg I. |
| contents | We propose a general procedure to study double integrals arising when considering wave propagation in periodic structures. This method, based on a complex deformation of the integration surface to bypass the integrands' singularities, is particularly efficient to estimate the Green's functions of such structures in the far field. We provide several illustrative examples and explicit asymptotic formulae. Special attention is devoted to the pathological cases of degeneracies, such as Dirac conical points for instance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures Shanin, Andrey V. Assier, Raphael C. Korolkov, Andrey I. Makarov, Oleg I. Analysis of PDEs Mathematical Physics Complex Variables We propose a general procedure to study double integrals arising when considering wave propagation in periodic structures. This method, based on a complex deformation of the integration surface to bypass the integrands' singularities, is particularly efficient to estimate the Green's functions of such structures in the far field. We provide several illustrative examples and explicit asymptotic formulae. Special attention is devoted to the pathological cases of degeneracies, such as Dirac conical points for instance. |
| title | A note on double Floquet-Bloch transforms and the far-field asymptotics of Green's functions tailored to periodic structures |
| topic | Analysis of PDEs Mathematical Physics Complex Variables |
| url | https://arxiv.org/abs/2402.08076 |