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

Pengfei ZHANG; Shu WANG; Pan LI

doi:10.11999/JEIT180247

Volume 41 Issue 6

Jun. 2019

Turn off MathJax

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2019 > 41(6): 1336-1343

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 & Information Technology, 2019, 41(6): 1336-1343. doi: 10.11999/JEIT180247

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 & Information Technology, 2019, 41(6): 1336-1343. doi: 10.11999/JEIT180247

Citation:

PDF( 1857 KB)

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

doi: 10.11999/JEIT180247

Key Laboratory of Antennas and Microwave Technology, Xidian University, Xi’an 710071, China

Received Date: 2018-03-19
Rev Recd Date: 2019-03-25

Available Online: 2019-04-20

Publish Date: 2019-06-01

Abstract

Abstract

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.
- Transformation Optics(TO),
- Stealth carpet cloak,
- Conformal transformation

FullText(HTML)

References(19)

References

PENDRY J B, SCHURIG D, and SMITH D R. Controlling electromagnetic fields[J]. Science, 2006, 312(5781): 1780–1782. doi: 10.1126/science.1125907

LEONHARDT U. Optical conformal mapping[J]. Science, 2006, 312(5781): 1777–1780. doi: 10.1126/science.1126493

CUMMER S A, POPA B I, SCHURIG D, et al. Full-wave simulations of electromagnetic cloaking structures[J]. Physical Review E, Covering Statistical, Nonlinear, Biological, and Soft Matter Physics, 2006, 74: 036621. doi: 10.1103/PhysRevE.74.036621

LAI Yun, NG J, CHEN Huanyang, et al. Illusion optics: The optical transformation of an object into another object[J]. Physical Review Letters, 2009, 102(25): 253902. doi: 10.1103/PhysRevLett.102.253902

LI Jensen and PENDRY J B. Hiding under the carpet: A new strategy for cloaking[J]. Physical Review Letters, 2008, 101(20): 203901. doi: 10.1103/PhysRevLett.101.203901

KHOSRAVI S, ROSTAMI A, DOLATYARI M, et al. Broadband carpet cloak designed using nanocomposite metamaterials for 3-5-μm wavelength range[J]. IEEE Transactions on Nanotechnology, 2017, 16(1): 44–48. doi: 10.1109/TNANO.2016.2625741

EBRAHIMPOURI M and QUEVEDO-TERUEL O. Bespoke lenses based on quasi-conformal transformation optics technique[J]. IEEE Transactions on Antennas and Propagation, 2017, 65(5): 2256–2264. doi: 10.1109/TAP.2017.2679494

YI Jianjia, BUROKUR S N, PIAU G P, et al. 3D printed broadband transformation optics based all-dielectric microwave lenses[J]. Journal of Optics, 2016, 18(4): 044010. doi: 10.1088/2040-8978/18/4/044010

JIANG Weixiang, BAO Di, and CUI Tiejun. Designing novel anisotropic lenses with transformation optics[J]. Journal of Optics, 2016, 18(4): 044022. doi: 10.1088/2040-8978/18/4/044022

YI Jianjia, BUROKUR S N, PIAU G P, et al. Coherent beam control with an all-dielectric transformation optics based lens[J]. Scientific Reports, 2016, 6: 18819. doi: 10.1038/srep18819

AGHANEJAD I, ABIRI H, and YAHAGHI A. Design of high-gain lens antenna by gradient-index metamaterials using transformation optics[J]. IEEE Transactions on Antennas and Propagation, 2012, 60(9): 4074–4081. doi: 10.1109/TAP.2012.2207051

MA Y G, WANG Ning, and ONG C K. Application of inverse, strict conformal transformation to design waveguide devices[J]. Journal of the Optical Society of America A: Optics Image Science & Vision, 2010, 27(5): 968–972. doi: 10.1364/JOSAA.27.000968

SCHURIG D, MOCK J J, JUSTICE B J, et al. Metamaterial electromagnetic cloak at microwave frequencies[J]. Science, 2006, 314(5801): 977–980. doi: 10.1126/science.1133628

POPA B I and CUMMER S A. Cloaking with optimized homogeneous anisotropic layers[J]. Physical Review A, 2009, 79(2): 023806. doi: 10.1103/PhysRevA.79.023806

XI Sheng, CHEN Hongsheng, ZHANG Baile, et al. Route to low-scattering cylindrical cloaks with finite permittivity and permeability[J]. Physical Review B, 2009, 79(15): 155122. doi: 10.1103/PhysRevB.79.155122

李艳秀. 基于变换光学的新型电磁功能器件的研究与设计[D]. [博士论文], 山东大学, 2016.

LI Yanxiu. Study and design of electromagnetic functional devices based on transformation optics method[D]. [Ph.D. dissertation], Shandong University, 2016.

JIANG Weixiang, CHIN J Y, LI Zhuo, et al. Analytical design of conformally invisible cloaks for arbitrarily shaped objects[J]. Physical Review E, Covering Statistical, Nonlinear, Biological, and Soft Matter Physics, 2008, 77(6): 066607. doi: 10.1103/PhysRevE.77.066607

LIU R, CUI Jiejun, MOCK J J, et al. Broadband ground-plane cloak[J]. Science, 2009, 323(5912): 366–369. doi: 10.1126/science.1166949

DRISCOLL T A. Schwarz-christoffel toolbox user’s guide version 2.1[EB/OL]. https://www.doc88.com/p-1826946369203.html, 2019.

Relative Articles

Supplements(0)

Cited By

Proportional views