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Published on: September 26, 2014
Why a harmonic solution for lossless, perfectly homogeneous, left-handed material cannot exist.
Daniel Maystre1, Stefan Enoch, Ross McPhedran
1Institut Fresnel, CNRS, Aix-Marseille Universite, CNRS, Domaine universitaire de St Jerome, Marseille, Cedex, France. daniel.maystre@fresnel.fr
Summary
This study offers a direct proof that harmonic solutions do not exist for left-handed materials with negative permittivity and permeability. This finding addresses previous concerns about analytical methods for metamaterials.
Area of Science:
- Electromagnetism
- Materials Science
- Optics
Background:
- Previous work suggested no harmonic solutions exist for specific left-handed materials (LHM) using analytic continuation.
- Concerns were raised regarding the applicability of the analytic continuation theorem in prior studies.
- A need existed for a more direct and universally applicable proof.
Purpose of the Study:
- To provide a direct and simple proof for the nonexistence of harmonic solutions in left-handed materials.
- To extend this proof to a broader class of left-handed materials.
- To address and circumvent the limitations of the analytic continuation theorem.
Main Methods:
- Direct mathematical proof, avoiding reliance on analytic continuation theorems.
- Analysis of the fundamental wave equations governing electromagnetic propagation in LHM.
- Generalization of the proof to arbitrary negative permittivity and permeability values.
Main Results:
- A direct proof demonstrates the nonexistence of harmonic solutions for homogeneous LHM with relative permittivity and permeability of -1.
- The proof is successfully extended to all left-handed materials exhibiting negative permittivity and permeability.
- The findings validate the nonexistence of such solutions irrespective of the specific analytical approach used.
Conclusions:
- Harmonic solutions are definitively shown to be non-existent for a wide range of left-handed materials.
- This work provides a robust and accessible proof, resolving prior theoretical debates.
- The results have implications for the understanding and design of metamaterials and electromagnetic wave propagation.
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