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Citation: Pengfei ZHANG, Shu WANG, Pan LI. Analysis of Some Mathematical Questions of Transformation Optics and Its Application to Stealth Carpet Design[J]. Journal of Electronics and Information Technology, ;2019, 41(6): 1336-1343. doi: 10.11999/JEIT180247 shu

Analysis of Some Mathematical Questions of Transformation Optics and Its Application to Stealth Carpet Design

  • Corresponding author: Pengfei ZHANG, zhangpf@mail.xidian.edu.cn
  • Received Date: 2018-03-19
    Accepted Date: 2019-03-25
    Available Online: 2019-06-01

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  • Transformation Optics (TO) is a hot topic in the research area of electrical-magnetic fields. For providing further theoretical support to the design of stealth carpet based on TO, three basic mathematic problems of TO are discussed in this paper. Firstly, the uniqueness of transformation form in three-dimensional transformation of Maxwell’s equations is analyzed. A new transformation model is proposed, which is different from the classical one shown in reference. The new model also leads to a new transformation method that can generate flexible characteristic impedance in transformation space. Based on this, a design method of stealth cloak or carpet that can be used to hide the target in an area surrounded by medium with given permittivity is discussed. During this process, only the field distribution in free space is required as the original field during mapping. Secondly, the two-dimensional transformation of the wave equation is studied. The transformation of the magnetic field component in the two-dimensional transformation based on the wave equation of the electric field component is analyzed. The boundary matching during transformation is also discussed. The two dimension design method of stealth cloak or carpet that can be used to hide a target in an area surrounded by medium with specified permittivity is also discussed. Finally, the sufficiency and necessity of conformal transformation for designing a two dimension stealth cloak with non-uniform and anisotropic medium are proved strictly. The simulation results of a stealth carpet embedded in material are given to verify the proposed method. The analysis and the related conclusion presented in the paper provide theoretical support to the related application based on TO.
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