Angular Spectrum Research Articles

Orietation-controlled synthesis and Raman study of 2D SnTe

Tin telluride (SnTe), as a narrow bandgap semiconductor material, has great potential for developing photodetectors with wide spectra and ultra-fast response. At the same time, it is also an important topological crystal insulator material, with different topological surface states on several common surfaces. Here, we introduce different Sn sources and control the growth of regular SnTe nanosheets along the (100) and (111) planes through the atmospheric pressure chemical vapor deposition method. It has been proven through various characterizations that the synthesized SnTe is a high-quality single crystal. In addition, the angular resolved Raman spectra of SnTe nanosheets grown on different crystal planes are first demonstrated. The experimental results showed that square SnTe nanosheets grown along the (100) plane exhibit in-plane anisotropy. At the same time, we use micro-nanofabrication technology to manufacture SnTe-based field effect transistors and photodetectors to explore their electrical and optoelectronic properties. It has been confirmed that transistors based on grown SnTe nanosheets exhibit p-type semiconductor characteristics and have a high response to infrared light. This work provides a new approach for the controllable synthesis of SnTe and adds new content to the research of SnTe-based infrared detectors.

Minkowski functionals of CMB polarization intensity with pynkowski: theory and application to Planck and future data

ABSTRACT The angular power spectrum of the cosmic microwave background (CMB) anisotropies is a key tool to study the Universe. However, it is blind to the presence of non-Gaussianities and deviations from statistical isotropy, which can be detected with other statistics such as Minkowski functionals (MFs). These tools have been applied to CMB temperature and E-mode anisotropies with no detection of deviations from Gaussianity and isotropy. In this work, we extend the MF formalism to the CMB polarization intensity, P2 = Q2 + U2. We use the Gaussian kinematic formula to derive the theoretical predictions of MFs for Gaussian isotropic fields. We develop a software that computes MFs on P2healpix maps and apply it to simulations to verify the robustness of both theory and methodology. We then estimate MFs of P2 maps from Planck, both in pixel space and needlet domain, comparing them with realistic simulations that include CMB and instrumental noise residuals. We find no significant deviations from Gaussianity or isotropy in Planck CMB polarization intensity. However, MFs could play an important role in the analysis of CMB polarization measurements from upcoming experiments with improved sensitivity. Therefore, we forecast the ability of MFs applied to P2 maps to detect much fainter non-Gaussian anisotropic signals than with Planck data for two future complementary experiments: the LiteBIRD satellite and the ground-based Simons Observatory. We publicly release the software to compute MFs in arbitrary scalar healpix maps as a fully documented python package called pynkowski.

The influence of bone model geometries on the determination of skull acoustic properties.

In this study, we investigated the impact of various simulated skull bone geometries on the determination of skull speed of sound and acoustic attenuation values via optimization using transmitted pressure amplitudes beyond the bone. Using the hybrid angular spectrum method (HAS), we simulated ultrasound transmission through four model sets of different geometries involving sandwiched layers of diploë and cortical bone in addition to three models generated from CT images of ex-vivo human skull-bones. We characterized cost-function solution spaces for each model and, using optimization, found that when a model possessed appreciable variations in resolvable layer thickness, the predefined attenuation coefficients could be found with low error (RMSE < 0.01 Np/cm). However, we identified a spatial frequency cutoff in the models' geometry beyond which the accuracy of the property determination begins to fail, depending on the frequency of the ultrasound source. There was a large increase in error of the attenuation coefficients determined by the optimization when the variations in layer thickness were above the identified spatial frequency cutoffs, or when the lateral variations across the model were relatively low in amplitude. For our limited sample of three CT-image derived bone models, the attenuation coefficients were determined successfully. The speed of sound values were determined with low error for all models (including the CT-image derived models) that were tested (RMSE < 0.4 m/s). These results illustrate that it is possible to determine the acoustic properties of two-component models when the internal bone structure is taken into account and the structure satisfies the spatial frequency constraints discussed.

General diffraction integral for converging freeform vectorial fields

Herein it is presented a new vector diffraction integral capable to compute the diffraction patterns for aspheric and freeform wavefronts, with different pupil shapes, and different polarization states. The aforementioned vector diffraction integral is based on the energy conservation theorem, the far field approximation, and the angular spectrum representation of optical fields. The integral is validated through illustrative examples whose results are as expected and coincides with the related works.

GW_CLASS: Cosmological Gravitational Wave Background in the cosmic linear anisotropy solving system

The anisotropies of the Cosmological Gravitational Wave Background (CGWB) retain information about the primordial mechanisms that source the gravitational waves and about the geometry and the particle content of the universe at early times. In this work, we discuss in detail the computation of the angular power spectra of CGWB anisotropies and of their cross correlation with Cosmic Microwave Background (CMB) anisotropies, assuming different processes for the generation of these primordial signals. We present an efficient implementation of our results in a modified version of CLASS which will be publicly available. By combining our new code GW_CLASS with MontePython, we forecast the combined sensitivity of future gravitational wave interferometers and CMB experiments to the cosmological parameters that characterize the cosmological gravitational wave background.

A 3D Numerical Study of Anisotropies in Supernova Remnants

We develop a suite of 3D hydrodynamic models of supernova remnants (SNRs) expanding against the circumstellar medium (CSM). We study the Rayleigh–Taylor instability forming at the expansion interface by calculating an angular power spectrum for each of these models. The power spectra of young SNRs are seen to exhibit a dominant angular mode, which is a diagnostic of their ejecta density profile as found by previous studies. The steep scaling of power at smaller modes and the time evolution of the spectra are indicative of the absence of a turbulent cascade. Instead, as the time evolution of the spectra suggests, they may be governed by an angular mode-dependent net growth rate. We also study the impact of anisotropies in the ejecta and in the CSM on the power spectra of velocity and density. We confirm that perturbations in the density field (whether imposed on the ejecta or the CSM) do not influence the anisotropy of the remnant significantly unless they have a very large amplitude and form large-scale coherent structures. In any case, these clumps can only affect structures on large angular scales. The power spectrum on small angular scales is completely independent of the initial clumpiness and governed only by the growth and saturation of the Rayleigh–Taylor instability.

Primordial non-Gaussianity f NL and anisotropies in scalar-induced gravitational waves

Primordial non-Gaussianity encodes vital information of the physics of the early universe, particularly during the inflationary epoch. To explore the local-type primordial non-Gaussianity f NL, we study the anisotropies in gravitational wave background induced by the linear cosmological scalar perturbations during radiation domination in the early universe. We provide the first complete analysis to the angular power spectrum of such scalar-induced gravitational waves. The spectrum is expressed in terms of the initial inhomogeneities, the Sachs-Wolfe effect, and their crossing. It is anticipated to have frequency dependence and multipole dependence, i.e., Cℓ (ν) ∝ [ℓ(ℓ+1)]-1 with ν being a frequency and ℓ referring to the ℓ-th spherical harmonic multipole. In particular, the initial inhomogeneites in this background depend on gravitational-wave frequency. These properties are potentially useful for the component separation, foreground removal, and breaking degeneracies in model parameters, making the non-Gaussian parameter f NL measurable. Further, theoretical expectations may be tested by space-borne gravitational-wave detectors in future.

Phase holograms for the three-dimensional patterning of microparticles in a traveling wave field

Acoustic fields can generate radiation forces that can align particles in patterns. Forces from standing waves pattern particles in three dimensions (3-D) at either nodal or anti-nodal regions. These patterns can be utilized to form 3-D microstructures for applications in tissue engineering or fabrication of layered materials. However, standing waves require more than one transducer or a reflector, which can complicate implementation. Here, we developed a method to suspend and align microspheres using a traveling wave from a single transducer. Acoustic fields were shaped to align polyethylene microspheres mimicking tissue cells in parallel planes along the axis of the transducer. A Bessel-like beam was developed using diffraction theory and an iterative angular spectrum approach were used to design phase holograms to shape pressure fields. Gor’kov potential was used to calculate radiation forces while minimizing the axial forces to create a stable trap. The resulting pressure fields and particle patterns matched predictions with a similarity index &amp;gt;0.92, where 1 is a perfect match. The transverse radiation force was ten times each microsphere’s weight and comparable to the standing wave radiation forces. Next steps are in vivo implementation of cell patterning for tissue engineering. [Work supported by NIH K25-DK132416 and P01-DK043881.]

Focusing performances of high numerical aperture Fresnel zone plates under different immersion media

The focusing performances of high-numerical-aperture (NA) Fresnel zone plates (FZP) under different immersion media are investigated by combining the vectorial angular spectrum (VAS) theory and the finite-difference time-domain method. It has been found that as the refractive index deviation increases, the focus approximately linearly shifts along the positive z-axis. Simultaneously, the transverse size of the focusing spot gradually decreases, and super-resolution focusing is realized. However, the peak intensity declines with an increase in the refractive index. In addition, when the deviation of the refractive index of the actual immersion medium from the design value is less than about 30%, VAS theory can correctly estimate the focusing light field distribution, except when the FZP has only one or two transparent annuli. On the contrary, VAS theory cannot achieve an accurate prediction when the deviation is larger. These findings will benefit the practical application of high-NA FZPs.

Efficient post-processing of electromagnetic plane wave simulations to model arbitrary structured beams incident on axisymmetric structures

The study of an optical beam interacting with material structures is a fundamental of nanophotonics. Computational electromagnetic solvers facilitate the rapid calculation of the scattering from material structures with arbitrary geometry and complexity, but have limited efficiency when employing structured excitation fields. We have developed a post-processing method and package that can efficiently calculate the full three-dimensional electric and magnetic fields for any optical beam incident on a particle or structure with at least one axis of continuous rotational symmetry, called an axisymmetric body (such as a sphere, cylinder, cone, torus or surface). Provided an initial batch of plane wave simulations is computed, this open-source package combines data from computational electromagnetic solvers in a post-processing fashion using the angular spectrum representation to create arbitrarily structured beams, including vector vortex beams. Any and all possible incident beams can be generated from the initial batch of PWSs, without the need for further simulations. This allows for efficiently performing parameter sweeps such as changing the angle of illumination or translating the particle position relative to the beam, all in post-processing, with no need for additional time-consuming simulations. We demonstrate some applications by numerically calculating optical force and torque maps for a spherical plasmonic nanoparticle in a tightly focused Gaussian beam, a plasmonic nanocone in an azimuthally polarised beam and compute the fields of a non-paraxial Laguerre–Gaussian vortex beam reflecting on a multilayered surface. We believe this package, called BEAMS, is a valuable tool for rapidly quantifying electromagnetic systems that are beyond traditional analytical methods.

Influence of optical surface distortion in a cylindrical Offner stretcher on the far-field signal-to-noise ratio.

In a stretcher, the surface distortion of the optical elements can introduce spectral phase modulations into the laser, which can affect the laser's signal-to-noise ratio. In this paper, by combining ray tracing methods and angular spectrum diffraction methods, the impact of the mid-frequency surface distortion of the optical elements in an cylindrical Offner stretcher on the far-field signal-to-noise ratio of the laser is simulated. The results show that reducing the spatial chirp on the convex cylindrical mirror can effectively improve the far-field signal-to-noise ratio of the laser, and two methods to improve the far-field signal-to-noise ratio are presented.

Cosmological constraints from low redshift 21 cm intensity mapping with machine learning

ABSTRACT The future 21 cm intensity mapping observations constitute a promising way to trace the matter distribution of the Universe and probe cosmology. Here, we assess its capability for cosmological constraints using as a case study the BINGO radio telescope, that will survey the Universe at low redshifts (0.13 &amp;lt; z &amp;lt; 0.45). We use neural networks (NNs) to map summary statistics, namely, the angular power spectrum (APS) and the Minkowski functionals (MFs), calculated from simulations into cosmological parameters. Our simulations span a wide grid of cosmologies, sampled under the ΛCDM scenario, {Ωc, h}, and under an extension assuming the Chevallier–Polarski–Linder (CPL) parametrization, {Ωc, h, w0, wa}. In general, NNs trained over APS outperform those using MFs, while their combination provides 27 per cent (5 per cent) tighter error ellipse in the Ωc–h plane under the ΛCDM scenario (CPL parametrization) compared to the individual use of the APS. Their combination allows predicting Ωc and h with 4.9 and 1.6 per cent fractional errors, respectively, which increases to 6.4 and 3.7 per cent under CPL parametrization. Although we find large bias on wa estimates, we still predict w0 with 24.3 per cent error. We also confirm our results to be robust to foreground contamination, besides finding the instrumental noise to cause the greater impact on the predictions. Still, our results illustrate the capability of future low-redshift 21 cm observations in providing competitive cosmological constraints using NNs, showing the ease of combining different summary statistics.

Focusing property of autofocusing Bessel beams.

We introduce what we believe to be a new family of abruptly autofocusing waves named autofocusing Bessel beams (ABBs). Since the beams only strongly influence the area near the focus, it holds promise for medical laser treatment and optical tweezers. By the angular spectrum method, ABBs are proved to be a class solution for the Helmholtz equation. The focal length is well-defined and easily tuned in our mathematical description. Under the finite energy limitation, the abruptly autofocusing and vortex characteristics of Gaussian-modulated ABBs are studied. Interestingly, we found a kind of abruptly autofocusing waves focusing twice on the propagation axis, which is formed by an ABB passing through a focusing lens. Dual-focus ABBs make it possible for a single laser to manipulate two particles on the propagation axis simultaneously. In the experiment, the autofocusing of ABBs and the dual focus of ABBs passing through a focusing lens are observed. This article provides a theoretical model and experimental protocol for studying abruptly autofocusing waves.

Real-time hybrid angular-interrogation surface plasmon resonance sensor in the near-infrared region for wide dynamic range refractive index sensing

Herein, we integrated angle-scanning surface plasmon resonance (SPR) and angle-fixed SPR as a hybrid angular-interrogation SPR to enhance the sensing performance. Galvanometer-mirror-based beam angle scanning achieves a 100-Hz acquisition rate of both the angular SPR reflectance spectrum and the angle-fixed SPR reflectance, whereas the use of near-infrared light enhances the refractive index (RI) sensitivity, range, and precision compared with visible light. Simultaneous measurement of the angular SPR reflectance spectrum and angle-fixed SPR reflectance boosts the RI change range, RI resolution, and RI accuracy to 10–1–10–6 RIU, 2.24 × 10−6 RIU, and 5.22 × 10−6 RIU, respectively. The proposed hybrid SPR is a powerful tool for wide-dynamic-range RI sensing with various applications.

A Simulation of Calibration and Map-making Errors of the Tianlai Cylinder Pathfinder Array

The Tianlai cylinder array is a pathfinder for developing and testing 21 cm intensity mapping techniques. In this paper, we use numerical simulation to assess how its measurement is affected by thermal noise and the errors in calibration and map-making process, and the error in the sky map reconstructed from a drift scan survey. Here we consider only the single frequency, unpolarized case. The beam is modeled by fitting to the electromagnetic simulation of the antenna, and the variations of the complex gains of the array elements are modeled by Gaussian processes. Mock visibility data are generated and run through our data processing pipeline. We find that the accuracy of the current calibration is limited primarily by the absolute calibration, where the error comes mainly from the approximation of a single dominating point source. We then studied the m-mode map-making with the help of Moore–Penrose inverse. We find that discarding modes with singular values smaller than a threshold could generate visible artifacts in the map. The impacts of the residue variation of the complex gain and thermal noise are also investigated. The thermal noise in the map varies with latitude, being minimum at the latitude passing through the zenith of the telescope. The angular power spectrum of the reconstructed map show that the current Tianlai cylinder pathfinder, which has a shorter maximum baseline length in the North–South direction, can measure modes up to l ≲ 2π b NS/λ ∼ 200 very well, but would lose a significant fraction of higher angular modes when noise is present. These results help us to identify the main limiting factors in our current array configuration and data analysis procedure, and suggest that the performance can be improved by reconfiguration of the array feed positions.

End-to-End Diverse Metasurface Design and Evaluation Using an Invertible Neural Network.

Employing deep learning models to design high-performance metasurfaces has garnered significant attention due to its potential benefits in terms of accuracy and efficiency. A deep learning-based metasurface design framework typically comprises a forward prediction path for predicting optical responses and a backward retrieval path for generating geometrical configurations. In the forward design path, a specific geometrical configuration corresponds to a unique optical response. However, in the inverse design path, a single performance metric can correspond to multiple potential designs. This one-to-many mapping poses a significant challenge for deep learning models and can potentially impede their performance. Although representing the inverse path as a probabilistic distribution is a widely adopted method for tackling this problem, accurately capturing the posterior distribution to encompass all potential solutions remains an ongoing challenge. Furthermore, in most pioneering works, the forward and backward paths are captured using separate models. However, the knowledge acquired from the forward path does not contribute to the training of the backward model. This separation of models adds complexity to the system and can hinder the overall efficiency and effectiveness of the design framework. Here, we utilized an invertible neural network (INN) to simultaneously model both the forward and inverse process. Unlike other frameworks, INN focuses on the forward process and implicitly captures a probabilistic model for the inverse process. Given a specific optical response, the INN enables the recovery of the complete posterior over the parameter space. This capability allows for the generation of novel designs that are not present in the training data. Through the integration of the INN with the angular spectrum method, we have developed an efficient and automated end-to-end metasurface design and evaluation framework. This novel approach eliminates the need for human intervention and significantly speeds up the design process. Utilizing this advanced framework, we have effectively designed high-efficiency metalenses and dual-polarization metasurface holograms. This approach extends beyond dielectric metasurface design, serving as a general method for modeling optical inverse design problems in diverse optical fields.

A Systematic Summary and Comparison of Scalar Diffraction Theories for Structured Light Beams

Structured light beams have recently attracted enormous research interest for their unique properties and potential applications in optical communications, imaging, sensing, etc. Since most of these applications involve the propagation of structured light beams, which is accompanied by the phenomenon of diffraction, it is very necessary to employ diffraction theories to analyze the obstacle effects on structured light beams during propagation. The aim of this work is to provide a systematic summary and comparison of the scalar diffraction theories for structured light beams. We first present the scalar fields of typical structured light beams in the source plane, including the fundamental Gaussian beams, higher-order Hermite–Gaussian beams, Laguerre–Gaussian vortex beams, non-diffracting Bessel beams, and self-accelerating Airy beams. Then, we summarize and compare the main scalar diffraction theories of structured light beams, including the Fresnel diffraction integral, Collins formula, angular spectrum representation, and Rayleigh–Sommerfeld diffraction integral. Finally, based on these theories, we derive in detail the analytical propagation expressions of typical structured light beams under different conditions. In addition, the propagation of typical structured light beams is simulated. We hope this work can be helpful for the efficient study of the propagation of structured light beams.

Generation of integer and fractional vortex beams based on liquid crystal electronically reconfigurable spiral phase plates.

The manufacturing and characterization of a large-size 72-electrode liquid crystal-based reconfigurable spiral phase plate (SPP) is presented. The SPP is addressed by a custom-made driver with 72 independent channels, which allows for the generation of any arbitrary integer or fractional optical vortex beam with topological charges ranging from -24 to +24. The 25 mm diameter device is fabricated using direct laser writing, leading to a fill factor over 99%. The device performance and flexibility exceed previous transparent reconfigurable SPP in terms of size, tuning range, and fill factor. The device and the light path have been simulated using the angular spectrum propagation method, showing excellent correspondence.

Capturing Statistical Isotropy Violation with Generalized Isotropic Angular Correlation Functions of Cosmic Microwave Background Anisotropy

The exquisitely measured maps of fluctuations in the cosmic microwave background (CMB) present the possibility of systematically testing the principle of statistical isotropy of the Universe. A systematic approach based on strong mathematical formulation allows any nonstatistical isotropic (nSI) feature to be traced to the nature of physical effects or observational artifacts. Bipolar spherical harmonics (BipoSH) representation has emerged as an overarching general formalism for quantifying the departures from statistical isotropy for a field on a 2D sphere. We adopt a little-known reduction of the BipoSH functions, dubbed minimal harmonics in the original paper by Manakov et al. We demonstrate that this reduction technique of BipoSH leads to a new generalized set of isotropic angular correlation functions referred to here as minimal BipoSH functions that are observable quantifications of nSI features in a sky map. This paper presents a novel observable quantification of deviation from statistical isotropy in terms of generalized angular correlation functions that are compact and complementary to the BipoSH spectra that generalize the angular power spectrum of CMB fluctuations.

The Simons Observatory: a new open-source power spectrum pipeline applied to the Planck legacy data

We present a reproduction of the Planck 2018 angular power spectra at ℓ > 30, and associated covariance matrices, for intensity and polarization maps at 100, 143 and 217 GHz. This uses a new, publicly available, pipeline that is part of the PSpipe package. As a test case we use the same input maps, ancillary products, and analysis choices as in the Planck 2018 analysis, and find that we can reproduce the spectra to 0.1σ precision, and the covariance matrices to 10%. We show that cosmological parameters estimated from our re-derived products agree with the public Planck products to 0.1σ, providing an independent cross-check of the Planck team's analysis. Going forward, the publicly-available code can be easily adapted to use alternative input maps, data selections and analysis choices, for future optimal analysis of Planck data with new ground-based Cosmic Microwave Background data.