Multiple-scattering Processes Research Articles

Comparative study of photoelectron momentum distributions from Kr and CO2 near a backward rescattering caustic by carrier-envelope-phase mapping

We study carrier-envelope-phase- (CEP-) dependent photoelectron momentum distributions (PEMDs) of Kr atoms and randomly oriented ${\mathrm{CO}}_{2}$ molecules exposed to sub-two-cycle intense infrared fields with linear polarization. The adiabatic theory predicts that, at fixed laser parameters (intensity, pulse duration, and CEP), the PEMDs for targets with equal ionization potentials considered across a backward rescattering caustic have identical shapes and only their absolute values depend on the target. We choose Kr and ${\mathrm{CO}}_{2}$ as targets with almost identical ionization potentials (approximately $14$ eV) to explore this behavior of PEMDs. We find that the measured PEMDs for Kr and ${\mathrm{CO}}_{2}$ have cutoff structures, which are associated with the caustics, with identical decaying profiles. We also reveal that CEP-dependent PEMDs around the cutoff exhibit target dependence, reflecting the differences in the differential cross sections (DCSs) of elastic rescattering and tunneling ionization rates. Furthermore, we extract the DCSs from the measured PEMDs around the cutoffs at different CEPs based on the adiabatic theory. The extracted DCSs agree with ones calculated by using the single-active-electron (SAE) scattering model, which includes all multiple-scattering processes, with orientation averaging for ${\mathrm{CO}}_{2}$. In contrast, the independent-atom model, which only considers single-scattering processes, cannot reproduce the extracted DCSs of ${\mathrm{CO}}_{2}$ at low scattering momenta. This finding indicates that multiple scattering is not negligible in the momentum range of 1.5--2.5 a.u. The extracted DCSs also show interference features assigned to multicenter scattering of O-O and C-O. These results confirm that the signature of electron interference is retained after orientation averaging, indicating that the internuclear distances of the constituent atoms can be retrieved from the CEP-dependent PEMDs for randomly oriented molecules using the SAE model.

Nonreciprocal acoustic transmission through dynamic multilayer structures

A time Floquet transfer-matrix method for the description of acoustic wave propagation through dynamic stratified structures, modulated by another, low-frequency, pump acoustic wave, is reported. The method is applied to a specific example of a GaAs/AlAs periodic superlattice, subject to a spatiotemporal modulation induced by an evanescent pump wave with frequency in the lowest acoustic band gap of the structure. By means of systematic numerical calculations, we provide compelling evidence for the occurrence of significant nonreciprocal transmission of an acoustic signal with frequency in a high-order acoustic band gap, through inelastic multiple-scattering processes. Our results indicate a promising route to design nonreciprocal acoustic devices.

Revisiting Multiple-Scattering Principles in a Crustal Waveguide: Equipartition, Depolarization and Coda Normalization

Seismic waves radiated by small crustal earthquakes are prone to multiple mode conversions caused by reflection and transmission at interfaces, and scattering by small-scale heterogeneities in the bulk of the medium. The goal of this study is to clarify the complex interplay between volume scattering and interface reflections in crustal waveguides and how it will impact the crustal energy propagation. To carry out this task, we have incorporated a rigorous description of wave polarization in the context of Monte–Carlo simulations of the multiple-scattering process by introducing a five-dimensional Stokes vector. To shed light on the wave content of the regional short-period seismic wavefield, we investigate the asymptotic partitioning of seismic energy onto P, SV and SH polarizations in the coda, as well as the angular distribution of energy flux in the waveguide. In full elastic space, equipartition theory predicts that (1) the energy ratio between P- and S-wave energies tends to $$\beta ^3/(2\alpha ^3)$$ , (2) an equal distribution of energy among SV- and SH-waves and (3) that energy fluxes are isotropic. In the presence of interfaces, we find that the isotropy of the wavefield is systematically broken and that energy ratios are shifted to the detriment of P-waves and in favor of SV-waves in a non-absorbing medium. This implies that a residual polarization is preserved in the waveguide. Through an extensive parametric study, we illustrate in detail how the anisotropy of the wavefield, the partitioning ratios and the shear wave polarization depend on the crustal attenuation parameters. The role of the initial polarization at the source has also been examined. In the case of an explosion and a shear dislocation with equal magnitude, we find that the energy level in the coda can differ by more than one order of magnitude when the effect of crustal scattering becomes very weak compared to reflections or transmissions at interfaces. When comparing different shear dislocation mechanisms, we find that the energy level in the coda can differ by up to 60%. While equipartition, depolarization and coda normalization remain fundamental guides to our understanding of the coda, their application requires a good a priori knowledge of the attenuation properties of the crust.

Enhanced Photocatalytic Activity of TiO2 Nanoparticles Immobilized on Porous-Sulfonated Polystyrene Microspheres through Multiple Scattering Process

Enhanced Photocatalytic Activity of TiO2 Nanoparticles Immobilized on Porous-Sulfonated Polystyrene Microspheres through Multiple Scattering Process

Spontaneous emission enhancement by rotationally-symmetric optical nanoantennas: impact of radially and axially propagating surface plasmon polaritons.

The excitation and radiation properties of rotationally-symmetric optical nanoantennas are independent of the azimuth angle, which enables great convenience and superior performances in practical applications. However, for rotationally-symmetric nanoantennas, the physical mechanisms behind their resonance properties remain to be clarified. In this paper, firstly, for a simple single-nanocylinder-on-mirror antenna (S-antenna), we establish a first-principles-based semianalytical model of surface plasmon polariton (SPP) by considering an intuitive multiple-scattering process of the radially-propagating gap surface plasmon (RGSP) in the nanogap and the axially-propagating surface plasmon (ASP) on the nanocylinder. The model can comprehensively reproduce all the radiation properties of the S-antenna such as the total and radiative emission rates, SPP excitation rates, and far-field radiation pattern. The model indicates that when the antenna radius is small (respectively, large), the enhancement of spontaneous emission mainly results from the resonance of ASP (respectively, RGSP). To show the wide applicability of the SPP model along with its unveiled decisive role of the RGSP and ASP in the spontaneous emission enhancement for other rotationally-symmetric nanoantennas of cylindrical shapes, we extend the SPP model to a more complex ring-nanocylinder-on-mirror antenna (R-antenna) that supports two ASPs. Moreover, to provide an explicit explanation of the resonance properties of the R-antenna, we further establish a semianalytical model for the resonant modes (called quasinormal modes, QNMs) supported by the R-antenna based on the SPP model, which quantitatively reveals the role of the RGSP and ASP in forming the antenna resonant modes and the resultant enhancement of spontaneous emission.

Broadband Enhancement of the Spontaneous Emission by an Optical Dipole Nanoantenna on Metallic Substrate: an Intuitive Model of Surface Plasmon Polariton

Optical nanoantennas can achieve electromagnetic-field enhancement under far-field excitation or spontaneous-emission enhancement under excitation by radiating emitters. Among them, nanoantennas on a metallic substrate (i.e., the so-called nanoparticle-on-mirror antennas) have drawn great research interests due to their ease in forming metallic gaps of sizes down to a few nanometers or even subnanometer. Here we propose an optical dipole nanoantenna on a metallic substrate with a broadband enhancement of spontaneous emission. Its total and radiative emission-rate enhancement factors can be up to 5454 and 1041, respectively. In the near-infrared band, the wavelength range of spontaneous-emission enhancement (Purcell factor over 1000) can reach 260nm. By changing the width of the slit between the two antenna arms and changing the length of the antenna arms, the spontaneous-emission enhancement bandwidth and enhancement factors can be adjusted, respectively, which brings great freedom and simplicity to the design process. The antenna can achieve a strong far-field radiation within a central anglular zone (polar angle <i>θ</i>≤60°) corresponding to a certain numerical aperture of objective lens, and therefore can increase the intensity of the fluorescence collected by the objective lens. Based on the above performances, the antenna can provide a broadband enhancement of spontaneous emission for fluorescent molecules or quantum dots (whose fluorescence spectrum usually covers a certain wavelength range), which is of great significance for applications such as high-speed and super-bright nanoscale light sources and high-sensitivity fluorescent-molecule sensing.<br>To clarify the underlying physical mechanisms, we build up a semi-analytical model by considering an intuitive excitation and multiple-scattering process of surface plasmon polaritons (SPPs) that propagate along the antenna arms. All the parameters used in the model (such as the SPP scattering coefficients) are obtained via rigorous calculations based on the first principle of Maxwell’s equations without any fitting process, which ensures that the model has a solid electromagnetic foundation and can provide quantitative predictions. The SPP model can comprehensively reproduce all the radiation properties of the antenna, such as the total and radiative emission rates and the far-field radiation pattern. Two phase-matching conditions are derived from the model for predicting the antenna resonance, and show that under these conditions, the SPPs on the antenna arms form a pair of Fabry-Perot resonance and therefore are enhanced, and the enhanced SPPs propagate to the emitter in the nanogap (or scattered into the free space), so as to enhance the total spontaneous emission rate (or the far-field radiative emission rate). Besides, this pair of Fabry-Perot resonance result in a pair of resonance peaks close to each other, which then forms the broadband enhancement of spontaneous emission.

Broadband enhancement of spontaneous emission by optical dipole nanoantenna on metallic substrate: An intuitive model of surface plasmon polariton

<sec>Optical nanoantennas can achieve electromagnetic-field enhancement under far-field excitation or spontaneous-emission enhancement under excitation by radiating emitters. Among them, nanoantennas on a metallic substrate (i.e. the so-called nanoparticle-on-mirror antennas) have aroused great research interest due to their ease in forming metallic gaps of sizes down to a few nanometers or even subnanometer. Here we propose an optical dipole nanoantenna on a metallic substrate with a broadband enhancement of spontaneous emission. Its total and radiative emission-rate enhancement factors can reach up to 5454 and 1041, respectively. In the near-infrared band, the wavelength range of spontaneous-emission enhancement (Purcell factor over 1000) can reach 260nm. By changing the width of the slit between the two antenna arms and also the length of the antenna arms, the spontaneous-emission enhancement bandwidth and enhancement factors can be adjusted, respectively, which brings great freedom and simplicity to the design process. The antenna can achieve a strong far-field radiation within a central anglular zone (polar angle <i>θ</i>≤60°) corresponding to a certain numerical aperture of objective lens, and therefore can increase the intensity of the fluorescence collected by the objective lens. Based on the above performances, the antenna can provide a broadband enhancement of spontaneous emission for fluorescent molecules or quantum dots (whose fluorescence spectrum usually covers a certain wavelength range), which is of great significance for the applications such as in high-speed and super-bright nanoscale light sources and high-sensitivity fluorescent-molecule sensing.</sec><sec>To clarify the underlying physical mechanisms, we build up a semi-analytical model by considering an intuitive excitation and multiple-scattering process of surface plasmon polaritons (SPPs) that propagate along the antenna arms. All the parameters used in the model (such as the SPP scattering coefficients) are obtained via rigorous calculations based on the first principle of Maxwell's equations without any fitting process, which ensures that the model has a solid electromagnetic foundation and can provide quantitative predictions. The SPP model can comprehensively reproduce all the radiation properties of the antenna, such as the total radiative emission rate and the far-field radiation pattern. Two phase-matching conditions are derived from the model for predicting the antenna resonance, and show that under these conditions, the SPPs on the antenna arms form a pair of Fabry-Perot resonance and therefore are enhanced, and the enhanced SPPs propagate to the emitter in the nanogap (or scattered into the free space), so as to enhance the total spontaneous emission rate (or the far-field radiative emission rate). Besides, this pair of Fabry-Perot resonance results in a pair of resonance peaks close to each other, then enhancing the spontaneous emission with a broadband.</sec>

Broadband Enhancement of the Spontaneous Emission by a Split-Ring Nanoantenna: Impact of Azimuthally Propagating Surface Plasmon Polaritons

We propose a split-ring optical nanoantenna which can achieve enhancement factors of total and radiative emission rates up to high values of 7411 and 1941, respectively, with a tunable bandwidth of enhanced emission (Purcell factor over 1000) up to 221 nm at visible wavelengths. To clarify the underlying physical mechanism, we build up a semi-analytical model by considering an intuitive multiple-scattering process of surface plasmon polaritons (SPPs) that propagate azimuthally along the curved antenna arms. The SPP model provides an intuitive picture that under two phase matching conditions, the SPPs form paired and tunable whispering-gallery-like resonances and are then coupled to the emitter in the nano-gap or scattered into free space, which results in an enhancement of the total or radiative emission rate, respectively. Based on the SPP model, we further build up a semi-analytical model for the quasi-normal modes (QNMs) supported by the antenna, which provides a frequency analyticity and indicates that the broadband enhancement of the spontaneous emission rate results from an excitation of paired symmetric and anti-symmetric QNMs with different eigenfrequencies. The proposed models clarify the impact of azimuthally propagating SPPs on the antenna radiation and may be extended to other optical antennas with curved arms.

Intuitive model of exceptional points in an optical whispering-gallery microcavity perturbed by nanoparticles

Exceptional points (EPs) in the optical whispering-gallery-mode (WGM) microcavity perturbed by Rayleigh scatterers have shown great potential in the areas of on-chip chiral photonics and enhanced sensors, creating a huge demand for deep theoretical insight into the unique physical properties of EPs. Here we propose an intuitive and first-principles-based model to clarify the formation of the EPs in the WGM microcavity perturbed by two nanoparticles. The model is constructed by considering a dynamical multiple-scattering process involving the clockwise and counterclockwise azimuthally propagating modes (APMs) at the nanoparticles. The complex resonance frequencies and resonant modes of the system can be comprehensively reproduced with the model. The conditions for the determination of EPs are derived, and the system parameters at the EP can be quantitatively predicted. The model unveils the relationship between the spatial chirality of the resonant modes near the EP and the scattering of APMs at the nanoparticles. The model quantitatively predicts the difference between the APM coefficients within different azimuthal regions divided by the two nanoparticles, which were considered to be identical in previous theoretical formalisms, and it exhibits the contributions of the APMs, other than those considered in the model, to forming the resonant modes. The proposition of the theoretical model will benefit the investigations of EPs in WGM microcavities and their applications.

Spin-orbit related power-law dependence of the diffusive conductivity on the carrier density in disordered Rashba two-dimensional electron systems

By using the momentum-space Lanczos recursive method which considers rigorously all multiple-scattering events, we unveil that the non-perturbative disorder effect has dramatic impact on the charge transport of a two-dimensional electron system with Rashba spin-orbit coupling in the low-density region. Our simulations find a power-law dependence of the dc longitudinal conductivity on the carrier density, with the exponent linearly dependent on the Rashba spin-orbit strength but independent of the disorder strength. Therefore, the classical charge transport influenced by complicated multiple-scattering processes also shows the characteristic feature of the spin-orbit coupling. This highly unconventional behavior is argued to be observable in systems with tunable carrier density and Rashba splitting, such as the LaAlO$_{3}$/SrTiO$_{3}$ interface, the heterostructure of Rashba semiconductors bismuth tellurohalides and the surface alloy Bi$_x$Pb$_y$Sb$_{1-x-y}$/Ag(111).

Complete Glauber calculations for proton–nucleus inelastic cross sections

We perform a parameter-free calculation for the high-energy proton–nucleus scattering based on the Glauber theory. A complete evaluation of the so-called Glauber amplitude is made by using the factorization of the single-particle wave functions. The multiple-scattering or multistep processes are fully taken into account within the Glauber theory. We demonstrate that proton-12C, 20Ne, and 28Si elastic and inelastic scattering (Jπ=0+→2+ and 0+→4+) processes are very well described in a wide range of the incident energies from ∼50 MeV to ∼1 GeV. We evaluate the validity of a simple one-step approximation and find that the approximation works fairly well for the inelastic 0+→2+ processes but not for 0+→4+ where the multistep processes become more important. As an application, we quantify the difference between the total reaction and interaction cross sections of proton-12C, 20Ne, and 28Si collisions.

Multiple-scattering effects in proton- and alpha-nucleus reactions with Glauber theory

We study the total reaction and elastic differential cross sections for proton-nucleus and 4He-nucleus reactions in the framework of the Glauber theory which describes multiplescattering processes. The input wave functions are obtained using the Skyrme-Hartree-Fock method and prepared for a wide range of mass numbers, O, Ca, Ni, Sn, and Pb isotopes. The theory reproduces experimental data very well. An effect of the multiple scattering is discussed by comparing with a standard optical-limit approximation. We see that the multiple-scattering effects play a crucial role, especially in enhancing the elastic differential cross sections at large scattering angles.

Effect of mineral dust aerosol aspect ratio on polarized reflectance

The effects of dust particle aspect ratios on single- and multiple-scattering processes are studied using the spheroidal model in order to obtain a better understanding of the radiance and polarization signals at the top of the atmosphere (TOA) under various dust-aerosol-loading conditions. Specifically, the impact of the particle aspect ratio on the polarization state of the TOA radiation field is demonstrated by comparing the normalized polarized radiances observed by the POLDER (POLarization and Directionality of the Earth׳s Reflectances) instrument on board the PARASOL (Polarisation et Anisotropie des Reflectances au sommet de l׳Atmosphère, couples avec un Satellite d׳Observation emportant un Lidar) satellite with the corresponding theoretical counterparts. Furthermore, presented are the aspect ratio values inferred from multi-angular polarized radiance measurements of Saharan and Asian dust by the POLDER/PARASOL.

Combined Sulfur K-Edge XANES–EXAFS Study of the Effect of Protonation on the Sulfate Tetrahedron in Solids and Solutions

Sulfur K-edge X-ray absorption spectroscopy (XAS) has been used to distinguish between aqueous and solid sulfates and to investigate changes in their speciation. Data have been collected for tetrahedrally coordinated S in K2SO4 and KHSO4 solids and aqueous solutions. With a first qualitative analysis of the X-ray absorption near-edge structure (XANES) spectra, it has been observed that those for solids are much more structured and distinguishable from those of aqueous solutions. The protonation state has a strong effect on the white line of sulfates and has been assigned to the different charge delocalization in the samples, the effect of the solvating water molecules and multiple scattering effects. In the extended X-ray absorption fine structure (EXAFS) spectra, the backscattering from the first O shell dominated the EXAFS fine structure function, χ(k), but the nonlinear multiple scattering contributions occurring in the first coordination shell are significant and must be considered in the EXAFS analysis. The intensity of these contributions strongly depend on the symmetry of the system. For a distorted tetrahedron, the intensity of the multiple scattering contributions is less than that found in a regular tetrahedron. The FEFF code has been used to model the contributions of the multiple-scattering processes. The observed experimental evidence in the XAS data can be used to distinguish between sulfates in solids and liquids. This is applicable to many chemical, geochemical, and biological systems.

Subgrid-scale cirrus observed by lidar at mid-latitude: variability effects of the cloud optical depth

The temporal variability of the 532-nm optical depth of cirrus clouds observed with a lidar at Observatory of Haute-Provence (43.9°N, 5.7°E, and 683-m altitude), has been analyzed. While advection dominates at the first order, variability of the optical depth on timescales of minutes can be related to spatial fluctuations of cloud properties on typical scales of a few kilometers. Log-normal distributions of the optical depth have been used to model the variability of the cirrus optical depth as observed by lidars. These investigations have been performed for three independent classes of cirrus. The log-normal distribution of the optical depth is applicable to the classes of thin clouds; however, for thick clouds, likely due to successive freezing/defreezing effects, the distribution is rather bimodal. This work compares the effects of visible solar light scattered by inhomogeneous cirrus to effects generated by homogeneous clouds having a constant geometrical thickness using the short-scale lidar observations of optical depth distribution and an analytical approach. In the case of thin cirrus, the scattering of solar light reaching the ground is stronger for inhomogeneous than homogeneous cirrus. In case of thick cirrus, multiple-scattering processes need to be considered. The conclusion is that log-normal distribution of the cirrus optical depth should be considered in any radiative calculation in case of model grids larger than a few kilometers whatever the cirrus type is.

Spectral line polarization with angle-dependent partial frequency redistribution

Context. The linear polarization of a strong resonance lines observed near the solar limb is created by a multiple-scattering process. Partial frequency redistribution (PRD) effects must be accounted for to explain the polarization profiles. The redistribution matrix describing the scattering process is a sum of terms, each containing a PRD function multiplied by a Rayleigh type phase matrix. A standard approximation made in calculating the polarization is to average the PRD functions over all the scattering angles, because the numerical work needed to take the angle-dependence of the PRD functions into account is large and not always needed for reasonable evaluations of the polarization. Aims. This paper describes a Stokes parameters decomposition method, that is applicable in plane-parallel cylindrically symmetrical media, which aims at simplifying the numerical work needed to overcome the angle-average approximation. Methods. The decomposition method relies on an azimuthal Fourier expansion of the PRD functions associated to a decomposition of the phase matrices in terms of the Landi Degl’Innocenti irreducible spherical tensors for polarimetry T K Q (i, Ω )( i Stokes parameter index, Ω ray direction). The terms that depend on the azimuth of the scattering angle are retained in the phase matrices. Results. It is shown that the Stokes parameters I and Q, which have the same cylindrical symmetry as the medium, can be expressed in terms of four cylindrically symmetrical components I K (K = Q = 0, K = 2, Q = 0, 1, 2). The components with Q = 1, 2a re created by the angular dependence of the PRD functions. They go to zero at disk center, ensuring that Stokes Q also goes to zero. Each component I K is a solution to a standard radiative transfer equation. The source term S K are significantly simpler than the source terms corresponding to I and Q. They satisfy a set of integral equations that can be solved by an accelerated lambda iteration (ALI) method.

Specific multiple-scattering process in acoustic cloak with multilayered homogeneous isotropic materials

It was qualitatively demonstrated through finite-element full-wave simulations that acoustic cloak can be constructed by using concentric multilayered structure with alternating homogeneous isotropic materials [Y. Cheng et al., Appl. Phys. Lett. 92, 151913 (2008)]. Here we present a sequential in-depth analysis of the proposed cloak by means of the multiple-scattering algorithms. Calculated pressure fields demonstrate that the cloak possesses low-reflection and wavefront-bending properties. The scattering patterns further characterize the directional cloaking performance in the far field, which is consistent with the pressure fields. The mechanism of the cloaking is ascribed to a specific multiple-scattering process determined by the microscopic material distribution and structural details of the cloak. We also discuss the behavior of the multilayered cloak as a function of wavelength.

Backscattered polarization patterns determined by conservation of angular momentum

It is demonstrated that the occurence of backscattered polarization patterns relates to the conservation of angular momentum of light. Using the geometrical phase formalism in the spin space, we develop a model where the helicity-maintaining and the helicity-flipping multiple-scattering processes can be accounted for. The model explains practically all the symmetries present in the spatially resolved Mueller matrices.

Quantum-mechanical formulation of light propagation: A multiple-scattering approach

Since in quantum optics light is represented in terms of photons, light propagation through a linear medium is discussed quantum mechanically in this paper by following the multiple-scattering process of one incident photon from the medium. To treat the photon and the medium on the same quantum footing, the medium is assumed to be an ensemble of uniformly distributed identical two-level atoms. It is found that inside the medium the incident photon follows the same propagation rules as a plane wave does in the classical domain, and has a possibility to become entangled with the atoms. It is also found that when interacting with a two-level test atom outside the medium, the output photon appears to be formally in a single mode identical to that of the incident photon.

Time evolution of electromagnetic wave packets through superlattices: Evidence for superluminal velocities

We study the space-time evolution of electromagnetic wave packets through optical superlattices. We present rigorous analytical solutions describing the multiple-scattering processes of Gaussian wave packets defined in the band gap and in the resonant energy regions. Following their space-time evolution, we obtain the Maxwell equations prediction for the time spent inside the superlattice. From a close and careful observation of the reflected and transmitted parts of Gaussian packets in a photonic band gap, we conclude unambiguously that the superluminal transmission and the Hartman effect are inherent properties of the electromagnetic theory. It is also shown that the theoretical predictions for the time spent inside an optical superlattice are in good agreement with the experimental results and the phase time predictions.