Multiband diffraction and refraction control in binary arrays of periodically curved waveguides

The possibility of controlling discrete diffraction and refraction in a multiband waveguide array by periodic waveguide bending is theoretically demonstrated. Resonance effects, leading to the enhancement or inhibition of discrete diffraction, are found and related to the quantum analog of field-induced n-photon resonances in semiconductor superlattices. A very distinct behavior for light refraction is found for odd or even resonances. In particular, for even resonances, the two-band behavior of the straight binary array is quenched, resulting in the inhibition of double refraction.     

Nature of Coulomb shifts of nuclear scattering resonances

Relations determining the shift of energies and widths of scattering resonances are obtained within the method of evolution in the coupling constant. These relations generalize the well-known relations for the shift of levels in a discrete spectrum. The problem of determining the Coulomb shifts of low-energy resonances manifesting themselves in the cross section for the scattering of some light nuclei is solved. Examples that are of importance for nuclear astrophysics and examples of problems that are associated with the production of chemical elements are considered. The character of Coulomb shifts is studied within simple nuclear models. Respective numerical estimates are given, which agree satisfactorily with experimental data.     

Temporary trapping of a light atom in between two heavy atoms

The temporary trapping of a light atom in between two heavy atoms is associated with short lived overlapping resonances. It is shown for the electronically excited ArHCl that these quantum diffraction resonances can be associated, within the framework of the adiabatic approximation, with the non-physical poles of the scattering matrix when the light atom is scattered through one-dimensional dynamical barriers.     

Application of the diffraction trace formula to the three-disk scattering system

The diffraction trace formula derived previously and the spectral determinant are tested on the open three-disk scattering system. The system contains a generic and exponentially growing number of diffraction periodic orbits. In spite of this it is shown that even the scattering resonances with large imaginary part can be reproduced semiclassically. The nontrivial interplay of the diffraction periodic orbits with the usual geometrical orbits produces the fine structure of the complicated spectrum of scattering resonances, which are beyond the resolution of the conventional periodic orbit theory.     

Optical fano resonances in photonic crystal slabs near diffraction threshold anomalies

Optical Fano resonances due to resonant eigenmodes in a layered periodically-modulated structure (photonic crystal slab) are investigated theoretically. The special attention is focused on the behavior of the resonances near a diffraction threshold. A new formulation of the resonant mode approximation for the optical scattering matrix near the diffraction threshold anomalies is proposed.     

Line shapes and threshold resonances for the scattering of waves from surfaces

An analytical study of threshold resonances in scattering of scalar waves from periodic surfaces is presented. Resonances are found with a variety of line shapes which provide characteristic information on the surface potential. The analytical predictions on line shapes are supported numerically. These resonances should be observed in atom-surface scattering and in scattering of light from large-amplitude gratings. We think that these resonances may be important for the field enhancement on surfaces.     

Light diffraction features in an ordered monolayer of spheres

The structure and optical diffraction properties of monolayers of monodisperse spheres crystallized on transparent dielectric substrates are studied. Two types of diffraction phenomena are considered: surface light diffraction on the lattice of spheres and waveguide resonances in the monolayer plane. For experimental study of these phenomena, optical retroreflection and transmission spectra are measured as functions of the light incidence angle and azimuthal orientation of the incidence plane. The monolayer structures determined by scanning electron microscopy and light diffraction methods are in quantitative agreement. It is concluded that one-dimensional Fraunhofer diffraction is applicable to describe surface diffraction in the hexagonal lattice of spheres. In the case of oblique light incidence, anisotropy of diffraction and transmission spectra depending on the light incidence plane orientation with respect to the sphere lattice and linear polarization of incident light is detected. Waveguide resonances of the planar two-dimensional photonic crystal are approximated within the light diffraction model in the “empty” hexagonal lattice. The best approximation of the waveguide resonance dispersion is achieved using the effective refractive index, depending on the wavelength. Surface diffraction suppression by waveguide resonances of the photonic crystal is demonstrated. Surface diffraction orders are identified as diffraction at singular points of the Brillouin zone of the planar twodimensional photonic crystal.     

Bound state resonances in atom-solid scattering

Theoretical studies and numerical calculations of bound state resonances (selective adsorption) in the elastic scattering of low-energy light atoms from a perfect crystalline surface are made. The surface-atom potential used is the sum of Yukawa-6 pair potentials with the pair potential parameters fixed to yield the correct bound state energies for the HeLiF system. The scattering equation is numerically integrated using basis sets of open and closed channels of varying number. It is found that numerically accurate solutions are obtained only if the basis set includes the bound state in resonance, all diffracted channels coupled strongly to it by the periodic surface potential, and the specular and other low-order diffracted channels. The calculations yield specular minimum and (11) and (21) diffraction maximum under (01) selective adsorption conditions in agreement with experimental observations for the HeLiF and HeNaF systems. These results appear independent of the potential model. The atomic band structure due to the surface periodic potential is found to yield splitting of the specular minima and/or broadening of the minima. It is suggested that studying such splittings will yield information on the periodic surface potential.     

Observation of phase-matched electromagnetic scattering in an active dielectric cylinder

A theoretical investigation of oblique plane-wave electromagnetic scattering in an active dielectric cylinder predicted the existence of anomalous resonances at discrete plane-wave angles of incidence. These resonances may be understood as being due to a leaky-wave phase-matching boundary condition. Experiments were performed with active dielectric cylinders to confirm the existence of discrete resonances. Cross coupling between TE and TM modes was clearly detected for both active and passive scattering. Enhancement of active scattered field intensities was observed in experiments with finite-diameter pump and probe laser beams. Optical pumping of a dye solution was used to provide the gain.     

Class of model problems in three-body quantum mechanics that admit exact solutions

An approach to solving scattering problems in three-body systems for cases where the mass of one of the particles is extremely small in relation to the masses of the other two particles and where the pair potentials of interaction between the particles involved are separable is developed. Exact analytic solutions to such model problems are found for the scattering of a light particle on two fixed centers and on two interacting heavy particles. It is shown that new resonances and a dynamical resonance enhancement may appear in a three-body system.     

A new spectral resonance of metallic nanorods

The extinction, integrated scattering, and absorption spectra of gold and silver nanorods with random and regular orientation are studied. The calculations are performed for spheroids, circular cylinders, circular cylinders with hemispherical ends (T-matrix method), and rectangular prisms (discrete dipole approximation). A new quadrupole resonance is discovered that arises between the usual plasmon dipole resonances excited by a field longitudinal or transverse with respect to the symmetry axis. The new resonance can be excited only by a TM incident wave and is the greatest for orientation of the symmetry axis of the particle at an angle of 54° with respect to the light beam.     

Neumann resonances in linear elasticity for an arbitrary body

We study resonances (scattering poles) associated to the elasticity operator in the exterior of an arbitrary obstacle inR ³ with Neumann boundary conditions. We prove that there exists a sequence of resonances tending rapidly to the real axis.Partly supported by BSF under grant MM 401.     

Description of Unstable Systems in Relativistic Quantum Mechanics in the Lax-Phillips Theory

We discuss some of the experimental motivation for the need for semigroup decay laws and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and, therefore, all physical properties of the resonant states can be computed. We show that the parametrized relativistic quantum theory is a natural setting for the realization of the Lax-Phillips theory.     

Nanoscale imaging of buried structures with elemental specificity using resonant x-ray diffraction microscopy

We report the first demonstration of resonant x-ray diffraction microscopy for element specific imaging of buried structures with a pixel resolution of approximately 15 nm by exploiting the abrupt change in the scattering cross section near electronic resonances. We performed nondestructive and quantitative imaging of buried Bi structures inside a Si crystal by directly phasing coherent x-ray diffraction patterns acquired below and above the Bi M5 edge. We anticipate that resonant x-ray diffraction microscopy will be applied to element and chemical state specific imaging of a broad range of systems including magnetic materials, semiconductors, organic materials, biominerals, and biological specimens.     

Frequency control of surface plasmons with oscillating metal-insulator-metal waveguides

A single frequency of surface plasmon polaritons (SPPs) will be converted to many discrete frequencies as they are transmitted through a metal-insulator-metal waveguide with its core width undergoing a harmonic oscillation. The process of the frequency conversion shares many key properties with the light diffraction in discrete optical systems. By employing the conception of optical diffraction management, we can control the discrete frequencies of SPPs such as the intensity and spectrum width by changing the initial phase of the waveguide oscillation. The study bridges the spatial discrete diffraction and frequency transition of SPP modes. Theoretical analysis based on the effective index method and coupled mode theory is provided in detail.     

Gamow Vectors for Resonances: A Lax-Phillips Point of View

Results from the Lax-Phillips Scattering Theory are used to analyze quantum mechanical scattering systems, in particular to obtain spectral properties of their resonances which are defined to be the poles of the scattering matrix. For this approach the interplay between the positive energy projection and the Hardy-space projections is decisive. Among other things it turns out that the spectral properties of these poles can be described by the (discrete) eigenvalue spectrum of a so-called truncated evolution, whose eigenvectors can be considered as the Gamow vectors corresponding to these poles. Further an expansion theorem of the positive Hardy-space part of vectors Sg (S scattering operator) into a series of Gamow vectors is presented.     

Mode oscillation and harmonic distortions associated with sinusoidal modulation of semiconductor lasers

Techniques to deal with Feshbach resonances are applied to describe resonant light scattering off one dimensional photonic crystal slabs. Accurate expressions for scattering amplitudes, free of any fitting parameter, are obtained for isolated as well as overlapping resonances. They relate the resonance properties to the properties of the optical structure and of the incident light. For the most common case of a piecewise constant dielectric function, the calculations can be carried out essentially analytically. After establishing the accuracy of this approach we demonstrate its potential in the analysis of the reflection coefficients for the diverse shapes of overlapping, interacting resonances.     

Distribution of Resonances and Decay Rate of the Local Energy for the Elastic Wave Equation

We study resonances (scattering poles) associated to the elasticity operator in the exterior of an arbitrary obstacle with Neumann or Dirichlet boundary conditions. We prove that there exists an exponentially small neighborhood of the real axis free of resonances. Consequently we prove that for regular data, the energy for the elastic wave equation decays at least as fast as the inverse of the logarithm of time. According to Stefanov–Vodev ([SV1, SV2]), our results are optimal in the case of a Neumann boundary condition, even when the obstacle is a ball of ℝ³. The main difference between our case and the case of the scalar Laplacian (see Burq [Bu]) is the phenomenon of Rayleigh surface waves, which are connected to the failure of the Lopatinskii condition. Received: 22 February 2000 / Accepted: 28 June 2000     

Incoherent and coherent backscattering of light by a layer of densely packed random medium

The problem of light scattering by a layer of densely packed discrete random medium is considered. The theory of light scattering by systems of nonspherical particles is applied to derive equations corresponding to incoherent (diffuse) and interference parts of radiation reflected from the medium. A solution of the system of linear equations describing light scattering by a system of particles is represented by iteration. It is shown that the symmetry properties of the T-matrices and of the translation coefficients for the vector Helmholtz harmonics lead to the reciprocity relation for an arbitrary iteration. This relation is applied to consider the backscattering enhancement phenomenon. Equations expressing the incoherent and interference parts of reflected light from statistically homogeneous and isotropic plane-parallel layer of medium are given. In the exact backscattering direction the relation between incoherent and interference parts is identical to that of sparse media.