2,165 research outputs found
Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics
Scattering theory has had a major roll in twentieth century mathematical
physics. Mathematical modeling and algorithms of direct,- and inverse
electromagnetic scattering formulation due to biological tissues are
investigated. The algorithms are used for a model based illustration technique
within the microwave range. A number of methods is given to solve the inverse
electromagnetic scattering problem in which the nonlinear and ill-posed nature
of the problem are acknowledged.Comment: 61 pages, 5 figure
Machine learning for knowledge acquisition and accelerated inverse-design for non-Hermitian systems
Non-Hermitian systems offer new platforms for unusual physical properties that can be flexibly manipulated by redistribution of the real and imaginary parts of refractive indices, whose presence breaks conventional wave propagation symmetries, leading to asymmetric reflection and symmetric transmission with respect to the wave propagation direction. Here, we use supervised and unsupervised learning techniques for knowledge acquisition in non-Hermitian systems which accelerate the inverse design process. In particular, we construct a deep learning model that relates the transmission and asymmetric reflection in non-conservative settings and propose sub-manifold learning to recognize non-Hermitian features from transmission spectra. The developed deep learning framework determines the feasibility of a desired spectral response for a given structure and uncovers the role of effective gain-loss parameters to tailor the spectral response. These findings offer a route for intelligent inverse design and contribute to the understanding of physical mechanism in general non-Hermitian systems.Postprint (published version
Dual polarization nonlinear Fourier transform-based optical communication system
New services and applications are causing an exponential increase in internet
traffic. In a few years, current fiber optic communication system
infrastructure will not be able to meet this demand because fiber nonlinearity
dramatically limits the information transmission rate. Eigenvalue communication
could potentially overcome these limitations. It relies on a mathematical
technique called "nonlinear Fourier transform (NFT)" to exploit the "hidden"
linearity of the nonlinear Schr\"odinger equation as the master model for
signal propagation in an optical fiber. We present here the theoretical tools
describing the NFT for the Manakov system and report on experimental
transmission results for dual polarization in fiber optic eigenvalue
communications. A transmission of up to 373.5 km with bit error rate less than
the hard-decision forward error correction threshold has been achieved. Our
results demonstrate that dual-polarization NFT can work in practice and enable
an increased spectral efficiency in NFT-based communication systems, which are
currently based on single polarization channels
Forward and inverse acoustic scattering problems involving the mass density
This investigation is concerned with the 2D acoustic scattering problem of a plane wave propagating in a non-lossy fluid host and soliciting a linear, isotropic, macroscopically-homogeneous, lossy, flat-plane layer in which the mass density and wavespeed are different from those of the host. The focus is on the inverse problem of the retrieval of either the layer mass density or the real part of the layer wavespeed. The data is the transmitted pressure field, obtained by simulation (resolution of the forward problem) in exact, explicit form via separation of variables. Another form of this solution, which is exact and more explicit in terms of the mass-density contrast (between the host and layer), is obtained by a domain-integral method. A perturbation technique enables this solution to be cast as a series of powers of the mass density contrast, the first three terms of which are employed as the trial models in the treatment of the inverse problem. The aptitude of these models to retrieve the mass density contrast and real part of the layer wavespeed is demonstrated both theoretically and numerically
Forward and inverse acoustic scattering problems involving the mass density
This investigation is concerned with the 2D acoustic scattering problem of a
plane wave propagating in a non-lossy fluid host and soliciting a linear,
isotropic, macroscopically-homogeneous, lossy, flat-plane layer in which the
mass density and wavespeed are different from those of the host. The focus is
on the inverse problem of the retrieval of either the layer mass density or the
real part of the layer wavespeed. The data is the transmitted pressure field,
obtained by simulation (resolution of the forward problem) in exact, explicit
form via separation of variables. Another form of this solution, which is exact
and more explicit in terms of the mass-density contrast (between the host and
layer), is obtained by a domain-integral method. A perturbation technique
enables this solution to be cast as a series of powers of the mass density
contrast, the first three terms of which are employed as the trial models in
the treatment of the inverse problem. The aptitude of these models to retrieve
the mass density contrast and real part of the layer wavespeed is demonstrated
both theoretically and numerically.
Keywords: 2D acoustics, forward scattering, inverse scattering, domain
integral equation, constant mass density assumption, small density contrast,
retrieval accurac
Modal Analysis and Coupling in Metal-Insulator-Metal Waveguides
This paper shows how to analyze plasmonic metal-insulator-metal waveguides
using the full modal structure of these guides. The analysis applies to all
frequencies, particularly including the near infrared and visible spectrum, and
to a wide range of sizes, including nanometallic structures. We use the
approach here specifically to analyze waveguide junctions. We show that the
full modal structure of the metal-insulator-metal (MIM) waveguides--which
consists of real and complex discrete eigenvalue spectra, as well as the
continuous spectrum--forms a complete basis set. We provide the derivation of
these modes using the techniques developed for Sturm-Liouville and generalized
eigenvalue equations. We demonstrate the need to include all parts of the
spectrum to have a complete set of basis vectors to describe scattering within
MIM waveguides with the mode-matching technique. We numerically compare the
mode-matching formulation with finite-difference frequency-domain analysis and
find very good agreement between the two for modal scattering at symmetric MIM
waveguide junctions. We touch upon the similarities between the underlying
mathematical structure of the MIM waveguide and the PT symmetric quantum
mechanical pseudo-Hermitian Hamiltonians. The rich set of modes that the MIM
waveguide supports forms a canonical example against which other more
complicated geometries can be compared. Our work here encompasses the microwave
results, but extends also to waveguides with real metals even at infrared and
optical frequencies.Comment: 17 pages, 13 figures, 2 tables, references expanded, typos fixed,
figures slightly modifie
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