A fast high-order solver for problems of scattering by heterogeneous bodies

A new high-order integral algorithm for the solution of scattering problems by heterogeneous bodies is presented. Here, a scatterer is described by a (continuously or discontinuously) varying refractive index n(x) within a two-dimensional (2D) bounded region; solutions of the associated Helmholtz equation under given incident fields are then obtained by high-order inversion of the Lippmann-Schwinger integral equation. The algorithm runs in O(Nlog(N)) operations where N is the number of discretization points. A wide variety of numerical examples provided include applications to highly singular geometries, high-contrast configurations, as well as acoustically/electrically large problems for which supercomputing resources have been used recently. Our method provides highly accurate solutions for such problems on small desktop computers in CPU times of the order of seconds

Inverse scattering problem for optical coherence tomography

We deal with the imaging problem of determining the internal structure of a body from backscattered laser light and low-coherence interferometry. Specifically, using the interference fringes that result when the backscattering of low-coherence light is made to interfere with the reference beam, we obtain maps detailing the values of the refractive index within the sample. Our approach accounts fully for the statistical nature of the coherence phenomenon; the numerical experiments that we present, which show image reconstructions of high quality, were obtained under noise floors exceeding those present for various experimental setups reported in the literature

Universal Kaluza-Klein reductions of type IIB to N=4 supergravity in five dimensions

We construct explicit consistent Kaluza-Klein reductions of type IIB supergravity on HK_4 x S^1, where HK_4 is an arbitrary four-dimensional hyper-Kaehler manifold, and on SE5, an arbitrary five-dimensional Sasaki-Einstein manifold. In the former case we obtain the bosonic action of D=5 N=4 (ungauged) supergravity coupled to two vector multiplets. For the SE_5 case we extend a known reduction, which leads to minimal D=5 N=2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the SE_5. We show that the resulting D=5 action is also consistent with N=4 gauged supergravity coupled to two vector multiplets. This theory has a supersymmetric AdS_5 vacuum, which uplifts to the class of supersymmetric AdS_5 x SE_5 solutions, that spontaneously breaks N=4 to N=2, and also a non-supersymmetric AdS_5 vacuum which uplifts to a class of solutions first found by Romans.Comment: 1+34 pages. v2: Minor typos corrected, three references added. Version to be published in JHE