Abstract
Abstract We propose a homogenization scheme for metamaterials that utilizes causality to determine their effective parameters. By requiring the Kramers-Kronig causality condition in the homogenization of metamaterials, we show that the effective parameters can be chosen uniquely, in contrast to the conventional parameter retrieval method which has unavoidable phase ambiguity arising from the multivalued logarithm function. We demonstrate that the effective thickness of metamaterials can also be determined to a specific value by saturating the minimum-error condition for the causality restriction. Our causal homogenization provides a robust and accurate characterization method for metamaterials.
Highlights
Metamaterials composed of artificial subwavelength structures, namely meta-atoms, can exhibit extraordinary optical properties not found in natural materials
We propose a homogenization scheme for metamaterials that utilizes causality to determine their effective parameters
By requiring the Kramers-Kronig causality condition in the homogenization of metamaterials, we show that the effective parameters can be chosen uniquely, in contrast to the conventional parameter retrieval method which has unavoidable phase ambiguity arising from the multivalued logarithm function
Summary
Metamaterials composed of artificial subwavelength structures, namely meta-atoms, can exhibit extraordinary optical properties not found in natural materials. The method has difficulty fixing parameters uniquely for two reasons: (i) the real part of the refractive index Re(n) obtained from the multivalued complex logarithm function possesses integer-labeled multiple branches and the rules needed to choose a specific branch are absent, and (ii) the effective thickness of the homogenized slab is not uniquely determined because of the lack of a well-defined boundary for inhomogeneous meta-atom collections and the thickness is usually selected according to the researcher’s own taste. Our homogenization method enables an algorithmic determination of the effective parameters and can be used as a general method for metamaterial homogenization
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