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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.15947 |
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| _version_ | 1866909767147978752 |
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| author | Mystilidis, Christos Fikioris, George Tserkezis, Christos Vandenbosch, Guy A. E. Zheng, Xuezhi |
| author_facet | Mystilidis, Christos Fikioris, George Tserkezis, Christos Vandenbosch, Guy A. E. Zheng, Xuezhi |
| contents | We investigate a fundamental electromagnetic theorem, namely the uniqueness theorem, in the context of nonlocal electromagnetics, as simulated by a popular semiclassical model, the Hydrodynamic Drude Model (HDM) and extensions thereof such as the Generalized Nonlocal Optical Response (GNOR). The derivations and proofs presented here give a theoretical foundation to the use of the Additional Boundary Conditions (ABCs), whose necessity is recognized and underlined in virtually all implementations and applications of HDM. Our proofs follow a mathematically relaxed style, borrowing from the literature of established electromagnetics textbooks that study the matter from an engineering perspective. Through this simpler route we deduce clear and intuitive material-response requirements for uniqueness to hold, while using a familiar parlance in a topic that is mostly studied through a physics perspective. Two numerical examples that examine the problem from either a semianalytical or a purely numerical viewpoint support our findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15947 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Uniqueness Theorem for Nonlocal Hydrodynamic Media Mystilidis, Christos Fikioris, George Tserkezis, Christos Vandenbosch, Guy A. E. Zheng, Xuezhi Applied Physics 78-10 We investigate a fundamental electromagnetic theorem, namely the uniqueness theorem, in the context of nonlocal electromagnetics, as simulated by a popular semiclassical model, the Hydrodynamic Drude Model (HDM) and extensions thereof such as the Generalized Nonlocal Optical Response (GNOR). The derivations and proofs presented here give a theoretical foundation to the use of the Additional Boundary Conditions (ABCs), whose necessity is recognized and underlined in virtually all implementations and applications of HDM. Our proofs follow a mathematically relaxed style, borrowing from the literature of established electromagnetics textbooks that study the matter from an engineering perspective. Through this simpler route we deduce clear and intuitive material-response requirements for uniqueness to hold, while using a familiar parlance in a topic that is mostly studied through a physics perspective. Two numerical examples that examine the problem from either a semianalytical or a purely numerical viewpoint support our findings. |
| title | The Uniqueness Theorem for Nonlocal Hydrodynamic Media |
| topic | Applied Physics 78-10 |
| url | https://arxiv.org/abs/2308.15947 |