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Active exterior cloaking for the 2D Laplace and Helmholtz equations
Fernando Guevara Vasquez1, Graeme W Milton, Daniel Onofrei
1Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA.
Physical Review Letters
|October 2, 2009
Summary
A novel cloaking method shields objects in 2D quasistatics and Helmholtz equations. A single device works for quasistatics, while three are needed for the Helmholtz equation, minimizing field scattering.
Area of Science:
- Physics
- Applied Mathematics
- Electromagnetism
Background:
- Metamaterials enable wave manipulation.
- Cloaking aims to render objects undetectable by controlling wave propagation.
- Previous methods often require complex structures or specific frequency ranges.
Purpose of the Study:
- To develop a new cloaking method for 2D quasistatic and Helmholtz problems.
- To demonstrate the effectiveness of exterior cloaking devices.
- To explore the potential extension to other linear wave equations.
Main Methods:
- Mathematical reduction of the 2D quasistatic problem to finding a specific polynomial.
- Construction of a polynomial approximating target values in distinct regions.
- Numerical simulations for the 2D Helmholtz equation using exterior cloaking devices.
Main Results:
- A single active exterior cloaking device effectively shields objects in 2D quasistatics.
- Very small scattered fields are produced by the cloaking device.
- Three exterior cloaking devices numerically demonstrated to hide objects in the 2D Helmholtz equation.
Conclusions:
- The proposed cloaking method is effective for 2D quasistatics and Helmholtz equations.
- Exterior cloaking devices offer a viable approach to wave shielding.
- The method shows promise for broader applications in linear wave phenomena.
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