Wiener-Hopf Techniques in Electromagnetic Scattering and Diffraction

The Wiener–Hopf technique is a powerful analytical method for solving boundary-value problems in semi-infinite geometries, notably those arising in electromagnetic scattering and diffraction. At its core, the approach involves transforming field equations into the spectral (often Fourier) domain, factorising kernel functions into multiplicative components analytic in complementary half-planes, and reconstructing physical solutions via inverse transforms. This framework underpins the rigorous analysis of wave interaction with edges, wedges, waveguides and open cavities, enabling exact or uniformly valid expressions for reflected, transmitted and diffracted fields. Over the past decade, advances in matrix-kernel factorisation, generalised Wiener–Hopf formulations and network representations have extended the technique to multi–layer media, anisotropic and bianisotropic materials, and complex angular regions. The incorporation of Fredholm factorisation, Riccati-equation methods and characteristic Green’s functions has enhanced stability and numerical implementability, while asymptotic and uniform approximations provide seamless descriptions across geometrical-optics transition zones. These developments support applications in antenna design, radar cross-section prediction, remote sensing and cavity-resonator analysis, reinforcing the Wiener–Hopf method as a cornerstone of theoretical electromagnetics with broad scientific and engineering significance.

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Wiener-Hopf Techniques in Electromagnetic Scattering and Diffraction publication trend

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Technical terms

Wiener–Hopf technique: A method that transforms boundary-value problems into spectral equations, factorises kernels into analytic parts, and reconstructs physical solutions via inverse transforms.

Fourier transform: A mathematical operation converting spatial or temporal field distributions into frequency or spectral components for algebraic manipulation.

Green’s function: A fundamental solution representing the response of a system to a point-source excitation, used to impose boundary conditions in scattering problems.

Diffraction coefficient: A complex amplitude quantifying the strength and phase of wave diffraction by edges or tips in high-frequency approximations.

Far-field approximation: An asymptotic expression for the scattered field observed at distances much larger than the characteristic dimensions of the scatterer, often obtained via saddle-point methods or steepest-descent integrals.

References

1. Network representations of angular regions for electromagnetic scattering. PLOS ONE (2017).
2. Spectral Analysis of Electromagnetic Diffraction Phenomena in Angular Regions Filled by Arbitrary Linear Media. Applied Sciences (2024).
3. Diffraction by a Semi-Infinite Parallel-Plate Waveguide with Five-Layer Material Loading: The Case of H-Polarization. Applied Sciences (2023).
4. A Uniform Diffraction Theory for Wide-Angle Cones. IEEE Transactions on Antennas and Propagation (2022).