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 $k\to \infty$. 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

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

Toroidal dipole induced transparency for core-shell nanoparticles

We investigate the scattering properties of spherical nanoparticles by employing a Cartesian multipole expansion method which has incorporated radiating toroidal multipoles. It is shown that toroidal dipoles, which are negligible under long-wavelength approximations, can be excited within high-permittivity dielectric nanoparticles and significantly influence the scattering profile in the optical regime. We further reveal that the scattering transparencies of core-shell plasmonic nanoparticles can be classified into two categories: i) the trivial transparency with no effective multipole excitations within the particle, and ii) the non-trivial one induced by the destructive interferences of induced electric and toroidal multipoles. The incorporation of toroidal moments offers new insights into the study into nanoparticle scattering in both the near- and far-fields, which may shed new light to many related applications, such as biosensing, nanoantennas, photovoltaic devices and so on.Comment: 15 pages and 3 figure