研究目的
To develop and demonstrate a parameter retrieval procedure for metamaterials using nonlocal constitutive relations to improve the prediction of optical responses beyond the paraxial regime.
研究成果
The nonlocal constitutive relation significantly improves the accuracy of effective material parameter retrieval for metamaterials, enabling better prediction of optical responses at oblique incidence angles and eliminating unphysical artifacts like anti-Lorentz resonances. The method is robust and applicable to various metamaterials, as demonstrated with isotropic and anisotropic examples. Future work could explore higher-order nonlocal terms and experimental verification.
研究不足
The retrieval procedure is computationally intensive and requires full-wave simulations. It is sensitive to the choice of constitutive model and may not capture all nonlocal effects if higher-order terms are neglected. The approach is demonstrated on specific metamaterials and may not generalize to all types. Experimental validation is not provided, and the method assumes subwavelength structures without diffraction orders.
1：Experimental Design and Method Selection:
The study uses a theoretical and numerical approach to retrieve effective material parameters by fitting analytically derived reflection and transmission coefficients for homogeneous slabs with nonlocal constitutive relations to reference data from full-wave simulations of metamaterial slabs. The Fresnel equations are derived for nonlocal models, and a merit function is minimized to find optimal parameters.
2：Sample Selection and Data Sources:
Two metamaterials are considered: isotropic dielectric spheres on a cubic lattice (with permittivity ε_SPH = 16, period a = 1 μm, sphere radius 0.45a) and an anisotropic fishnet metamaterial (with specific geometric parameters, silver layers described by a Drude model, and magnesium fluoride spacer). Reference reflection and transmission data are obtained numerically using the Korringa-Kohn-Rostoker (KKR) method for the spheres and the Fourier modal method (FMM) for the fishnet.
3：45a) and an anisotropic fishnet metamaterial (with specific geometric parameters, silver layers described by a Drude model, and magnesium fluoride spacer). Reference reflection and transmission data are obtained numerically using the Korringa-Kohn-Rostoker (KKR) method for the spheres and the Fourier modal method (FMM) for the fishnet.
List of Experimental Equipment and Materials:
3. List of Experimental Equipment and Materials: No physical equipment is used; the study is computational. Materials include dielectric spheres (e.g., germanium), silver (modeled with Drude parameters: ω_p = 13700 THz, Γ = 85 THz), magnesium fluoride (ε_MgF2 = 1.9044), and air (ε = 1).
4：9044), and air (ε = 1).
Experimental Procedures and Operational Workflow:
4. Experimental Procedures and Operational Workflow: For each frequency and angle of incidence, reflection and transmission coefficients are computed numerically for the metamaterial slabs. These are compared to coefficients from homogeneous slab models with local (WSD) and nonlocal (SSD) constitutive relations. A merit function is minimized to retrieve effective parameters (ε, μ, γ) by fitting the analytical expressions to the reference data.
5：Data Analysis Methods:
The analysis involves minimizing the merit function using optimization techniques, evaluating deviations between model and reference data, and performing sensitivity analysis using Jacobi matrices. Spectral continuity is enforced to ensure physical plausibility of the retrieved parameters.
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