Bragg Components Research Articles

Polarization-independent photonic Bragg grating filter with cladding asymmetry.

A photonic Bragg grating is a fundamental building block that reflects the direction of wave propagation through spatial phase modulation and can be implemented using sidewall corrugation. However, due to the asymmetric aspect ratio of a waveguide cross section, typical Bragg gratings exhibit a strong polarization sensitivity. Here, we show that photonic Bragg gratings with cladding asymmetry can enable polarization-independent notch filters by rotating input polarizations. Such Bragg gratings strongly couple transverse electric (TE) and transverse magnetic (TM) modes propagating in opposite directions, filtering the input signal and reflecting the rotated mode. We analyzed this polarization-rotating Bragg grating using the coupled-mode theory and experimentally demonstrated it on a silicon-on-insulator platform. Our device concept is simple to implement and compatible with other platforms, readily available as polarization transparent Bragg components.

New Features of Bragg and Non-Polarized Radar Backscattering from Film Slicks on the Sea Surface

Suppression of radar backscattering from the sea surface has been studied in field experiments with surfactant films carried out from an Oceanographic Platform on the Black Sea and from onboard a research vessel on the Gorky Water Reservoir using an X-C-S-band two co-polarized radar instrument. Bragg and non-polarized (non-Bragg) radar backscatter components, BC and NBC, respectively, were retrieved when measuring the radar backscatter at vertical (VV-) and horizontal (HH-) polarizations. New features of microwave backscattering from the sea surface have been revealed, including a non-monotonic dependence of radar backscatter suppression (contrasts) in slicks on azimuth angle and particularities of BC contrasts on radar wave number. Namely, it is demonstrated that the backscatter contrasts achieve maximum values at azimuth angles in between the upwind and crosswind radar look directions, and BC contrasts increase with radar wave number along the wind and decrease in the crosswind directions. The suppression of BC is discussed in the frame of Bragg’s theory of microwave scattering and of a simple model of the wind wave spectrum, while the suppression of NBC is considered associated with the micro-breaking of wind waves. The obtained new features of radar contrasts can be used for the identification and characterization of marine films.

Ka-Band Radar Cross-Section of Breaking Wind Waves

The effective normalized radar cross section (NRCS) of breaking waves, σwb, is empirically derived based on joint synchronized Ka-band radar and video records of the sea surface from a research tower. The σwb is a key parameter that, along with the breaker footprint fraction, Q, defines the contribution of non-polarized backscattering, NP =σwbQ, to the total sea surface NRCS. Combined with the right representation of the regular Bragg and specular backscattering components, the NP component is fundamental to model and interpret sea surface radar measurements. As the first step, the difference between NRCS values for breaking and non-breaking conditions is scaled with the optically-observed Q and compared with the geometric optics model of breaker backscattering. Optically-derived Q might not be optimal to represent the effect of breaking waves on the radar measurements. Alternatively, we rely on the breaking crest length that is firmly detected by the video technique and the empirically estimated breaker decay (inverse wavelength) scale in the direction of breaking wave propagation. A simplified model of breaker NRCS is then proposed using the geometric optics approach. This semi-analytical model parameterizes the along-wave breaker decay from reported breaker roughness spectra, obtained in laboratory experiments with mechanically-generated breakers. These proposed empirical breaker NRCS estimates agree satisfactorily with observations.

The Role of Micro Breaking of Small-Scale Wind Waves in Radar Backscattering from Sea Surface

The study of the microwave scattering mechanisms of the sea surface is extremely important for the development of radar sensing methods. Some time ago, Bragg (resonance) scattering of electromagnetic waves from the sea surface was proposed as the main mechanism of radar backscattering at moderate incidence angles of microwaves. However, it has been recently confirmed that Bragg scattering is often unable to correctly explain observational data and that some other physical mechanisms should be taken into consideration. The newly introduced additional scattering mechanism was characterized as non-polarized, or non-Bragg scattering, from quasi-specular facets appearing due to breaking wave crests, the latter usually occurring in moderate and strong winds. In this paper, it was determined experimentally that such non-polarized radar backscattering appeared not only for rough sea conditions in which wave crests strongly break and “white caps” occur, but also at very low wind velocities close to their threshold values for the wave generation process. The experiments were performed using two polarized Doppler radars. The experiments demonstrated that a polarization ratio, which characterizes relative contributions of non-polarized and Bragg components to the total backscatter, changed slightly with wind velocity and wind direction. Detailed analysis of radar Doppler shifts revealed two types of scatterers responsible for the non-polarized component. One type of scatterer, moving with the velocities of decimeter-scale wind waves, determined radar backscattering at low winds. We identified these scatterers as “microbreakers” and related them to nonlinear features in the profile of decimeter-scale waves, like bulges, toes and parasitic capillary ripples. The scatterers of the second type were associated with strong breaking, moved with the phase velocities of meter-scale breaking waves and appeared at moderate winds additionally to the “microbreakers”. Along with strong breakers, the impact of microbreaking in non-polarized backscattering at moderate winds remained significant; specifically the microbreakers were found to be responsible for about half of the non-polarized component of the radar return. The presence of surfactant films on the sea surface led to a significant suppression of the small-scale non-Bragg scattering and practically did not change the non-Bragg scatterer speed. This effect was explained by the fact that the nonlinear structures associated with dm-scale waves were strongly reduced in the presence of a film due to the cascade mechanism, even if the reduction of the amplitude of dm waves was weak. At the same time, the velocities of non-Bragg scatterers remained practically the same as in non-slick areas since the phase velocity of dm waves was not affected by the film.

K-space algorithmic reconstruction (KAREN): a robust statistical methodology to separate Bragg and diffuse scattering

Diffuse scattering occurring in the Bragg diffraction pattern of a long-range-ordered structure represents local deviation from the governing regular lattice. However, interpreting the real-space structure from the diffraction pattern presents a significant challenge because of the dramatic difference in intensity between the Bragg and diffuse components of the total scattering function. In contrast to the sharp Bragg diffraction, the diffuse signal has generally been considered to be a weak expansive or continuous background signal. Herein, using 1D and 2D models, it is demonstrated that diffuse scattering in fact consists of a complex array of high-frequency features that must not be averaged into a low-frequency background signal. To evaluate the actual diffuse scattering effectively, an algorithm has been developed that uses robust statistics and traditional signal processing techniques to identify Bragg peaks as signal outliers which can be removed from the overall scattering data and then replaced by statistically valid fill values. This method, described as a `K-space algorithmic reconstruction' (KAREN), can identify Bragg reflections independent of prior knowledge of a system's unit cell. KAREN does not alter any data other than that in the immediate vicinity of the Bragg reflections, and reconstructs the diffuse component surrounding the Bragg peaks without introducing discontinuities which induce Fourier ripples or artifacts from underfilling `punched' voids. The KAREN algorithm for reconstructing diffuse scattering provides demonstrably better resolution than can be obtained from previously described punch-and-fill methods. The superior structural resolution obtained using the KAREN method is demonstrated by evaluating the complex ordered diffuse scattering observed from the neutron diffraction of a single plastic crystal of CBr4 using pair distribution function analysis.

Modulation of Dual-Polarized X-Band Radar Backscatter Due to Long Wind Waves

Investigation of microwave scattering mechanisms is extremely important for developing methods for ocean remote sensing. Recent studies have shown that a common two-scale scattering model accounting for resonance (Bragg) scattering has some drawbacks, in particular it often overestimates the vertical-to-horizontal polarization radar return ratio and underestimates the radar Doppler shifts if the latter are assumed as associated with quasi linear resonance surface waves. It is supposed nowadays that radar backscattering at moderate incidence angles is determined not only by resonance Bragg mechanism but also contains non polarized (non Bragg) component which is associated supposedly with wave breaking but which is still insufficiently studied. Better understanding of the scattering mechanisms can be achieved when studying variations of radar return due to long wind waves. In this paper, results of experiments from an Oceanographic Platform on the Black Sea using dual co-polarized X-band scatterometers working at moderate incidence are presented and variations of Bragg and non-Bragg components (BC and NBC, respectively) and radar Doppler shifts are analysed. It is established that BC and NBC are non-uniformly distributed over profile of dominant (decametre-scale) wind waves (DWW). Variations of BC are characterized by some “background” return weakly modulated with the dominant wind wave periods, while NBC is determined mostly by rare and strong spikes occurred near the crests of the most intense individual waves in groups of DWW. We hypothesize that the spikes are due to intensification of nonlinear structures on the profile of short, decimetre-scale wind waves when the latter are amplified by intense DWW. Bragg scattering in slicks under the experimental conditions was suppressed stronger than NBC and spikes dominated in total radar return. It is obtained that radar Doppler shifts at HH-polarization are larger than at VV-polarization, particularly in slicks, the same relation is for NBC and BC Doppler shifts, thus indicating different scattering mechanisms for these components.

Remote Sensing of Organic Films on the Water Surface Using Dual Co-Polarized Ship-Based X-/C-/S-Band Radar and TerraSAR-X

Microwave radar is a well-established tool for all-weather monitoring of film slicks which appear in radar imagery of the surface of water bodies as areas of reduced backscatter due to suppression of short wind waves. Information about slicks obtained with single-band/one-polarized radar seems to be insufficient for film characterization; hence, new capabilities of multi-polarization radars for monitoring of film slicks have been actively discussed in the literature. In this paper the results of new experiments on remote sensing of film slicks using dual co-polarized radars—a satellite TerraSAR-X and a ship-based X-/C-/S-band radar—are presented. Radar backscattering is assumed to contain Bragg and non-Bragg components (BC and NBC, respectively). BC is due to backscattering from resonant cm-scale wind waves, while NBC is supposed to be associated with wave breaking. Each of the components can be eliminated from the total radar backscatter measured at two co-polarizations, and contrasts of Bragg and non-Bragg components in slicks can be analyzed separately. New data on a damping ratio (contrast) characterizing reduction of radar returns in slicks are obtained for the two components of radar backscatter in various radar bands. The contrast values for Bragg and non-Bragg components are comparable to each other and demonstrate similar dependence on radar wave number; BC and NBC contrasts grow monotonically for the cases of upwind and downwind observations and weakly decrease with wave number for the cross-wind direction. Reduction of BC in slicks can be explained by enhanced viscous damping of cm-scale Bragg waves due to an elastic film. Physical mechanisms of NBC reduction in slicks are discussed. It is hypothesized that strong breaking (e.g., white-capping) weakly contributes to the NBC contrast because of “cleaning” of the water surface due to turbulent surfactant mixing associated with wave crest overturning. An effective mechanism of NBC reduction due to film can be associated with modification of micro-breaking wave features, such as parasitic ripples, bulge, and toe, in slicks.

Diffraction by nanocrystals

X-ray femtosecond nanocrystallography is a new, potentially powerful technique for imaging biological macromolecules that uses ensemble-averaged measurements of diffraction of x-ray free-electron laser pulses from nanocrytalline specimens. Nanocrystals have some diffraction characteristics that are distinct from those of macroscopic crystals, due to the presence of different kinds of unit cell in the crystal and of truncated unit cells on the crystal surface. Expressions are derived for diffraction by nanocrystals with variable and incomplete unit cells, averaged over a distribution of crystal sizes and shapes. The diffraction contains differently modulated Bragg components that are due to interference effects within and between the full and incomplete unit cells. Estimates are obtained for the relative magnitudes of the components. The nature of the diffraction is illustrated by two-dimensional simulations. Implications for molecular imaging are discussed.

Facet-based simulator for bistatic scattering of the maritime scene with electrically large ships: Slope Summation Facet Model

This article developed a bistatic facetized sea scattering model, in which the sea surface is envisaged as a profile that is locally approximated by planar facets. The radar return from each local facet is associated to a so-called semi-deterministic scheme, which is established by combining the geometric optics limit of the Kirchhoff approximation with the Bragg components of the Bass–Fuks' two-scale model. In order to evaluate the complex reflective function of the facetized sea surface, a Slope Summation Facet Model is presented by simply associating the facet phase with its relative path delay. Significant computational efficiency and good agreement with experimental data are observed, which make the proposed facet model well suited for application to fast estimation on sea scattering, as well as further simulations on synthetic aperture radar imagery and the composite pattern of ship–sea scattering.

FACET-BASED TREATMENT ON MICROWAVE BISTATIC SCATTERING OF THREE-DIMENSIONAL SEA SURFACE WITH ELECTRICALLY LARGE SHIP

A feasible simulator, of which formulation and mechanism should be simple and time saving, is developed in this paper to overcome the di-culties of prediction on the EM scattering from three- dimensional (3-D) electrically very large ship-sea models. The work in this paper is twofold. First, the sea surfaces are supposed to be a combination of many locally-tilted slightly rough facets with two-scale proflles. The radar return from each local facet is associated to a semi- deterministic scheme which is established by combining the geometric optics limit of Kirchhofi Approximation (KA-GO) with the Bragg components of Bass-Fuks' two-scale model (BFTSM). Furthermore, we associate the complex re∞ective function of the respective facet by a so-called Phase-modifled Facet Model (PMFM), in which the facet's phase is treated approximately as a combination of inherent part that follows a homogeneous random distribution and coherent part associated with the relative path-delay. Second, in companion with the semi-deterministic treatment of the sea scattering model, a hybrid approximate algorithm is proposed to deal with the composite scattering of electrically large ship-sea model, which is entirely evolved through facets (for the sea surface) and wedges (for the ship target). The method of equivalent currents (MEC) and a hybrid frame which combines the four path model (FPM) with the quasi-image method (QIM) are employed to calculate the scattering characteristics of the ship-like target and ship-sea interactions, respectively. The entire simulator is of comparatively signiflcant computational e-ciency, and suitable for providing a preliminary prediction on the instantaneous complex re∞ective functions and normalized radar cross sections (NRCS) mean levels for electrically very large ship-sea model.

Comparison of short-range ion–ion correlations in the α, β and δ phases of Bi 2O 3

Neutron total scattering data for α-Bi 2O 3 and δ-Bi 2O 3, considering both the Bragg and diffuse components, have been analysed by the reverse Monte Carlo (RMC) method to extract experimental information concerning the short-range correlations between pairs of ions. These results complement the average structural information provided by conventional Rietveld refinement of the Bragg scattering alone. The radial and angular distribution functions in the stable ambient temperature α phase and superionic δ phase of Bi 2O 3 are presented and compared with the corresponding data for the metastable β phase reported previously. These data provide an important insight into the nature of the anion disorder within the highly conducting δ phase and the relationship between the δ phase and its ordered α and β counterparts.

Oxygen vacancy ordering within anion-deficient Ceria

The structural properties of anion deficient ceria, CeO 2− δ , have been studied as a function of oxygen partial pressure, p(O 2), over the range 0≥log 10 p(O 2)≥−18.9 at 1273(2) K using the neutron powder diffraction technique. Rietveld refinement of the diffraction data collected on decreasing p(O 2) showed increases in the cubic lattice parameter, a, the oxygen nonstoichiometry, δ, and the isotropic thermal vibration parameters, u Ce and u O, starting at log 10 p(O 2)~−11. The increases are continuous, but show a distinct kink at log 10 p(O 2)~−14.5. Analysis of the total scattering (Bragg plus diffuse components) using reverse Monte Carlo (RMC) modelling indicates that the O 2− vacancies preferentially align as pairs in the 〈 111 〉 cubic directions as the degree of nonstoichiometry increases. This behaviour is discussed with reference to the chemical crystallography of the CeO 2–Ce 2O 3 system at ambient temperature and, in particular, to the nature of the long-range ordering of O 2− vacancies within the crystal structure of Ce 7O 12.

Scattering of decimetric acoustic waves from the sea’s surface

The influence of the sea’s surface slopes caused by wind waves whose wavelength exceeds that of the Bragg components on the backscattering of acoustic radiation is discussed. The analysis is performed for long waves whose wavelengths are greater than 1.5 m. The study is based on the data of full-scale measurements of the sea’s surface slopes. Expressions relating the backscattering coefficient to the statistical characteristics of the sea’s surface slopes caused by long waves are presented.

Bragg scattering of centimeter electromagnetic radiation from the sea surface: The effect of waves longer than Bragg components

The effect of sea surface waves longer than Bragg components on the backscattering of centimeter electromagnetic radiation is studied on the basis of data on direct field measurements of sea-surface slopes. A situation in which waves with wavelengths greater than 10 cm are longer than the Bragg components is considered. The increase in the backscattering cross section that is due to the presence of long waves is numerically estimated for sounding at horizontal and vertical polarization. Nonlinear effects in the field of surface waves result in the departure of the distribution of sea-surface slopes from a Gaussian distribution and lead to a change in the backscattering cross section. At a sounding angle of 35°, this change may reach 15% with respect to the cross section calculated for a Gaussian surface.

О соотношении зеркальной и брегговской составляющих при рассеянии радиоволн квазигауссовой морской поверхностью

О соотношении зеркальной и брегговской составляющих при рассеянии радиоволн квазигауссовой морской поверхностью

Precise analysis of the components of diffraction by cylindrical crystals

A detailed quantitative analysis of the various Bragg and Laue components of the integrated reflection power ratio for cylindrical crystals, and the dependence of these components on the Bragg angle, thetaB, the reduced radius, tau0 = sigma0rho, and the ratio of absorption coefficient to diffraction cross section, mu/sigma0 = xi0, is presented. The result indicates that the percentage of Laue and Bragg components of the integrated reflection power ratio is larger than 50% when thetaB < or = 20 degrees and murho < or = 1, and when thetaB > or = 10 degrees and murho > or = 5. The reflection power ratio profile for cylindrical crystals with large murho is also discussed.

A Michelson interferometer for X-rays capable of high-order measurement

The first Michelson interferometer which was capable of working in the hard X-ray range featured geometric path-length differences of interfering beams of about 120 nm, corresponding to a scan range of more than 750 orders at a wavelength λ ≃ 0.15 nm. The new instrument uses the same principle,i.e.mixing of Laue- and Bragg-case beams diffracted by only one set of Bragg planes of two separate structures of perfect silicon crystals. Through modifying the geometry of beam paths, it has been possible to extend the scan range by a factor of 3.6 and to measure 2700 interference orders for the same wavelength. Six beat nodes of the CuKα1–Kα2doublet were recorded in Fourier spectrometric mode. Allowing for realistic reflection curves of Laue and Bragg components, the output spectrum was calculated and found to be in good agreement with the measured spectrum. The influence of thermal, acoustic and vibrational disturbances was studied in detail and special means were developed to cope with them. Applying the know-how obtained in this study in scaling up the present design, it should be feasible to extend the scanning range to ∼40000 orders, which would allow hard X-ray Fourier spectroscopy at spectroscopic resolutions λ/Δλ ≃ 20000.

A new decomposition of radar polarization signatures

A method for the decomposition of radar polarization signatures is developed. The polarization backscattering model is assumed to consist of odd, double, Bragg, and cross backscattering components, and the Mueller matrix is the sum of the Mueller matrices of these four scattering mechanisms. The technique of least squares (LS) is then used to find the best combination of these four components. Using NASA/Jet Propulsion Laboratory (JPL) AirSAR data, the results of the decomposition agree with the general understanding of radar backscatter. In most cases, the accuracy of the decomposition is more than 95% for linear polarizations and more than 85% for any other polarizations.

Parametric estimation of ocean surface currents with HF radar

Ocean surface currents can be estimated, over a large coastal area, by utilizing the backscatter of high frequency (HF) radar waves from ocean gravity waves. Although the overall backscatter mechanism is complicated, the surface current information is contained within the spectral characteristics of two dominant Bragg components. The accuracy of the current estimate, following the usual FFT-based spectral estimate, is limited by the frequency resolution of the FFT and the time-varying characteristics of the Bragg components. This paper describes a high resolution parametric estimation of the ocean currents based on a recently proposed technique for analyzing time-varying signals. This technique, together with a time-domain ocean clutter model, allows all the Bragg signal information to be extracted from the two dominant eigenvalues and eigenvectors of a matrix constructed from the radar data. Using signals from an operational coastal surveillance radar, current estimates made using this technique are compared with those estimated by the conventional FFT-based method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bragg and diffuse components of X-ray reflection measured using acoustic excitation of an Si crystal with oxide precipitates

Bragg and diffuse scattering contributions to a reflection can be separated using the intensity dependence on the amplitude of transverse ultrasound excited in the crystal. The method is based on the fact that a weak ultrasound with wavelength equal to the extinction length suppresses almost completely the anomalous transmission of the coherent (Bragg) beam in a sufficiently thick absorbing crystal and does not affect diffuse scattering. Both parameters characterizing diffraction in a slightly imperfect crystal, the static Debye–Waller factor and the coefficient of additional absorption due to diffuse scattering, have been determined for a silicon crystal containing oxide precipitates after heat treatment.