Document Type : Research
Author
jahrom university
Abstract
Subwavelength layered metamaterials are widely used platforms for engineering effective electromagnetic responses. In such structures, the effective permittivity along the directions parallel and perpendicular to the layers can be controlled by adjusting the fill fraction, enabling tuning of the effective refractive index and impedance. Although classical effective-medium relations for these systems are well established, the derivative behavior of these relations and the quantitative sensitivity of effective parameters to small variations in fill fraction have not been systematically addressed. In practical fabrication, unavoidable deviations in layer thickness directly translate into fill-fraction variations; therefore, the stability of the effective response depends on its functional dependence on this parameter. Within the subwavelength effective-medium regime, we derive analytical expressions for the derivatives of the effective permittivity with respect to fill fraction and extend the analysis to refractive index and impedance. The results show that in certain parametric regions, particularly near near-zero permittivity conditions, the effective response can become highly sensitive to small fill-fraction changes. The main contribution of this work is a quantitative analytical formulation for estimating the allowable variation range of the fill fraction based on the permittivity contrast of the constituent materials. This framework enables prediction of design stability without numerical optimization and provides a practical analytical tool for selecting suitable fill-fraction ranges and material contrasts in layered metamaterial design.
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