Metamaterials represent one of the most vibrant fields of modern science and technology. They are generally dispersive structures in the direct and reciprocal space and time domains. Upon this consideration, I overview here a number of metamaterial innovations developed by colleagues and myself in the holistic framework of space and time dispersion engineering. Moreover, I provide some thoughts regarding the future perspectives of the area.
This paper presents the authors vision of the emerging field of spacetime metamaterials in a cohesive and pedagogical perspective. For this purpose, it systematically builds up the physics, modeling and applications of these media upon the foundation of their pure-space and pure-time counterparts.
We propose a simple singularity-free coordinate transformation that could be implemented in Maxwells equations in order to simulate one aspect of a Kerr black hole. Kerr black holes are known to force light to rotate in a predetermined direction inside the ergoregion. By making use of cosmological analogies and the theoretical framework of transformation optics, we have designed a metamaterial that can make light behave as if it is propagating around a rotating cosmological massive body. We present numerical simulations involving incident Gaussian beams interacting with the materials to verify our predictions. The ergoregion is defined through the dispersion curve of the off-axis permittivities components.
A new formalism for electromagnetic and mechanical momenta in a metamaterial is developed by means of the technique of wave-packet integrals. The medium has huge mass density and can therefore be regarded as almost stationary upon incident electromagnetic waves. A clear identification of momentum density and momentum flow, including their electromagnetic and mechanical parts, is obtained by employing this formalism in a lossless dispersive metamaterial (including the cases of impedance matching and mismatching with vacuum). It is found that the ratio of the electromagnetic momentum density to the mechanical momentum density depends on the impedance and group velocity of the electromagnetic wave inside the metamaterial. One of the definite results is that both the electromagnetic momentum and the mechanical momentum in the metamaterial are in the same direction as the energy flow, instead of in the direction of the wave vector. The conservation of total momentum is verified. In addition, the law of energy conservation in the process of normal incidence is also verified by using the wave-packet integral of both the electromagnetic energy density and the electromagnetic power density, of which the latter is caused by the interaction between the induced (polarized) currents and the electromagnetic wave.
Traditionally, a black hole is a region of space with huge gravitational field, which absorbs everything hitting it. In history, the black hole was first discussed by Laplace under the Newton mechanics, whose event horizon radius is the same as the Schwarzschilds solution of the Einsteins vacuum field equations. If all those objects having such an event horizon radius but different gravitational fields are called as black holes, then one can simulate certain properties of the black holes using electromagnetic fields and metamaterials due to the similar propagation behaviours of electromagnetic waves in curved space and in inhomogeneous metamaterials. In a recent theoretical work by Narimanov and Kildishev, an optical black hole has been proposed based on metamaterials, in which the theoretical analysis and numerical simulations showed that all electromagnetic waves hitting it are trapped and absorbed. Here we report the first experimental demonstration of such an electromagnetic black hole in the microwave frequencies. The proposed black hole is composed of non-resonant and resonant metamaterial structures, which can trap and absorb electromagnetic waves coming from all directions spirally inwards without any reflections due to the local control of electromagnetic fields and the event horizon corresponding to the device boundary. It is shown that the absorption rate can reach 99% in the microwave frequencies. We expect that the electromagnetic black hole could be used as the thermal emitting source and to harvest the solar light.
Electromagnetic pulses are typically treated as space-time (or space-frequency) separable solutions of Maxwells equations, where spatial and temporal (spectral) dependence can be treated separately. In contrast to this traditional viewpoint, recent advances in structured light and topological optics have highlighted the non-trivial wave-matter interactions of pulses with complex topology and space-time non-separable structure, as well as their potential for energy and information transfer. A characteristic example of such a pulse is the Flying Doughnut (FD), a space-time non-separable toroidal few-cycle pulse with links to toroidal and non-radiating (anapole) excitations in matter. Here, we propose a quantum-mechanics-inspired methodology for the characterization of space-time non-separability in structured pulses. In analogy to the non-separability of entangled quantum systems, we introduce the concept of space-spectrum entangled states to describe the space-time non-separability of classical electromagnetic pulses and develop a method to reconstruct the corresponding density matrix by state tomography. We apply our method to the FD pulse and obtain the corresponding fidelity, concurrence, and entanglement of formation. We demonstrate that such properties dug out from quantum mechanics quantitatively characterize the evolution of the general spatiotemporal structured pulse upon propagation.