NIM dispersion makes waves very inhomogeneous.

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Plane wave movie

Wave decay movie

What does happen to light entering NIM?
Our paper shows that the key in understanding wave propagation in NIM without making mistakes is never to forget wave dispersion.

The NIM wave dispersion causes large angles between the phase and the signal directions as shown above. This leads to very inhomogeneous waves that decay rapidly . This happens mainly because the shape of the modulations depends on the relative phases of the carriers.

Since proximity to narrow resonances is essential for realizing the low-loss NIM region of main interest, the magnitude of the refractive index is always much smaller than its fractional variation with frequency. This causes large wave dispersion and decay and can be found from the causality-based Kramers-Kronig relations.

This rapid wave decay is shown on left ( see movies too ). The wave is practically gone within about 20 wavelengths in NIM. At optical frequencies this is a very small distance of decay. Even within this distance the shape of the envelope gets severely distorted.

Note that all simulations shown here are just plots of exact analytic solutions of the linear wave equation obtained by matching the electromagnetic boundary conditions at the PIM-NIM interface. The numerical solutions used in the plots and movies are for illustrating our points. Our proof of the impossibility negative wave (signal) refraction does not depend on numerical calculations or modeling of any specific system. Our causality arguments apply to all physically realizable waves and materials. (A pure monochromatic wave lives forever and is not physically realizable).
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