Coherent backscattering of ultrasound without a source

– Coherent backscattering is due to constructive interferences of reciprocal paths and leads to an enhancement of the intensity of a multiply scattered field near its source. To observe this enhancement an array of receivers is conventionally placed close to the source. Our approach here is different. In a first experiment, we recover the coherent backscattering effect (CBE) within an array of sources and a distant receiver using time correlation of diffuse fields. The enhancement cone has an excellent spatial resolution. The dynamics of the enhancement factor is studied in a second experiment using correlation of thermal phonons at the same ultrasonic frequencies, without any active source. Coherent Backscattering Enhancement (CBE) is a consequence of interferences in multiple scattering or multiple reverberations of waves in a complex environment. It was first observed for electrons [1], then in optics [2, 3] where it exhibited as a doubling of the backscattered energy in the incident direction. Later, it was applied to various fields of wave physics, like ultrasound [4–6], laser in cold atoms [7], and more recently to seismology [8]. In these fields, CBE was shown to be an accurate way to measure transport mean-free paths of the medium, a quantity that characterizes its degree of heterogeneity. The origin of CBE is the constructive interference between long reciprocal paths in wave scattering or reverberation. This enhances the probability for the wave to return to the source by a factor of exactly two in open media, and three in closed cavities, which results in the local energy density enhancement by the same factor [9, 10]. In a reverberant body, it was proved that the CBE factor increases from two to three with a dynamics driven by the Heisenberg time TH (also referred to as the break time of the cavity) [6]. When the source and the receivers are placed inside the diffusive medium, the spatial extent of the cone is the order of the wavelength [6, 11]. In all of these active experiments, the observation of CBE requires that a receiver be placed close to the source. Unfortunately, the source-receiver configuration is sometime disadvantaging. First, it may break the reciprocity condition if the source and the receiver have not exactly the same orientation [12]. Second, placing a source close to the receiver is hard to perform as soon as the sizes of source and recording device are not negligible compared to the wavelength. In