Acoustic Analogies for Quantum Mechanics

Abstract

In Chap. 2, we considered the analogy between the propagation of electromagnetic waves and quantum waves, based on the formal similarity between the Helmholtz and the Schrödinger equation. However, a similar analogy holds for sound waves. This is to be expected since sound waves are not so different from electromagnetic waves. In fact acoustical devices made of periodic distributions of rigid cylinders in air which are similar to refractive optical components have been demonstrated recently (Cervera et al., 2002) and solitary elastic surface pulses similar to optical solitons have been reported (Lomonosov et al., 2002). However, there are also differences between electromagnetic and acoustic systems. For example, transient acoustic waves propagating through a disordered medium in the high-order multiple scattering regime can converge to their source and recover their original wave form with the help of an acoustic time-reversal mirror (Derode et al. 1995). Such a time-reversal mirror, similar to the phase conjugation method that holds for monochromatic waves, has not been demonstrated for optical waves.