Far-field Plane Research Articles

A note on near-field site amplification effects of ground motion from a radially inhomogeneous valley

To improve the understanding of the near-field soil and topographic amplification effects, an analytical solution by the authors for the scattering of plane SH waves by a radially inhomogeneous semi-cylindrical valley is extended to the case of a line source of cylindrical SH waves. Upon confirmation of its accuracy with past exact solutions for a homogeneous and an inhomogeneous semi-cylindrical valley under far-field plane SH waves, the extended solution is used to calculate the ground motion amplification factors for both the homogeneous and inhomogeneous valleys subjected to near-field waves. A comprehensive parametric study is conducted with respect to the location of the wave source, the dimensionless frequency of the incident waves, and the inhomogeneity degree of the covering soil layer. It is found that more amplifications and reductions of ground motions will occur within a certain range in and around the valley as the sources are located further. Consistent with the far-field case, it is confirmed that an increase of the degree of inhomogeneity of the covering soil layer generally amplifies the ground motions significantly.

Modeling and analysis of surface plasmon microscopy with radial polarization

This paper is to present a model of surface plasmon microscopy (SPM) with radial polarization and numerically examine its far-field imaging performance. More preciously, we analyze the SP distribution on the back focal plane (BFP) of an immersion objective lens and explore how it is focused on the far-field image plane. We show that many of the effects of large angles are eliminated since the image plane is magnified many times with normal NA lens. Specifically, we show that the strong longitude component in focal plane vanishes in image plane and the calculations of transverse component distributions of the two planes are also different. We establish the model which gives the mathematical model on SPM imaging area and shows great potentials in relevant field such as confocal configuration or interferometric SPM.

Measurements of polarization-dependent angle-resolved light scattering from individual microscopic samples using Fourier transform light scattering.

We present a method to measure the vector-field light scattering of individual microscopic objects. The polarization-dependent optical field images are measured with quantitative phase imaging at the sample plane, and then numerically propagated to the far-field plane. This approach allows the two-dimensional polarization-dependent angle-resolved light scattered patterns from individual object to be obtained with high precision and sensitivity. Using this method, we present the measurements of the polarization-dependent light scattering of a liquid crystal droplet and individual silver nanowires over scattering angles of 50°. In addition, the spectroscopic extension of the polarization-dependent angle-resolved light scattering is demonstrated using wavelength-scanning illumination.

Radial-variant nonlinear ellipse rotation.

The nonlinear ellipse rotation usually occurs when an elliptically polarized beam propagates through an isotropic nonlinear medium owing to the existence of χ1221(3). Here we report the radial-variant nonlinear ellipse rotation of a vector beam with structured elliptical polarization through isotropic Kerr nonlinearities. Due to the interaction of elliptically polarized vector beams (EPVBs) with isotropic nonlinear media, the distributions of both the orientation angle and the ellipticity angle of beams at the far-field observational plane exhibit multiple concentric ring structures with the circularly symmetry. Numerical simulations show that the self-diffraction intensity pattern, the distribution of the state of polarization, and the spin angular momentum (SAM) distribution of an EPVB could be manipulated by tuning both the isotropic optical nonlinearity and the chirality parameter of the vector beam, which may find direct applications in polarization-control optical switching, SAM manipulation, and optical polarization encoding or detection.

A high-precision centroid detecting method based on two-dimension orthogonal gratings

In order to detect high-precision far-field spots centroid, a multiple spots centroid detecting method is proposed. Using two-dimension orthogonal diffraction gratings, a single spot on the far-field focal plane is developed into a multiple spots array. By increasing the input information of the far-field detected spots, the centroid detection accuracy can be improved. The experimental results show that the centroid detecting accuracy of multiple spots is 4 times larger than that of single spot. The root mean square (RMS) of single spot centroid detecting error is 0.0385 pixels and the RMS of 16 spots centroid detecting error is 0.0099 pixels. Compared with the conventional method of the centroid detecting, the far-field multiple spots centroid detecting method proposed is simpler and more convenient.

On the van Cittert–Zernike theorem for intensity correlations and its applications

A reciprocal relationship between the autocovariance of the light intensity in the source plane and in the far-field detector plane is presented in a form analogous to the classical van Cittert-Zernike theorem, but involving intensity correlation functions. A "classical" version of the reciprocity relationship is considered first, based on the assumption of circular Gaussian statistics of the complex amplitudes in the source plane. The result is consistent with the theory of Hanbury Brown-Twiss interferometry, but it is shown to be also applicable to estimation of the source size or the spatial resolution of the detector from the noise power spectrum of flat-field images. An alternative version of the van Cittert-Zernike theorem for intensity correlations is then derived for a quantized electromagnetic beam in a coherent state, which leads to Poisson statistics for the intrinsic intensity of the beam.

Optimized Finite Element Method for Acoustic Scattering Analysis With Application to Head-Related Transfer Function Estimation

Obtaining head-related transfer functions (HRTFs) is a challenging task, in spite of its importance in localizing sound in a three-dimensional (3D) environment or improving the performance of hearing aids, among their various applications. In this paper, an optimized finite element method through adaptive dimension size based on wavelength (frequency) for acoustic scattering analyses using ansys is presented. Initial investigation of the validity of our method is conducted by simulating scattered sound field for a solid sphere exposed to a far-field plane sound wave at 100 (equally spaced in logarithmic scale) frequencies between 20 and 20 kHz. Comparison of the equivalent HRTF results between the two methods shows a maximum deviation of less than 0.6 dB between our method and the analytical solution depending on the angle of rotation of the sphere with respect to sound source.

On the influence of Sommerfeld’s radiation boundary condition on the propagation direction of oblique modes in streamwise corner flow

Linear stability of a laminar boundary-layer flow in a streamwise corner can only be treated with an ansatz that considers two-dimensional eigenfunctions with inhomogeneous boundary conditions in cross-flow directions. It is common practice to use Sommerfeld’s radiation condition with a certain wavenumber $\unicode[STIX]{x1D6FD}$ at the lateral domains of the integration domain which are at the same time the far-field domains for each wall. So far, this radiation condition has been exclusively used in a ‘symmetrical’ way, i.e. with the same $\unicode[STIX]{x1D6FD}$ on either far-field boundary plane. This has led to wave patterns that either enter or leave the corner region from the lateral sides for $\unicode[STIX]{x1D6FD}<0$ or $\unicode[STIX]{x1D6FD}>0$ respectively. Here, an ‘asymmetric’ use of Sommerfeld’s radiation condition is suggested, i.e. $\unicode[STIX]{x1D6FD}<0$ on one far side of the corner and $\unicode[STIX]{x1D6FD}>0$ on the other. With this modification, waves enter the corner area from one side and leave it through the other, i.e. they travel obliquely through the corner. In contrast to before, their amplification rate is always symmetric with respect to $\unicode[STIX]{x1D6FD}=0$ and there is no amplification-rate increase or decrease due to information that either continuously enters the corner from both sides or continuously leaves it through the far sides. The present analysis also shows that the inviscid corner modes are unaffected by the parameters of the far-field radiation boundary conditions. Nevertheless, superposition of two oppositely running single waves obtained by the modified application of the radiation condition leads to a similar wave pattern to that in the case with $\unicode[STIX]{x1D6FD}<0$ on both sides; however, with a slightly smaller amplification rate and a strictly streamwise propagation direction.

Low-Cost Dielectric Reflective Surface for Low-Level Backscattered Diffuse Reflections

This article presents the design of non-subwavelength, non-resonant, and non-absorptive dielectric surface that creates a low-level backward diffuse reflections under illumination of a far-field plane wave at millimeter wave regime. Thus, radar cross section reduction of a solid metallic object can be achieved. The dielectric surface is consist of unit cells of only two different electric permittivity (er1 = 6.14 and er2 = 3.49) distributed across the surface aperture to achieve low-level backscattered diffuse reflections. The unit cells used are having non-subwavelength size (0.53λ80GHz) which ensures an easier fabrication of the presented surface using low cost simple PCB technology, in particular at high frequencies. RCS reduction of more than 10 dBsm is achieved from 70 to 87 GHz (BW ≈ 21.65 %) using the presented dielectric surface of optimized permittivity distribution. The RCS reduction capabilities of the presented surface are studied theoretically under both normal and oblique incidences and then fabricated and verified experimentally by reflectivity measurements.

Effects of a near-field rigid sphere scatterer on the performance of linear microphone array beamformers.

Beamformers enable a microphone array to capture acoustic signals from a sound source with high signal to noise ratio in a noisy environment, and the linear microphone array is of particular importance, in practice, due to its simplicity and easy implementation. A linear microphone array sometimes is used near some scattering objects, which affect its beamforming performance. This paper develops a numerical model with a linear microphone array near a rigid sphere for both far-field plane wave and near-field sources. The effects of the scatterer on two typical beamformers, i.e., the delay-and-sum beamformer and the superdirective beamformer, are investigated by both simulations and experiments. It is found that the directivity factor of both beamformers improves due to the increased equivalent array aperture when the size of the array is no larger than that of the scatter. With the increase of the array size, the directivity factor tends to deteriorate at high frequencies because of the rising side-lobes. When the array size is significantly larger than that of the scatterer, the scattering has hardly any influence on the beamforming performance.

Varying polarization and spin angular momentum flux of radially polarized beams by anisotropic Kerr media.

Light fields with structured polarization distribution interacting with structured media will result in many novel optical effects in both the linear and nonlinear regimes. In this work, we report a theoretical investigation of both vectorial self-diffraction behaviors and polarization evolution characteristics of a radially polarized beam induced by anisotropic Kerr nonlinearity. By taking the polarization-orientation dependence of the third-order refractive nonlinearity, we study the far-field vectorial self-diffraction patterns of the radially polarized beam using the vectorial Rayleigh-Sommerfeld formulas. Numerical results reveal that the self-diffraction patterns with a four-fold rotational symmetry exhibit hybrid states of polarization. Moreover, the interaction of radially polarized beams with the anisotropic nonlinear Kerr media leads to the redistribution of the spin angular momentum (SAM) flux in the far-field plane. The presented work opens up new avenues for varying polarization and SAM through anisotropic optical nonlinearity.

Measuring different types of transverse momentum correlations in the biphoton's Fourier plane.

In this Letter, we present a theoretical and experimental study about the spatial correlations of paired photons generated by Type II spontaneous parametric down-conversion. In particular, we show how these correlations can be positive or negative, depending on the direction in which the far-field plane is scanned and the polarization postselected. Our results provide a straightforward way to observe different kind of correlations that complement other well-known methods to tune the spatial correlations of paired photons.

Vectorial structural properties of a Gaussian vortex beam in the far-field

In the far-field, the Gaussian vortex beam is just a sum of the TE and TM terms. The TE and TM terms are called the vectorial structure. The vectorial structural properties of a Gaussian vortex beam, which are related to the energy flux distributions of the Gaussian vortex beam and its TE and TM terms, are investigated in the far-field. The analytical expressions of the energy flux distributions of the Gaussian vortex beam and its TE and TM terms are derived in the far-field. The integral expressions of the power, the beam widths, the divergence angles, and the kurtosis parameters of the TE term, the TM term, and the Gaussian vortex beam are also derived in the far-field, which are concise and convenient to calculate. The relations of the beam widths, the far-field divergence angles, and the kurtosis parameters among the TE term, the TM term, and the Gaussian vortex beam are presented, respectively. The energy flux distributions of the Gaussian vortex beam and its TE and TM terms are demonstrated in the far-field plane. The influences of the beam parameters and the topological charge on the contributions of the TE and TM terms to the whole power, the beam widths, the far-field divergence angles, and the kurtosis parameters are numerically examined.

A BEM–FEM model for the dynamic analysis of building structures founded on viscoelastic or poroelastic soils

This paper presents a time-harmonic boundary element–finite element three–dimensional model for the dynamic analysis of building structures founded on viscoelastic or poroelastic soils. The building foundation and soil domains are modelled as homogeneous, isotropic, viscoelastic or poroelastic media using boundary elements. The foundation can also be modelled as a perfectly rigid body coupled to soil and structure. The buildings are modelled using Timoshenko beam finite elements that include the torsional eccentricity of non-symmetrical buildings. The excitation model includes far-field plane seismic waves of P, S or Rayleigh type for viscoelastic soils and P1 and S type for poroelastic soils. Modelling foundation and structure as rigid body and Timoshenko beam respectively conveys important benefits such as a significant reduction in the number of degrees of freedom in the problem, which allows to study problems involving several building structures and the interactions between them with acceptable computational effort. Results are presented for validation purposes first, and for studying the influence of modelling the soil as a viscoelastic or poroelastic region afterwards. Results involving structure–soil–structure interaction are also presented for illustration purposes.

Super-resolved optical lithography with phase controlled source

Recently, we have demonstrated that second-order subwavelength interference could be realized in an optical lithography scheme with an effective entangled source [P. Hong and G. Zhang, Phys. Rev. A 88, 043838 (2013)]. In this paper, by considering the correlation function in both the source plane and observation plane, we show how the coherence property of such a source is controlled via introduction of random-phase correlation, which finally affects the two-photon interference effect observed in the far-field plane. Furthermore, by introducing different but similar random-phase correlations, we generalize the phase controlled source with particular high-order coherence properties to obtain higher-order subwavelength interference, i.e., high-order super-resolved optical lithography. These results show the importance of phase control in generating a light field with particular high-order coherence properties.

Phase-sensitive structured illumination to detect nanosized asymmetries in silicon trenches

A metrology approach to detect nanoscale asymmetries in structures on a silicon wafer is being introduced through simulation investigations. The simulations were performed based on a rigorous coupled-wave analysis. A structured spot focused on the wafer with a high-numerical aperture (NA=0.7) has been scanned over the wafer. Having access to the complex amplitude of the wavefront over the field, both the intensity and the phase profile of the spot have been investigated in the far-field image plane. To show the proof of concept, we considered a 10-nm asymmetry that appears in the radius of the bottom roundings of a trench on the wafer. The results have been compared to the case of using a conventional spot and it has been shown that the structured illumination provides more sensitivity to the presence of asymmetry. In both illumination cases, the phase distribution along the spot was shown to be more sensitive to the changes due to the presence of asymmetry in the wafer.

Spatiotemporal noise characterization for chirped-pulse amplification systems.

Optical noise, the core of the pulse-contrast challenge for ultra-high peak power femtosecond lasers, exhibits spatiotemporal (ST) coupling induced by angular dispersion. Full characterization of such ST noise requires two-dimensional measurements in the ST domain. Thus far, all noise measurements have been made only in the temporal domain. Here we report the experimental characterization of the ST noise, which is made feasible by extending cross-correlation from the temporal domain to the ST domain. We experimentally demonstrate that the ST noise originates from the optical surface imperfections in the pulse stretcher/compressor and exhibits a linear ST coupling in the far-field plane. The contrast on the far-field axis, underestimated in the conventional measurements, is further improved by avoiding the far-field optics in the stretcher. These results enhance our understanding of the pulse contrast with respect to its ST-coupling nature and pave the way toward the design of high-contrast ultra-high peak power lasers.

Einstein-Podolsky-Rosen paradox in twin images.

Spatially entangled twin photons provide both promising resources for modern quantum information protocols, because of the high dimensionality of transverse entanglement, and a test of the Einstein-Podolsky-Rosen paradox in its original form of position versus impulsion. Usually, photons in temporal coincidence are selected and their positions recorded, resulting in a priori assumptions on their spatiotemporal behavior. In this Letter, we record, on two separate electron-multiplying charge coupled devices cameras, twin images of the entire flux of spontaneous down-conversion. This ensures a strict equivalence between the subsystems corresponding to the detection of either position (image or near-field plane) or momentum (Fourier or far-field plane). We report the highest degree of paradox ever reported and show that this degree corresponds to the number of independent degrees of freedom, or resolution cells, of the images.

Response of distributed fiber optic sensor cables to spherical wave incidence

A generalized multi-layered infinite-length fiber optic cable is modeled using the exact theory of three-dimensional elasticity in cylindrical coordinates. A cable is typically composed of a fiber optic (glass) core surrounded by various layered materials such as plastics, metals, and elastomers. The cable is excited by an acoustic spherical wave radiated by a monopole source at an arbitrary location in the acoustic field. For a given source location and frequency, the radial and axial strains within the cable are integrated over a desired sensor zone length to determine the optical phase sensitivity using an equation that relates the strain distribution in an optical fiber to changes in the phase of an optical signal. Directivity results for the cable in a free-field water environment are presented at several frequencies for various monopole source locations. Some comparisons of the sensor directional response resulting from nearfield (spherical wave) incidence and farfield (plane wave) incidence are made. [Work supported by NAVSEA Division Newport ILIR Program.]

Three-dimensional position accuracy in circular synthetic aperture radar

This article evaluates the three-dimensional (3-D) location information provided by spotlight-mode circular synthetic aperture radar (SAR). The circular synthetic aperture refers to a single circular flight path of 360° azimuth at a constant altitude and broadside squint angle. The motivating operational concept is persistent wide-area surveillance from a single airborne radar platform. The circular SAR data collection geometry inherently presents a near-field inverse scattering problem; however, the far-field plane wave propagation assumption is accurate for a region about the scene center. Early SAR manuscripts noted that nonlinear flight paths provide k-space data not confined to a plane, thus providing some 3-D resolution [1]. Resolution in 3-D was likewise demonstrated for ultrahigh frequency (UHF) and X-band systems using circular apertures [2].