Plane-wave scattering-matrix theory of antennas and antenna-antenna interactions /

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Resolvent and Scattering Matrix at the Maximum of the Potential

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.

First-principles calculation of carrier-phonon scattering in n-type Si1−xGex alloys

First-principles electronic structure methods are used to find the rates of inelastic intravalley and intervalley n-type carrier scattering in Si1-xGex alloys. Scattering parameters for all relevant Delta and L intra- and intervalley scattering are calculated. The short-wavelength acoustic and the optical phonon modes in the alloy are computed using the random mass approximation, with interatomic forces calculated in the virtual crystal approximation using density functional perturbation theory. Optical phonon and intervalley scattering matrix elements are calculated from these modes of the disordered alloy. It is found that alloy disorder has only a small effect on the overall inelastic intervalley scattering rate at room temperature. Intravalley acoustic scattering rates are calculated within the deformation potential approximation. The acoustic deformation potentials are found directly and the range of validity of the deformation potential approximation verified in long-wavelength frozen phonon calculations. Details of the calculation of elastic alloy scattering rates presented in an earlier paper are also given. Elastic alloy disorder scattering is found to dominate over inelastic scattering, except for almost pure silicon (x approximate to 0) or almost pure germanium (x approximate to 1), where acoustic phonon scattering is predominant. The n-type carrier mobility, calculated from the total (elastic plus inelastic) scattering rate, using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys..

First-principles calculation of P-type alloy scattering in Si1-xGex

The p-type carrier scattering rate due to alloy disorder in Si1-xGex alloys is obtained from first principles. The required alloy scattering matrix elements are calculated from the energy splitting of the valence bands, which arise when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Alloy scattering within the valence bands is found to be characterized by a single scattering parameter. The hole mobility is calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation. The results are in good agreement with experiments on bulk, unstrained alloys..

First-principles calculation of alloy scattering in GexSi1-x

First-principles electronic structure methods are used to find the rates of intravalley and intervalley n-type carrier scattering due to alloy disorder in Si1-xGex alloys. The required alloy scattering matrix elements are calculated from the energy splitting of nearly degenerate Bloch states which arises when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Scattering parameters for all relevant Delta and L intravalley and intervalley alloy scattering are calculated. Atomic relaxation is found to have a substantial effect on the scattering parameters. f-type intervalley scattering between Delta valleys is found to be comparable to other scattering channels. The n-type carrier mobility, calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys.

Absorbance enhancement in microplate wells for improved-sensitivity biosensors

A generic optical biosensing strategy was developed that relies on the absorbance enhancement phenomenon occurring in a multiple scattering matrix. Experimentally, inserts made of glass fiber membrane were placed into microplate wells in order to significantly lengthen the trajectory of the incident light through the sample and therefore increase the corresponding absorbance. Enhancement factor was calculated by comparing the absorbance values measured for a given amount of dye with and without the absorbance-enhancing inserts in the wells. Moreover, the dilution of dye in solutions with different refractive indices (RI) clearly revealed that the enhancement factor increased with the ΔRI between the membrane and the surrounding medium, reaching a maximum value (EF>25) when the membranes were dried. On this basis, two H2O2-biosensing systems were developed based on the biofunctionalization of the glass fiber inserts either with cytochrome c or horseradish peroxidase (HRP) and the analytical performances were systematically compared with the corresponding bioassay in solution. The efficiency of the absorbance-enhancement approach was particularly clear in the case of the cytochrome c-based biosensor with a sensitivity gain of 40 folds and wider dynamic range. Therefore, the developed strategy represents a promising way to convert standard colorimetric bioassays into optical biosensors with improved sensitivity.

Maximum-likelihood estimation of specific differential phase and attenuation in rain

Precise estimation of propagation parameters inprecipitation media is of interest to improve the performanceof communications systems and in remote sensing applications.In this paper, we present maximum-likelihood estimators ofspecific attenuation and specific differential phase in rain. Themodel used for obtaining the cited estimators assumes coherentpropagation, reflection symmetry of the medium, and Gaussianstatistics of the scattering matrix measurements. No assumptionsabout the microphysical properties of the medium are needed.The performance of the estimators is evaluated through simulateddata. Results show negligible estimators bias and variances closeto Cramer–Rao bounds.

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H2(ν, j) → HD(ν′, j′) + H reaction for J = 0.

Planar Topological Defects in Unconventional Superconductors

In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.

Contribución al análisis eficiente y a la mejora de prestaciones de antenas reflectarray

El diseño de una antena reflectarray bajo la aproximación de periodicidad local requiere la determinación de la matriz de scattering de estructuras multicapa con metalizaciones periódicas para un gran número de geometrías diferentes. Por lo tanto, a la hora de diseñar antenas reflectarray en tiempos de CPU razonables, se necesitan herramientas númericas rápidas y precisas para el análisis de las estructuras periódicas multicapa. En esta tesis se aplica la versión Galerkin del Método de los Momentos (MDM) en el dominio espectral al análisis de las estructuras periódicas multicapa necesarias para el diseño de antenas reflectarray basadas en parches apilados o en dipolos paralelos coplanares. Desgraciadamente, la aplicación de este método numérico involucra el cálculo de series dobles infinitas, y mientras que algunas series convergen muy rápidamente, otras lo hacen muy lentamente. Para aliviar este problema, en esta tesis se propone un novedoso MDM espectral-espacial para el análisis de las estructuras periódicas multicapa, en el cual las series rápidamente convergente se calculan en el dominio espectral, y las series lentamente convergentes se calculan en el dominio espacial mediante una versión mejorada de la formulación de ecuaciones integrales de potenciales mixtos (EIPM) del MDM. Esta versión mejorada se basa en la interpolación eficiente de las funciones de Green multicapa periódicas, y en el cálculo eficiente de las integrales singulares que conducen a los elementos de la matriz del MDM. El novedoso método híbrido espectral-espacial y el tradicional MDM en el dominio espectral se han comparado en el caso de los elementos reflectarray basado en parches apilados. Las simulaciones numéricas han demostrado que el tiempo de CPU requerido por el MDM híbrido es alrededor de unas 60 veces más rápido que el requerido por el tradicional MDM en el dominio espectral para una precisión de dos cifras significativas. El uso combinado de elementos reflectarray con parches apilados y técnicas de optimización de banda ancha ha hecho posible diseñar antenas reflectarray de transmisiónrecepción (Tx-Rx) y polarización dual para aplicaciones de espacio con requisitos muy restrictivos. Desgraciadamente, el nivel de aislamiento entre las polarizaciones ortogonales en antenas DBS (típicamente 30 dB) es demasiado exigente para ser conseguido con las antenas basadas en parches apilados. Además, el uso de elementos reflectarray con parches apilados conlleva procesos de fabricación complejos y costosos. En esta tesis se investigan varias configuraciones de elementos reflectarray basadas en conjuntos de dipolos paralelos con el fin de superar los inconvenientes que presenta el elemento basado en parches apilados. Primeramente, se propone un elemento consistente en dos conjuntos apilados ortogonales de tres dipolos paralelos para aplicaciones de polarización dual. Se ha diseñado, fabricado y medido una antena basada en este elemento, y los resultados obtenidos para la antena indican que tiene unas altas prestaciones en términos de ancho de banda, pérdidas, eficiencia y discriminación contrapolar, además de requerir un proceso de fabricación mucho más sencillo que el de las antenas basadas en tres parches apilados. Desgraciadamente, el elemento basado en dos conjuntos ortogonales de tres dipolos paralelos no proporciona suficientes grados de libertad para diseñar antenas reflectarray de transmisión-recepción (Tx-Rx) de polarización dual para aplicaciones de espacio por medio de técnicas de optimización de banda ancha. Por este motivo, en la tesis se propone un nuevo elemento reflectarray que proporciona los grados de libertad suficientes para cada polarización. El nuevo elemento consiste en dos conjuntos ortogonales de cuatro dipolos paralelos. Cada conjunto contiene tres dipolos coplanares y un dipolo apilado. Para poder acomodar los dos conjuntos de dipolos en una sola celda de la antena reflectarray, el conjunto de dipolos de una polarización está desplazado medio período con respecto al conjunto de dipolos de la otra polarización. Este hecho permite usar solamente dos niveles de metalización para cada elemento de la antena, lo cual simplifica el proceso de fabricación como en el caso del elemento basados en dos conjuntos de tres dipolos paralelos coplanares. Una antena de doble polarización y doble banda (Tx-Rx) basada en el nuevo elemento ha sido diseñada, fabricada y medida. La antena muestra muy buenas presentaciones en las dos bandas de frecuencia con muy bajos niveles de polarización cruzada. Simulaciones numéricas presentadas en la tesis muestran que estos bajos de niveles de polarización cruzada se pueden reducir todavía más si se llevan a cabo pequeñas rotaciones de los dos conjuntos de dipolos asociados a cada polarización. ABSTRACT The design of a reflectarray antenna under the local periodicity assumption requires the determination of the scattering matrix of a multilayered structure with periodic metallizations for quite a large number of different geometries. Therefore, in order to design reflectarray antennas within reasonable CPU times, fast and accurate numerical tools for the analysis of the periodic multilayered structures are required. In this thesis the Galerkin’s version of the Method of Moments (MoM) in the spectral domain is applied to the analysis of the periodic multilayered structures involved in the design of reflectarray antennas made of either stacked patches or coplanar parallel dipoles. Unfortunately, this numerical approach involves the computation of double infinite summations, and whereas some of these summations converge very fast, some others converge very slowly. In order to alleviate this problem, in the thesis a novel hybrid MoM spectral-spatial domain approach is proposed for the analysis of the periodic multilayered structures. In the novel approach, whereas the fast convergent summations are computed in the spectral domain, the slowly convergent summations are computed by means of an enhanced Mixed Potential Integral Equation (MPIE) formulation of the MoM in the spatial domain. This enhanced formulation is based on the efficient interpolation of the multilayered periodic Green’s functions, and on the efficient computation of the singular integrals leading to the MoM matrix entries. The novel hybrid spectral-spatial MoM code and the standard spectral domain MoM code have both been compared in the case of reflectarray elements based on multilayered stacked patches. Numerical simulations have shown that the CPU time required by the hybrid MoM is around 60 times smaller than that required by the standard spectral MoM for an accuracy of two significant figures. The combined use of reflectarray elements based on stacked patches and wideband optimization techniques has made it possible to design dual polarization transmit-receive (Tx-Rx) reflectarrays for space applications with stringent requirements. Unfortunately, the required level of isolation between orthogonal polarizations in DBS antennas (typically 30 dB) is hard to achieve with the configuration of stacked patches. Moreover, the use of reflectarrays based on stacked patches leads to a complex and expensive manufacturing process. In this thesis, we investigate several configurations of reflectarray elements based on sets of parallel dipoles that try to overcome the drawbacks introduced by the element based on stacked patches. First, an element based on two stacked orthogonal sets of three coplanar parallel dipoles is proposed for dual polarization applications. An antenna made of this element has been designed, manufactured and measured, and the results obtained show that the antenna presents a high performance in terms of bandwidth, losses, efficiency and cross-polarization discrimination, while the manufacturing process is cheaper and simpler than that of the antennas made of stacked patches. Unfortunately, the element based on two sets of three coplanar parallel dipoles does not provide enough degrees of freedom to design dual-polarization transmit-receive (Tx-Rx) reflectarray antennas for space applications by means of wideband optimization techniques. For this reason, in the thesis a new reflectarray element is proposed which does provide enough degrees of freedom for each polarization. This new element consists of two orthogonal sets of four parallel dipoles, each set containing three coplanar dipoles and one stacked dipole. In order to accommodate the two sets of dipoles in each reflectarray cell, the set of dipoles for one polarization is shifted half a period from the set of dipoles for the other polarization. This also makes it possible to use only two levels of metallization for the reflectarray element, which simplifies the manufacturing process as in the case of the reflectarray element based on two sets of three parallel dipoles. A dual polarization dual-band (Tx-Rx) reflectarray antenna based on the new element has been designed, manufactured and measured. The antenna shows a very good performance in both Tx and Rx frequency bands with very low levels of cross-polarization. Numerical simulations carried out in the thesis have shown that the low levels of cross-polarization can be even made smaller by means of small rotations of the two sets of dipoles associated to each polarization.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Spin and spatial dynamics in electron-impact scattering off S-wave He using R-matrix with Time-Dependence theory

R-matrix with time-dependence theory is applied to electron-impact ionisation processes for He in the S-wave model. Cross sections for electron-impact excitation, ionisation and ionisation with excitation for impact energies between 25 and 225 eV are in excellent agreement with benchmark cross sections. Ultra-fast dynamics induced by a scattering event is observed through time-dependent signatures associated with autoionisation from doubly excited states. Further insight into dynamics can be obtained through examination of the spin components of the time-dependent wavefunction.

Structure of disordered gold-polymer thin films using small angle x-ray scattering

We have investigated the structure of disordered gold-polymer thin films using small angle x-ray scattering and compared the results with the predictions of a theoretical model based on two approaches-a structure form factor approach and the generalized Porod law. The films are formed of polymer-embedded gold nanoclusters and were fabricated by very low energy gold ion implantation into polymethylmethacrylate (PMMA). The composite films span (with dose variation) the transition from electrically insulating to electrically conducting regimes, a range of interest fundamentally and technologically. We find excellent agreement with theory and show that the PMMA-Au films have monodispersive or polydispersive characteristics depending on the implanted ion dose. (C) 2010 American Institute of Physics. [doi:10.1063/1.3493241]

Possible hyperdeformed band in (36)Ar observed in (12)C+(24)Mg elastic scattering

Fifteen strongly oscillating angular distributions of the elastic scattering of (12)C + (24)Mg at energies around the Coulomb barrier (E(c.m). = 10.67-16.00 MeV) are reproduced by adding five Breit-Wigner resonance terms to the l = 2, 4, 6, 7, and 8 elastic S matrix. The nonresonant, background elastic scattering S matrix S(l)(0) is calculated using the Sao Paulo potential. The J = 2, 4, 6, 7, and 8 (h) over bar molecular resonances fit well into a rotational molecular band, together with other higher lying resonances observed in the (16)O + (20)Ne elastic scattering. We propose that the presently observed, largely deformed molecular band corresponds to the hyperdeformed band, which has been found previously in alpha-cluster calculations, as well as in a new Nilsson model calculation. Systematic study of its possible clusterizations predicts the preference of the (12)C + (24)Mg and (16)O + (20)Ne molecular structure, in accordance with our present results.