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General conformal transformation method based on Schwarz-Christoffel approach.
Linlong Tang1, Jinchan Yin, Guishan Yuan
1Physics Department, Sichuan University, Chengdu 610064, China.
Optics Express
|September 22, 2011
Summary
A new conformal transformation method (CTM) enables mapping between irregular geometries. This approach approximates shapes with polygons, yielding material parameters for TE and TM waves, validated with devices like Luneburg lenses.
Area of Science:
- Electromagnetics and Optics
- Computational Mathematics
Background:
- Conformal mapping is crucial for designing electromagnetic devices.
- Irregular geometries pose challenges for traditional conformal transformation methods.
Purpose of the Study:
- To propose a general conformal transformation method (CTM) for irregular geometries.
- To determine material parameters for conformal transformations between complex shapes.
Main Methods:
- Approximating irregular geometries with polygons.
- Utilizing an intermediate geometry for mapping.
- Calculating Schwarz-Christoffel (SC) mappings for material parameters.
- Finite element method (FEM) for simulation and validation.
Main Results:
- The CTM successfully constructs conformal mappings for irregular geometries.
- Approximate material parameters for TE and TM waves were obtained.
- Simulations of a phase modulator and Luneburg lens validated the method's effectiveness.
Conclusions:
- The proposed CTM is a generalizable approach for conformal transformations involving irregular geometries.
- This method expands the applicability of conformal mapping in electromagnetic device design.
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