Scattering Matrix Approach Research Articles

Exact finite-time correlation functions for multiterminal setups: Connecting theoretical frameworks for quantum transport and thermodynamics

Transport in open quantum systems can be explored through various theoretical frameworks, including the quantum master equation, scattering matrix, and Heisenberg equation of motion. The choice of framework depends on factors such as the presence of interactions, the coupling strength between the system and environment, and whether the focus is on steady-state or transient regimes. Existing literature mainly treats these frameworks independently. Our work establishes connections between them by clarifying the role and status of these approaches using two paradigmatic models for single and multipartite quantum systems in a two-terminal setup under voltage and temperature biases. We derive analytical solutions in both steady-state and transient regimes for the populations, currents, and current correlation functions. Exact results from the Heisenberg equation are shown to align with scattering matrix and master equation approaches within their respective validity regimes. Crucially, we establish a protocol for the weak-coupling limit, bridging the applicability of master equations at weak-coupling with Heisenberg or scattering matrix approaches at arbitrary coupling strength. Published by the American Physical Society 2024

A scattering matrix approach to the effective mass dependence of tunneling current through heterojunctions

A scattering matrix technique is used to calculate the longitudinal and transverse energy dependence of the transmission probability through various heterostructures using both the BenDaniel–Duke (BD) and the lesser known Zhu–Kroemer (ZK) boundary conditions to take into account the spatial dependence of the effective mass. We first illustrate the large difference in the transmission probabilities calculated using both boundary conditions for the simple problems of tunneling through a potential step, a single rectangular barrier, and a resonant tunneling device. Then, we present numerical calculations of the external electric field dependence of the field emission (FE) current from a n-doped GaAs semiconductor/vacuum interface using both boundary conditions, showing that the BD boundary conditions underestimate the FE current for large values of the applied external electrostatic field. A comparison of calculated FE characteristics with FE data may be a way to determine the appropriate boundary conditions to solve tunneling problems through heterostructures with spatially varying effective mass.

Exotic spin-Hall effect in non-Hermitian optical systems

Abstract We systematically explore the origin and evolution of the exceptional points (EP) when a light beam is scattered by a parity-time (PT)-symmetric system using a scattering matrix approach and a full-wave theory. It is demonstrated that the PT-symmetric system switches between symmetry and symmetry-breaking phases at the EPs, giving rise to singular features in the Fresnel coefficients and causing the spin-Hall effect (SHE) near the EPs to exhibit anomalous features such as significantly enhanced transverse spin-Hall shifts and additional in-plane spin-Hall shifts. This exotic SHE can be explained by the significant beam intensity distortion caused by the destructive interference between the spin-maintained normal modes and the spin-reversed abnormal modes in the scattered light. This phenomenon can further be understood in terms of vortex mode decomposition, wherein it can be interpreted as the competition and superposition of three vortex modes with topological charges of −1, 0, and 1, respectively. These findings elucidate the mechanism of the unusual SHE around the EPs and offer potential avenues for EP-based sensing and structured light manipulation.

Tomographic cross correlations between galaxy surveys and the CMB gravitational lensing potential. Effect of the redshift bin mismatch

Upcoming surveys of the large-scale structure of our Universe will employ a large coverage area of about half of the sky and will significantly increase the observational depth. With these surveys, we will be able to cross-correlate cosmic microwave background (CMB) gravitational lensing and galaxy surveys divided into narrow redshift bins to map the evolution of the cosmological parameters with redshift. We study the effect of the redshift bin mismatch of objects that is due to photometric redshift errors in tomographic cross-correlation measurements. We used the code FLASK to create Monte Carlo simulations of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) and Planck CMB lensing convergence. We simulated log-normal fields and divided galaxies into nine redshift bins with the Gaussian and modified Lorentzian photometric redshift errors. To estimate the parameters, we used angular power spectra of CMB lensing and galaxy density contrast fields and the maximum likelihood estimation method. We show that even with simple Gaussian errors with a standard deviation of $ the galaxy auto-power spectra in tomographic bins are offset by $2-15<!PCT!>$. The estimated cross-power spectra between galaxy clustering and CMB lensing are also biased, with smaller deviations $<5<!PCT!>$. As a result, the $ $ parameter deviates between $0.2-1.2\ due to the redshift bin mismatch of the objects. We propose a computationally fast and robust method based on the scattering matrix approach to correct for the redshift bin mismatch of the objects. The estimates of the parameters in tomographic studies such as the linear galaxy bias, the cross-correlation amplitude, and $ $ are biased due to the redshift bin mismatch of the objects. The biases in these parameters are alleviated with our scattering matrix approach.

The generation and detection of the spin-valley-polarization in semi-Dirac materials

We investigated the transport properties in a normal metal/ferromagnet/normal metal/superconductor junction based on semi-Dirac materials with inverted energy gap. With a scattering matrix approach, we show that the electron transport in the junction is spin-valley-polarized due to the ferromagnetic exchange energy. It is also shown that the Andreev reflection is strongly suppressed, which is a clear experimental signal for the spin-valley-polarization in semi-Dirac materials.

Fully Reconfigurable Photonic Filter for Flexible Payloads

Reconfigurable photonic filters represent cutting-edge technology that enhances the capabilities of space payloads. These advanced devices harness the unique properties of light to deliver superior performance in signal processing, filtering, and frequency selection. They offer broad filtering capabilities, allowing for the selection of specific frequency ranges while significantly reducing Size, Weight, and Power (SWaP). In scenarios where satellite communication channels are crowded with various signals sharing the same bandwidth, reconfigurable photonic filters enable efficient spectrum management and interference mitigation, ensuring reliable signal transmission. Furthermore, reconfigurable photonic filters demonstrate their ability to adapt to the dynamic space environment, withstanding extreme temperatures, radiation exposure, and mechanical stress while maintaining stable and reliable performance. Leveraging the inherent speed of light, these filters enable high-speed signal processing operations, paving the way to various space payload applications, such as agile frequency channelization. This capability allows for the simultaneous processing and analysis of different frequency bands. In this theoretical study, we introduce a fully reconfigurable filter comprising two decoupled ring resonators, each with the same radius. Each resonator can be independently thermally tuned to achieve reconfigurability in both central frequency and bandwidth. The precise reconfiguration of both central frequency and bandwidth is achieved by using the thermo-optic effect along the whole ring resonator path. A stopband rejection of 45 dB, with a reconfigurable bandwidth and central frequency of 20 MHz and 180 MHz, respectively, has been numerically achieved, with a maximum electrical power of 11.50 mW and a reconfiguration time of 9.20 µs, by using the scattering matrix approach, where the elements have been calculated through Finite Element Method-based and Beam Propagation Method-based simulations. This performance makes the proposed device suitable as key building block of RF optical filters, useful in the next-generation telecommunication payload domain.

Multi-frequency and wide-angle nonreciprocity arising from non-uniform magnetic field

We investigate the effect of non-uniform external static magnetic field on the scattering nonreciprocity of a deep-subwavelength gyrotropic particle system. Based on a scattering matrix approach, we show analytically that asymmetrical extinction cross section of the scattering system for opposite illumination directions can be accessed at multi-frequency and wide-angle regimes, in the presence of magnetic field with weak spatial non-uniformity. A simplified dual-dipole model is further employed to capture the generic physics of nonreciprocal scattering, essentially attributed to the asymmetrical magneto-electric cross interactions. In addition, typical examples are provided with full-wave numerical verifications. Our finding may open a straightforward and efficient pathway to manipulate nonreciprocal scattering at the subwavelength scale.

Polaritonic linewidth asymmetry in the strong and ultrastrong coupling regime

Abstract The intriguing properties of polaritons resulting from strong and ultrastrong light–matter coupling have been extensively investigated. However, most research has focused on spectroscopic characteristics of polaritons, such as their eigenfrequencies and Rabi splitting. Here, we study the decay rates of a plasmon–microcavity system in the strong and ultrastrong coupling regimes experimentally and numerically. We use a classical scattering matrix approach, approximating our plasmonic system with an effective Lorentz model, to obtain the decay rates through the imaginary part of the complex quasinormal mode eigenfrequencies. Our classical model automatically includes all the interaction terms necessary to account for ultrastrong coupling without dealing with the rotating-wave approximation and the diamagnetic term. We find an asymmetry in polaritonic decay rates, which deviate from the expected average of the uncoupled system’s decay rates at zero detuning. Although this phenomenon has been previously observed in exciton–polaritons and attributed to their disorder, we observe it even in our homogeneous system. As the coupling strength of the plasmon–microcavity system increases, the asymmetry also increases and can become so significant that the lower (upper) polariton decay rate reduction (increase) goes beyond the uncoupled decay rates, γ − < γ 0,c < γ +. Furthermore, our findings demonstrate that polaritonic linewidth asymmetry is a generic phenomenon that persists even in the case of bulk polaritons.

Analysis of the process e+e- → h0a0 in ihdm in the presence of a linearly polarized laser field

We consider the process of neutral Higgs production from e+e- annihilation in Inert Higgs Doublet Model (IHDM) in the absence and presence of an external eld. The latter is assumed to be a plane and monochro-matic wave with linear polarization. In the theoretical framework, we present the analytic calculation of the lowest order di erential cross section by using the scattering matrix approach and Dirac-Volkov formalism for charged incident particles. The total cross section is computed by performing a numerical integration of the di erential cross section over the solid angle. The results obtained are analyzed and discussed for di erent centre of mass energies and laser parameters. We found that inserting a laser wave with linear polarization is a suitable mechanism to enhance the total cross-section of the process. Indeed, the probability of the process to occur increases with the presence of a linearly polarized laser eld, especially with low frequency and high strength.

Wideband circular polarizer for a photoconductive antenna.

We report a thin-film circular polarizer consisting of three metal-grid layers to be used with a photoconductive antenna (PCA) to generate terahertz (THz) circularly polarized (CP) radiation. The polarizer has a high transmission with a measured 3 dB axial-ratio bandwidth of 54.7% from 0.57 to 1 THz. We further developed a generalized scattering matrix approach to provide insight into the underlying physical mechanism of the polarizer. We revealed that the Fabry-Pérot-like multi-reflection among gratings enables the high-efficiency polarization conversion. The successful realization of the CP PCA can find widespread application, such as THz circular dichroism spectroscopy, THz Mueller imaging, and ultrahigh-speed THz wireless communications.

Casimir effect for a stack of graphene sheets

We consider a stack of parallel sheets composed of conducting planes with tensorial conductivities. Using the scattering matrix approach, we derive explicit formulas for the Casimir energy of two, three, and four planes as well as a recurrence relation for arbitrary planes. Specifically, for a stack of graphene, we solve the recurrence relations and obtain formulas for the Casimir energy and force acting on the planes within the stack. Moreover, we calculate the binding energy in the graphene stack with graphite interplane separation, which amounts to ${E}_{ib}=9.9$ meV/atom. Notably, the Casimir force on graphene sheets decreases rapidly for planes beyond the first one. For the second graphene layer in the stack, the force is 35 times smaller than that experienced by the first layer.

(Ann. Phys. 4/2023)

Annalen der PhysikVolume 535, Issue 4 2370007 Cover PictureFree Access (Ann. Phys. 4/2023) First published: 13 April 2023 https://doi.org/10.1002/andp.202370007AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Graphical Abstract Quantum Pumping When quasiparticles of Weyl/multi-Weyl and nodal-line semimetals are subjected to a time-periodic potential well, the presence of the oscillating potential of frequency ω creates equispaced Floquet side-bands. Using the Floquet theory and the scattering matrix approach, in the zero-temperature non-adiabatic pumping limit, characteristic Fano resonance patterns are found in the transmission coefficients, which depend on the nature of the dispersion. See article number 2200460 for more details. Volume535, Issue4April 20232370007 RelatedInformation

Floquet Transmission in Weyl/Multi‐Weyl and Nodal‐Line Semimetals through a Time‐Periodic Potential Well

AbstractA quantum pumping protocol through which the quasiparticles of Weyl/multi‐Weyl and nodal‐line semimetals are subjected to a time‐periodic rectangular potential well is considered. The presence of an oscillating potential of frequency ω creates equispaced Floquet side‐bands with spacing . As a result, a Fano resonance is observed when the difference in the Fermi energy (i.e., the energy of the incident quasiparticle), and the energy of one of the (quasi)bound state levels of the well, coincides with the energy of an integer number of photons (each carrying energy quantum ). Using the Floquet theory and the scattering matrix approach in the zero‐temperature non‐adiabatic pumping limit, characteristic Fano resonance patterns are found in the transmission coefficients. The inflection points in the pumped shot noise spectra also serve as a proxy for the corresponding Fano resonances. Therefore, the pumped shot noise is also numerically evaluated. Finally, the existence of the Fano resonance points is correlated to the (quasi)bound states of the well, by explicitly calculating the bound states of the static well (which are a subset of the bound states of the driven system). Since semimetals with anisotropic dispersions are considered, all the features observed depend on the orientation of the potential well.

Modeling of spontaneous emission in presence of cylindrical nanoobjects: the scattering matrix approach

We propose a method of analysis of spontaneous emission of a quantum emitter (an atom, a luminescence center, a quantum dot) inside or in vicinity of a cylinder. At the focus of our method are analytical expressions for the scattering matrix of the cylindrical nanoobject. We propose the approach to electromagnetic field quantization based of eigenvalues and eigenvectors of the scattering matrix. The method is applicable for calculation and analysis of spontaneous emission rates and angular dependences of radiation for a set of different systems: semiconductor nanowires with quantum dots, plasmonic nanowires, cylindrical hollows in dielectrics and metals. Relative simplicity of the method allows obtaining analytical and semi-analytical expressions for both cases of radiation into external medium and into guided modes.

Extraction of Attenuation Parameter in Periodic Shorted Reflectors of One-Port SAW Resonator Using Scattering Matrix Approach

In this work, the well-known scattering matrix approach to the design of one-port surface acoustic wave (SAW) resonators is adapted toward extraction of the coupling-of-modes (COM) attenuation parameter, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> for Rayleigh SAW propagation on a periodic shorted aluminum grating. The attenuation close to resonance inside the reflectors of the one-port SAW resonator is extracted by matching the measured conductance of the resonator to its version calculated from the experimentally measured interdigital transducer (IDT) scattering coefficients, intrinsic substrate parameters, and geometry of the resonator. Based on the extracted value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> , it was observed that the proposed method could predict the unloaded <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor of the resonator at a minor discrepancy of ~7.02%. At the same time, since the proposed method utilizes the measured IDT scattering coefficients to consider the effect of IDT losses on the measured conductance of the resonator, it offers a convenient scheme to directly extract the attenuation of SAW contributed by the reflectors of the device through numerical means while operating purely in the frequency domain. The proposed method could be applied to quantify the increase in attenuation caused by viscous damping of SAW inside sensing film-coated reflectors of one-port SAW resonator sensors, and thereby, aid to optimize the sensing film thickness to deploy these devices for high-resolution frequency-based sensing applications.

Effect of the laser beam geometry on laser-assisted muon pair production process at collider

In this research paper, we have investigated the process of muon pair production in high energy collisions via the exchange of γ and Z-bosons in the presence of the laser field for different directions. Analytical calculations of the cross-section are done within the scattering matrix approach by using the Dirac-Volkov states for electron and positron. The numerical computation of the cross-section shows that it behaves differently by changing the laser wave direction. For a laser field propagating in parallel with the incident beam, the cross-section is strongly affected from low intensities. In addition, for a given laser field strength and frequency, the required number of photons to be transferred increases by increasing the centre of mass energy. Therefore, the acceleration gradient provided by a collinear laser field further enhances the centre of mass energy.

Muon pair production via e + e − annihilation in the presence of a circularly polarized laser field

In this paper, we have investigated the elementary particle reaction that results from the electron–positron interaction, at the leading order, with an intense laser wave of circular polarization. We have derived, by analytical means, the laser-assisted differential cross section expression by using the scattering matrix approach. We have analysed the energy and the number of exchanged photons dependence of muon pair production in electron–positron annihilation at different centre of mass energies including the Z-boson peak. For this reason, a wide range of high centre of mass energies relevant to future collider were covered to study the cross section behaviour. We have found that, for a given number of exchanged photons, laser field strength and frequency, the circularly polarized laser field decreases the total cross section by several orders of magnitudes.

Ultralow Scattering Design of Wideband Conformal Arrays Based on Optimally Loaded Resistors

A novel approach based on the use of a resistor-loaded meta-surface (RL-MS) with optimized resistor values is proposed for scattering control in wideband conformal phased arrays. Specifically, the resistance of the loaded resistor in each RL-MS element is varied. As a result, the proposed RL-MS structure not only absorbs incident EM waves but also scatters the remainders away from threatening directions. To accelerate the design process, the scattering matrix approach is used to calculate the scattering patterns efficiently. Proper resistor element distribution can be achieved by optimizing the scattering characteristics. The RL-MS structure is used as the cover layer of a wideband conformal array. By loading the optimized resistors, scattering in the proposed array is reduced to a relatively low level with little degradation of radiation performances. The final designed array achieves 3:1 impedance bandwidth with scanning up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm 60^{\circ }/\pm 45^{\circ }$ </tex-math></inline-formula> in the E-/H-plane. Remarkably, a monostatic scattering reduction of approximately 30 dB is observed throughout the X-band in the simulated results of the optimized array. To demonstrate the effectiveness of this design, prototype arrays are fabricated and measured. The measured results are in reasonable agreement with the simulated results.

Dual resonance modes in two-port SAW resonator sensors: an analysis through scattering matrix approach

We report dual resonance modes occurring in two-port surface acoustic wave (SAW) resonators attached with typical sensing film and investigated the significance in sensing applications. Two-port SAW resonators operating at 303 MHz frequency were modelled using the scattering matrix approach and resonance frequency characteristics of the resonators were studied for mass loading caused by an arbitrary film attached between the interdigital transducers of the resonator. Depending on the mass loading, symmetric and antisymmetric modes occur around the near resonance frequency of the SAW device. Either a single-mode or both modes are dominant depending on the phase shift caused by the mass loading of the film. Choosing arbitrary film thickness could result in complexity to track the resonance frequency shift and degrade sensing performance. The approach used for analysis can aid to determine the optimum sensing film thickness for two port SAW resonator-based sensors that can exhibit better linearity.

Broadband and high-efficiency ultrathin wavefront manipulation based on the Pancharatnam-Berry phase principle.

A broadband and high-efficiency metasurface is proposed based on the Pancharatnam-Berry (PB) principle. The PB phase principle is analyzed using the scattering matrix approach and proposed to achieve the abrupt phase with an equal amplitude of the transmission coefficient. The abrupt phase φ has a linear relationship with the rotation angle θ, namely, φ=±2θ. A 1-D gradient metasurface was designed, and the circular polarized waves in the frequency range 8.2-10 GHz were refracted anomalously when left-handed circular polarization or right-handed circular polarization waves were irradiated vertically on the metasurface and the refraction angle of the circular polarized waves, depending on the chirality of the incident wave. Finally, a 2-D parabolic metasurface that not only converts planar circular polarized waves into spherical circular polarized waves, but also converges the parallel wave into a focus point, was designed. The focal distance of the 2-D parabolic metasurface decreases as the frequency of the incident wave decreases, and the half-maximum at full width shows the opposite trend.