Doctoral thesis viva voce: Fabrice Lemoult

This thesis follows on studies realized at the Institut Langevin concerning the spatio-temporal control of waves. In this context, we first show that random multiple scattering media give more opportunities than their homogeneous counterpart. We quantify these benefits and interpret them in terms of spatio-temporal degrees of freedom that can be controlled through the use of large bandwidth signals and multiple sources. We then study locally resonant complex media and make the link between different models (effective medium, polariton, hybridization) to describe the propagation inside such media. When the typical spatial scale of the medium is smaller than the free space wavelength, we demonstrate theoretically the existence of propagating waves that oscillate faster than the free space wavelength. By exploiting the spatio-temporal degrees of freedom of the medium, we show the possibility to excite and control those modes from the far field region. Thus, we give experimental and numerical results of focusing and imaging beyond the diffraction limit from the far field in three branches of wave physics : microwaves, acoustics and optics. We eventually focus on the frequency range where no propagating modes exist : a photonic (phononic) bandgap. We show that the introduction of a locally resonant defect inside the medium permits to build a resonant cavity or a waveguide, characterized by a deeply subwavelength spatial scale.