Scattering Matrix Formalism Research Articles

Tunable optical response at the plasmon-polariton frequency in dielectric-graphene-metamaterial systems

By using the scattering matrix formalism, it is studied the optical properties of one dimensional photonic crystals made of multiple layers of dielectric and uniaxial anisotropic single negative electric metamaterial with Drude type responses, with inclusions of graphene in between the dielectric-dielectric interfaces (DGMPC). The transmission spectra for transverse electric (TE) and magnetic (TM) polarization are presented as a function of the incidence angle, the graphene chemical potential, and the metamaterial plasma frequencies. It is found for the TM polarization the tunability of the DGMPC optical response with the graphene chemical potential, which can be observed by means of transmission or reflexion bands around the metamaterial plasmon-polariton frequency, with bandwidths depending on both the incidence angle and the metamaterial plasma frequency. Also, the transmission band is observed when losses in the metamaterial slabs are considered for finite systems. The conditions for the appearance of these bands are shown analytically. We consider this work contributes to open new possibilities to the design of photonic devices with DGMPCs.

Quantum transport in defective phosphorene nanoribbons: Effects of atomic vacancies

Defects are almost inevitably present in realistic materials and defective materials are expected to exhibit very different properties than their nondefective (perfect) counterparts. Here, using a combination of the tight-binding approach and the scattering matrix formalism, we investigate the electronic transport properties of defective phosphorene nanoribbons (PNRs) containing atomic vacancies. We find that for both armchair PNRs (APNRs) and zigzag PNRs (ZPNRs), single vacancies can create quasilocalized states, which can affect their conductance. With increasing vacancy concentration, three different transport regimes are identified: ballistic, diffusive, and Anderson localized ones. In particular, ZPNRs that are known to be metallic due to the presence of edge states become semiconducting: edge conductance vanishes and transport gap appears due to Anderson localization. Moreover, we find that for a fixed vacancy concentration, both APNRs and ZPNRs of narrower width and/or longer length are more sensitive to vacancy disorder than their wider and/or shorter counterparts, and that for the same ribbon length and width, ZPNRs are more sensitive to vacancy disorder than APNRs.

Spin Transport and Dynamics in Multilayer Magnetic Nanostructures

The interconnection between the spin current and spin dynamics via the spin-dependent scattering and an accompanying by spin torque effect in ferromagnetic/normal metal based magnetic multilayer nanostructures is studied including a high fast out-of-equilibrium spin dynamics. Features of the spin transport through interfaces and its impact on spin dynamics are described on the base of the scattering matrix formalism for spin flows. The dependence of the spin torque effect on conductance character of the normal metal layers is considered. The exchange processes between the itinerant <i>s</i> and the localized <i>d</i> electrons are described by kinetic rate equations for electron-magnon spin-flop scattering. It is shown that the magnon distribution function remains nonthermalized on the relevant time scales of the demagnetization process, and the relaxation of the out-of-equilibrium spin accumulation among itinerant electrons provides the principal channel for dissipation of spin angular momentum from the combined electronic system.

Квантование электромагнитного поля в трехмерных фотонных структурах на основе формализма матрицы рассеяния (S-квантование)

AbstractA technique for quantization of the electromagnetic field in photonic nanostructures with three-dimensional modulation of the dielectric constant is developed on the basis of the scattering matrix formalism ( S quantization in the three-dimensional case). Quantization is based on equating the eigenvalues of the scattering matrix to unity, which is equivalent to equating each other the sets of Fourier expansions for the fields of the waves incident on the structure and propagating away from the structure. The spatial distribution of electromagnetic fields of the modes in a photonic nanostructure is calculated on the basis of the R and T matrices describing the reflection and transmission of the Fourier components by the structure. To calculate the reflection and transmission coefficients of individual real-space and Fourier-space components, the structure is divided into parallel layers within which the dielectric constant varies as a function of two-dimensional coordinates. Using the Fourier transform, Maxwell’s equations are written in the form of a matrix connecting the Fourier components of the electric field at the boundaries of neighboring layers. Based on the calculated reflection and transmission vectors for all polarizations and Fourier components, the scattering matrix for the entire structure is formed and quantization is carried out by equating the eigenvalues of the scattering matrix to unity. The developed method makes it possible to obtain the spatial profiles of eigenmodes without solving a system of nonlinear integro-differential equations and significantly reduces the computational resources required for calculating the probability of spontaneous emission in three-dimensional systems.

Transmission scanning electron microscopy: Defect observations and image simulations

The new capabilities of a FEG scanning electron microscope (SEM) equipped with a scanning transmission electron microscopy (STEM) detector for defect characterization have been studied in parallel with transmission electron microscopy (TEM) imaging. Stacking faults and dislocations have been characterized in strontium titanate, a polycrystalline nickel-base superalloy and a single crystal cobalt-base material. Imaging modes that are similar to conventional TEM (CTEM) bright field (BF) and dark field (DF) and STEM are explored, and some of the differences due to the different accelerating voltages highlighted. Defect images have been simulated for the transmission scanning electron microscopy (TSEM) configuration using a scattering matrix formulation, and diffraction contrast in the SEM is discussed in comparison to TEM. Interference effects associated with conventional TEM, such as thickness fringes and bending contours are significantly reduced in TSEM by using a convergent probe, similar to a STEM imaging modality, enabling individual defects to be imaged clearly even in high dislocation density regions. Beyond this, TSEM provides significant advantages for high throughput and dynamic in-situ characterization.

Nonlinear transport theory in the metal with tunnel barrier

Within the framework of the scattering matrix formalism, the nonlinear Kubo theory for electron transport in the metal with a tunnel barrier has been considered. A general expression for the mean electrical current was obtained. It significantly simplifies the calculation of nonlinear contributions to the conductivity of various hybrid structures. In the model of the tunnel Hamiltonian, all linear and nonlinear contributions to a mean electrical current are evaluated. The linear approximation agrees with results of other theories. For effective barrier transmission , the ballistic transport is realised with a value of the Landauer conductivity equal to .

Quantization of an electromagnetic field in two-dimensional photonic structures based on the scattering matrix formalism (S-quantization)

Based on the scattering matrix formalism, we have developed a method of quantization of an electromagnetic field in two-dimensional photonic nanostructures (S-quantization in the two-dimensional case). In this method, the fields at the boundaries of the quantization box are expanded into a Fourier series and are related with each other by the scattering matrix of the system, which is the product of matrices describing the propagation of plane waves in empty regions of the quantization box and the scattering matrix of the photonic structure (or an arbitrary inhomogeneity). The quantization condition (similarly to the onedimensional case) is formulated as follows: the eigenvalues of the scattering matrix are equal to unity, which corresponds to the fact that the set of waves that are incident on the structure (components of the expansion into the Fourier series) is equal to the set of waves that travel away from the structure (outgoing waves). The coefficients of the matrix of scattering through the inhomogeneous structure have been calculated using the following procedure: the structure is divided into parallel layers such that the permittivity in each layer varies only along the axis that is perpendicular to the layers. Using the Fourier transform, the Maxwell equations have been written in the form of a matrix that relates the Fourier components of the electric field at the boundaries of neighboring layers. The product of these matrices is the transfer matrix in the basis of the Fourier components of the electric field. Represented in a block form, it is composed by matrices that contain the reflection and transmission coefficients for the Fourier components of the field, which, in turn, constitute the scattering matrix. The developed method considerably simplifies the calculation scheme for the analysis of the behavior of the electromagnetic field in structures with a two-dimensional inhomogeneity. In addition, this method makes it possible to obviate difficulties that arise in the analysis of the Purcell effect because of the divergence of the integral describing the effective volume of the mode in open systems.

Deterministic and statistical characterization of rigid frame porous materials from impedance tube measurements.

A method to characterize macroscopically homogeneous rigid frame porous media from impedance tube measurements by deterministic and statistical inversion is presented. Equivalent density and bulk modulus of the samples are reconstructed with the scattering matrix formalism, and are then linked to its physical parameters via the Johnson-Champoux-Allard-Lafarge model. The model includes six parameters, namely the porosity, tortuosity, viscous and characteristic lengths, and static flow and thermal permeabilities. The parameters are estimated from the measurements in two ways. The first one is a deterministic procedure that finds the model parameters by minimizing a cost function in the least squares sense. The second approach is based on statistical inversion. It can be used to assess the validity of the least squares estimate, but also presents several advantages since it provides valuable information on the uncertainty and correlation between the parameters. Five porous samples with a range of pore properties are tested, and the pore parameter estimates given by the proposed inversion processes are compared to those given by other characterization methods. Joint parameter distributions are shown to demonstrate the correlations. Results show that the proposed methods find reliable parameter and uncertainty estimates to the six pore parameters quickly with minimal user input.

Efficient full wave code for the coupling of large multirow multijunction LH grills

The full wave code OLGA, for determining the coupling of a single row lower hybrid launcher (waveguide grills) to the plasma, is extended to handle multirow multijunction active passive structures (like the C3 and C4 launchers on TORE SUPRA) by implementing the scattering matrix formalism. The extended code is still computationally fast because of the use of (i) 2D splines of the plasma surface admittance in the accessibility region of the k-space, (ii) high order Gaussian quadrature rules for the integration of the coupling elements and (iii) utilizing the symmetries of the coupling elements in the multiperiodic structures. The extended OLGA code is benchmarked against the ALOHA-1D, ALOHA-2D and TOPLHA codes for the coupling of the C3 and C4 TORE SUPRA launchers for several plasma configurations derived from reflectometry and interferometery. Unlike nearly all codes (except the ALOHA-1D code), OLGA does not require large computational resources and can be used for everyday usage in planning experimental runs. In particular, it is shown that the OLGA code correctly handles the coupling of the C3 and C4 launchers over a very wide range of plasma densities in front of the grill.

Quasiguided modes of opaline photonic crystals covered by Ge2Sb2Te5

The physical origin of resonant Wood's anomalies in the reflection spectra of three-dimensional (3D) opaline photonic crystals covered with ${\mathrm{Ge}}_{2}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{5}$ (GST225) is discussed. For this purpose, the optical reflection spectra are studied for different incident angles of light both experimentally and theoretically. The performed eigenmode analysis reveals that the Wood's anomalies originate from the quasiguided modes which appear in the GST225 capping layer. This conclusion is supported by the simulated electromagnetic near-field distributions of incident light at resonant frequencies. The experimental reflection spectra are in good agreement with theoretical calculations performed by the Fourier modal method in the scattering matrix form.

Analytical theory and possible detection of the ac quantum spin Hall effect

We develop an analytical theory of the low-frequency ac quantum spin Hall (QSH) effect based upon the scattering matrix formalism. It is shown that the ac QSH effect can be interpreted as a bulk quantum pumping effect. When the electron spin is conserved, the integer-quantized ac spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes, which also equal to the bulk spin Chern numbers of the QSH material. Furthermore, a possible experimental scheme by using ferromagnetic metals as electrodes is proposed to detect the topological ac spin current by electrical means.

Analysis of the Purcell effect in the waveguide mode by S-quantization

A method for calculating the spontaneous-emission probability for arbitrary layered structures in the waveguide mode has been developed based on the scattering matrix formalism. The results of calculating the mode Purcell factor for the TE and TM modes of a planar waveguide are shown. Analytical estimates for the mode Purcell factor are obtained, and the conditions for achieving maximum amplification of spontaneous emission in a waveguide are determined.

PT-Symmetric Scattering in Flow Duct Acoustics.

We show theoretically and experimentally that the propagation of an acoustic wave in an airflow duct going through a pair of diaphragms, with equivalent amounts of mean-flow-induced effective gain and loss, displays all the features of a parity-time (PT) symmetric system. Using a scattering matrix formalism, we observe, experimentally, the properties which reflect the PT symmetry of the scattering acoustical system: the existence of spontaneous symmetry breaking with symmetry-broken pairs of scattering eigenstates showing amplification and reduction, and the existence of points with unidirectional invisibility.

Quantum charge pumping through resonant crossed Andreev reflection in a superconducting hybrid junction of silicene

We theoretically investigate the phenomena of adiabatic quantum charge pumping through a normal-insulator-superconductor-insulator-normal (NISIN) setup of silicene within the scattering matrix formalism. Assuming thin barrier limit, we consider the strength of the two barriers ($\chi_{1}$ and $\chi_{2}$) as the two pumping parameters in the adiabatic regime. Within this geometry, we obtain crossed Andreev reflection (CAR) with probability unity in the $\chi_{1}$-$\chi_{2}$ plane without concomitant transmission or elastic cotunneling (CT). Tunability of the band gap at the Dirac point by applying an external electric field perpendicular to the silicene sheet and variation of the chemical potential at the normal silicene region, open up the possibility of achieving perfect either CAR or transmission process through our setup. This resonant behavior is periodic with the barrier strengths. We analyze the behavior of the pumped charge through the NISIN structure as a function of the pumping strength and angles of the incident electrons. We show that large ($Q\sim2e$) pumped charge can be obtained through our geometry when the pumping contour encloses either the CAR or transmission resonance in the pumping parameter space. We discuss possible experimental feasibility of our theoretical predictions.

Conductance spectroscopy of nontopological-topological superconductor junctions

We calculate the zero-temperature differential conductance $dI/dV$ of a voltage-biased one-dimensional junction between a nontopological and a topological superconductor for arbitrary junction transparency using the scattering matrix formalism. We consider two representative models for the topological superconductors: (i) spinful $p$-wave and (ii) $s$-wave with spin-orbit coupling and spin splitting. We verify that in the tunneling limit (small junction transparencies) where only single Andreev reflections contribute to the current, the conductance for voltages below the nontopological superconductor gap $\Delta_s$ is zero and there are two symmetric conductance peaks appearing at $eV = \pm \Delta_s$ with the quantized value $(4-\pi)2e^2/h$ due to resonant Andreev reflection from the Majorana zero mode. However, when the junction transparency is not small, there is a finite conductance for $e|V| < \Delta_s$ arising from multiple Andreev reflections. The conductance at $eV = \pm \Delta_s$ in this case is no longer quantized. In general, the conductance is particle-hole asymmetric except for sufficiently small transparencies. We further show that, for certain values of parameters, the tunneling conductance from a zero-energy conventional Andreev bound state can be made to mimic the conductance from a true Majorana mode.

Connected hidden singularities and toward successive state flipping in degenerate optical microcavities

Using scattering matrix formalism, we report the formation of a special hidden singular line connecting multiple second-order hidden singular points, in a non-uniformly pumped degenerate optical microcavity. Such singularities are known as exceptional points (EPs), and the line is proposed as an exceptional line. Exploring the unconventional behavior of cavity resonances created by a spatially imbalanced gain–loss profile, we have established the adiabatic state-flipping mechanism of coupled resonances encountering such EPs. Various interesting encircling situations, incorporating smooth as well as fluctuating variations of the control parameters, have been analyzed. We exploit the above scheme for the first time, to the best of our knowledge, to analyze the optical performance and stability of the cascaded flip-of-state phenomenon assisted by successive encirclement of either single or multiple singularities following the exceptional line in the context of optical mode converters.

Quantum jumps, superpositions, and the continuous evolution of quantum states

The apparent dichotomy between quantum jumps on the one hand, and continuous time evolution according to wave equations on the other hand, provided a challenge to Bohr's proposal of quantum jumps in atoms. Furthermore, Schrödinger's time-dependent equation also seemed to require a modification of the explanation for the origin of line spectra due to the apparent possibility of superpositions of energy eigenstates for different energy levels. Indeed, Schrödinger himself proposed a quantum beat mechanism for the generation of discrete line spectra from superpositions of eigenstates with different energies.However, these issues between old quantum theory and Schrödinger's wave mechanics were correctly resolved only after the development and full implementation of photon quantization. The second quantized scattering matrix formalism reconciles quantum jumps with continuous time evolution through the identification of quantum jumps with transitions between different sectors of Fock space. The continuous evolution of quantum states is then recognized as a sum over continually evolving jump amplitudes between different sectors in Fock space.In today's terminology, this suggests that linear combinations of scattering matrix elements are epistemic sums over ontic states. Insights from the resolution of the dichotomy between quantum jumps and continuous time evolution therefore hold important lessons for modern research both on interpretations of quantum mechanics and on the foundations of quantum computing. They demonstrate that discussions of interpretations of quantum theory necessarily need to take into account field quantization. They also demonstrate the limitations of the role of wave equations in quantum theory, and caution us that superpositions of quantum states for the formation of qubits may be more limited than usually expected.

Broadband quasi perfect absorption using chirped multi-layer porous materials

This work theoretically analyzes the sound absorption properties of a chirped multi-layer porous material including transmission, in particular showing the broadband unidirectional absorption properties of the system. Using the combination of the impedance matching condition and the balance between the leakage and the intrinsic losses, the system is designed to have broadband unidirectional and quasi perfect absorption. The transfer and scattering matrix formalism, together with numerical simulations based on the finite element method are used to demonstrate the results showing excellent agreement between them. The proposed system allows to construct broadband sound absorbers with improved absorption in the low frequency regime using less amount of material than the complete bulk porous layer.

Scattering phenomenon ofPT-symmetric dielectric-nanosphere structure

The scattering properties of the $\mathcal{PT}$-symmetric dielectric dual nanosphere structure are investigated through scattering matrix formalism. We calculate the extinction, scattering, and absorption cross sections of the $\mathcal{PT}$-symmetric scatterer illuminated by the monochromatic linearly polarized plane wave with different incident direction. When the size parameter of distance between the dielectric spheres' centers is small, the $\mathcal{PT}$ scatterer is in the unbroken phase due to strong interaction between the active and dissipated spheres. The extinction cross section of the $\mathcal{PT}$ scatterer is always the same when the plane wave is incident from opposite directions with the same polarization. It implies that the light transmission is reciprocal whether the $\mathcal{PT}$ scatterer is in the broken or unbroken phase, because the $\mathcal{PT}$ scatterer is a linear optical scattering system for which the Lorentz reciprocity holds. However, the scattering cross section is different when the plane wave is incident from the loss and gain regions, respectively, and the scattering asymmetry is large when the interaction between active and dissipated spheres is strong. In addition, we find that the absorption cross section of the scattering structure is always negative in the broken phase due to the dominated light scattering of the active sphere.

Waiting Time Correlations in Transport through Two Coupled Quantum Dots

Current fluctuations can give useful information about the underlying mechanism of the mesoscopic transport. There are two approaches to the study of these fluctuations. Full counting statistics (FCS) analyses the number of transferred particles in the given time interval. In an alternative approach, distribution of time delays between subsequent physical events, known as waiting time distribution (WTD), is studied [1]. In quantum dots both FCS and WTD can be studied using charge detection techniques [2]. Dasenbrock et al. [3] have shown the correlation of subsequent waiting times in the coherent transport through a quantum point contact described within the scattering matrix formalism. Here the study is extended to the case of quantum dots. I show the presence of the waiting time correlation in the sequential tunneling transport through the capacitively interacting quantum dots, where the transport in one quantum dot is modulated by the charge state of the other. All calculations are made within the Markovian master equation formalism.