Using the freedom of design that metamaterials provide, we show how electromagnetic fields can be redirected at will and propose a design strategy. The conserved fields-electric displacement field D, magnetic induction field B, and Poynting vector B-are all displaced in a consistent manner. A simple illustration is given of the cloaking of a proscribed volume of space to exclude completely all electromagnetic fields. Our work has relevance to exotic lens design and to the cloaking of objects from electromagnetic fields.

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Controlling Electromagnetic Fields

Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

https://depts.washington.edu/clawpack/book2/sample.pdf

Finite Volume Methods for Hyperbolic Problems

We present the design for an absorbing metamaterial (MM) with near unity absorbance A(omega). Our structure consists of two MM resonators that couple separately to electric and magnetic fields so as to absorb all incident radiation within a single unit cell layer. We fabricate, characterize, and analyze a MM absorber with a slightly lower predicted A(omega) of 96%. Unlike conventional absorbers, our MM consists solely of metallic elements. The substrate can therefore be optimized for other parameters of interest. We experimentally demonstrate a peak A(omega) greater than 88% at 11.5 GHz.

Perfect metamaterial absorber.

A modified set of Maxwell's equations is presented that includes complex coordinate stretching along the three Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow the specification of absorbing boundaries with zero reflection at all angles of incidence and all frequencies. The modified equations are also related to the perfectly matched layer that was presented recently for 2D wave propagation. Absorbing-material boundary conditions are of particular interest for finite-difference time-domain (FDTD) computations on a single-instruction multiple-data (SIMD) massively parallel supercomputer. A 3D FDTD algorithm has been developed on a connection machine CM-5 based on the modified Maxwell's equations and simulation results are presented to validate the approach. © 1994 John Wiley & Sons, Inc.

A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates

A new, freely available third party MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields is described. The toolbox, named k-Wave, is designed to make realistic photoacoustic modeling simple and fast. The forward simulations are based on a k-space pseudo-spectral time domain solution to coupled first-order acoustic equations for homogeneous or heterogeneous media in one, two, and three dimensions. The simulation functions can additionally be used as a flexible time reversal image reconstruction algorithm for an arbitrarily shaped measurement surface. A one-step image reconstruction algorithm for a planar detector geometry based on the fast Fourier transform (FFT) is also included. The architecture and use of the toolbox are described, and several novel modeling examples are given. First, the use of data interpolation is shown to considerably improve time reversal reconstructions when the measurement surface has only a sparse array of detector points. Second, by comparison with one-step, FFT-based reconstruction, time reversal is shown to be sufficiently general that it can also be used for finite-sized planar measurement surfaces. Last, the optimization of computational speed is demonstrated through parallel execution using a graphics processing unit.

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k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave fields

A perfectly matched layer for the absorption of electromagnetic waves

Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves

The wave-structure interactions are the most usual applications of the finite-difference method, in electromagnetic compatibility and radar cross-section computations. The aim of this paper is to get a detailed insight into the implementation of the perfectly matched layer (PML) technique when dealing with such important applications. The PML is a new technique developed for the simulation of free space with the finite-difference time-domain (FDTD) method. This paper deals with the application of this technique to the solution of wave-structure interaction problems. It is shown that the absorbing layer can be set very close to the structure, provided some specifications are satisfied, with the consequence that the computational requirements of the PML technique are far shorter than those of the other methods of free space simulation.

Perfectly matched layer for the FDTD solution of wave-structure interaction problems

This lecture presents the perfectly matched layer (PML) absorbing boundary condition (ABC) used to simulate free space when solving the Maxwell equations with such finite methods as the finite difference time domain (FDTD) method or the finite element method. The frequency domain and the time domain equations are derived for the different forms of PML media, namely the split PML, the CPML, the NPML, and the uniaxial PML, in the cases of PMLs matched to isotropic, anisotropic, and dispersive media. The implementation of the PML ABC in the FDTD method is presented in detail. Propagation and reflection of waves in the discretized FDTD space are derived and discussed, with a special emphasis on the problem of evanescent waves. The optimization of the PML ABC is addressed in two typical applications of the FDTD method: first, wave-structure interaction problems, and secondly, waveguide problems. Finally, a review of the literature on the application of the PML ABC to other numerical techniques of elec...

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Perfectly Matched Layer (PML) for Computational Electromagnetics

The author shows that the complex frequency shifted PML (CFS PML) can be optimized in view of absorbing both the evanescent and traveling waves at the end of waveguiding structures. Numerical results are provided to illustrate the effectiveness of the optimized CFS PML in FDTD computations.

Jean-Pierre Berenger

Papers

A perfectly matched layer for the absorption of electromagnetic waves

Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves

Perfectly matched layer for the FDTD solution of wave-structure interaction problems

Perfectly Matched Layer (PML) for Computational Electromagnetics

Application of the CFS PML to the absorption of evanescent waves in waveguides