LEGRAND , Olivier

This chapter is an introduction to the semiclassical approach for the Helmholtz equation in complex systems originating in the field of quantum chaos. A particular emphasis will be made on the applications of trace formulae in paradigmatic wave cavities known as wave billiards. Its connection with random matrix theory (RMT) and disordered...

We report non-invasive measurements of the complex field of elastic quasimodes of a silicon wafer with chaotic shape. The amplitude and phase spatial distribution of the flexural modes are directly obtained by Fourier transform of time measurements. We investigate the crossover from real mode to complex-valued quasimode, when absorption is...

The description of open quantum system successfully uses the concept of the effective Hamiltonian, which takes into account the coupling to the environment. The concept can be extended to classical waves. Exper- imentally, classical waves are very convenient as they allow to control boundaries, coupling and absorption. We combine here recent...

In a 2D rectangular microwave cavity dressed with one point-like scatterer, a semiclassical approach is used to analyze the spectrum in terms of periodic orbits and diffractive orbits. We show, both numerically and experimentally, how the latter can be accounted for in the so-called length spectrum which is retrieved from 2-point correlations...

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We experimentally study the widths of resonances in a two-dimensional microwave cavity at room temperature. By developing a model for thecoupling antennas, we are able to discriminate their contribution from those of ohmic losses to the broadening of resonances. Concerning ohmic losses, we experimentally put to evidence two mechanisms: damping...

In a two-dimensional microwave chaotic cavity ohmic losses located at the contour of the cavity result in different broadenings of different modes. We provide an analytic description and establish the link between such an inhomogeneous damping and the complex (non-real) character of biorthogonal wave functions. This substantiates the...

In this letter, we demonstrate that a non-Hermitian Random Matrix description can account for both spectral and spatial statistics of resonance states in a weakly open chaotic wave system with continuously distributed losses. More specifically, the statistics of resonance states in an open 2D chaotic microwave cavity are investigated by solving...

We present a formal analogy between the eigenvalue problem for guided scalar modes in a low-contrast photonic bandgap fiber and quasi-stationary TM modes of a two-dimensional (2D) photonic structure. Using this analogy, we numerically study the confinement losses of disordered microstructured fibers through the leakage rate of an open 2D system...

In a two-dimensional microwave chaotic cavity ohmic losses located at the contour of the cavity result in different broadenings of different modes. We provide an analytic description and establish the link between such an inhomogeneous damping and the complex (non-real) character of biorthogonal wave functions. This substantiates the...

We experimentally study the various manifestations of ohmic losses in a two-dimensional microwave chaotic cavity and exhibit two different contributions to the resonance widths. We show that the parts of these widths, which vary from mode to mode, are associated to ohmic losses located at the boundary of the cavity. We also describe how this...

In this letter, we demonstrate that a non-Hermitian Random Matrix description can account for both spectral and spatial statistics of resonance states in a weakly open chaotic wave system with continuously distributed losses. More specifically, the statistics of resonance states in an open 2D chaotic microwave cavity are investigated by solving...

Electromagnetic reverberation chambers (RC) are nowadays commonly used for electromagnetic immunity testing applications. Thanks to the presence of a mechanical stirrer (generally a rotating metallic object), electronic devices under test are submitted to an isotropic, statistically uniform and depolarised electromagnetic field. The latter...

Electromagnetic reverberation chambers (RC) are nowadays commonly used for electromagnetic immunity testing applications. Thanks to the presence of a mechanical stirrer (generally a rotating metallic object), electronic devices under test are submitted to an isotropic, statistically uniform and depolarised electromagnetic field. The latter...

A Reverberation Chamber (RC) is analyzed with techniques issued from the wave chaos domain. The first 200 modes are determined numerically: their cumulated number is separated into a smooth part, predicted by the Weyl formula, and an oscillating part, interpreted in term of periodic orbits. The technique of the nearest-neighbor spacing...

A multimode optical fiber with a D-shaped cross section has already been proved to constitute a privileged system to image wavefunctions of a chaotic system. Nevertheless, diffraction of light at the fiber input precludes the excitation of individual wavefunctions and particularly the "scar" modes we want to investigate. We show that a...

La théorie des cavités chaotiques montre que dans ces dernières les champs répondent aux critères statistiques voulus dans les chambres réverbérantes. C'est pourquoi nous cherchons à nous inspirer des connaissances sur ces cavités pour optimiser les chambres réverbérantes. Dans ce résumé, nous présentons des résultats de simulations et de...

Using the knowledge gained from the wave chaos theory, we present a simple modification of the shape of a reverberation chamber (RC) consisting in inserting a metallic hemisphere on a cavity wall. The presented simulation results show a significant improvement of the field statistical properties, and this without resorting to a mode stirrer.