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Conformal mappings to achieve simple material parameters for transformation optics devices
Jeremiah P Turpin1, Ayah T Massoud, Zhi Hao Jiang
1Department of Electrical Engineering Pennsylvania State University, University Park, PA 16802, USA.
Optics Express
|February 23, 2010
Summary
Transformation optics simplifies electromagnetic device design using conformal mapping. This enables practical metamaterial fabrication for creating lenses that convert cylindrical waves into multiple planar beams.
Area of Science:
- Electromagnetism
- Metamaterials
- Optics
Background:
- Transformation optics offers advanced control over electromagnetic waves for novel device design.
- Current implementation is hindered by metamaterial design and fabrication challenges.
Purpose of the Study:
- To simplify transformation optics implementation by restricting spatial transformations to conformal mappings.
- To demonstrate a practical application through the design and simulation of a novel lens.
Main Methods:
- Utilized conformal mapping to derive simplified material parameters for transformation optics.
- Designed a flat cylindrical-to-plane-wave conversion lens.
- Validated performance using numerical simulations.
- Proposed and analyzed two metamaterial designs for the lens.
Main Results:
- The conformal mapping approach significantly simplifies material parameter requirements.
- The designed lens can generate one, two, or four directive planar beams by adjusting dimensions and source location.
- Two viable metamaterial designs were identified for implementing the lens.
Conclusions:
- Conformal mapping is a viable strategy to overcome practical limitations in transformation optics.
- The proposed lens design offers a flexible and efficient method for cylindrical-to-planar wave conversion.
- The study paves the way for more accessible and practical metamaterial-based optical devices.
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