Plane wave and Coulomb asymptotics

A simple plane wave solution of the Schrodinger-Helmholtz equation is a quantum eigenfunction obeying both energy and linear momentum correspondence principles. Inclusion of the outgoing wave with scattering amplitude f asymptotic development of the plane wave, we show that there is a problem with angular momentum when we consider forward scattering at the point of closest approach and at large impact parameter given semiclassically by (l + 1/2)/k where l is the azimuthal quantum number and may be large (J. Leech et al., Phys. Rev. Lett. 88. 257901 (2002)). The problem is resolved via non- uniform, non-standard analysis involving the Heaviside step function, unifying classical, semiclassical and quantum mechanics, and the treatment is extended to the case of pure Coulomb scattering.

Spontaneous spin polarization and electron localization in constrained geometries: The Wigner transition in nanowires

The Wigner transition in a jellium model of cylindrical nanowires has been investigated by density-functional computations using the local spin-density approximation. A wide range of background densities rho(b) has been explored from the nearly ideal metallic regime (r(s)=[3/4 pi rho(b)](1/3)=1) to the high correlation limit (r(s)=100). Computations have been performed using an unconstrained plane wave expansion for the Kohn-Sham orbitals and a large simulation cell with up to 480 electrons. The electron and spin distributions retain the cylindrical symmetry of the Hamiltonian at high density, while electron localization and spin polarization arise nearly simultaneously in low-density wires (r(s)similar to 30). At sufficiently low density (r(s)>= 40), the ground-state electron distribution is the superposition of well defined and nearly disjoint droplets, whose charge and spin densities integrate almost exactly to one electron and 1/2 mu(B), respectively. Droplets are arranged on radial shells and define a distorted lattice whose structure is intermediate between bcc and fcc. Dislocations and grain boundaries are apparent in the droplets' configuration found by our simulations. Our computations aim at modeling the behavior of experimental low-carried density systems made of lightly doped semiconductor nanostructures or conducting polymers.

Second-order distorted wave calculation for electron impact ionization of hydrogen

The triple differential cross sections for ionization of atomic hydrogen by electron impact are analysed in the case of coplanar, asymmetric geometry within the framework of second- order distorted wave theory. Detailed calculations are performed without making any approximations (other than numerical) in the evaluation of the second-order amplitude. The present results are compared with experimental measurements and other theoretical calculations for incident energies of 250, 150 and 54.4 eV. It is found that the second-order calculations represent a marked improvement over the results obtained from first-order theories for impact energies of 150 eV and higher. The close agreement between the present second-order plane wave calculation and those of Byron et al calculated using the closure approximation at an incident energy of 250 eV implies that the closure approximation is valid for this energy. The large difference between the present second-order distorted wave calculations and experiment at an incident energy of 54.4 eV suggests that higher order effects are important for incident energies less than 100 eV.

Convergence acceleration of the doubly periodic Green's function for the analysis of thin wire arrays

A method is proposed to accelerate the evaluation of the Green's function of an infinite double periodic array of thin wire antennas. The method is based on the expansion of the Green's function into series corresponding to the propagating and evanescent waves and the use of Poisson and Kummer transformations enhanced with the analytic summation of the slowly convergent asymptotic terms. Unlike existing techniques the procedure reported here provides uniform convergence regardless of the geometrical parameters of the problem or plane wave excitation wavelength. In addition, it is numerically stable and does not require numerical integration or internal tuning parameters, since all necessary series are directly calculated in terms of analytical functions. This means that for nonlinear problem scenarios that the algorithm can be deployed without run time intervention or recursive adjustment within a harmonic balance engine. Numerical examples are provided to illustrate the efficiency and accuracy of the developed approach as compared with the Ewald method for which these classes of problems requires run time splitting parameter adaptation.

Sub-Wavelength Profile 2-D Leaky-Wave Antennas With Two Periodic Layers

A fast and accurate analysis and synthesis technique for high-gain sub-wavelength 2-D Fabry-Perot leaky-wave antennas (LWA) consisting of two periodic metallodielectric arrays over a ground plane is presented. Full-wave method of moments (MoM) together with reciprocity is employed for the estimation of the near fields upon plane wave illumination and the extraction of the radiation patterns of the LWA. This yields a fast and rigorous tool for the characterisation of this type of antennas. A thorough convergence study for different antenna designs is presented and the operation principles of these antennas as well as the radiation characteristics are discussed. Moreover, design guidelines to tailor the antenna profile, the dimensions of the arrays as well as the antenna directivity and bandwidth are provided. A study on the radiation efficiency for antennas with different profiles is also presented and the trade off between directivity and radiation bandwidth is discussed. Numerical examples are given throughout to demonstrate the technique. A finite size antenna model is simulated using commercial software (CST Microstripes 2009) which validates the technique.

Design optimisation of ring elements for broadband reflectarray antennas

Plane wave scattering from a flat surface consisting of two periodic arrays of ring elements printed on a grounded dielectric sheet is investigated. It is shown that the reflection phase variation as a function of ring diameter is controlled by the difference in the centre resonant frequency of the two arrays. Simulated and measured results at X-band demonstrate that this parameter can be used to reduce the gradient and improve the linearity of the reflection phase versus ring size slope. These are necessary conditions for the re-radiating elements to maximise the bandwidth of a microstrip reflectarray antenna. The scattering properties of a conventional dual resonant multilayer structure and an array of concentric rings printed on a metal backed dielectric substrate are compared and the trade-off in performance is discussed.

Quality factor assessment of subwavelength resonant cavities at FIR frequencies

Subwavelength resonators at FIR are presented and studied. The structures consist of 1D cavities formed between a metallized (silver) surface and a metamaterial surface comprising a periodic array of silver patches on a silver-backed silicon substrate. The concept derives from recent discoveries of artificial magnetic conductors (AMC). By studying the currents excited on the metamaterial surface by a normally incident plane wave, the nature of the emerging resonant phenomena and the physical mechanism underlying the AMC operation are investigated. Full wave simulations, based on finite element method and time-domain transmission line modelling technique, have been carried out to demonstrate the effective AMC boundary condition and prove the possibilities for subwavelength cavities. The quality factor of the resonant cavities is assessed as a function of the cavity profile. It is demonstrated that the quality factor drops to about 1/8 of the half-wavelength value for lambda/8 resonant cavity.

Efficient modelling technique for fractal electromagnetic band-gap arrays

An efficient modelling technique is proposed for the analysis of a fractal-element electromagnetic band-gap array. The modelling is based on a method of moments modal analysis in conjunction with an interpolation scheme, which significantly accelerates the computations. The plane-wave and the surface-wave responses of the structure have been studied by means of transmission coefficients and dispersion diagrams. The multiband properties and the compactness of the proposed structure are presented. The technique is general and can be applied to arbitrary-shaped element geometries.

Electron shell contributions to gamma-ray spectra of positron annihilation in noble gases

Gamma-ray positron annihilation spectra of the noble gases are simulated using computational chemistry tools for the bound electron wavefunctions and plane-wave approximation for the low-energy positron. The present annihilation line shapes, i.e. the full width at half maximum, Delta epsilon, of the gamma-ray annihilation spectra for He and Ar (valence) agree well with available independent atomic calculations using a different algorithm. For other noble gases they achieve moderate agreement with the experimental measurements. It is found that the contributions of various atomic electron shells to the spectra depend significantly on their principal quantum number n and orbital angular momentum quantum number l. The present study further reveals that the outermost ns electrons of the noble gases exhibit spectral line shapes in close agreement with those measured, indicating (as expected) that the measurements are not due to a simple sum over the momentum densities for all atomic electrons. The robust nature of the present approach makes it possible for us to proceed to more complex molecular systems using the tools of modern computational chemistry.

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrodinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Power Stored and Quality Factors in Frequency Selective Surfaces at THz Frequencies

A study of the external, loaded and unloaded quality factors for frequency selective surfaces (FSSs) is presented. The study is focused on THz frequencies between 5 and 30 THz, where ohmic losses arising from the conductors become important. The influence of material properties, such as metal thickness, conductivity dispersion and surface roughness, is investigated. An equivalent circuit that models the FSS in the presence of ohmic losses is introduced and validated by means of full-wave results. Using both full-wave methods as well as a circuit model, the reactive energy stored in the vicinity of the FSS at resonance upon plane-wave incidence is presented. By studying a doubly periodic array of aluminium strips, it is revealed that the reactive power stored at resonance increases rapidly with increasing periodicity. Moreover, it is demonstrated that arrays with larger periodicity-and therefore less metallisation per unit area-exhibit stronger thermal absorption. Despite this absorption, arrays with higher periodicities produce higher unloaded quality factors. Finally, experimental results of a fabricated prototype operating at 14 THz are presented.

Nonlinear excitations in ferromagnetic chains with nearest and next nearest neighbor exchange interactions

Weakly nonlinear excitations in one-dimensional isotropic Heisenberg ferromagnetic chains with nearest- and next-nearest-neighbor exchange interactions are considered. Based on the properties of modulational stability of corresponding linear spin waves, the existence regions of bright and dark magnetic solitons of the system are discussed in the whole Brillouin zone. The antidark soliton mode which is convex soliton super-imposed with a plane wave component is obtained near the zero-dispersion points of the spin wave frequency spectrum. The analytical results are checked by numerical simulations. [S0163;1829(98)01838-4].

Effect of positron-atom interactions on the annihilation gamma spectra of molecules

Calculations of ?-spectra for positron annihilation on a selection of molecules, including methane and its fluoro-substitutes, ethane, propane, butane and benzene are presented. The annihilation ?-spectra characterise the momentum distribution of the electron-positron pair at the instant of annihilation. The contribution to the ?-spectra from individual molecular orbitals is obtained from electron momentum densities calculated using modern computational quantum chemistry density functional theory tools. The calculation, in its simplest form, effectively treats the low-energy (thermalised, room-temperature) positron as a plane wave and gives annihilation ?-spectra that are about 40% broader than experiment, although the main chemical trends are reproduced. We show that this effective 'narrowing' of the experimental spectra is due to the action of the molecular potential on the positron, chiefly, due to the positron repulsion from the nuclei. It leads to a suppression of the contribution of small positron-nuclear separations where the electron momentum is large. To investigate the effect of the nuclear repulsion, as well as that of short-range electron-positron and positron-molecule correlations, a linear combination of atomic orbital description of the molecular orbitals is employed. It facilitates the incorporation of correction factors which can be calculated from atomic many-body theory and account for the repulsion and correlations. Their inclusion in the calculation gives -spectrum linewidths that are in much better agreement with experiment. Furthermore, it is shown that the effective distortion of the electron momentum density, when it is observed through positron annihilation -spectra, can be approximated by a relatively simple scaling factor. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Chemical structural effects on γ-ray spectra of positron annihilation in fluorobenzenes

Spectra of ?-ray Doppler shifts for positron annihilation in benzene and its fluoro-derivatives are simulated using low energy plane wave positron (LEPWP) approximation. The results are compared with available measurements. It is found that the Doppler shifts in these larger aromatic compounds are dominated by the contributions of the valence electrons and that the LEPWP model overestimates the measurements by approximately 30%, in agreement with previous findings in noble gases and small molecules. It is further revealed that the halogen atoms not only switch the sign of the charges on carbon atoms that they bond to, but that they also polarize other C-H bonds in the molecule leading to a redistribution of the molecular electrostatic potentials. As a result, it is likely that the halogen atoms contribute more significantly to the annihilation process. The present study also suggests that, while the Doppler shifts are sensitive to the number of valence electrons in the molecules, they are less sensitive to the chemical structures of isomers that have the same numbers and type of atoms and, hence, the same numbers of electrons. Further investigation of this effect is warranted. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2012.