Manipulating Spatiotemporal Degrees of Freedom of Waves in Random Media

We show that all the spatiotemporal degrees of freedom available in a complex medium can be harnessed and converted into spatial ones. This is demonstrated experimentally through an instantaneous spatial inversion, using broadband ultrasonic waves in a multiple scattering sample. We show theoretically that the inversion convergence is governed by the total number of degrees of freedom available in the medium for a fixed bandwidth and demonstrate experimentally its use for complex media investigation. We believe our approach has potential in sensing, imagery, focusing, and telecommunication.

Figure 1

Schematic representation of a broadband time reversal operation (a) and the iterative focusing (b). Each arrow (a Fresnel vector) represents a frequency component. (a) Frequency components add constructively at the source, and randomly outside. (b) Outside the source, the corrections (red arrows) cancel the initial field.

Figure 2

(Top) Focal spot for time reversal (black dashed-dotted line) and emission of iterative signals (red dashed line) with one transducer source. The blue line represents the instantaneous spot with emission of the iterative signals. The focused pulses for TR and iterative signals emissions are represented in the inset. (Bottom) The 21 instantaneous focal spots for time reversal (left) and iterative signals (right): a true inversion over 21 points with only one source is shown.

Figure 3

Evolution with frequency of the reconstructed elastic mean free path. The reconstruction is done, according to Eq. (12), using convergence criterion. The red asterisks represent a theoretical prediction for a Gaussian distribution of radii [17] (mean radius 0.4 mm, standard deviation 8 mm).