Negative reflection of elastic guided waves in chaotic and random scattering media
Résumé
The propagation of waves in complex media can be harnessed either by taming the incident wave-field impinging on the medium or by forcing waves along desired paths through its careful design. These two alternative strategies have given rise to fascinating concepts such as time reversal or negative refraction. Here, we show how these two processes are intimately linked through the negative reflection phenomenon. A negative reflecting mirror converts a wave of positive phase velocity into its negative counterpart and vice versa. In this article, we experimentally demonstrate this phenomenon with elastic waves in a 2D billiard and in a disordered plate by means of laser interferometry. Despite the complexity of such configurations, the negatively reflected wave field focuses back towards the initial source location, thereby mimicking a phase conjugation operation while being a fully passive process. The super-focusing capability of negative reflection is also highlighted in a monochromatic regime. The negative reflection phenomenon is not restricted to guided elastic waves since it can occur in zero-gap systems such as photonic crystals, chiral metamaterials or graphene. Negative reflection can thus become a tool of choice for the control of waves in all fields of wave physics. Controlling the propagation of acoustic or electromagnetic waves, is of fundamental interest for many applications ranging from imaging the living and detecting hazardous components, to information processing and structural health monitoring. In the past decades, there has been many proposals in this regards, which can be separated within two approaches. On the one hand, the wave fields can be tamed in order to take advantage of the complexity of propagation media, for instance, to focus waves or image various objects. This is realized in the temporal domain using time reversal (TR) mirrors 1-3 or in the spatial domain using phase conjugation (PC) 4-6 and wave-front shaping techniques 7 developed in optics. On the other hand, one can force waves along desired paths through a careful design of man-made materials. This can be achieved using metamaterials, an arrangement of tailored sub-wavelength building blocks from which the material gains its unusual properties 8-10. The advent of such structures has given rise to fascinating concepts such as negative refraction 11-13 , transformation optics 14,15 or metasurfaces 16. Although the concepts of TR and negative refraction have been developed in an independent fashion, they are intimately linked processes 17,18. Here, we want to push forward this analogy by investigating the negative reflection (NR) phenomenon. A NR mirror is an interface at which light or sound is retro-reflected. There is a strong similarity with a PC mirror. In a PC experiment, if the incident wave is divergent, the PC wave is converging [Fig. 1(a)]. It follows the same path as the incident wave but in an opposite way, thus back-focusing exactly on the source location. Let us now consider a NR mirror and an incident forward wave with a Poynting vector, P i , and a wave vector, k i , pointing in the same direction (i.e. with a positive phase velocity, v φ > 0) [see Fig. 1(b,c)]. The NR mirror gives rise to a reflected backward wave (v φ < 0), i.e. with a Poynting vector, P r , and a wave vector, k r , of opposite direction [see Fig. 1(b,c)]. By virtue of the Snell-Descartes law, the incident and reflected wave vectors are strictly identical (k r = k i) but their Poynting vectors shall be in opposite directions (P r = −P i) [Fig. 1(b)]. Negative reflection is a perfectly reciprocal phenomenon: A backward incident wave with anti-parallel k i and P i will be negatively reflected into a forward mode with parallel k r and P r. If the incident wave is divergent, the NR wave back-converges towards the initial source position. We thus recover a similar effect as in PC, although the reflected wave vectors in each case are in opposite directions [Fig. 1(a,c)]. The PC concept and its temporal equivalent, TR, have shown to be particularly powerful in
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