Possible techniques for optical measurement of temperature and concentration profiles in a supersonic ramjet

Optical measurement techniques of temperature and concentration profiles in supersonic ramje

Controlling Light Through Optical Disordered Media : Transmission Matrix Approach

We experimentally measure the monochromatic transmission matrix (TM) of an optical multiple scattering medium using a spatial light modulator together with a phase-shifting interferometry measurement method. The TM contains all information needed to shape the scattered output field at will or to detect an image through the medium. We confront theory and experiment for these applications and we study the effect of noise on the reconstruction method. We also extracted from the TM informations about the statistical properties of the medium and the light transport whitin it. In particular, we are able to isolate the contributions of the Memory Effect (ME) and measure its attenuation length

Quasi Two-dimensional Transfer of Elastic Waves

A theory for multiple scattering of elastic waves is presented in a random medium bounded by two ideal free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. This geometry is relevant for seismic wave propagation in the Earth crust. We derive a time-dependent, quasi-2D radiative transfer equation, that describes the coupling of the eigenmodes of the layer (surface Rayleigh waves, SH waves, and Lamb waves). Expressions are found that relate the small-scale fluctuations to the life time of the modes and to their coupling rates. We discuss a diffusion approximation that simplifies the mathematics of this model significantly, and which should apply at large lapse times. Finally, coherent backscattering is studied within the quasi-2D radiative transfer equation for different source and detection configurations.Comment: REVTeX, 36 pages with 10 figures. Submitted to Phys. Rev.

Nonlinear Parabolic Equations arising in Mathematical Finance

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387

Localization of electromagnetic waves in a two dimensional random medium

Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many randomly distributed two dimensional dipoles. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for the total electromagnetic field. The results show that spatially localized electromagnetic waves are possible in such a simple but realistic disordered system. When localization occurs, a coherent behavior appears and is revealed as a unique property differentiating localization from either the residual absorption or the attenuation effects

Coherent Backscattering of Light by Cold Atoms

Light propagating in an optically thick sample experiences multiple scattering. It is now known that interferences alter this propagation, leading to an enhanced backscattering, a manifestation of weak localization of light in such diffuse samples. This phenomenon has been extensively studied with classical scatterers. In this letter we report the first experimental evidence for coherent backscattering of light in a laser-cooled gas of Rubidium atoms.Comment: 4 pages REVTEX, 1 page color image GIF, accepted for publication in Phys. Rev. Let

Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium

In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B {\bf 10}, 391 (1993)). A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with travelling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases that the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems (Asatryan, et al., Phys. Rev. E {\bf 67}, 036605 (2003).)Comment: 8 pages 9 figure

Eigenvalue distributions of correlated multichannel transfer matrices in strongly scattering systems

We experimentally study the effects of correlations in the propagation of ultrasonic waves in water from a multielement source to a multielement detector through a strongly scattering system of randomly placed vertical rods. Due to the strong scattering, the wave transport in the sample is in the diffusive regime. The correlation between the waves is induced when the distance between transducer elements is within the coherence region of the scattered sound. We measure the multichannel transfer matrix H, each element of which represents the signal strength between the m individual transmitters and n receivers. The observed eigenvalue distribution of the matrix HH dagger clearly shows the effect of correlations between channels and can be interpreted using random matrix theory. These results are of practical importance in many areas, e.g., for evaluating the information transfer capacity of such a complex scattering system