Keller’s theorem revisited
Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assu...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2018-01-01
|
| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aaa7e1 |
| _version_ | 1797750682101481472 |
|---|---|
| author | Guillermo P Ortiz W Luis Mochán |
| author_facet | Guillermo P Ortiz W Luis Mochán |
| author_sort | Guillermo P Ortiz |
| collection | DOAJ |
| description | Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations. |
| first_indexed | 2024-03-12T16:36:21Z |
| format | Article |
| id | doaj.art-5639900649854ee680d0cd4fda97fb90 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:36:21Z |
| publishDate | 2018-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-5639900649854ee680d0cd4fda97fb902023-08-08T14:51:04ZengIOP PublishingNew Journal of Physics1367-26302018-01-0120202302810.1088/1367-2630/aaa7e1Keller’s theorem revisitedGuillermo P Ortiz0W Luis Mochán1Departamento de Física, Facultad de Ciencias Exactas Naturales y Agrimensura, Universidad Nacional del Nordeste , Corrientes, ArgentinaInstituto de Ciencias Físicas, Universidad Nacional Autónoma de México , Apartado Postal 48-3, 62251 Cuernavaca, Morelos, MéxicoKeller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.https://doi.org/10.1088/1367-2630/aaa7e1effective mediarecursive algorithmcompositesplasmonsrandom mediaoptics |
| spellingShingle | Guillermo P Ortiz W Luis Mochán Keller’s theorem revisited New Journal of Physics effective media recursive algorithm composites plasmons random media optics |
| title | Keller’s theorem revisited |
| title_full | Keller’s theorem revisited |
| title_fullStr | Keller’s theorem revisited |
| title_full_unstemmed | Keller’s theorem revisited |
| title_short | Keller’s theorem revisited |
| title_sort | keller s theorem revisited |
| topic | effective media recursive algorithm composites plasmons random media optics |
| url | https://doi.org/10.1088/1367-2630/aaa7e1 |
| work_keys_str_mv | AT guillermoportiz kellerstheoremrevisited AT wluismochan kellerstheoremrevisited |