Interference Maxima Research Articles

Insights into the Thermal Expansion of Amorphous Polymers.

We investigated the thermal expansion of amorphous polystyrene (PS) and poly(methyl methacrylate) (PMMA) homopolymers using the temperature dependence of spatial electron-density correlations. The strong and broad X-ray interference maxima arising from inter- and intramolecular correlation distances were distinct, maintaining their shape during the heating of the samples to 250 °C. Three maxima characteristic of electron density correlations between the backbones, substituents along the chain, and repeat-units were observed. A remarkable temperature dependence was identified in the largest correlation distances arising from the intermolecular interactions. Based on the temperature dependence of the correlation distances, the coefficients of molecular expansion were very close to the coefficients of thermal expansion. This study provides a simple yet accurate way to correlate macroscopic volume expansions with the molecular expansion obtained from wide-angle X-ray scattering (WAXS) data.

Determination of the structure of weakly ordered films according to x-ray diffraction data

A method for searching for parameters of structural models of weakly ordered thin films based on X-ray diffraction data containing a small number of reflexes is proposed. The developed method makes it possible to narrow down the number of possible structural models, despite the small number of interference maxima, determine the parameters of possible elementary cells and index the corresponding peaks on diffractograms. It is shown how the use of a priori data makes it possible to obtain physically adequate solutions. The method of determining structural parameters is demonstrated by analyzing an experimental curve containing only 3 diffraction peaks (maxima). The corresponding search algorithms are implemented within the framework of the analytical software package BARD (Basic Analisys of xRay Diffraction).

Ultrashort-pulse-laser ablation of freestanding dielectric thin films

Ultrashort-pulse-laser ablation of dielectric thin films is strongly affected by the interference of the exciting laser pulse with itself, which causes the deposited energy to be confined to narrow regions equidistantly spaced along the propagation direction of the laser. We investigate how this affects the ablation mechanism of freestanding Al2O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Al}_2\\hbox {O}_3$$\\end{document} thin films by analyzing the laser-generated structures with several post-mortem imaging and spectroscopic techniques. Close to the ablation threshold, the laser-irradiated region exhibits surface blistering. Higher intensities cause layers of material to be removed corresponding to ejection of material initiated from the regions of high excitation. Significantly above the ablation threshold, the laser-generated structure is remarkably stable and consists of a membrane of thickness corresponding to the distance between neighboring interference maxima, which is uniquely determined by the central wavelength of the laser pulse and the refractive index of the film. The electronic excitation as a function of depth is simulated using a multiple-rate-equation model in combination with finite-difference-time-domain propagation of the laser field. The simulations confirm the strongly localized excitation and thus correlate well with the observed laser-generated structures.

Modeling the Determination of Wavelength Using a Diffraction Grating in Python

To model a laboratory experiment for determining the wavelength of light using a diffraction grating in Python, it is proposed to use the libraries numpy, matplotlib, and ipywidgets. A simulation is created to model the positions of maxima on the screen. The developed code can be run in an environment that supports ipywidgets, such as Jupyter Notebook, to obtain an interactive simulation for determining the wavelength of light using a diffraction grating. The code includes the following steps: 1. Import the necessary libraries: numpy for numerical calculations, matplotlib for plotting graphs, ipywidgets for creating interactive widgets. 2. Define constants: d - the distance between the slits of the diffraction grating, L - the distance from the grating to the screen. 3. Create the function calculate_maxima to calculate the positions of the maxima. 4. Create the function plot_diffraction_pattern to plot the diffraction pattern. 5. Create interactive widgets: wavelength_slider to change the wavelength of light, order_max_slider to change the maximum order of the interference maxima. 6. Run the interactive simulation, which allows parameters to be adjusted and results to be observed in real-time.

Formation of multibeam dynamic gradient interference light fields with refractive optical elements

This paper presents methods for the formation and properties of light fields that controllably vary in time and space, obtained as a result of the interference of three or four coherent light beams using refractive optical elements. The formation of three-beam and four-beam interference fields is carried out using trihedral and tetrahedral glass pyramids respectively. The possibility of the interference field displacement in the transverse plane is ensured by devices for controlled phase changes of at least two of the interfering beams. The directions of propagation of these beams do not lie in the same plane with the optical axis of the original beam incident on the pyramid. In threeand four-beam dynamic interference fields the peak intensity values are higher than in the original laser beams and two-beam interference fields, so it is advisable to use them for processing flat objects with laser radiation, moving the interference maxima along the surface of the object. With a pairwise azimuthal displacement of the propagation directions of four interfering beams around the longitudinal axis, a dynamic interference field is formed, the periodically structured maxima of which cyclically smoothly change their shape from cells to band and back. At different speeds of pairs of directions the interference structure of the maxima rotates around the longitudinal axis. Therefore, this field can be used for therapeutic effects on biological tissues and for mixing microparticles in suspensions and emulsions. Since the local maxima of the intensity of all these interference fields have dimensions of the order of several micrometers while exceeding in value the maximum intensity of the initial light beam, these fields in the cross section are gradient and therefore can be used not only for laser exposure, but also for moving ensembles of microparticles including for sorting and changing concentration.

Mathematical simulation of radar scattering characteristics of ultra-short-pulse signals on complex shape objects

The article discusses the method of mathematical modeling of characteristics of scattering of ultrashort-pulse signals of complex shape objects, taking into account the shape of the envelope of the ultrashort-pulse radio signal and the features of radiation of an ultrawideband antenna. To estimate the reflecting properties of objects, the determination of the ultra-short-pulse radar cross section of complex shape objects with their radar location by non-harmonic signals is given. The mathematical model of radar scattering characteristics of location objects under ultra-short-pulse signals takes into account the shape of the envelope of the signal generated by a transmitter of a single-chip microchip NVA 6100 with duration of 300 ps and obtained through direct measurements. The electric scattering field of a location object in the frequency domain is determined on the use of a polygonal model of the object and asymptotic methods of diffraction theory. The transfer function of the Vivaldi antenna to radiation obtained by numerical modeling using the method of moments was used in the electric field calculations. Verification of the developed mathematical model was carried out on the basis of determining the ultra-short pulse radar cross section of perfect electric conductive sphere. A diagram of the ultra-short-pulse radar cross section of the GPS satellite was obtained, taking into account the radiation of the ultra-short-pulse signal by the Vivaldi antenna. The diagram of ultra-short pulse radar cross section of GPS satellite does not contain interference maxima and minima, and the averaged values ultra-short radar cross section of GPS satellite from lateral angles are on average 3..8 times less than radar cross section at the center frequency of the spectrum. The mathematical model of radar scattering characteristics of location objects under ultra-short-pulse signals is intended for preliminary estimates of the ultra-short-pulse radar cross section at an early step of designing ultra-wideband radars. The obtained estimates of the ultra-short-pulse radar cross section of the GPS satellite make it possible to identify the main features in the scattering of ultra-short-pulse signals at the location of extended targets.

Highly Ordered Monolayers of μm-Sized Polystyrene Spheres Studied by Grazing-Incidence Small-Angle X-ray Scattering, Simulations, and Geometrical Calculations.

Unraveling the two-dimensional (2D) structural ordering of colloidal particles assembled at a flat surface is essential for understanding and optimizing their physical properties. So far, grazing-incidence small-angle X-ray scattering (GISAXS) has been widely used to determine crystallographic information on 2D self-assembled structures of nanosize objects. However, solving the structure of 2D lattices consisting of micrometer (μm)-sized objects still remains a challenge using scattering methods. Here, a model 2D SCALMS (supported catalytically active liquid metal solution) template is fabricated from μm-sized polystyrene (PS) spheres that form a monolayer on top of the flat solid support. GISAXS patterns of the sample were collected for rotation angles around its surface normal in steps of 3°. For every rotation angle, different Bragg-type interference maxima along the out-of-plane (qz) direction were observed. On the basis of simulations of GISXAS patterns of single domains of ordered particle arrangements using the distorted wave Born approximation (DWBA) and validation against a simple geometrical scattering model, the interference maxima could nicely be interpreted to originate from a monolayer of the μm-sized spherical particles which are arranged in domains of hexagonal 2D paracrystalline order. This novel GISAXS evaluation technique serves as a proof of principle for determining the μm-size periodicity of 2D crystalline domains and demonstrates its potential to spatially resolve the relative orientations of such domains with respect to a reference direction.

Single-photon ionization of aligned H with near-ionization-threshold photon energy

We study single-photon ionization of aligned H in a high-frequency low-intensity laser field. We focus on the cases where the laser frequency is near to or somewhat larger than the ionization potential of the target. The calculated photoelectron momentum distribution through numerical solution of time-dependent Schrödinger equation shows clear interference patterns. However, different from the cases of photon energy far larger than the ionization potential usually explored in experiments, the positions of interference maxima and minima for the present cases can not be explained by the interference of the electronic wave with the observed momentum between these two atomic centers of the molecule. By developing a theory model applicable for ionization of molecules in high-frequency laser field, we show that the Coulomb potential plays an important role in the momentum component of the emitting electronic wave near the nuclei, resulting in a remarkable shift of the interference pattern. A simple expression with Coulomb-modified momentum is obtained to predict the interference extrema, which gives suggestions for probing the structure and electron dynamics of the aligned molecule in single-photon ionization with lower photon energy.

Method of spatial-temporal coding of signals in the antenna array of millimeter-wave radar

Currently, most antenna systems are built based on MIMO technology. Its main advantage compared to classical antenna arrays is the possibility of a significant reduction of the number of physical transmitting and receiving channels keeping the resolution in angular coordinates. This feature is achieved due to the fact that the transmitting or receiving array is designed to be sparse, that is, the distance between the phase centers is significantly higher than half the wavelength. The cost of simplifying the design is presence of energy losses. In addition, the presence of several transmitting signals leads to the need to separate them from each other at the receiving position. The most popular method for separating orthogonal signals in MIMO arrays is code division signal separation. To implement this method, various types of orthogonal sequences are used. The most common are the Walsh, Fourier, and pseudo-random sequences. The use of orthogonal codes leads to the arising of multiple maximums in two-dimensional spectrum of the signal reflected from the object, exactly in dimension of Doppler frequency, with regular intervals. The number of maximums corresponds to the number of orthogonal sequences. Moreover, these maximums are formed in both case when using a sequence decoder and in the absence of a decoder. This feature is explained by the fact that when the sum of signals modulated in phase by Walsh sequences is multiplied by one of these sequences, one of the signals is demodulated, and the rest receive additional phase modulation. The level of additional maximum corresponds to the level of the main maximum. As a result, the ambiguity in determining the Doppler frequency appears. The indicated problem is very actual at the present time. To solve this problem, in the present paper the method of spatial-temporal coding of signals in millimeter-wave antenna array has been considered, based on the simultaneous operation of all sparse transmitters encoded by Walsh or Fourier sequences and spatial selection of transmitting beams by receiving one. The geometry of the placement of the elements of the transmitting and receiving antenna arrays corresponds to the geometry of the elements of MIMO array. At the same time, in contrast to the classical approach of beam forming for MIMO array, when individual transmitting antennas radiate orthogonal signals, and the irradiation of the target by each of them is considered separately, in the proposed method, the target is irradiated with a beam formed for transmission due to coherent spatial addition of signals from individual sparse transmitting array elements shifted in phase in accordance with the required slope of the phase front. As a result, the directivity pattern (DP) of the transmitting and receiving antenna is formed, which is equal to the product of the DP of the transmitting and receiving arrays. In this case, the interference maxima of DP of the transmitting antenna are at the zeros of DP of the receiving antenna, and the resulting DP coincides with the DP of the virtual receiving antenna formed using the classical MIMO approach. In the course of the studies and simulations, results have been obtained that show the effectiveness of the described method in terms of Doppler frequency ambiguity elimination when encoding signals in MIMO antenna arrays of the millimeter range.

Decoherent phonon effects in fast atom-surface scattering

The study of the influence of phonon-mediated processes on grazing-incidence fast atom diffraction (GIFAD) patterns is relevant for the use of GIFAD as a surface analysis technique. In this work, we apply the Phonon-Surface Initial Value Representation (P-SIVR) approximation to investigate lattice vibration effects on GIFAD patterns for the He/LiF(001) system at room temperature. The main features introduced by thermal lattice vibrations in the angular distributions of the scattered helium atoms are analyzed by keeping a fixed impact energy and varying the incidence angle to consider normal energies in the 0.1–3 eV range. In all the cases, thermal fluctuations introduce a wide polar spread that transforms the interference maxima into elongated strips. We found that the log-normal polar widths of the specular and outermost maxima do not depend on the normal energy, as it was experimentally observed. In addition, when the normal energy increases, not only the relative intensities of interference peaks are affected by the crystal vibrations, but also the visibility of the interference structures, which disappear completely for normal energies approximately equal to 3 eV. These findings qualitatively agree with recent experimental data, but the simulated polar widths underestimate the experimentally-derived limit, suggesting that there are other mechanisms, such as inelastic processes involving the net exchange of phonons, that contribute to the polar dispersion of the GIFAD patterns.

Universal rotation gauge via quantum anomalous Hall effect

Integer quantum Hall effect allows to gauge the resistance standard up to more than one part in a billion. Combining it with the speed of light, one obtains the fine-structure constant α ≈ 1/137, a dimensionless reference number that can be extracted from a physical experiment. Most exact notion of this value and especially its possible variation on the cosmological time scales is of enormous relevance for fundamental science. In an optical experiment, the fine-structure constant can be directly obtained as purely geometrical angle by measuring the quantized rotation of light polarization in two-dimensional quantum wells. In realistic conditions, high external magnetic fields have to be applied, which strongly affects possible attainable accuracy. An elegant solution of this problem is provided by quantum anomalous Hall effect where a universal quantized value can be obtained in zero magnetic field. Here, we measure the fine-structure constant in a direct optical experiment that requires no material adjustments or technical calibrations. By investigating the Faraday rotation at the interference maxima of the dielectric substrate, the angle close to one α is obtained at liquid helium temperatures without using a dilution refrigerator. Such calibration and parameter-free experiment provides a system-of-unit-independent access to universal quantum of rotation.

Interference patterns in ionization of Kramers–Henneberger atom

We combine IR pump and XUV probe laser pulses to visualize the Kramers–Henneberger (KH) state of the potassium atom. We demonstrate that ionization of such an atom exhibits some molecular-like features such as low order interference maxima in photoelectron momentum spectra. The locations of these maxima allow to estimate spatial dimensions of the KH atom and can be used for accurate calibration of high intensity laser fields. At the same time, we show that an analogy between the KH atom and a homo-nuclear diatomic molecule cannot be extended too far. In particular, higher order interference maxima are very difficult to observe in the case of the KH state. We attribute this to a particular structure of the KH potential which does not confine electron motion to a well-defined potential well unlike in real diatomic molecules.

Multi-angle spectrophotometry as a tool for determination of film parameters on single-layer structures

Ta–Si–C–N single-layer films have been synthesized by direct current magnetron sputtering on fused quartz substrates. The structural perfection of the films has been studied using X-ray diffraction, scanning electron microscopy and glow discharge optical emission spectroscopy. The optical parameters of the films have been studied using multi-angle spectrophotometry. The spectral dependences of the transmission coefficients of substrates and structures were measured for normal incidence of light in the wavelength range 200–2500 nm. We show that the transmittance spectrum of the specimen has an oscillating pattern due to interference phenomena that are typical for layered structures. The reflectance of the films and the substrates has been measured in the 200–2500 nm region for small incidence angles. The difference between the reflection coefficient at the maximum of the interference of the film and the corresponding reflection coefficient of the substrate at the same wavelength shows that the absorption in the film is low. A formula for determination of the film absorption index based on the measured parameters has been derived. The experimental and calculated data have been used for plotting the absorption spectra of the substrate, structure and film. Discrete refractive indices in the 400–1200 nm region have been calculated for reflections at two incidence angles by determining the positions of interference maxima in the reflectivity spectral responses. The results have been approximated using the Cauchy equation. The film thickness has been estimated to be df = 1046 nm ± 13%. The spectra of film extinction coefficients have been plotted with and without allowance for reflection. Obtained values of the refractive and absorption indices with and without reflection have been summarized in a table.

Impurities and other defects in correlated lattice electrons: Friedel oscillations and interference patterns

We study interference patterns and Friedel oscillations (FO) due to scattering from two or more localized impurities and scattering from extended inhomogeneities in the two-dimensional lattice systems of interacting fermions. Correlations between particles are accounted for by using an approximate method based on the real-space dynamical mean-field theory and a homogeneous self-energy approximation (HSEA), where the site-dependent part of the self-energy is neglected. We find that the interference maxima and minima change systematically as we vary the relative distance between the two impurities. At the same time, the increase of the interaction does not shift the position of interference fringes but only reduces their intensities. A comparison with the single impurity cases clearly shows complex patterns in FO fringes induced by additional multiple scattering processes. In the case of an extended step like potential the system becomes more homogeneous when the interaction increases. FO and interference patterns are not present in the Mott insulating phase in both single and many impurity models.

Reversible and Irreversible Laser Interference Patterning of MOF Thin Films

Laser interference patterning on top of a thin film and inside a crystal is a powerful tool today to create the desired patterns for optical data processing. Here, we demonstrate reversible and irreversible laser interference patterning on a metal-organic framework (MOF) thin film through the water desorption and thermal decomposition processes, respectively. The irreversible interference pattern with a period of the strips of up to 5 µm has been realized, and its morphology has been characterized using confocal Raman and reflection spectroscopy as well as atomic force microscopy. We revealed that reducing the distance between the interference maxima from 10.5 to a record of 5 µm for MOFs yields a 10-fold increase in the surface roughness of the irreversible pattern; on the other hand, the reversible laser pattern provides a completely non-destructive effect of variable optical contrast. The experimental results obtained open up prospects for the use of MOF crystals as photosensitive materials in the template drawing of the desired patterns for different application scopes.

2D Microwave Simulation Using Finite Differences

We derive a finite difference scheme to numerically simulate the propagation of microwaves in a 2D domain with reflective obstacles. An analysis of the consistency and stability of this method is performed, leading to a rigorous justification of its convergence. Following this, we discuss the boundary conditions and derive the mathematical form for energy flux. Finally, the numerical approximation is compared against prior experimental results. The simulation was found to have been able to predict the distribution of interference maxima and minima with some accuracy, but it was seen to be less effective in predicting average intensities. The advantages and disadvantages of these techniques are then discussed along with possible avenues for improvement.

Uniform subwavelength high-aspect ratio nanogratings on metal-protected bulk silicon produced by laser-induced periodic surface structuring

Formation of highly ordered nanostructures on a crystalline silicon surface is highly demanded for novel optoelectronic and nanophotonic designs pushing toward development of inexpensive and high-performing nanostructuring technologies. Here, we demonstrate that laser-induced periodic surface structuring of c-Si protected by a thin Hf over-layer allows one to fabricate extremely uniform high-aspect-ratio gratings with a characteristic periodicity of ≈900–950 and 450 nm. Corresponding ordering originates from interference of incident IR femtosecond laser pulses with surface plasmons as well as doubling of the grating period via interference of counter-propagating plasmons. A high-melting-point Hf over-layer regulates the c-Si ablation in the plasmon-mediated interference maxima and prevents its excessive oxidation upon multi-pulse exposure in ambient environment. Considering unique high-aspect ratio morphology (a depth-to-period ratio of up to 1.24 and a depth-to-width ratio of up to 8) of the reported nanogratings, their outstanding uniformity, and rather fast printing rate of ≈0.2 mm2/s as well as possibility for its further upscaling, we envision high practical applicability of this technology in novel optoelectronic devices, visible and near-IR optics, all-dielectric metasurfaces, and sensors.

Metallic nanoparticle-on-mirror: Multiple-band light harvesting and efficient photocurrent generation under visible light irradiation

We present a photoanode concept for photoelectrochemical (PEC) water splitting based on metal nanoparticles (Au, Ag, Cu) deposited on a Ti mirror (NPoM) to photosensitize an intermediate TiO2 layer to induce the harvesting of light with sub-bandgap photon energies. The generation of hot electron-hole pairs in metallic nanostructures can occur either by intraband excitation, i.e., plasmon electrons, or by the interband transition of the d-band electrons to the unoccupied conduction band states. Our results demonstrate that the underlying Ti mirror significantly amplifies the PEC activity of such NPoM systems in the visible spectral range. We show that the PEC enhancement in the visible spectral range is not limited to the intraband excitations but is affected mainly by the light trapping pathway within the TiO2 layer, i.e. due to a favorable interplay between thin-film interference cavity modes with both intraband and interband excitations. Among tested metals, Cu and Ag NPs demonstrate a ~3-fold higher enhancement factor than that of Au NPs, while in both former cases the nature of the excited electrons is different. The experimentally determined internal quantum efficiency demonstrates alternating behavior with wavelength showing higher efficiencies at short wavelengths, which is attributed to the reduced Schottky barrier of the NPoMs at constructive interference maxima.

A Bi-Axial Quantum State That Controls Molecular Collisions Like a Double-Slit Interferometer

To control molecular scattering, we consider hydrogen molecules prepared in a coherent superposition of m states within a single rovibrational (v, j) energy eigenstate using Stark-induced adiabatic Raman passage (SARP). Specifically, SARP can prepare a bi-axial state of the HD molecule in which the HD bond axis exists simultaneously in two possible alignments at right angles to one another with a well-defined relative phase. We show that scattering from this biaxial state will interfere, resulting in a φ -dependent scattering intensity distribution, where φ is the azimuthal angle about the collision velocity direction. Using the scattering matrix extracted from our experiments on the rotationally inelastic collisions of quantum state prepared HD at low temperatures, we calculate the differential scattering cross-section dσ/dΩ, which shows an interference pattern as function of θ and φ in the image plane perpendicular to the collision velocity. The calculated scattering image shows that scattering from the bi-axial state directs molecules along well-defined angles, corresponding to interference maxima. Thus, the bi-axial state behaves like a double slit for molecular scattering. Moreover, by rotating the polarizations of the SARP preparation lasers, we can control the interference thereby altering the scattering angular distribution. This molecular interferometer, which experimentally measures the relative phases of the scattering matrix elements, allows a direct test of theoretical calculations on important, fundamental collision processes.

Electron interference in atomic ionization by two crossing polarized ultrashort pulses

Formation of geometrically regular interference patterns in the photoelectron momentum distributions (PMDs) corresponding to the photoionization of atoms by two single-color, crossing ultrashort pulses is investigated both analytically and numerically. It is shown that, in contrast to the photoionization by monochromatic pulses, PMDs for the ionization by crossing and co-propagating broadband pulses are essentially different (unless both pulses are linearly polarized), namely, when one pulse is linearly polarized along the propagation direction, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}$, of the circularly polarized (CP) pulse, then interference maxima (minima) of the ionization probability have the form of three-dimensional single-arm regular spirals which are wound along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbf{k}}$. Next, the interference maxima (minima) of the ionization probability by a pair of crossing elliptically polarized pulses have the form of either Newton's rings or two-arm Fermat's spirals, depending on the position of a detection plane. Remarkably, these regular patterns occur only for certain values of the pulse ellipticities, and they become distorted for CP pulses. For both above-mentioned pulse configurations, the features of interference patterns depend on the time delay between pulses, their relative electric field amplitude, and relative carrier-envelope phase. Our predictions, illustrated by the numerical results for the ionization of H and He atoms by two orthogonal pulses, are quite general and we expect them to be valid for the ionization of any randomly oriented atomic or molecular target.