182 research outputs found
Experimental Observation of a Fundamental Length Scale of Waves in Random Media
Waves propagating through a weakly scattering random medium show a pronounced
branching of the flow accompanied by the formation of freak waves, i.e.,
extremely intense waves. Theory predicts that this strong fluctuation regime is
accompanied by its own fundamental length scale of transport in random media,
parametrically different from the mean free path or the localization length. We
show numerically how the scintillation index can be used to assess the scaling
behavior of the branching length. We report the experimental observation of
this scaling using microwave transport experiments in quasi-two-dimensional
resonators with randomly distributed weak scatterers. Remarkably, the scaling
range extends much further than expected from random caustics statistics.Comment: 5 pages, 5 figure
Array imaging of localized objects in homogeneous and heterogeneous media
We present a comprehensive study of the resolution and stability properties
of sparse promoting optimization theories applied to narrow band array imaging
of localized scatterers. We consider homogeneous and heterogeneous media, and
multiple and single scattering situations. When the media is homogeneous with
strong multiple scattering between scatterers, we give a non-iterative
formulation to find the locations and reflectivities of the scatterers from a
nonlinear inverse problem in two steps, using either single or multiple
illuminations. We further introduce an approach that uses the top singular
vectors of the response matrix as optimal illuminations, which improves the
robustness of sparse promoting optimization with respect to additive noise.
When multiple scattering is negligible, the optimization problem becomes linear
and can be reduced to a hybrid- method when optimal illuminations are
used. When the media is random, and the interaction with the unknown
inhomogeneities can be primarily modeled by wavefront distortions, we address
the statistical stability of these methods. We analyze the fluctuations of the
images obtained with the hybrid- method, and we show that it is stable
with respect to different realizations of the random medium provided the
imaging array is large enough. We compare the performance of the
hybrid- method in random media to the widely used Kirchhoff migration
and the multiple signal classification methods
Ultrasonic scattering from decorated grain boundaries
The microstructure of polycrystalline materials is manipulated in many ways to create materials with superior engineering properties. Alloying pure materials, for example, can alter crystallographic structure to strengthen or stiffen the material, but when impurities collect along grain boundaries, the material may become embrittled. This undesirable condition is generally associated with improper heat treatment during fabrication, but it may also occur during the service life of alloys exposed to penetrating radiation or severe thermal conditions. This dissertation studies scattering from decorated grain boundaries theoretically and experimentally, and ties results for isolated scatterers to grain noise measurements on materials composed entirely of scattering structures. The theoretical analysis begins with a treatment of a grain with decorated boundaries. This is modelled as an isolated isotropic spherical scatterer with a shell of spherically orthotropic material surrounding the core. This composite scatterer is embedded in a homogeneous isotropic host, and exact equations for scattering of an incident plane longitudinal wave are developed. Approximate and exact solutions for these equations are derived, and compared to prior solutions in the limiting case of an isotropic shell. The solution is then extended to focused incident fields, using a generalized Fourier series to represent the incident field in a form compatible with the separation of variables method of solving the spherical scatterer problem. Good agreement for scattering from isolated spherical scatterers, without and with a shell, and in a focused field, is obtained when theoretical results are compared with observations on microspheres of titanium - 6 aluminum - 4 vanadium (Ti64) and similar microspheres having a shell of nitrided Ti64. Finally, isolated scatterer theory is incorporated into backscattering models which allow multiple independent scatterers, scattering due to crystallographic anisotropy, and scattering from phase contrast in multiphase materials. Calculations based on these backscattering theories compare favorably with ultrasonic grain noise measurements on solid samples compacted from the Ti64 and nitrided Ti64 microspheres
Filtering random layering effects in imaging
Objects that are buried deep in heterogeneous media produce faint echoes which are difficult to distinguish from the backscattered field. Sensor array imaging in such media cannot work unless we filter out the backscattered echoes and enhance the coherent arrivals that carry information about the objects that we wish to image. We study such filters for imaging in strongly backscattering, finely layered media. The filters are based on a travel time transformation of the array data, the normal move-out, used frequently in connection with differential semblance velocity estimation in seismic imaging. In a previous paper [10] we showed that the filters can be used to remove coherent signals from strong plane reflectors. In this paper we show theoretically and with extensive numerical simulations that these filters, based on the normal move-out, can also remove the incoherent arrivals in the array data that are due to fine random layering in the medium. Key words. array imaging, randomly layered media, filtering
Coherent multiple scattering of light in (2+1) dimensions
We formulate a multiple scattering theory of light in media spatially
disordered along two directions and homogeneous along the third one, without
making any paraxial approximation on the wave equation and fully treating the
vector character of light. With this formalism, we calculate the distribution
of transverse momenta of a beam as it evolves along the optical axis, and
unveil a phenomenon not captured by the paraxial equation: a cross-over from a
scalar to a vector regime, visible in the coherent backscattering peak as
polarization gets randomized.Comment: 10 page
Beam shaping using genetically optimized two-dimensional photonic crystals
We propose the use of two-dimensional photonic crystals with engineered
defects for the generation of an arbitrary-profile beam from a focused input
beam. The cylindrical harmonics expansion of complex-source beams is derived
and used to compute the scattered wavefunction of a 2D photonic crystal via the
multiple scattering method. The beam shaping problem is then solved using a
genetic algorithm. We illustrate our procedure by generating different orders
of Hermite-Gauss profiles, while maintaining reasonable losses and tolerance to
variations in the input beam and the slab refractive index
Multiple scattering of polarized light in disordered media exhibiting short-range structural correlations
We develop a model based on a multiple scattering theory to describe the
diffusion of polarized light in disordered media exhibiting short-range
structural correlations. Starting from exact expressions of the average field
and the field spatial correlation function, we derive a radiative transfer
equation for the polarization-resolved specific intensity that is valid for
weak disorder and we solve it analytically in the diffusion limit. A
decomposition of the specific intensity in terms of polarization eigenmodes
reveals how structural correlations, represented via the standard anisotropic
scattering parameter , affect the diffusion of polarized light. More
specifically, we find that propagation through each polarization eigenchannel
is described by its own transport mean free path that depends on in a
specific and non-trivial way
Helicity and duality symmetry in light matter interactions: Theory and applications
In my thesis, I first develop the theoretical basis and tools for the use of
helicity and duality in the study, understanding and engineering of
interactions between electromagnetic radiation and material systems. Then,
within the general framework of symmetries and conservation laws, I apply the
theoretical results to several different problems: Optical activity, zero
backscattering, metamaterials for transformation optics and nanophotonics
phenomena involving the electromagnetic angular momentum. The tool has provided
new insights and design guidelines in all these cases.Comment: PhD Thesis, Department of Physics and Astronomy, Macquarie
University. Fixed a very slow figure from the previous versio
- …