445 research outputs found
Engineering Fano resonances in discrete arrays
We study transmission properties of discrete arrays composed of a linear waveguide coupled to a system of N side defect states. This simple system can be used to model discrete networks of coupled defect modes in photonic crystals, complex waveguide arrays in two-dimensional nonlinear lattices, and ring-resonator structures. We demonstrate the basic principles of the resonant scattering management through engineering Fano resonances and find exact results for the wave transmission coefficient. We reveal conditions for perfect reflections and transmissions due to either destructive or constructive interferences, and associate them with Fano resonances, also demonstrating how these resonances can be tuned by nonlinear defects
On the Heisenberg condition in the presence of redundant poles of the S-matrix
For the same potential as originally studied by Ma [Phys. Rev. {\bf 71}, 195
(1947)] we obtain analytic expressions for the Jost functions and the residui
of the S-matrix of both (i) redundant poles and (ii) the poles corresponding to
true bound states. This enables us to demonstrate that the Heisenberg condition
is valid in spite of the presence of redundant poles and singular behaviour of
the S-matrix for . In addition, we analytically determine the
overall contribution of redundant poles to the asymptotic completeness
relation, provided that the residuum theorem can be applied. The origin of
redundant poles and zeros is shown to be related to peculiarities of analytic
continuation of a parameter of two linearly independent analytic functions.Comment: The Heisenberg condition has been reduced down to analytic relation
(35) for the cylindrical Bessel functions (7 pages, 1 figure
Scattering invisibility with free-space field enhancement of all-dielectric nanoparticles
Simultaneous scattering invisibility and free-space field enhancement have
been achieved based on multipolar interferences among all-dielectric
nanoparticles. The scattering properties of all-dielectric nanowire quadrumers
are investigated and two sorts of scattering invisibilities have been
identified: the trivial invisibility where the individual nanowires are not
effectively excited; and the nontrivial invisibility with strong multipolar
excitations within each nanowire, which results in free-space field enhancement
outside the particles. It is revealed that such nontrivial invisibility
originates from not only the simultaneous excitations of both electric and
magnetic resonances, but also their significant magnetoelectric
cross-interactions. We further show that the invisibility obtained is both
polarization and direction selective, which can probably play a significant
role in various applications including non-invasive detection, sensing, and
non-disturbing medical diagnosis with high sensitivity and precision.Comment: 7 pages, 4 figures and comments are welcom
Spectroscopy of Discrete Breathers
In this work the interaction between a spatial localized and time periodic state (discrete breather) and small amplitude plane waves is studied
Sharp bends in photonic crystal waveguides as nonlinear Fano resonators
We demonstrate that high transmission through sharp bends in photonic crystal
waveguides can be described by a simple model of the Fano resonance where the
waveguide bend plays a role of a specific localized defect. We derive effective
discrete equations for two types of the waveguide bends in two-dimensional
photonic crystals and obtain exact analytical solutions for the resonant
transmission and reflection. This approach allows us to get a deeper insight
into the physics of resonant transmission, and it is also useful for the study
and design of power-dependent transmission through the waveguide bends with
embedded nonlinear defects.Comment: 8 pages, 5 figures, submitted to Optics Expres
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