Statistics of resonance states in a weakly open chaotic cavity

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 the Maxwell equations with lossy boundaries subject to Ohmic dissipation. We successfully compare the statistics of its complex-valued resonance states and associated widths with analytical predictions based on a non-Hermitian effective Hamiltonian model defined by a finite number of fictitious open channels

Microfabricated rubber microscope using soft solid immersion lenses

We show here a technique of soft lithography to microfabricate efficient solid immersion lenses (SIL) out of rubber elastomers. The light collection efficiency of a lens system is described by its numerical aperture (NA), and is critical for applications as epifluorescence microscopy [B. Herman, Fluorescence Microscopy (BIOS Scientific, Oxford/Springer, United Kingdom, 1998). While most simple lens systems have numerical apertures less than 1, the lenses described here have NA=1.25. Better performance can be engineered though the use of compound designs; we used this principle to make compound solid immersion lenses (NA=1.32). An important application of these lenses will be as integrated optics for microfluidic devices. We incorporated them into a handheld rubber microscope for microfluidic flow cytometry and imaged single E. Coli cells by fluorescence

Complete S-matrix in a microwave cavity at room temperature

We experimentally study the widths of resonances in a two-dimensional microwave cavity at room temperature. By developing a model for the coupling 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 along propagation and absorption at the contour, the latter being responsible for variations of widths from mode to mode due to its dependence on the spatial distribution of the field at the contour. A theory, based on an S-matrix formalism, is given for these variations. It is successfully validated through measurements of several hundreds of resonances in a rectangular cavity.Comment: submitted to PR

Diffractive orbits in the length spectrum of a 2D microwave cavity with a small scatterer

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 of a finite range frequency spectrum. Beyond its fundamental interest, this first experimental evidence of the role played by diffractive orbits in the spectrum of an actual cavity, can be the first step towards a novel technique to detect and track small defects in wave cavities.Comment: 14 pages, format IO

Localized Modes in a Finite-Size Open Disordered Microwave Cavity

We present measurements of the spatial intensity distribution of localized modes in a two-dimensional open microwave cavity randomly filled with cylindrical dielectric scatterers. We show that each of these modes displays a range of localization lengths and successfully relate the largest value to the measured leakage rate at the boundary. These results constitute unambiguous signatures of the existence of strongly localized electromagnetic modes in two-dimensionnal open random media

Avoided level crossing statistics in open chaotic billiards

We investigate a two-level model with a large number of open decay channels in order to describe avoided level crossing statistics in open chaotic billiards. This model allows us to describe the fundamental changes of the probability distribution of the avoided level crossings compared with the closed case. Explicit expressions are derived for systems with preserved and broken Time Reversal Symmetry (TRS). We find that the decay process induces a modification at small spacings of the probability distribution of the avoided level crossings due to an attraction of the resonances. The theoretical predictions are in complete agreement with the recent experimental results of Dietz \textit{et al.} (Phys. Rev. E {\bf 73} (2006) 035201)

Universal behaviour of a wave chaos based electromagnetic reverberation chamber

In this article, we present a numerical investigation of three-dimensional electromagnetic Sinai-like cavities. We computed around 600 eigenmodes for two different geometries: a parallelepipedic cavity with one half- sphere on one wall and a parallelepipedic cavity with one half-sphere and two spherical caps on three adjacent walls. We show that the statistical requirements of a well operating reverberation chamber are better satisfied in the more complex geometry without a mechanical mode-stirrer/tuner. This is to the fact that our proposed cavities exhibit spatial and spectral statistical behaviours very close to those predicted by random matrix theory. More specifically, we show that in the range of frequency corresponding to the first few hundred modes, the suppression of non-generic modes (regarding their spatial statistics) can be achieved by reducing drastically the amount of parallel walls. Finally, we compare the influence of losses on the statistical complex response of the field inside a parallelepipedic and a chaotic cavity. We demonstrate that, in a chaotic cavity without any stirring process, the low frequency limit of a well operating reverberation chamber can be significantly reduced under the usual values obtained in mode-stirred reverberation chambers