Waves and metamaterials illustrations

Polarized electromagnetic waves. E: electric field. B: magnetic field, k: wave vector. This k vector determines the direction of the wave phase. The vectors E and B determine the wave packet way (the energy of this wave is following the wave packet).
 
On the left, the wave packet and the wave phase are going in the same way.
 
On the right, E and B stay the same, the wave packet follow the same way as figure "a" but the k vector is going in the opposite way. The wave phase and packet are in the opposite way. This is a metamaterial with a negative refractive index.
Acoustic wave: propagation of a vibrational stat
 
a                                                               pressure field
b        density oscillation induce by this pressure field
Representation of a mechanical phase shift. The objet is expanding under a pressure. This is the behavior of a phase shift between an acoustic wave and a resonant object.
 
Brunet, T., J. Leng, and O. Mondain-Monval, Soft Acoustic Metamaterials. Science, 2013.
342: p. 323-324.
Representation of a mechanical phase shift. Acceleration and applied force on the object are going in opposite way. This is the behavior of a phase shift between an acoustic wave and a resonant object.
 

Brunet, T., J. Leng, and O. Mondain-Monval, Soft Acoustic Metamaterials. Science, 2013.
342: p. 323-324.
Propagation of an acoustic monochromatic wave in a medium with a positive refractive index (real part of n). The horizontal axis is the time (or distance) and the vertical one, the pressure variation. In bleu, wave packet. In red, different phase of the wave. For a medium with a positive refractive index (common materials) Group and phase are going in the same way.
Propagation of an acoustic monochromatic wave in a medium with a negative refractive index (real part of n). The horizontal axis is the time (or distance) and the vertical one, the pressure variation. In bleu, wave packet. In red, different phase of the wave. For a medium with a negative refractive index (metamaterials) group and phase are going in the opposite way.
Refraction effect between two mediums. On red, refraction in a common material. In bleu, refraction in a metamaterial.
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