Borrmann Effect Research Articles

Bragg-Primakoff axion photoconversion in crystal detectors

Axions and axion-like pseudoscalar particles with dimension-5 couplings to photons exhibit coherent Primakoff scattering with ordered crystals at keV energy scales, making for a natural detection technique in searches for solar axions. We find that there are large suppressive corrections, potentially greater than a factor of O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(103), to the coherent enhancement when taking into account absorption of the final state photon. This effect has already been accounted for in light-shining-through-wall experiments through the language of Darwin classical diffraction, but is missing from the literature in the context of solar axion searches that use a matrix element approach. We extend the treatment of the event rate with a heuristic description of absorption effects to bridge the gap between these two languages. Furthermore, we explore the Borrmann effect of anomalous absorption in lifting some of the event rate suppression by increasing the coherence length of the conversion. We study this phenomenon in Ge, NaI, and CsI crystal experiments and its impact on the projected sensitivities of SuperCDMS, LEGEND, and SABRE to the solar axion parameter space. Lastly, we comment on the reach of multi-tonne scale crystal detectors and strategies to maximize the discovery potential of experimental efforts in this vein.

Effects of viscous dissipation in propagation of sound in periodic layered structures

Propagation and attenuation of sound through a layered phononic crystal with viscous constituents is theoretically studied. The Navier–Stokes equation with appropriate boundary conditions is solved and the dispersion relation for sound is obtained for a periodic layered heterogeneous structure where at least one of the constituents is a viscous fluid. Simplified dispersion equations are obtained when the other component of the unit is either elastic solid, viscous fluid, or ideal fluid. The limit of low frequencies when periodic structure homogenizes and the frequencies close to the band edge when propagating Bloch wave becomes a standing wave are considered and enhanced viscous dissipation is calculated. Angular dependence of the attenuation coefficient is analyzed. It is shown that transition from dissipation in the bulk to dissipation in a narrow boundary layer occurs in the region of angles close to normal incidence. Enormously high dissipation is predicted for solid–fluid structure in the region of angles where transmission practically vanishes due to appearance of so-called “transmission zeros,” according to El Hassouani, El Boudouti, Djafari-Rouhani, and Aynaou [Phys. Rev. B 78, 174306 (2008)]. For the case when the unit cell contains a narrow layer of high viscosity fluid, the anomaly related to acoustic manifestation of Borrmann effect is explained.

Resonant scattering of surface acoustic waves by arrays of magnetic stripes

Owing to magnetoelastic coupling, surface acoustic waves (SAWs) may be scattered resonantly by magnetic elements, such as nickel stripes. The scattering may be further enhanced via the Borrmann effect when the elements are organized into an array that matches the acoustic wavelength. We use finite-element modeling to consider single- and double-layer stripes patterned on top of a lithium niobate surface that carries Love surface waves. We do observe enhancement in the coupling for single-layer stripes, but only for Gilbert damping below its realistic value. For double-layered stripes, a weak yet clear and distinct signature of Bragg reflection is identified far away from the acoustic band edge, even for a realistic damping value. Double-layered stripes also offer better magnetic tunability when their magnetic period is different from the periodicity of elastic properties of the structure because of staggered magnetization patterns. The results pave the way for the design of magnetoacoustic metamaterials with an enhanced coupling between propagating SAWs and local magnetic resonances and for the development of reconfigurable SAW-based circuitry.

Three-dimensional distribution and propagation of dislocations in β-Ga2O3 revealed by Borrmann effect x-ray topography

Synchrotron radiation x-ray topography (XRT) in a transmission configuration based on the Borrmann effect (BE) was carried out to observe characteristic dislocation structures and three-dimensional distribution and propagation of dislocations in β-Ga2O3 grown via the edge-defined film-fed growth (EFG) method. Substrates with a range of surface orientations of (001), (010), and (2¯01), cut perpendicular or parallel to the ⟨010⟩ growth direction of the EFG, were observed to understand the whole picture of dislocations distributed in the bulk crystals. Using the (001)-oriented substrate, we found characteristic dislocation structures such as dislocation helices, damage-related (001)-plane dislocation networks, and tangled dislocation complexes, which exist universally in EFG crystals but have rarely been reported before. A careful measurement of the dislocation length in BE-XRT images taken with different g-vectors allows us to determine the crystal plane on which a dislocation lies. The BE-XRTs taken from the (010)-oriented and (2¯01)-oriented substrates suggested that the dislocations propagating along the [010] growth direction were dominant. Most of these b-axis threading dislocations had a Burgers vector of [010] or [001], and they tended to align in the (100) plane. The BE-XRT observations in this study provide valuable knowledge for understanding the structure and character of dislocations in β-Ga2O3.

Combining Borrmann and weak-beam diffraction images to study defects in a high-quality CdTe(Zn) crystal

In this work, synchrotron radiation rocking curve imaging (RCI) is used to visualize and characterize dislocations and second-phase defects in a highly perfect and absorbing CdTe(Zn) crystal. This technique requires recording a series of Bragg diffracted images along the rocking curve to produce maps of the `local' integrated intensity, full width at half-maximum and peak position. The diffraction conditions of the reported experiment are such that anomalous transmission (Borrmann effect) is a crucial ingredient for the formation of the image of the defects. The images recorded and maps produced allow the investigation of a series of topics that, to the authors' knowledge, have not been previously studied. The first of these topics is the variation of the position and width of the Borrmann image of a defect when sitting on the peak and on the flanks of the diffraction curve. The second topic is the way Borrmann images show up on the usual RCI maps. The final topic is the combination of Borrmann and weak-beam images to infer the depth of the defect within the crystal.

Study of X-ray topography using the super-Borrmann effect.

X-ray topography exerting the super-Borrmann effect has been performed using synchrotron radiation to display dislocation images with a high-speed and high-resolution CMOS camera. Forward-transmitted X-rays are positively employed instead of reflected X-rays to reveal dislocations in relatively thick crystals by simultaneously exciting a pair of adjacent {111} planes owing to the super-Borrmann effect. Before the experiment, minimum values of the attenuation coefficients AminP for σ and π polarizations of the incident X-rays in the three-beam case are calculated. Results demonstrate that AminP for both polarizations are almost 20 times larger than those in the two-beam (usual Borrmann effect) case. The transmitted X-rays can be used to confirm the efficacy of taking topographs under the super-Borrmann conditions, as well as under multiple-diffraction conditions. Furthermore, super-Borrmann topographs can be considered for relatively thick crystals, where a conventional Lang X-ray topography technique is difficult to apply.

Observation of dislocations in thick β-Ga2O3 single-crystal substrates using Borrmann effect synchrotron x-ray topography

We performed Borrmann effect x-ray topography (XRT) to observe dislocations and other structural defects in a thick β-Ga2O3 (001) substrate. The Borrmann effect was realized by working in a symmetrical Laue geometry (g = 020). Anomalous transmission occurred under the exact Bragg condition, producing a strong diffraction beam that allowed us to image defects across the entire thickness of the substrate. The analysis clearly revealed straight b-axis screw-type and curved dislocations and allowed assessing the corresponding behaviors. Other structural defects, including pipe-shaped voids and dislocation loops produced by mechanical damage, were also observed. Finally, we compared Borrmann effect transmission topography and conventional reflection topography and explained the appearance of some characteristic defects in the two modes. Our results show that Borrmann effect XRT is a powerful and effective technique to study the spatial distribution and structural properties of defects in highly absorbing β-Ga2O3.

Structural Analysis of Low Defect Ammonothermally Grown GaN Wafers by Borrmann Effect X-ray Topography.

X-ray topography defect analysis of entire 1.8-inch GaN substrates, using the Borrmann effect, is presented in this paper. The GaN wafers were grown by the ammonothermal method. Borrmann effect topography of anomalous transmission could be applied due to the low defect density of the substrates. It was possible to trace the process and growth history of the GaN crystals in detail from their defect pattern imaged. Microscopic defects such as threading dislocations, but also macroscopic defects, for example dislocation clusters due to preparation insufficiency, traces of facet formation, growth bands, dislocation walls and dislocation bundles, were detected. Influences of seed crystal preparation and process parameters of crystal growth on the formation of the defects are discussed.

Quantum Borrmann effect for dissipation-immune photon-photon correlations

We study theoretically the second-order correlation function $g^{(2)}(t)$ for photons transmitted through a periodic Bragg-spaced array of superconducting qubits, coupled to a waveguide. We demonstrate that photon bunching and anti-bunching persist much longer than both radiative and non-radiative lifetimes of a single qubit. The photon-photon correlations become immune to non-radiative dissipation due to the Borrmann effect, that is a strongly non-Markovian collective feature of light-qubit coupling inherent to the Bragg regime. This persistence of quantum correlations opens new avenues for enhancing the performance of setups of waveguide quantum electrodynamics.

Kossel Lines and X-ray Localized Conical Modes

An alternative way of describing X-ray Kossel lines based on the theory of X-ray localized conical modes existing in perfect crystals is proposed. The theory of Kossel lines is presented within the approximation of a two-wave dynamical diffraction theory. The theoretical results are compared with known experimental data and demonstrate good general agreement with an experiment. The influence of essential crystal parameters (perfection, size, Borrmann effect, etc.) on the shape of Kossel lines is discussed. To prove the direct link between Kossel lines and X-ray localized conical modes, it is proposed to use an X-ray time-delay detection technique.

Hybrid magnetoacoustic metamaterials for ultrasound control

We propose a class of metamaterials in which the propagation of acoustic waves is controlled magnetically through magnetoelastic coupling. The metamaterials are formed by a periodic array of thin magnetic layers (“resonators”) embedded in a nonmagnetic matrix. Acoustic waves carrying energy through the structure hybridize with the magnetic modes of the resonators (“Fano resonance”). This leads to a rich set of effects, enhanced by Bragg scattering and being most pronounced when the magnetic resonance frequency is close to or lies within acoustic bandgaps. The acoustic reflection from the structure exhibits magnetically induced transparency and Borrmann effect. Our analysis shows that the combined effect of the Bragg scattering and Fano resonance may overcome the magnetic damping, ubiquitous in realistic systems. This paves a route toward the application of such structures in wave computing and signal processing.

Optical Kossel Lines and Fluorescence in Photonic Liquid Crystals

We propose a general analytical way to describe the fluorescence peculiarities in photonic liquid crystals (revealing themselves as an optical analog of the X-ray Kossel lines in conventional crystals) based at the localized optical edge modes existing in perfect photonic liquid crystal layers. The proposed approach allows us to predict theoretically the properties of optical Kossel lines in photonic liquid crystal (fluorescence polarization, spectral and angular fluorescence distribution, influence of the light absorption in liquid crystal, and, in particular, existing the optical Borrmann effect if the absorption in liquid crystal is locally anisotropic). Comparison of the theoretical results and the known experimental data shows that the theory reproduces sufficiently well the observation results on the fluorescence in photonic liquid crystals. For confirming a direct connection of the optical Kossel lines to the localized optical edge modes in perfect photonic liquid crystal, we propose the application of time-delayed techniques in studying the optical Kossel lines.

Bragg Diffraction Imaging of CdZnTe Single Crystals

A high-quality CdZnTe single crystal has been imaged with micrometer resolution using monochromatic x-ray Bragg diffraction at the bending magnet (BM)-05 beamline of the European Synchrotron Radiation Facility. Since this material is used to produce substrates for the epitaxial growth of infrared sensitive HgCdTe photon detectors, imaging the defects is of strong interest to visualize their arrangement within the bulk. We show that large field-of-view rocking curve projection maps can be acquired in transmission geometry using samples as thick as 0.5 mm thanks to the Borrmann effect. Furthermore, section topography can be applied to provide information on the depth of the observed defects allowing for a complete 3D localization of lattice distortions. Examples of 1.5 mm × 1.5 mm full width at half-maximum maps are given to illustrate the spatial arrangement of dislocations in a number of samples cut with respect to different crystallographic planes in a particular CdZnTe ingot.

Anomalous transmission through periodic resistive sheets

This work investigates anomalous transmission effects in periodic dissipative media, which is identified as an acoustic analogue of the Borrmann effect. For this, the scattering of acoustic waves on a set of equidistant resistive sheets is considered. It is shown both theoretically and experimentally that at the Bragg frequency of the system, the transmission coefficient is significantly higher than at other frequencies. The optimal conditions are identified: one needs a large number of sheets, which induce a very narrow peak, and the resistive sheets must be very thin compared to the wavelength, which gives the highest maximal transmission. Using the transfer matrix formalism, it is shown that this effect occurs when the two eigenvalues of the transfer matrix coalesce (i.e., at an exceptional point). Exploiting this algebraic condition, it is possible to obtain similar anomalous transmission peaks in more general periodic media. In particular, the system can be tuned to show a peak at an arbitrary long wavelength.

New kind of interference in the case of X-ray Laue diffraction in a single crystal with uneven exit surface under the conditions of the Borrmann effect. Analytical solution.

The analytical solution of the problem of X-ray spherical-wave Laue diffraction in a single crystal with a linear change of thickness on the exit surface is derived. General equations are applied to a specific case of plane-wave Laue diffraction in a thick crystal under the conditions of the Borrmann effect. It is shown that if a thickness increase takes place at the side of the reflected beam, the related reflected wave amplitude is calculated as a sum of three terms, two of which are complex. If all three terms have a comparable modulus, it can lead to an increase in the reflected beam intensity by up to nine times due to interference compared with the value for a plane parallel shape of the crystal. The equation for the related transmitted wave amplitude contains only two terms. Therefore, the possibility to increase intensity is smaller compared with the reflected beam. The analytical solution is obtained after a solution of the integral equations by means of the Laplace transformation. A general integral form of the Takagi equations derived earlier is used. The results of relative intensity calculations by means of analytical equations coincide with the results of direct computer simulations.

Absorption of 1D meta-liquids with continuum distribution of the refraction index

Absorption and emission in isotropic one-dimensional photonic crystals with continuous distribution of the refraction index have been investigated. It was assumed that the photonic crystal under investigation was fabricated by introducing micro and nano-scale particles (either ferroelectric or ferromagnetic, or both) into a specially chosen liquid and it is periodically inhomogeneous with respect to both the dielectric and magnetic properties. The peculiarities for the absorption, emission and light localization were investigated. The absorption suppression in the photonic band gap was demonstrated. Anomalously strong absorption and anomalously weak absorption (or the anomalous increase in the intensity of the light transmitted through a crystal or, simply, the Borrmann effect) were observed near the band edges, depending on either the absorption due to the imaginary part of the dielectric permittivity or the imaginary part of the magnetic permeability. These effects were exhibited stronger for periodic inhomogeneity of absorption. The effects are different for the absorption changes in-phase and out-of-phase in the real part of the corresponding permeability or permittivity. The features of the revealed effects for the oblique incidence of the light were also investigated.

Imaging of microdefects in ZnGeP2 single crystals by X-ray topography

The contrast from microdefects in ZnGeP2 crystals is studied. Simulation of images in X-ray topography based on the Borrmann effect is carried out for a model of a coherent inclusion of spherical form in an infinite isotropic matrix. For this simulation, a semi-phenomenological theory of contrast from defects with a slowly changing deformation field is applied. It is shown that the contrast from the inclusion is a complex function, depending on the nature of defect (sign of the deformation of the matrix), the magnitude of the deformation caused by the defect, its depth in the crystal, the modulus of the diffraction vector g and the topography used (reflection or transmission). The most common images are intensity rosettes of double or triple contrast, whose lobes are elongated along the diffraction vector. These are created by inclusions, located near the X-ray exit surface of the sample. Analysis of experimental data shows that the majority of microdefects in ZnGeP2 revealed by Borrmann method (~96%) show good agreement with proposed model. All the features of the experimental images are explained by the theory. Additionally, the contrast from dislocation loops and from groups of big inclusions which have non-Coulombic deformation fields is observed.

Dynamic plasma/metal/dielectric photonic crystals in the mm-wave region: Electromagnetically-active artificial material for wireless communications and sensors

Inexorable demand for increasing bandwidth is driving future wireless communications systems into the 100 GHz–1 THz region, thereby fueling demand for new sources and modulators but also complementary devices such as resonators, phase shifters, and filters. Few such devices exist at present, and the electromagnetic properties of those available at millimeter-wavelengths are generally fixed and characterized by broad (i.e., low Q) resonances. We introduce a class of 3D plasma/metal/dielectric photonic crystals (PPCs), operating in the 120–170 GHz spectral range, that are dynamic (tunable and reconfigurable at electronic speeds) and possess attenuation and transmission resonances with bandwidths below 50 MHz. Interference between sublattices of the crystal, which controls the resonance line shapes, is manipulated through the crystal structure. Incorporating Bragg arrays of low-temperature plasma microcolumns into a dielectric/metal scaffold that is itself a static crystal forms two interwoven and electromagnetically coupled crystals. Plasma-scaffold lattices produce multiple, narrowband attenuation resonances that shift monotonically to higher frequencies by as much as 1.6 GHz with increasing plasma electron density. Controlling the longitudinal geometry of the PPC through electronic activation of successive Bragg planes of plasma columns reveals an unexpected double-crystal symmetry interaction at 138.4 GHz and resonance Q values above 5100. The introduction of point or line defects into plasma column/polymer/metal crystals increases transparency at resonances of the scaffold (Borrmann effect) and yields Fano line shapes characteristic of coupled resonators. The experimental results suggest the suitability of PPC-based metamaterials for applications including multichannel communications, millimeter-wave spectroscopy, and fundamental studies of multiple, coupled resonators.

Borrmann modulation of terahertz absorption in 3D printing microlattices

We have fabricated a three-dimensional (3D) microlattice, composed of orthogonal polymer rods along three dimensions and featured with a sub-millimeter scale size, with a photopolymerizing 3D printer. The reflection and transmission spectra of the microlattice have been measured in terahertz time-domain spectroscopy and compared with numerical simulations. Due to Debye relaxation loss of the constituent photopolymer, the microlattice gives rise to absorption in the measured frequencies. In particular, the absorption modulation is observed across the bandgap, corresponding to the lower/upper band edges, and is a straightforward manifestation of the Borrmann effect.

Computer Simulations of X‐Ray Spherical Wave Laue Diffraction in a Thick Perfect Crystal with a Triangular Cutout on the Exit Surface

The results of computer simulations of X‐ray spherical wave dynamical Laue diffraction in a perfect crystal of a special shape are presented. Namely, the crystal has a triangular cutout on the exit surface with the angle 2θ less than 2θB, where θB is the Bragg angle. The effect of a strong increase in the intensity near the triangular cutout is found in the case of a thick crystal. It is demonstrated that the X‐ray beam intensity can be increased up to seven times under the conditions of the Borrmann effect. The fast Fourier transform (FFT) algorithm is used at the first step where simulations of spherical wave Laue diffraction in a perfect crystal slab are performed. Thus, the X‐ray fields are obtained in front of the triangular cutout which are used as boundary conditions for the second step. At the second step, a direct numerical solution of the Takagi equations is used. The effect of a strong increase in intensity is observed for all source‐to‐crystal distances including the distance of diffraction focusing. This effect is explained in terms of a crystal propagator.