The higher order multipoles above the electric quadrupole are commonly neglected in metamaterial homogenization. We show that they nevertheless can be significant when second order spatial dispersive effects, such as the magnetic response, are considered. In this respect, they can be equally important as the magnetization and quadrupole terms, and should not automatically be neglected.
The idealization of monochromatic plane waves leads to considerable simplifications in the analysis of electromagnetic systems. However, for active systems this idealization may be dangerous due to the presence of growing waves. Here we consider a gainy slab, and use a realistic incident beam, which is both causal and has finite width. This clarifies some apparent paradoxes arising from earlier analyses of this setup. In general it turns out to be necessary to involve complex frequencies ω and/or complex transversal wavenumbers kx. Simultaneously real ω and kx cannot describe amplified waves in a slab which is infinite in the transversal direction. We also show that the only possibility to have an absolute instability for a finite width beam, is if a normally incident plane wave would experience an instability.
The analysis of wave propagation in linear, passive media is usually done by considering a single real frequency (the monochromatic limit) and also often a single plane wave component (plane wave limit). For gain media, we demonstrate that these two limits generally do not commute; for example, one order may lead to a diverging field, while the other order leads to a finite field. Moreover, the plane wave limit may be dependent on whether it is realized with a finite support excitation or gaussian excitation, eventually of infinite widths. We consider wave propagation in gain media by a Fourier-Laplace integral in space and time, and demonstrate how the correct monochromatic limit or plane wave limit can be taken, by deforming the integration surface in complex frequency-complex wavenumber space. We also give the most general criterion for absolute instabilities. The general theory is applied in several cases, and is used to predict media with novel properties. In particular, we show the existence of isotropic media which in principle exhibit simultaneous refraction, meaning that they refract positively and negatively at the same time.
Magnetic permeabilities derived for infinite, periodic media are used in the Fresnel equation to calculate the reflection from corresponding semi-infinite media. By comparison to finite-differencetime-domain (FDTD) simulations, we find that the Fresnel equation gives accurate results for 2D metamaterials which mimic natural magnetism, in a frequency range where the magnetic moment density dominates the O(k 2 ) part of the total Landau-Lifshitz permittivity. For a 1D layered structure, or for large frequencies, the correspondence is poor. We also demonstrate that even if a medium is described accurately by a local permittivity and permeability, the Fresnel equation is not necessarily valid.
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