21 research outputs found
Electromagnetic radiation in a time-varying background medium
Analytical solutions are presented for the electromagnetic radiation by an
arbitrary pulsed source into a homogeneous time-varying background medium. In
the constant-impedance case an explicit radiation formula is obtained for the
synchronous permittivity and permeability described by any positive function of
time. As might be expected, such a medium introduces significant spectral
shifts and spatio-temporal modulation, which are analized here for the linear
and exponential time-variations of the medium parameters. In the
varying-impedance case the solution is obtained for the fourth-order polynomial
time-dependence of the permittivity. In addition to the spectral shifts and
modulation this spatially homogeneous medium scatters the field introducing
causal echoes at the receiver location.Comment: 17 pages, no figure
Transverse electric scattering on inhomogeneous objects: spectrum of integral operator and preconditioning
The domain integral equation method with its FFT-based matrix-vector products
is a viable alternative to local methods in free-space scattering problems.
However, it often suffers from the extremely slow convergence of iterative
methods, especially in the transverse electric (TE) case with large or negative
permittivity. We identify the nontrivial essential spectrum of the pertaining
integral operator as partly responsible for this behavior, and the main reason
why a normally efficient deflating preconditioner does not work. We solve this
problem by applying an explicit multiplicative regularizing operator, which
transforms the system to the form `identity plus compact', yet allows the
resulting matrix-vector products to be carried out at the FFT speed. Such a
regularized system is then further preconditioned by deflating an apparently
stable set of eigenvalues with largest magnitudes, which results in a robust
acceleration of the restarted GMRES under constraint memory conditions.Comment: 20 pages, 8 figure
Classification of electromagnetic resonances in finite inhomogeneous three-dimensional structures
We present a simple and unified classification of macroscopic electromagnetic
resonances in finite arbitrarily inhomogeneous isotropic dielectric 3D
structures situated in free space. By observing the complex-plane dynamics of
the spatial spectrum of the volume integral operator as a function of angular
frequency and constitutive parameters we identify and generalize all the usual
resonances, including complex plasmons, real laser resonances in media with
gain, and real quasi-static resonances in media with negative permittivity and
gain.Comment: 4 pages, 2 figure