# Wave front shaping with chaotic cavities : RMT model and application

**Speaker:** Jean-Baptiste Gros, ESPCI, Institut Langevin, Paris

**Title:** Wave front shaping with chaotic cavities : RMT model and application

**Abstract: **For decades, wave chaos has been an attractive field of fundamental research concerning a wide variety of physical systems such as quantum physics , room acoustics or ocean acoustics, elastodynamics, guided-wave optics, microwave cavities ,etc. The success of wave chaos is mainly due to its ability to describe such a variety of complex systems through a unique formalism which permits us to derive a universal statistical behaviour.

Indeed, since the Bohigas-Giannoni-Schmit conjecture concerning the universality of level fluctuations in chaotic quantum spectra, it has become customary to analyse spectral and spatial statistics of wave systems whose ray counterpart is chaotic with the help of statistical tools introduced by random matrix theory (RMT).

In recent years electromagnetic (EM) chaotic cavities have been involved in a variety of applications ranging from reverberation chambers for electromagnetic compatibility (EMC) to microwave imaging , wavefront shaping or telecommunication and energy harvesting. Among all the universal statistics of chaotic cavities, one of the most important for applications is the field ergodicity of the responses and eigenfields. It means that fields in chaotic systems are statistically equivalent to an appropriate random superposition of plane waves.

During this talk, I will present a new approach to build a chaotic reverberation chamber from a regular cavity without modification of its geometry. Traditionally, a chaotic cavity is build from a regular one by modifying its geometry ( for instance by adding spherical caps or hemisphere) until its spatial and/or spectral statistics follow the RMT predictions. Here we propose to use spatial microwave modulators (SMM). SMM are commonly used in wavefront shaping applications to control locally the boundary conditions and create a reconfigurable cavity.

In the second part of the talk, I will show that reconfigurable cavities, because they permit to create chaotic cavities, are in fact excellent reverberation chambers for electromagnetic compatibility testing. In this part, I will compare different quantities introduced by the EMC Standard with those measured in a chaotic reconfigurable cavity.

In the last part of the talk, I will present a RMT model for wavefront shaping in chaotic cavities. This model is able to reproduce the experimentally observed behaviour of reconfigurable cavities.