Bragg Region Research Articles

P‐45: A simulation method for crossed‐type exit pupil based on polarization volume grating

We propose a simulation method for two‐dimensional (2D) crossed‐type exit pupil expansion based on polarization volume grating (PVG) applied in diffractive waveguide holographic display. The functions of turning and decoupling of the PVG are realized through two continuous Bragg regions, and the spatial director distribution of liquid crystal is combined with RCWA to model its diffractive characteristics and ray tracing simulation.

Development of a new base isolation system using the concept of metamaterials

Metamaterials are making a breakthrough in seismic wave manipulation with their ability to yield wave filtration properties that cannot be realized inherently through conventional construction materials. The popularly used seismic vibrational control techniques, such as base isolation, fall short at low-frequency regions of the spectrum and fail to encompass both flexible and rigid structures. Using the concept of metamaterials, the phenomena of local resonance and Bragg scattering can create a stop band region of frequencies that undergo vibrational wave filtration. This study proposes a two-dimensional periodic foundation system with steel-silicone embedded assemblies to serve as local resonators. The proposed foundation can cover a wide and ultra-low frequency region in its band gap, enveloping the principal frequencies of seismic waves (i.e., 0.2 Hz to 10 Hz). This two-dimensional periodic foundation can also exhibit a Bragg region without local resonators but is made more efficient with the help of steel-silicone resonators (SSR). Upon experimental testing, the scaled-down prototype of the proposed foundation with three locally resonant panels embedded with SSR showed an average of 50 % attenuation of displacement within the frequency band gap (i.e., 2.54 Hz to 8.08 Hz). Moreover, the experimentation showed a 73 % attenuation at the resonant frequency of SSR. Experimental testing affirmed the frequency band gap obtained through mathematical formulation. Furthermore, the theoretical results demonstrate that the full-scale proposed periodic foundation would be able to achieve a band gap that covers frequencies from as low as 0.3 Hz to 7.35 Hz. This study is the first attempt to set the baseline for periodic foundations capable of fully mitigating the entire spectrum of seismic vibrational effects on structures.

Bragg-region recognition of high-frequency radar spectra based on deep learning and image fusion processing

ABSTRACT In previous research, the identification of the Bragg region, which is often achieved using image recognition, was easily affected by ionospheric interference and different manual parameter settings. Strong disturbances from the ionosphere and other environmental noise may interfere with high-frequency radar (HFR) systems when determining first-order Bragg regions and thus may directly influence the surface current mapping performance. To avoid human intervention in first-order Bragg-region recognition, deep learning methods were used to extract multiple levels of feature abstractions of the first-order Bragg region. In this study, to assist in developing sufficient training data, a procedure integrating a morphological approach and Otsu’s method was proposed to provide manual labelled data for a U-Net deep learning model. Additionally, several sets of activation functions and optimizers were used to achieve optimal deep learning model performance. The best combination of model parameters results in an accuracy of over 90%, an F1 score of over 80%, and an intersection over union (IoU) reaching 60%. The identification time of one image is approximately 70 ms. These results demonstrate that this deep learning model can predict the position of first-order Bragg regions under ionospheric interference and avoid being affected by strong noise that could cause prediction errors. Hence, deep learning and image fusion processing can effectively recognize the first-order Bragg regions under strong interference and noise and can thereby improve the surface current mapping accuracy.

A Quality Control Method for Broad-Beam HF Radar Current Velocity Measurements

This paper describes a method to provide quality control for radial velocity maps derived from radar echo voltage cross spectra measured by broad-beam high frequency radars. The method involves the comparison of voltage cross spectra measured at Doppler frequencies in the Bragg region with values predicted from basic equations defining the complex voltage cross spectra in terms of the measured antenna patterns and the radar cross section. Poor agreement at a given Doppler frequency indicates contamination of the spectra, usually due to interference; velocity results from that Doppler frequency are then eliminated. Examples are given of its application to broad-beam radars operating at four sites.

Multiple scattering of proton via stochastic differential equations

Multiple scattering of protons through a target is explained by a set of coupled stochastic differential equations. The motion of protons in matter is calculated by analytical random sampling from Moliere and Landau probability density functions (PDF). To satisfy the Vavilov theory, the moments for energy distribution of a 49.1MeV proton beam in aluminum target are obtained. The skewness for the PDF of energy demonstrates that the energy distribution of protons in thin thickness becomes a Landau function, whereas, by increasing the thickness of the target it does not follow a Gaussian function completely. Afterwards, the depth-dose distributions are calculated for a 60MeV proton beam traversing soft tissue and for a 160MeV proton beam travelling through water. The results prove that when elastic scattering is taken into account, the Bragg-peak position is decreased, while the dose deposited in the Bragg region is increased. The results obtained in this article are benchmarked by comparison of our results with the experimental data reported in the literature.

Distribution of energy flow by dielectric waveguide with rhombic dielectric structure along a middle layer

Light propagation in periodic structure waveguide such as photonic crystals [1] waveguide is both theoretical and practical interest in many areas of physics and engineering. As these applications, there are devices such as an optical resonator, an optical waveguide filter, and integrated optical devices[2]. Consequently, in the design of photonic crystal structures with periodic constants identical to the optical wavelength, it is important to investigate the stop band region or photonic band-gaps. Though it is not analyzed the propagation constants in detailed in Bragg region, many analysis results are shown only the distribution of the electromagnetic fields by using the FDTD method[2] or another numerical techniques[3]-[6].

Breather-like collision of gap solitons in Bragg gap regions within nonlocal nonlinear photonic crystals

We analyze the existence, stability and mobility of gap solitons in a periodic photonic structure with nonlocal nonlinearity. Within the Bragg region of bandgaps, gap solitons exhibit better stability and higher mobility due to the combinations of nonlocality effect and the oscillation nature of Bloch waves. Using linear stability analysis and calculating the Peierls–Nabarro potentials, we demonstrate that gap solitons can revive a nontrivial breather-like collision even in the periodic systems with the help of nonlocal nonlinearity. Such interesting behaviors of gap solitons in nonlocal nonlinear photonic crystals are believed to be useful in optical switching devices.

Effect of grating surface loss on the Smith–Purcell free-electron laser

The effect of dissipative loss in the grating surface on a Smith–Purcell free-electron laser is investigated with the help of a two-dimensional particle-in-cell simulation. The simulation model supposes an open grating driven by a continuous electron beam. With present parameters, simulation results show that such a device can oscillate on absolute instability, Bragg condition and convective instability when ignoring the surface loss. The growth rate is found to be dependent of beam energy, and it decreases when the surface loss is involved. It is shown that surface loss impacts a lot on the Bragg region. Comparisons of simulation results with the latest theory are reported.

Many-hit model calculations for track etch rate in CR-39 SSNTD using confocal microscope data

The present work studied an important part of ion tracks: the Bragg peak region. Information about the microscopic nature of ion-energy dissipation based on zero-approximation in frame of the many-hit model of the track structure theory was studied. The detector response, Vt, was calculated in terms of Poisson’s distribution as a function of the ion’s linear energy transfer (LET). This approach can be considered to be a zero-approximation since LET is a special case of restricted energy losses with a cut off energy wcutoff=∞: LET=REL∞. Confocal microscopic data allows the visualising and analysing of the etched tracks one by one with high precision. A three-dimensional track image was observed and the track etch rate was measured. On the basis of χ2 analysis of the experimental track etch rate (square of the least deviation), with respect to that of the theoretical value, information about the energy transfer process can be obtained. Light ions of little MeV energy were slowed down in the CR-39 detector and the detectors responses close to the Bragg peak region were studied. It was shown that in the zero-approximation no one to one relation can be found between the primary linear energy transfer (LET) and the measured specific track etch rate. The statistical analysis can be split into two separate parts; before the Bragg peak (Bethe–Bloch) and after the Bragg peak (Thin Down). The two parts analysed reflect the separated domains where the etching rate increases or decreases, due to the different role of the delta-electrons in each of these domains. The main aim of this study is to develop a method for any ion describing Vt in this very sensitive Bragg region. This would allow ion identification at low velocities on the one hand, and on the other hand to have a better understanding of the physical processes involved during high velocity ion stopping.

Heavy ion RBE and microdosimetric spectra.

Reliable values for the relative biological effectiveness (RBE) of the complex field of heavy ions is essential for radiation therapy with carbon beams. Clinical experience with this novel form of therapy is still quite narrow and it is, therefore, desirable to compare and combine relevant clinical findings and theoretical approaches. One major source of available information comes from neutron therapy. The approach towards the determination of RBE for neutron therapy is, therefore, tentatively applied to the heavy ion therapy. This includes the determination of microdosimetric spectra and their numerical evaluation towards the determination of RBE. A microdosimetric detector on the basis of a tissue-equivalent proportional counter (TEPC) was developed for measurements in the heavy ion fields of the GSI, Darmstadt. Measurements were performed first near the perspex phantom surface with carbon ion energies between 89 MeV.amu-1 and 430 MeV.amu-1. Subsequently, measurements were taken at various depths in the neighbourhood of the Bragg region. The numerical techniques that were developed for neutron therapy lead to tentative values of the RBE that are compared to the RBE values from the biophysical model developed at the GSI. The comparison is still preliminary but can be helpful in modifying the microdosimetric approach for its application in heavy ion therapy.

Automation of the particle dosimetry and the dose application for radiobiological experiments at a vertical proton beam

A facility with a vertical beam for radiobiological experiments with low-energy protons has been setup at the Tandem accelerator at Erlangen. This energy region is optimal to investigate the biological effects of the linear energy transfer in the Bragg region under physiological conditions. A new automated data acquisition system for dosimetry and monitoring based on a personal computer was developed and optimized for this setup. A specially designed sample holder offers possibilities of cooling or changing of atmosphere during irradiation. First irradiations of biological samples have shown the functionality of the setup.

Nonsymmetrical X-ray diffraction in a perfect rectangular t × l crystal. Extinction and absorption

A theoretical investigation of diffraction in a rectangular t x l crystal for nonsymmetrical coplanar scattering has been undertaken. The asymmetry in the scattering geometry, measured by an angle gamma, causes different weights for the mixed Laue-Bragg contributions to the integrated power. Primary extinction and ordinary absorption are only moderately affected when the value of the geometrical parameter zeta = (t/l)tanstraight theta(oh) < 1, straight theta(oh) being the Bragg angle. For increasing values of zeta and gamma the surface integration set-up for the Laue and Bragg regions is extensively changed, leading to pronounced effects. Analytical results for the normal absorption factor are presented.

Inversion in x-ray Bragg diffraction: A practical technique to compensate for dynamical scattering features

A new numerical technique to compensate for the dynamical effects in experimental x-ray intensity profiles is proposed and implemented to enhance the crystal-lattice strain determination algorithm which is applicable to x-ray diffraction data collected from nearly perfect crystals. A practical procedure for the preliminary treatment of experimental data exhibiting dynamical features was tested using three sets of data representing different cases of near-surface distorted layers. It is shown that the influence of the substrate peak on the overall diffraction pattern can be removed by an iterative modification of the very vicinity of the Bragg region in experimental intensity profile.

Structural characterization of a Mo/Si multilayer reflector by means of x-ray diffraction measurements

The physical and optical characteristics of a multilayered synthetic microstructure (MLSM) have a significant structural dependence. Knowledge of the structure and its correlation to physical properties is needed in order to control the fabrication of MLSMs to obtain desired properties. Important parameters for the description of the structure are the thickness of a repeating unit, the thickness ratio of composite materials within the repeating unit and the degree of interdiffusion and roughness at interfaces. The effects of these various structural parameters on the small-angle x-ray diffraction (XRD) pattern are investigated for a molybdenum-silicon MLSM. The angular positions of the Bragg peaks are sensitive to the thickness of the repeating unit (Mo/Si bilayer in this study), and the pattern of the subsidiary peaks in the low-order Bragg region has a strong dependence on the thickness ratio. The major effect of interfacial diffusion is the overall reduction of the intensities of high-order Bragg peaks. However, the atomic concentration profile correlates with their relative intensities. The uncorrelated roughness is responsible for the increased linewidths of the Bragg peaks and the increase of the relative intensities of the subsidiary peaks to those of the Bragg peaks. Based on the above results, we present an analysis of the experimental XRD data in order to deduce the structural parameters of a molybdenum-silicon MLSM.

Radiation in spherically symmetric structures. I. The coupled-amplitude equations for vector spherical waves.

A scalar Green's-function technique is used to derive coupled-amplitude equations for electromagnetic waves propagating in a three-dimensional structure with a radially varying refractive index. The vector nature of the problem is discussed and a method is outlined for reducing the vector wave equations to characteristic scalar equations. These scalar equations are then solved via an exact coupled-amplitude formalism, and closed-form solutions are compared with numerical results for the particular case of a spherical Bragg region. The derivation of the coupled-amplitude equations for vector spherical waves is a significant portion of the calculation, described in the companion paper [Sullivan and Hall, following paper, Phys. Rev. A 50, 2708 (1994)], of the radiative effects due to the presence of a spherical Bragg structure. Furthermore, the formulation is a powerful complement to previously developed Debye potential and transfer-matrix methods.

Beam propagation model for vertical-cavity surface-emitting lasers: threshold properties

A novel beam propagating method model for vertical-cavity surface-emitting lasers is presented. The Bloch wave concept is used for wave propagation in the Bragg region, and the numerical model includes the structure of Bragg reflectors, carrier, and thermal effects. Based on this model the optical field in the cavity is calculated. The numerical results show that weak index guiding should be introduced to maintain the low threshold current property when the temperature difference between the center and edge is comparable with that of edge-emitting laser diodes, especially in the small contact case. The effects of the mismatch between the lasing wavelength and the gain peak and the reflectivity of the facet are investigated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Integrated mode-locked laser design with a distributed-Bragg reflector

The design of actively mode locked semiconductor lasers integrated onto a single substrate is studied using a new variation on the transmission-line laser model. The laser includes a distributed Bragg reflector to provide wavelength selective feedback. The behaviour of the device under various drive conditions is investigated. Pulses below 3 ps can be achieved by careful design of the Bragg region.

Light diffraction by ultrasonic pulses: Analytical and numerical solutions of the extended Raman–Nath equations

Light diffraction by ultrasonic pulses at normal incidence is studied as well in the Raman–Nath region (low frequencies) as in the Bragg region (high frequencies). Based on a generating function method, an analytical expression for the Raman–Nath-like diffraction has been derived and compared with earlier work. Only small corrections within its validity region were observed. In order to extend these existing theories toward higher frequencies, numerical expressions for the intensity of the diffracted light waves are obtained by means of the Laplace transform theory. This powerful method leads to the same results for Raman–Nath-like diffraction and can easily be applied for much higher frequencies, too. Examples are provided showing the frequency dependence of the ultrasound, the influence of the Raman–Nath parameter v, and the spectral composition of the pulse on the diffraction pattern. When the pulse approaches a continuous wave, both theories converge to known results. A general condition concerning the symmetry properties of the diffraction spectrum has been derived.

TWO GENERALISED THEORIES DESCRIBING LIGHT DIFFRACTION BY ULTRASONIC PULSES :A. GENERATING-FUNCTION METHODB. LAPLACE-TRANSFORM METHOD

As an extension from previous studies concerning the interaction of light with ultrasound of a purely sinusoidal form, two theoretical models describing light diffraction by ultrasonic pulses are derived starting from the Maxwell equations. Based on a generating function, the first model provides finite solutions for the amplitudes and intensities of the diffraction pattern and is restricted in validity to the Raman-Nath region. The second model consists of a numerical method developed by means of Laplacetransformations and covers as well the Raman-Nath as the Bragg region. Both new methods are compared with a theory based on the diffraction-integral theory, leading to the conclusion that the results of this latter method can be obtained from our models considering the extreme Raman-Nath regime ρ = 0. A general rule concerning the (a)symmetry properties of the diffraction spectrum at normal incidence has been derived from the extended Raman-Nath equations, using the generating function method.

Theoretical Description of Light Diffraction on Acoustic Pulses in Bragg's Region

AbstractAs a result of theoretical analysis an equation is obtained describing the dependence of deflected light intensity on diffraction angle and time. Considerations are carried out for an isotropic, nonmagnetic dielectric medium and Gaussian light beam. The inverse problem is solved, too. Basing on its solution an acousto‐optic method for acoustic pulse parameter analysis is proposed. It allows to reconstruct the acoustic wave envelope basing on the diffraction pattern. This method may be used in investigations of acoustic properties of solids and liquids.