First-order Born Approximation Research Articles

Scattering and radiation forces of two types of partially coherent twisted beams

Based on the first-order Born approximation and the Rayleigh scattering theory, the analytical expressions of the weak scattering and the radiation force of two types of partially coherent twisted beams are derived, respectively. Numerical examples show that the scattering's directionality and the radiation force's magnitude can be controlled by the twist factor and the cross-strength factor. Moreover, it can be obtained that these two beams can capture particles into the beams' center transversely and push the particles to move forward in the axial direction, which may be useful in optical micromanipulation. For example, we can use these beams to filter out high refractive index particles from clusters and separate them through axial force. This paper will be helpful to the fields of optical tweezers, optical communication, and so on.

Scattering of the generalized multi-Gaussian correlated Schell-model beam upon a deterministic medium with semi-hard boundary

In this paper, based on the first-order Born approximation, the scope of scattering theory was broadened by analyzing the scattering of generalized multi-Gaussian correlated Schell-model (GMGCSM) beam upon a deterministic medium with semi-hard boundary. It was revealed that the scattering spectral density and degree of coherence (DOC) are affected by several parameters, covered semi-hard boundary medium’s summation index L and effective radius σR, and GMGCSM beam’s coherence length δ, index M and transverse width σ0. The valuable and meaningful results obtained here could contribute to the expansion of the application range of scattering theory, making it applicable in various fields such as optical communication, remote sensing, and medicine.

Reciprocally tailored transparent artificial media for frequency and direction dependent light trapping

We propose a quasiperiodic leveled-wave structure whose reciprocal space is represented by spherical belt sections, designed to achieve scattering only for the defined wavelength and direction of incident light. At the same time light is scattered only towards directions of k-vectors for which the waves are trapped by total internal reflection in the structured slab. The trapped light is only weakly scattered and thus spends a long time inside the slab and is attenuated by weak absorption in the slab. The incident light of other direction and/or wavelength is transmitted through the slab almost undisturbed. We quantitatively estimated the scattering mean free paths for incident and trapped light from the first-order Born approximation and develop an analytical model which predicts the absorption for a given slab thickness, refractive index contrast and spherical belt parameters. Reducing the refractive index contrast and thickness of the belt, the selectivity can be increased and the absorption contrast for incident light of different wavelengths can reach 70%. We present numerical simulations with absorption contrast of 63% for refractive index contrast of 0.1, which is in good agreement with our analytical model.

Nonlinear least-squares reverse time migration of prismatic waves for delineating steeply dipping structures

Prismatic reflections in seismic data carry abundant information about subsurface steeply dipping structures, such as salt flanks or near-vertical faults, playing an important role in delineating these structures when effectively used. Conventional linear least-squares reverse time migration (L-LSRTM) fails to use prismatic waves due to the first-order Born approximation, resulting in a blurry image of steep interfaces. We develop a nonlinear LSRTM (NL-LSRTM) method to take advantage of prismatic waves for the detailed characterization of subsurface steeply dipping structures. Compared with current least-squares migration methods of prismatic waves, our NL-LSRTM is nonlinear and thus avoids the challenging extraction of prismatic waves or the prior knowledge of L-LSRTM results. The gradient of NL-LSRTM consists of the primary and prismatic imaging terms, which can accurately project observed primary and prismatic waves into the image domain for the simultaneous depiction of near-horizontal and near-vertical structures. However, we find that the full Hessian-based Newton normal equation has two similar terms, which prompts us to make further comparison between the Newton normal equation and our NL-LSRTM. We determine that the Newton normal equation is problematic when applied to the migration problem because the primary reflections in the seismic records will be incorrectly projected into the image along the prismatic wavepath, resulting in an artifact-contaminated image. In contrast, the nonlinear data-fitting process included in the NL-LSRTM contributes to balancing the amplitudes of primary and prismatic imaging results, thus making NL-LSRTM produce superior images compared with the Newton normal equation. Several numerical tests validate the applicability and robustness of NL-LSRTM for the delineation of steeply dipping structures and illustrate that the imaging results are much better than the conventional L-LSRTM.

Scattering of radially polarized partially coherent vortex beams from a random medium with semi-hard boundary

In this paper, scattering medium with a semi-hard boundary is extended to the case of a quasi-homogeneous random medium for the first time. Applying the first-order Born approximation, far-field distribution of radially polarized partially coherent vortex beams scattered upon the random medium with semi-hard boundary is studied. Spectral density distribution, degree of spectral polarization, polarization angle, and degree of ellipticity of the scattering field in the far zone are investigated. Influence of characteristics of the incident beam and scattering medium on the far-zone scattering field are discussed. In addition, phase singularity of the scattering field’s center is also described. It is interesting to find that the far-field scattering field is circularly polarized with a Gaussian distribution, though the incident field is radially polarized with a dark-hollow distribution. The center of the scattering field is completely polarized, while on the edge of the scattering field, degree of polarization shows obvious fluctuations with the change of parameters of the incident beam and medium. Results obtained here could find application in the acquisition of medium structure information.

Nonlinear polarization tensor measurement with a vectorial complex field in second-harmonic-generation microscopy

Polarization-sensitive second-harmonic-generation microscopy (pSHGM) allows one to determine the molecular orientation of harmonophores. Conventional point scanning based pSHGM is time consuming and subject to the assumption of the cylinder symmetry of the sample. Here, we propose a wide-field pSHGM measurement scheme that is able to measure the second-order nonlinear polarization tensor. The measurement scheme is based on first-order Born approximation, from which the relation between incident fundamental wave, second harmonic wave, and nonlinear polarization tensor has been established. It suggests that the polarization tensor can be solved by measuring the vectorial second harmonic complex fields corresponding to three independent polarization states of the incident fundamental wave. An experiment on measuring the supramolecular orientations, in terms of their symmetric axis, of myosin in rat muscle tissue has been carried out to demonstrate the proposed measurement scheme. Benefiting from the ability of recording the second harmonic signal from different positions parallelly, the proposed method possesses a higher imaging frame rate compared to point scanning based pSHGM. With the present configuration, it takes 0.01 s to acquire a 128\ifmmode\times\else\texttimes\fi{}128 pixels image, which is mainly limited by the excitation power density for wide-field illumination. For the same data throughput using pixel-by-pixel scanning, 0.16 s acquisition time is required for a pixel dwell time of 10 \textmu{}s. Having the ability of wide-field imaging and polarization measurement, the present work also lays a foundation for high-resolution SHG microscopy using computed tomography.

Phase-preserving theory and its linearization approximation for forward scattering field of scalar acoustic wave equation

The conventional wave-equation linearization methods, such as the first-order Born or Rytov approximation, always implicitly imply a weak-scattering assumption, making it valid only for weak perturbation models. To extend the wave-equation linearization theory to strong perturbation models, we consider a scenario that the reference model is smooth within the scale of the incident wave length, and propose a phase-preserving method which can predict the phase perturbation of forward scattering wave field. First, we introduce the WKBJ approximation to the scattered- and incident wave fields so that the integral of the unknown solution (i.e. the scattered field) in the nonlinear Ricatti integral equation can be replaced by the integral of scattering-angle and model perturbation, yielding an explicit expression of the scattered field. Theoretical derivation shows that the proposed phase-preserving method can accurately predict the phase-perturbation of forward scattered wave field regardless of the strength of velocity perturbations for one-dimensional wave propagation problem. To apply the phase-preserving approximation to the inverse problem, we further consider a scenario of small-angle forward propagation. In this case, the phase-preserving approximation can be linearized by neglecting the influence of scattering angles, leading to a linear relation between the scattered field and the model perturbation, which we refer to as the generalized Rytov approximation. Numerical experiments demonstrate that the generalized Rytov approximation can predict the phase perturbation of the scattered field with higher accuracy for small-angle forward propagation, and is suitable for strong model perturbations. The generalized Rytov approximation extends the validity and the scope of application of the traditional Rytov approximation. In specific application fields such as the seismic traveltime tomography or medical ultrasonic transmission imaging, a new traveltime/phase sensitivity kernel can be derived by replacing the conventional Rytov approximation with the proposed method, which can increase the inversion accuracy and speed up the convergence.

Experimental setup for interaction between highly charged ions and laser-produced plasma near Bohr velocity energy region

Ion energy loss in the interaction between highly charged ions and dense plasma near Bohr velocity energy region is one of the important physical problems in the field of high-energy density physics driven by intense heavy ion beams. Based on the 320 kV experimental platform at the Institute of Modern Physics, Chinese Academy of Sciences, a new experimental setup was built for the research of interaction between ions and laser-produced plasma near the Bohr velocity, where the ion energy loss and charge state distribution can be experimentally investigated. In this paper we introduce the new setup in detail, including the generation and controlling of pulsed ion beam ( ≥ 200 ns); the preparation of high-density laser plasma target (10<sup>17</sup>—10<sup>21</sup> cm<sup>–3</sup>); the diagnostics of plasma and the developed high energy resolution ion measurement system (< 1%). In the experiment, the charge distribution of Xe<sup>15+</sup> ions with 4 MeV penetrating through the laser-produced Al plasma target is measured. The charge-state analysis device observes different results without and with the plasma, in which the outgoing Xe ion charge-state changes correspondingly from the 15+ to 10+, thus the electron capture process is believed to be dominant. In addition, the proton energy loss is also measured by using the magnetic spectrometer, showing that the experimental energy loss is about 2.0 keV, 30% higher than those theoretical predictions , which can be attributed to the fact that in the near Bohr velocity energy regime, the first-order Born approximation condition is not valid, thus the Bethe model and SSM model are inapplicable to the experimental results. In future, a systematic study will be performed based on our ions-plasma ineteraction setup, and the energy loss and charge state data will be introduced.

Optical diffraction tomography of second-order nonlinear structures in weak scattering media: theoretical analysis and experimental consideration.

Computed tomography (CT) allows for high lateral and axial resolution imaging of the endogenous structure of matter thanks to its large spatial frequency support and has been realized in X-ray and linear optical domain known as optical diffraction tomography (ODT). Here, we present the theoretical basis and experimental considerations for ODT of second-order nonlinear structures in weak scattering media. We have derived the relation between second harmonic wave and the anisotropic nonlinear tensor in spatial frequency domain under first-order Born approximation. Our results show that, under a plane wave illumination, the two dimensional (2D) spatial spectra of generated second harmonic complex field relates to the inverse lattice of nonlinear structure on Ewald sphere shells. The centers of the Ewald spheres are determined by 2 times wavevector of the incident fundamental wave and the radii are determined by the modulus of the second harmonic wavevector. More importantly, it shows that the 2D spatial spectra is a superposition of the Ewald spheres of different components of the anisotropic nonlinear tensor. We propose to solve the inverse problem by controlling the polarizations of the fundamental and second harmonic signal. We tested the feasibility of the proposed method using a numerical phantom and make some discussions on practical implementations, including angular scanning schemes, polarization detection and illumination profile for optimizing reconstruction region. Possessing high resolution, wide-field imaging and polarization-sensitive property, we believe that the proposed scheme would have important applications in nonlinear microscopy.

Scattering of light waves from a collection of particles of L types.

A new, to the best of our knowledge, pathway is paved within the first-order Born approximation to access light scattering from a collection of particles of L types. Two L×L matrices called a pair-potential matrix (PPM) and a pair-structure matrix (PSM) are introduced to jointly characterize the scattered field. We show that the cross-spectral density function of the scattered field equals the trace of the product of the PSM and the transpose of the PPM, and thus these two matrices allow us to determine all the second-order statistical properties of the scattered field. Based on this, the spectral degree of coherence (SDOC) of the scattered field is further analyzed. In a special case where the spatial distributions of the scattering potentials of particles of different types are similar and the same is true of their density distributions, it is found that the PPM and the PSM will reduce to two new matrices whose elements separately quantify the degree of angular correlation of the scattering potentials of particles and their density distributions, and the number of species of particles in this special case will appear as a scaled factor to ensure the normalization of the SDOC. The importance of our new approach is illustrated by an example.

High Sound-Contrast Inverse Scattering by MR-MF-DBIM Scheme

In ultrasound tomography, cross-sectional images represent the spatial distribution of the physical parameters of a target of interest, which can be obtained based on scattered ultrasound measurements. These measurements can be obtained from dense datasets collected at different transmitter and receiver locations, and using multiple frequencies. The Born approximation method, which provides a simple linear relationship between the objective function and the scattering field, has been adopted to resolve the inverse scattering problem. The distorted Born iterative method (DBIM), which utilizes the first-order Born approximation, is a productive diffraction tomography scheme. In this article, the range of interpolation applications is extended at the multilayer level, taking into account the advantages of integrating this multilayer level with multiple frequencies for the DBIM. Specifically, we consider: (a) a multi-resolution technique, i.e., a multi-step interpolation for the DBIM: MR-DBIM, with the advantage that the normalized absolute error is reduced by 18.67% and 37.21% in comparison with one-step interpolation DBIM and typical DBIM, respectively; (b) the integration of multi-resolution and multi-frequency techniques with the DBIM: MR-MF-DBIM, which is applied to image targets with high sound contrast in a strongly scattering medium. Relative to MR-DBIM, this integration offers a 44.01% reduction in the normalized absolute error.

Dressing effects in the laser-assisted ( e,2e ) process in fast-electron–hydrogen-atom collisions in an asymmetric coplanar scattering geometry

We present the theoretical treatment of laser-assisted $(e,2e)$ ionizing collisions in hydrogen for fast electrons, in the framework of the first-order Born approximation at moderate laser intensities and photon energies beyond the soft-photon approximation. The interaction of the laser field with the incident, scattered, and ejected electrons is treated nonperturbatively by using Gordon-Volkov wave functions, while the atomic dressing is treated by using first-order perturbation theory. Within this semiperturbative formalism, we obtain a closed-form formula for the nonlinear triple differential cross section (TDCS), which is valid for linear as well circular polarizations. Analytical simple expressions of TDCS are derived in the weak field domain and low-photon energy limit. It was found that for nonresonant $(e,2e)$ reactions, the analytical formulas obtained for the atomic matrix element in the low-photon energy limit give a good agreement, qualitative and quantitative, with the numerical semiperturbative model calculations. We study the influence of the photon energy as well of the kinetic energy of the ejected electron on the TDCS, in the asymmetric coplanar geometry, and show that the dressing of the atomic target strongly influences the $(e,2e)$ ionization process. We discuss the exchange effects between the ejected and scattered electrons in the TDCS.

Analytical and numerical study of diffusion and localization of cold atoms in 3D optical speckles.

This paper aims to study the diffusion and localization of cold atoms in three-dimensional (3D) optical speckles by using the theory of self-energy for N diffusers. In this paper, the Self-consistent Born approximation (SCBA) is used to study the diffusion and localization of cold atoms in an optical disordered speckles, while the spectral function is adopted to study the effect of the matter waves energy and the disorder amplitude on the behaviour of cold atoms. For this purpose, the models of SCBA and spectral function are computed by a numerical algorithm. The calculation of the latter quantity involves the application of Simpson’s integration methods. The diffusion and localization of a Bose–Einstein Condensate for First-order Born Approximation (FBA) and SCBA models are presented. In addition, the diffusion time and the mean free path between two diffusers are illustrated. Moreover, the effect of disorder amplitude and the scattering of matter waves in 3D disordered potentials are highlighted. In this study, the results show that the time response of cold atoms localization and metal–insulator transition in SCBA is faster and yields lower energy than the FBA approximation.

Spin accumulation without spin current

The spin Hall (SH) effect is a phenomenon in which the spin current flows perpendicular to an applied electric field and causes the spin accumulation at the boundaries. However, in the presence of spin-orbit couplings, the spin current is not well defined. Here, we calculate the spin response to an electric field gradient, which naturally appears at the boundaries. We derive a generic formula using the Bloch wave functions and the phenomenological relaxation time. We also calculate the response for the Rashba model with $\delta$-function nonmagnetic disorder within the first-order Born approximation and corresponding vertex corrections. We find the nonzero spin accumulation, although the SH conductivity exactly vanishes.

Quasielastic least-squares reverse time migration of PS reflections

Conventional analysis of amplitude variation with offset for elastic PS reflections is based on analytical reflection coefficients in a layered medium, and wave-equation-based PS migration is mainly used to produce a structural image. To overcome this problem, we have developed a least-squares reverse time migration (LSRTM) method for elastic PS reflections based on a quasielastic wave equation. The quasielastic wave equation can accurately model PS reflections with elastic amplitudes under the first-order Born approximation. Our LSRTM method inverts for perturbations of the S-wave velocity and density by minimizing the [Formula: see text] norm of the difference between recorded and predicted PS reflections modeled using a quasielastic wave equation. We refer to our new method as quasielastic LSRTM of PS reflections. Numerical tests on synthetic and field data indicate that our method can properly handle the amplitudes of elastic PS reflections and provides an accurate estimate of the perturbations of S-wave velocity and density. Extending the method to the 3D case is not straightforward and might require incorporating certain PS data processing techniques into the inversion itself.

Scattering of Partially Coherent Vector Beams by a Deterministic Medium Having Parity-Time Symmetry

We study the scattering properties of the partially coherent vector beams with the deterministic media having the classic symmetric and parity-time (PT) symmetric scattering potential functions. The closed-form expressions for the intensity and polarization matrix of the far-zone scattered field are obtained, under first-order Born approximation, when the partially coherent vector beams are taken to be radially polarized and the deterministic media are assumed as the four-point scatterers. We demonstrate both analytically and numerically that the far-zone scattered field becomes noncentrosymmetric and the directionality appears in the scattering pattern when the scattering potential function is switched from classic symmetry to PT symmetry. We show the effect of spatial coherence of the incident partially coherent vector beam on the directionality in scattering. We find that by turning the symmetry property of the spatial coherence function of the incident beam, i.e., into PT symmetry, the directionality in the far-zone scattering can be suppressed or enhanced, depending on the joint effect from the symmetry of the scattering potential and the symmetry of the spatial coherence. Our findings may be useful in the application of dynamic control of the directionality in light scattering.

Elastic least-squares reverse time migration of steeply dipping structures using prismatic reflections

The migration of prismatic reflections can be used to delineate steeply dipping structures, which is crucial for oil and gas exploration and production. Elastic least-squares reverse time migration (ELSRTM), which considers the effects of elastic wave propagation, can be used to obtain reasonable subsurface reflectivity estimations and interpret multicomponent seismic data. In most cases, we can only obtain a smooth migration model. Thus, conventional ELSRTM, which is based on the first-order Born approximation, considers only primary reflections and cannot resolve steeply dipping structures. To address this issue, we develop an ELSRTM framework, called Pris-ELSRTM, which can jointly image primary and prismatic reflections in multicomponent seismic data. When Pris-ELSRTM is directly applied to multicomponent records, near-vertical structures can be resolved. However, the application of imaging conditions established for prismatic reflections to primary reflections destabilizes the process and leads to severe contamination of the results. Therefore, we further improve the Pris-ELSRTM framework by separating prismatic reflections from recorded multicomponent data. By removing artificial imaging conditions from the normal equation, primary and prismatic reflections can be imaged based on unique imaging conditions. The results of synthetic tests and field data applications demonstrate that the improved Pris-ELSRTM framework produces high-quality images of steeply dipping P- and S-wave velocity structures. However, it is difficult to delineate steep density structures because of the insensitivity of the density to prismatic reflections.

Determination of phases of complex scattering amplitudes and two-particle structure factors by investigating diffractograms of thin amorphous foils

Abstract In this study we analyse diffractograms of elastically filtered images of thin amorphous foils of carbon, silicon and germanium using the weak object approximation. The use of this approximation leads to a contrast transfer function containing a phase η(u) depending on the spatial frequency u. Furthermore, the derivative of this phase is included in the envelope function of the contrast transfer function. The phase can be attributed to the breakdown of the first-order Born approximation leading to complex scattering amplitudes characterized by this phase η(u). We analyse contrast transfer characteristics to determine the phase of complex scattering amplitudes of carbon, silicon and germanium as a function of spatial frequency and to measure the two-particle structure factor of the corresponding amorphous specimens. The contrast transfer characteristics were calculated from diffractograms of focal series of elastically filtered images. The phases measured show a decay with increasing spatial frequency and additional oscillations. The results for the two-particle structure factor also decay with increasing spatial frequency and contain low local maxima. Both can be attributed to voids or inhomogeneities within the amorphous structure.

The probe particle scattering cross-section off the many-fermion systems in the impulse approximation

In this work, we study the differential scattering cross-section (DSCS) in the first-order Born approximation. It is not difficult to show that the DSCS can be simplified in terms of the system response function. Also, the system response function has this property to be written in terms of the spectral function and the momentum distribution function in the impulse approximation (IA) scheme. Therefore, the DSCS in the IA scheme can be formulated in terms of the spectral function and the momentum distribution function. On the other hand, the DSCS for an electron off the [Formula: see text] and [Formula: see text] nuclei is calculated in the harmonic oscillator shell model. The obtained results are compared with the experimental data, too. The most important result derived from this study is that the calculated DSCS in terms of the spectral function has a high agreement with the experimental data at the low-energy transfer, while the obtained DSCS in terms of the momentum distribution function does not. Therefore, we conclude that the response of a many-fermion system to a probe particle in IA must be written in terms of the spectral function for getting accurate theoretical results in the field of collision. This is another important result of our study.

Elastic full-waveform inversion of steeply dipping structures with prismatic waves

High-resolution reconstruction of steeply dipping structures is an important but challenging subject in seismic exploration. Prismatic reflections that contain information on these structures are helpful for reconstructing steeply dipping structures. Elastic full-waveform inversion (EFWI) is a powerful tool that can accurately estimate subsurface parameters from multicomponent seismic data, which can provide information useful for characterizing oil and gas reservoirs. We have constructed the relationship between the forward and inverse problems related to the prismatic reflections by considering the multiparameter exact Hessian in realistic elastic media. We numerically analyze the characteristics of the multiparameter exact Hessian and determine that, when prismatic reflections are apparent in multicomponent data, the multiparameter delta Hessian has a strong influence. We develop this in more detail through forward analysis and determine that the multiparameter delta Hessian considers not only the prismatic reflections but also compensates for the primary reflections in multicomponent data. To use the prismatic waves, we develop a migration/demigration approach-based truncated Newton (TN) method in frequency-domain EFWI, whose storage requirements and computational costs are the same as those of the truncated Gauss-Newton (TGN) method. Realistic 2D numerical examples demonstrate that, compared with the TGN method based on the first-order Born approximation, the TN method can converge faster and obtain higher accuracy in the reconstruction of steeply dipping structures.