研究目的
To develop a unified asymptotic approach for solving high-frequency electromagnetic diffraction problems at curved dielectric, conducting, and absorbing layers, incorporating curvature corrections.
研究成果
The asymptotic method provides accurate solutions for high-frequency diffraction at curved layers, with curvature corrections significantly improving accuracy over plane-slab approximations. It is validated against analytical and numerical benchmarks, showing good agreement and applicability to various layer types and thicknesses.
研究不足
The method assumes small parameters (η and ξ) and specific relations between them; it may not be applicable for large dielectric permittivities (beyond ε ~ 10) or very thick layers. The approximation of piece-wise constant dielectric permittivity with continuous functions has limitations, and the approach is validated primarily for 2D and 3D canonical problems.
1：Experimental Design and Method Selection:
The study employs an asymptotic method combining ray representations and boundary-layer expansions to derive solutions for diffraction problems. It involves formal power series expansions with respect to small parameters (e.g., η = κ0/k0 and ξ = κ0δ) and solving boundary-value problems for successive terms.
2：Sample Selection and Data Sources:
Canonical problems are used for validation, including analytical solutions from references and numerical solutions from integral equation methods (e.g., Müller boundary integral equations for homogeneous layers and volume integral equations for layers with piece-wise constant dielectric permittivity).
3：List of Experimental Equipment and Materials:
No specific equipment or materials are mentioned; the work is theoretical and computational.
4：Experimental Procedures and Operational Workflow:
The procedure involves formulating Maxwell equations and boundary conditions, introducing curvilinear coordinates, expanding fields into series, and solving the resulting equations. Numerical validation is performed by comparing asymptotic results with analytical and numerical benchmarks.
5：Data Analysis Methods:
Data analysis includes comparison of field magnitudes and other parameters with reference solutions to assess accuracy, using methods such as integral equation techniques for validation.
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