Spectral Pollution

We discuss the problems arising when computing eigenvalues of self-adjoint operators which lie in a gap between two parts of the essential spectrum. Spectral pollution, i.e. the apparent existence of eigenvalues in numerical computations, when no such eigenvalues actually exist, is commonplace in problems arising in applied mathematics. We describe a geometrically inspired method which avoids this difficulty, and show that it yields the same results as an algorithm of Zimmermann and Mertins.Comment: 23 page

Planar metamaterial with transmission and reflection that depend on the direction of incidence

We report that normal incidence reflection and transmission of circularly polarized electromagnetic waves from and through planar split-ring microwave metamaterials with chiral symmetry breaking depends on the incidence direction and handedness of circular polarization. The effect has a resonant nature and is linked to the lack of mirror symmetry in the metamaterial pattern leading to a polarization-sensitive excitation of electric and magnetic dipolar responses in the meta-molecules. It has striking phenomenological resemblance with the reflective circular dichroism of high-temperature "anyon" superconductors

Reconfigurable photonic metamaterials drive by Coulomb, Lorentz and optical forces

Metamaterials offer a huge range of enhanced and novel functionalities that natural materials cannot provide. They promise applications in superresolution imaging, optical data storage, optical filters, polarization control, cloaking, fraud prevention and many more. However, their unique optical properties are often narrowband and usually fixed. Here we demonstrate how the mechanical rearrangement of metamaterial structures at the nanoscale provides a powerful platform for controlling metamaterial properties dynamically. Using thermal, electrical, magnetic and optical control signals we demonstrate large-range tuning, high-contrast switching and modulation of metamaterial optical properties at megahertz frequencies and beyond. Beyond the obvious benefit of adding tunability to known metamaterial functionalities, this unlocks many new opportunities in areas such as light modulation and highly nonlinear & bistable optical device

Nano-electromechanical switchable photonic metamaterials

We introduce mechanically reconfigurable electrostatically-driven photonic metamaterials (RPMs) as a generic platform for large-range tuning and switching of photonic metamaterial properties. Here we illustrate this concept with a high-contrast metamaterial electro-optic switch exhibiting relative reflection changes of up to 72% in the optical part of the spectrum

Coherent control of birefringence and optical activity

Control of polarization of light with light is demonstrated in thin slabs of linear material promising ultrafast all-optical data processing at arbitrarily low intensities. In proof-of-principle experiments we access any polarization azimuth and any ellipticity

Controlling light with light in a plasmonic nanooptomechanical metamaterial

We demonstrate metamaterial with a cubic optical nonlinearity that is ten orders of magnitude greater than the reference nonlinearity of CS2. The nonlinearity has optomechanical nature and is underpinned by light-induced electromagnetic near-field interactions

Two-Stream Instability Model With Electrons Trapped in Quadrupoles

We formulate the theory of the two-stream instability (e-cloud instability) with electrons trapped in quadrupole magnets. We show that a linear instability theory can be sensibly formulated and analyzed. The growth rates are considerably smaller than the linear growth rates for the two-stream instability in drift spaces and are close to those actually observed

Lorentz force metamaterial with giant optical magnetoelectric response

We demonstrate the first reconfigurable photonic metamaterial controlled by electrical currents and magnetic fields, providing first practically useful solutions for sub-megahertz and high contrast modulation of metamaterial optical properties

Dynamics of the black soliton in a regularized nonlinear Schrodinger equation

We consider a family of regularized defocusing nonlinear Schrodinger (NLS) equations proposed in the context of the cubic NLS equation with a bounded dispersion relation. The time evolution is well-posed if the black soliton is perturbed by a small perturbation in the Sobolev space $H^s(\R)$ with s > 1/2. We prove that the black soliton is spectrally stable (unstable) if the regularization parameter is below (above) some explicitly specified threshold. We illustrate the stable and unstable dynamics of the perturbed black solitons by using the numerical finite-difference method. The question of orbital stability of the black soliton is left open due to the mismatch of the function spaces for the energy and momentum conservation.Comment: 15 pages; 5 figures