Spectral asymptotics of Pauli operators and orthogonal polynomials in complex domains

We consider the spectrum of a two-dimensional Pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value. The rate of accumulation of eigenvalues to zero is described in terms of the logarithmic capacity of the support of the electric potential. A connection between these eigenvalues and orthogonal polynomials in complex domains is established.Comment: 16 page

On a spectrum of nonlinear internal waves in the oceanic coastal zone

This paper studies the internal wave band of temperature fluctuation spectra in the coastal zone of Pacific ocean. It is observed that on the central Mexican Pacific Shelf in the high-frequency band of temperature spectra the spectral exponent tends to ~ω<sup>-1</sup> at the time of spring tide and ω<sup>-2</sup> at the time of neap tide. On the western shelf of the Japan/East Sea, in the Ω<<ω<< N<sub>*</sub> range, where N<sub>*</sub> is the representative buoyancy frequency and Ω is the inertial frequency, the rate tends to ~ω<sup>-3</sup>. These features of spectra are simulated by the model spectrum of nonlinear internal waves in the shallow water. Interaction of high-frequency internal waves with an internal wave of semidiurnal frequency is considered. It is shown that as a result of the interaction the spectrum of high-frequency internal waves take the universal form and the spectral exponent tends to ~ω<sup>-1</sup>

Switching from visibility to invisibility via Fano resonances: theory and experiment

Subwavelength structures demonstrate many unusual optical properties which can be employed for engineering functional metadevices, as well as scattering of light and invisibility cloaking. Here we demonstrate that the suppression of light scattering for any direction of observation can be achieved for an uniform dielectric object with high refractive index, in a sharp contrast to the cloaking with multilayered plasmonic structures suggested previously. Our finding is based on the novel physics of cascades of Fano resonances observed in the Mie scattering from a homogeneous dielectric rod. We observe this effect experimentally at microwaves by employing high temperature-dependent dielectric permittivity of a glass cylinder with heated water. Our results open a new avenue in analyzing the optical response of hight-index dielectric nanoparticles and the physics of cloaking.Comment: 8 pages, 4 figure

Phase diagram for the transition from photonic crystals to dielectric metamaterials

Photonic crystals and metamaterials represent two seemingly different classes of artificial electromagnetic media but often they are composed of similar structural elements arranged in periodic lattices. The important question is how to distinguish these two types of periodic photonic structures when their parameters, such as dielectric permittivity and lattice spacing, vary continuously. Here, we discuss transitions between photonic crystals and all-dielectric metamaterials and introduce the concept of a phase diagram and an order parameter for such structured materials, based on the physics of Mie and Bragg resonances. We show that a periodic photonic structure transforms into a metamaterial when the Mie gap opens up below the lowest Bragg bandgap where the homogenization approach can be justified and the effective permeability becomes negative. Our theoretical approach is confirmed by detailed microwave experiments for a metacrystal composed of a square lattice of glass tubes filled with heated water. This analysis yields deep insight into the properties of periodic photonic structures, and it also provides a useful tool for designing different classes of electromagnetic materials in a broad range of parameters.Comment: 7 pages, 6 figure