Mathematical Analysis of Electromagnetic Scattering Phenomena
Summary
The mathematical analysis of electromagnetic scattering investigates how incident electromagnetic waves interact with objects and inhomogeneities, giving rise to reflected, transmitted and diffracted fields. At its core, the subject rests on Maxwell’s equations, cast as boundary value problems that enforce continuity or prescribed conditions on material interfaces. Analytical techniques range from separation of variables in canonical geometries to spectral analysis of boundary integral operators. Asymptotic expansions in the low- and high-frequency limits yield compact formulae for the leading scattering terms, while homogenisation theories describe effective behaviour in composite media. Modern developments exploit variational formulations and limiting absorption principles to characterise resonant phenomena, such as plasmonic excitations at sharp corners or anomalous localised resonance in metamaterials. Numerical approaches—including extended Foldy–Lax systems, integral‐equation solvers and hybrid deterministic-stochastic methods—complement analytical results by enabling accurate computation in complex configurations. These mathematical insights underpin practical applications in radar cross-section reduction, remote sensing, biomedical imaging, nondestructive evaluation and the design of cloaking devices. By uniting rigorous theory with computational strategies, the field continues to elucidate fundamental scattering mechanisms and to drive innovation in wave-based technologies.
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Mathematical Analysis of Electromagnetic Scattering Phenomena publication trend
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Technical terms
Maxwell’s equations: Fundamental partial differential equations governing electric and magnetic fields in space and time.
Boundary value problem: Mathematical formulation in which fields satisfy differential equations and prescribed conditions on material interfaces or at infinity.
Asymptotic expansion: Representation of a field or quantity as a series in a small parameter, valid in limiting regimes.
Neumann–Poincaré operator: Boundary integral operator arising in potential theory, central to spectral analysis of scattering and resonance.
Foldy–Lax approximation: Self-consistent system for multiple scattering by small particles, yielding coupled equations for scattering amplitudes.
Plasmonic resonance: Resonant oscillation of free electrons at a metal–dielectric interface, leading to strong localisation of electromagnetic fields.
References
- A Revisit of Electromagnetic Wave Scattering by a Metal Isotropic Body in a Lossless Environment with Magnetic Sensor Excitation. Sensors (2024).
- HOMOGENIZATION OF THE SYSTEM OF HIGH‐CONTRAST MAXWELL EQUATIONS. Mathematika (2015).
- Plasmonic eigenvalue problem for corners: Limiting absorption principle and absolute continuity in the essential spectrum. Journal de Mathématiques Pures et Appliquées (2021).
- Extended Foldy–Lax Approximation on Multiple Scattering. Mathematical Modelling and Analysis (2014).
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