Green Function Analysis Research Articles

Second harmonic conversions of surface-plasmon-polariton–enhanced optical fields in nonlinear optics polymer/Ag/glass structures

Optical fields enhanced by surface plasmon polaritons (SPPs) on metal-dielectric interfaces are useful for increasing several light-matter interactions, and application to nonlinear optics (NLO) is one of the most important uses of this type of structure. Most previous studies on this subject took advantage of the nonlinear susceptibilities of metal surfaces. However, the limited NLO light-matter interaction lengths prevented the transfer of the technologies to practical use. In the present paper, we tried to overcome this problem by growing NLO polymer thin films on metal surfaces. The NLO responses of the system were characterized by second-harmonic generation (SHG) spectroscopy. Our experimental results suggested that SPP-enhanced optical fields induced not only surface nonlinearities in Ag but also bulk nonlinearities in NLO polymer. There was an optimal polymer thickness for the SHG conversions, and a greater thickness did not always result in higher conversion. The maximum conversion efficiency was approximately 40 times higher than that of the nonpolymer-coated bare Ag surface. The growth and propagation of the SHG waves were addressed with a numerical approach combining the transfer matrix method and Green's function analysis. The SHG conversion efficiencies were determined by three factors, the SPP-field enhancement factor, the nonlinear light-matter interaction length, and the degree of interference between the forward- and backward-propagating SHG waves. The latter two factors predominantly determined the optimal SHG conversion efficiencies. The proposed strategy of hybridizing NLO polymers brings us closer to practical uses for nonlinear plasmonics.

A simulation-based model for understanding the time dependent x-ray drive asymmetries and error bars in indirectly driven implosions on the National Ignition Facility

Time-dependent low-mode asymmetries are believed to play a leading role in limiting the performance of current inertial confinement fusion implosions on the National Ignition Facility (NIF) [E. I. Moses et al., Phys. Plasmas 16, 041006 (2009)]. These long wavelength modes are initiated and driven by asymmetries in the x-ray flux from the hohlraum; however, the underlying hydrodynamics of the implosion also act to modify and amplify these asymmetries. We present here a simulation-based model connecting the time-dependent drive asymmetry seen by the capsule to the measured inflight and hot spot symmetries. This approach is based on a Green's function analysis for which we evaluate the response of the capsule to impulses of drive asymmetry at a series of times. Our model sheds new light on the sensitivity to the drive asymmetry of an imploded capsule, giving a new tool for design. Inverting the problem and finding the drive asymmetry needed to match the experimental data allow us to tightly constrain the drive asymmetry seen by the capsule, providing an error estimate on the result. Doing so, we are able to point out when and how the complex hohlraum simulations start to deviate from what they should obtain to match the experimental data. Ultimately, we project to use this model to make some experimental recommendations to fix the time-dependent low-mode asymmetry of indirectly driven implosions and identify additional measurements to further constrain the asymmetries with a view to improving target design on the NIF.

First-principles calculations of solute transport in zirconium: Vacancy-mediated diffusion with metastable states and interstitial diffusion

Zirconium alloys are the most widely used nuclear fuel cladding materials for light water power reactors where irradiation damage causes solute redistribution, leading to degradation of alloy properties such as corrosion resistance. Designing radiation-tolerant zirconium alloys requires a thorough understanding of the atomic-scale transport behavior of the alloying elements in Zr. We perform density function theory calculations to investigate the diffusion of Sn, Cr, Fe, Be, Al, and Ni in the hexagonal close-packed (HCP) Zr matrix. We develop a methodology to accurately model the metastable vacancy states along the basal migration path, known to occur in group IV metals. We compute the vacancy-mediated solute diffusion coefficients and drag ratios using the kinetic Monte Carlo method and an analytic Green's function method---the agreement between the two validates our methodology. The computed diffusion coefficients of Sn and Al show good agreement with the experimental data and we expect these solutes to diffuse via the vacancy-mediated mechanism. We use a Green's function approach, parameterized with data from density functional theory calculations, to compute the interstitial diffusion coefficients of Cr, Fe, Be, and Ni in the HCP Zr lattice. The computed diffusion coefficients of Cr, Ni, and Be agree with the experimental measurements within one order of magnitude, while those of Fe are within two orders of magnitude of the experimental measurements. The drag ratios for Cr, Fe, Be, and Ni are positive up to 1235 K, which suggests that nonequilibrium vacancy fluxes could drag these solutes toward sinks such as dislocation loops and grain boundaries. We also compute the transport coefficients without including the metastable states, and using the eight- and thirteen-frequency model. Our results show significant differences in drag ratio for the eight- and thirteen-frequency model predictions compared with the Green's function methodology, but smaller errors in the solute diffusivity. Combining interstitial and vacancy-mediated diffusivities, we predict the unusual result that increased vacancy concentration slows down solute diffusivity, while a sufficiently high vacancy concentration can change the dominant mechanism to an accelerated vacancy-mediated diffusion.

Theory and experiments of coherent photon coupling in semiconductor nanowire waveguides with quantum dot molecules

We present a quantum optics theory, numerical calculations, and experiments on coupled quantum dots in semiconductor nanowire waveguides. We first present an analytical Green function theory to compute the emitted spectra of two coupled quantum dots, treated as point dipoles, fully accounting for retardation effects, and demonstrate the signatures of coherent and incoherent coupling through a pronounced splitting of the uncoupled quantum dot resonances and modified spectral broadening. In the weak excitation regime, the classical Green functions used in models are verified and justified through full three-dimensional solutions of Maxwell equations for nanowire waveguides, specifically using finite-difference time-domain techniques, showing how both waveguide modes and near-field evanescent mode coupling is important. The theory exploits an ensemble-based quantum description, and an intuitive eigenmode-expansion-based Maxwell theory. We then demonstrate how the molecular resonances (in the presence of coupling) take on the form of bright and dark (or quasidark) resonances, and study how these depend on the excitation and detection conditions. To go beyond the weak excitation regime, we also introduce a quantum master-equation approach to model the nonlinear spectra from an increasing incoherent pump field, which shows the role of the pump field on the oscillator strengths and broadening of the molecular resonances, with and without pure dephasing. Next, we present experimental photoluminescence spectra for spatially separated quantum dot molecules (InAsP) in InP nanowires, which show clear signatures of pronounced splittings, although they also highlight additional mechanisms that are not accounted for in the dipole-dipole coupling model. Two different approaches are taken to control the spatial separation of the quantum dot molecules, and we discuss the advantages and disadvantages of each.

Analytic form of the size distribution in irreversible growth of nanoparticles.

We study theoretically the size distributions of nanoparticles (surface islands, droplets, molecular chains, and semiconductor nanowires) which grow without decay and with arbitrary size and time-dependent growth rates. Using a special transformation of variables, the analytic Green's function is obtained in the form of a Gaussian the variance of which is determined by the size dependence of the growth rate k(s). In the case of the power-law growth rates k(s)=(a+s)^{α}, the explicit formulas for the expectation and variance are given that contain earlier results in the limiting regimes. In the case of heterogeneous nucleation in a closed system, by convoluting Green's function with the exponential nucleation rate, we find an analytic size distribution which takes into account a delay in forming the smallest dimer and shows how it affects the distribution shapes. The recently discovered sub-Poissonian narrowing of the size distribution by nucleation antibunching is also included in the treatment. We briefly consider the length distribution of vapor-liquid-solid nanowires in the context of the obtained results. Overall, simple analytic size distributions obtained here under rather general assumptions may be useful for understanding and modeling statistical properties of different growth systems.

Coupled Topological Surface Modes in Gyrotropic Structures: Green's Function Analysis

At a transition in a wave-guiding structure, part of the incident energy is transmitted and part of the energy is reflected. When the waveguide has non-trivial topological properties, however, the transition may occur with no backscattering, and with unusual modal coupling/transformations. Within this context, we discuss the response of a nonreciprocal topological structure composed of two nearby interfaces between oppositely-biased gyrotropic media and an isotropic medium, which support unidirectional surface modes (topological modes). We provide an exact Green's function analysis of this structure, and we discuss how the topological surface modes are modified when the two interfaces are brought closer and eventually merged. We show that the resulting mode conversion is independent of the transition geometry.

Effects of dielectric inhomogeneity on electrostatic twist rigidity of a helical biomolecule in Debye-Hückel regime.

The electrostatic interactions play a crucial role in biological systems. Here we consider an impermeable dielectric molecule in the solvent with a different dielectric constant. The electrostatic free energy in the problem is studied in the Debye-Hückel regime using the analytical Green function that is calculated in the paper. Using this electrostatic free energy, we study the electrostatic contribution to the twist rigidity of a double stranded helical molecule such as a DNA and an actin filament. The dependence of the electrostatic twist rigidity of the molecule to the dielectric inhomogeneity, structural parameters, and the salt concentration is studied. It is shown that, depending on the parameters, the electrostatic twist rigidity could be positive or negative.

Coherent Seismic Arrivals in the P Wave Coda of the 2012 Mw 7.2 Sumatra Earthquake: Water Reverberations or an Early Aftershock?

AbstractTeleseismic records of the 2012 Mw 7.2 Sumatra earthquake contain prominent phases in the P wave train, arriving about 50 to 100 s after the direct P arrival. Azimuthal variations in these arrivals, together with back‐projection analysis, led Fan and Shearer (, https://doi.org/10.1002/2016GL067785) to conclude that they originated from early aftershock(s), located ∼150 km northeast of the mainshock and landward of the trench. However, recently, Yue et al. (, https://doi.org/10.1002/2017GL073254) argued that the anomalous arrivals are more likely water reverberations from the mainshock, based mostly on empirical Green's function analysis of a M6 earthquake near the mainshock and a water phase synthetic test. Here we present detailed back‐projection and waveform analyses of three M6 earthquakes within 100 km of the Mw 7.2 earthquake, including the empirical Green's function event analyzed in Yue et al. (, https://doi.org/10.1002/2017GL073254). In addition, we examine the waveforms of three M5.5 reverse‐faulting earthquakes close to the inferred early aftershock location in Fan and Shearer (, https://doi.org/10.1002/2016GL067785). These results suggest that the reverberatory character of the anomalous arrivals in the mainshock coda is consistent with water reverberations, but the origin of this energy is more likely an early aftershock rather than delayed and displaced water reverberations from the mainshock.

Strained zigzag graphene nanoribbon devices with vacancies as perfect spin filters.

The transport properties of zigzag graphene nanoribbons (zGNRs) were studied by density functional theory (DFT) in conjunction with Green's function analysis. In particular, spin transport through a zGNR (12,0) device was investigated under the constraint of ferromagnetic coordination of the ribbon edges. Several configurations with two vacant sites in the edge and the bulk region of the zGNR device were derived from this system. For all structures, magnetocurrent ratios (MCRs) were recorded as a function of the bias as well as the amount of strain applied longitudinally to the devices. ZGNR devices with vacancies in the edge regime turn out to exhibit perfect spin-filter activity for well-defined choices of the strain and the bias, carrying completely polarized minority spin currents. In the alternative structure, characterized by vacancies in the bulk regime, spin currents with majority orientation prevail. With respect to both the sign and the size, the MCR is seen to depend sensitively on the device parameters, i.e., the vacancy locations, the bias, and the amount of strain. These results are interpreted in terms of density-of-states distributions, transmission spectra, and transmission operator eigenstates.

Spin waves in superlattice nanowires formed by two different ferromagnetic materials

A Green function analysis is used to study spin-wave excitations in a nanowire ferromagnetic superlattice. The dispersion equation for spin waves propagating along the nanowires, which are modeled as having a hexagonal cross section, is derived. The results are illustrated numerically for a particular choice of parameters.

Time domain nearfield acoustical holography without wrap-around error and spectral leakage for forward propagation.

Nearfield acoustical holography can be used to visualize time domain evolution of non-stationary sound fields. It requires sampling of the pressure field with a microphone array to calculate the sound field on other parallel surfaces, either toward the source or farther away from it. This paper focuses on forward propagation of fields sampled with a planar array. Several formulations exist to perform such calculation; however, despite being mathematically well-posed, they generate significant errors, especially for larger propagation distances. These errors are mainly due to wrap-around and spectral leakage. It is shown in this paper that generation of leakage can be avoided by sampling the analytical Green's function in the time and space domains. Such formulation allows the application of linear convolution, which completely suppresses wrap-around errors. The results obtained from the proposed formulation are compared to the analytical solution of a baffled piston with transient displacement. The average discrepancy is below 3.5% for propagation distances of 5 to 55 cm. In comparison, the relative error obtained with other propagators varies from 6% to 73%, depending on the propagation distance and method used. Finally, the proposed formulation is applied to experimental data obtained from an impacted plate.

Heat conduction in convectively cooled eccentric spherical annuli: A boundary integral moment method

In this paper heat conduction equation for an eccentric spherical annulus with the inner surface kept at a constant temperature and the outer surface subjected to convection is solved analytically. Eccentric problem domain is first transformed into a concentric domain via formulating the problem in bispherical co-ordinate system. Since an analytical Green?s function for the heat conduction equation in bispherical co-ordinate for an eccentric sphere subject to boundary condition of third type can not be found, an analytical Green's function obtained for Dirichlet boundary condition is employed in the solution. Utilizing this Green's function yields a boundary integral equation for the unknown normal derivative of the surface temperature distribution. The resulting boundary integral equation is solved analytically using method of moments. The method has been applied to heat generating eccentric spherical annuli and results are compared to the simulation results of FLUENT CFD code. A very good agreement was observed in temperature distribution computations for various geometrical configurations and a wide range of Biot number. Variation of heat dissipation with radii and eccentricity ratios are studied and a very good agreement with FLUENT has been observed

Internal Tide Generation Using Green Function Analysis: To WKB or Not to WKB?

AbstractAn established analytical technique for modeling internal tide generation by barotropic flow over bottom topography in the ocean is the Green function–based approach. To date, however, for realistic ocean studies this method has relied on the WKB approximation. In this paper, the complete Green function method, without the WKB approximation, is developed and tested, and in the process, the accuracy of the WKB approximation for realistic ridge geometries and ocean stratifications is considered. For isolated Gaussian topography, the complete Green function approach is shown to be accurate via close agreement with the results of numerical simulations for a wide range of height ratios and criticality; in contrast, the WKB approach is found to be inaccurate for small height ratios in the subcritical regime and all tall topography that impinges on the pycnocline. Two ocean systems are studied, the Kaena and Wyville Thomson Ridges, for which there is again excellent agreement between the complete Green function approach and numerical simulations, and the WKB approximate solutions have substantial errors. This study concludes that the complete Green function approach, which is typically only modestly more computationally expensive than the WKB approach, should be the go-to analytical method to model internal tide generation for realistic ocean ridge scenarios.

Validation of low frequency noise attenuation using locally resonant patches.

Since conventional silencers in acoustic ducts have problems of size limitations at low frequencies and being prone to high backpressure, locally resonant aluminum patches are introduced in acoustic duct walls aiming at creating frequency stop bands in the low frequency region (below 1 KHz). With these flush mounted patches, promising noise reductions, with no such drawbacks, can be obtained, building on local resonance phenomenon implemented in acoustic metamaterials techniques. The objective of the current paper is to experimentally validate the performance of an array of flexible side-wall-mounted patches inside ducts. The experimental results are compared with Analytical Green's function method as well as Numerical Finite Element Method and a close agreement was found. The results show that the presence of the patches singly or periodically can play a prominent role in designing any acoustic bandgap materials. The effect of the arrays of patches on the effective dynamic density and bulk modulus has also been investigated.

A DGTD Scheme for Modeling the Radiated Emission From DUTs in Shielding Enclosures Using Near Electric Field Only

To meet the electromagnetic interference regulation, the radiated emission from device under test such as electronic devices must be carefully manipulated and accurately characterized. Instead of resorting to the direct far-field measurement, in this paper, a novel approach is proposed to model the radiated emission from electronic devices placed in shielding enclosures by using the near electric field only. Based on the Schelkkunoff's equivalence principle and Raleigh–Carson reciprocity theorem, only the tangential components of the electric field over the ventilation slots and apertures of the shielding enclosure are sufficient to obtain the radiated emissions outside the shielding box if the inside of the shielding enclosure was filled with perfectly electric conductor (PEC). In order to efficiently model wideband emission, the time-domain sampling scheme is employed. Due to the lack of analytical Green's function for arbitrary PEC boxes, the radiated emission must be obtained via the full-wave numerical methods by considering the total radiated emission as the superposition between the direct radiation from the equivalent magnetic currents in free space and the scattered field generated by the PEC shielding box. In this study, the state-of-the-art discontinuous Galerkin time-domain (DGTD) method is utilized, which has the flexibility to model irregular geometries, keep high-order accuracy, and more importantly involves only local operations. For open-region problems, a hybridized DGTD and time-domain boundary integration method applied to rigorously truncate the computational domain. To validate the proposed approach, several representative examples are presented and compared with both analytical and numerical results.

Multidimensional quasiballistic thermal transport in transient grating spectroscopy

Transient grating spectroscopy has emerged as a useful technique to study thermal phonon transport because of its ability to perform thermal measurements over length scales comparable to phonon mean free path (MFPs). Although several prior works have performed theoretical studies of quasiballistic heat conduction in transient grating, the analysis methods are either restricted to one spatial dimension or require phenomenological fitting parameters. Here, we analyze quasiballistic transport in a two-dimensional transient grating experiment in which heat conduction can occur both in and cross plane using an analytic Green's function of the Boltzmann equation we recently reported that is free of fitting parameters. We demonstrate a method by which phonon MFPs can be extracted from these measurements, thereby extending the MFP spectroscopy technique using transient grating to opaque bulk materials.

Local spin excitations in the rectangular ferromagnetic semiconductor nanowires

A Green function analysis is used to study spin-waves excitations in a ferromagnetic semiconductor nanowires. The expressions of Green function for different spins of ferromagnetic nanowires are derived. The nanowire is modeled as having a cubic cross section. The results are illustrated numerically for a particular choice of parameters

Plasmon excitation on flat graphene by s-polarized beams using four-wave mixing.

Graphene plasmons have received significant attention recently due to its attractive properties such as high spatial confinement and tunability. However, exciting plasmons on graphene effectively still remains a challenge owing to the large wave-vector mismatch between the optical beam in air and graphene plasmon. In this paper, we present a novel scheme capable of exciting graphene surface plasmons (GSPs) on a flat suspended graphene by using only s-polarized optical beams through four-wave mixing (FWM) process, where the GSPs fields were derived analytically based on the Green's function analysis, under the basis of momentum conservation. By incorporating the merits of nonlinear optics, the presented scheme avoids any patterning of either graphene or substrate. We believe that the proposed scheme potentially paves the way towards an efficient pure optical excitation, switching and modulation of GSPs for realizing graphene-based nano-photonic and optoelectronic integrated circuits.

Stability of Viscous Weak Detonation Waves for Majda’s Model

Continuing the program initiated by Humpherys, Lyng, & Zumbrun [17] for strong detonation waves, we use a combination of analytical and numerical Evans-function techniques to analyze the spectral stability of weak detonation waves in a simplified model for gas-dynamical combustion. Combining these new spectral stability results with the pointwise Green function analysis of Lyng, Raoofi, Texier, & Zumbrun [22], we conclude that these waves are nonlinearly stable. The principal novelty of this analysis is the treatment of weak detonation waves. In contrast to the case of strong detonation waves, weak detonation waves are undercompressive and the stability of these waves is delicate and has not been treated by standard weighted-norm techniques. The present analysis thus provides a case study illustrating the flexibility and power of the Evans-function- based approach to stability. As in the case of strong detonations, we find that all tested waves are spectrally stable, hence nonlinearly stable.

Interaction of a Guided Wave with a Crack in an Embedded Multilayered Anisotropic Plate: Global Matrix with Laplace Transform Formalism

We solve the problem of the interaction of a transient guided elastic wave by a planar crack with an indirect Boundary Element approach in the Laplace domain (t → s). The originality of this work is to use the numerical Green function of the layered plate rather than the analytical Green function of each layer. As a consequence, the BEM matrices are small. To obtain the Green function in the (x,z,s) domain we first solve the equations in the Fourier transform (k,z,s) domain with a Global Matrix approach, and then perform a numerical inverse FFT. Comparisons with finite element show excellent agreement. This approach is fast and low memory consuming for planar defects in arbitrary layered media, and can be extended to arbitrary shapes and boundary conditions for a higher computational cost. It is valid in 3D, however only the 2D case is considered in this work.