2,522 research outputs found
Lorenz-Mie theory for 2D scattering and resonance calculations
This PhD tutorial is concerned with a description of the two-dimensional
generalized Lorenz-Mie theory (2D-GLMT), a well-established numerical method
used to compute the interaction of light with arrays of cylindrical scatterers.
This theory is based on the method of separation of variables and the
application of an addition theorem for cylindrical functions. The purpose of
this tutorial is to assemble the practical tools necessary to implement the
2D-GLMT method for the computation of scattering by passive scatterers or of
resonances in optically active media. The first part contains a derivation of
the vector and scalar Helmholtz equations for 2D geometries, starting from
Maxwell's equations. Optically active media are included in 2D-GLMT using a
recent stationary formulation of the Maxwell-Bloch equations called
steady-state ab initio laser theory (SALT), which introduces new classes of
solutions useful for resonance computations. Following these preliminaries, a
detailed description of 2D-GLMT is presented. The emphasis is placed on the
derivation of beam-shape coefficients for scattering computations, as well as
the computation of resonant modes using a combination of 2D-GLMT and SALT. The
final section contains several numerical examples illustrating the full
potential of 2D-GLMT for scattering and resonance computations. These examples,
drawn from the literature, include the design of integrated polarization
filters and the computation of optical modes of photonic crystal cavities and
random lasers.Comment: This is an author-created, un-copyedited version of an article
published in Journal of Optics. IOP Publishing Ltd is not responsible for any
errors or omissions in this version of the manuscript or any version derived
from i
Entanglement properties of bound and resonant few-body states
Studying the physics of quantum correlations has gained new interest after it
has become possible to measure entanglement entropies of few body systems in
experiments with ultracold atomic gases. Apart from investigating trapped atom
systems, research on correlation effects in other artificially fabricated
few-body systems, such as quantum dots or electromagnetically trapped ions, is
currently underway or in planning. Generally, the systems studied in these
experiments may be considered as composed of a small number of interacting
elements with controllable and highly tunable parameters, effectively described
by Schr\"odinger equation. In this way, parallel theoretical and experimental
studies of few-body models become possible, which may provide a deeper
understanding of correlation effects and give hints for designing and
controlling new experiments. Of particular interest is to explore the physics
in the strongly correlated regime and in the neighborhood of critical points.
Particle correlations in nanostructures may be characterized by their
entanglement spectrum, i.e. the eigenvalues of the reduced density matrix of
the system partitioned into two subsystems. We will discuss how to determine
the entropy of entanglement spectrum of few-body systems in bound and resonant
states within the same formalism. The linear entropy will be calculated for a
model of quasi-one dimensional Gaussian quantum dot in the lowest energy
states. We will study how the entanglement depends on the parameters of the
system, paying particular attention to the behavior on the border between the
regimes of bound and resonant states.Comment: 22 pages, 3 figure
Stability of networks of nonlinear elements with logical properties
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