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Exact analytical solutions of continuously graded models of flat lenses based on transformation optics
Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.
Penn State Univ, USA.
2017 (English)In: Facta Universitatis Series: Electronics and Energetics, ISSN 0353-3670, E-ISSN 2217-5997, Vol. 30, no 4, p. 639-646Article in journal (Refereed) Published
Abstract [en]

We present a study of exact analytic solutions for electric and magnetic fields in continuously graded flat lenses designed utilizing transformation optics. The lenses typically consist of a number of layers of graded index dielectrics in both the radial and longitudinal directions, where the central layer in the longitudinal direction primarily contributes to a bulk of the phase transformation, while other layers act as matching layers and reduce the reflections at the interfaces of the middle layer. Such lenses can be modeled as compact composites with continuous permittivity (and if needed) permeability functions which asymptotically approach unity at the boundaries of the composite cylinder. We illustrate the proposed procedures by obtaining the exact analytic solutions for the electric and magnetic fields for one simple special class of composite designs with radially graded parameters. To this purpose we utilize the equivalence between the Helmholtz equation of our graded flat lens and the quantummechanical radial Schrodinger equation with Coulomb potential, furnishing the results in the form of Kummer confluent hypergeometric functions. Our approach allows for a better physical insight into the operation of our transformation optics-based graded lenses and opens a path toward novel designs and approaches.

Place, publisher, year, edition, pages
2017. Vol. 30, no 4, p. 639-646
Keyword [en]
Flat lenses, Graded permittivity and permeability models, Transformation Optics, Exact analytical solutions
National Category
Physical Sciences
Research subject
Natural Science, Physics
Identifiers
URN: urn:nbn:se:lnu:diva-72112DOI: 10.2298/FUEE1704639DISI: 000418505200012OAI: oai:DiVA.org:lnu-72112DiVA, id: diva2:1195068
Available from: 2018-04-04 Created: 2018-04-04 Last updated: 2018-04-04Bibliographically approved

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Dalarsson, Mariana

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf