Angular Spectrum Research Articles

Multiplane Holographic Imaging Using the Spatial Light Modulator

The optimization of imaging accuracy and speed is a crucial issue in the development of computer-generated holograms (CGH) for three-dimensional (3D) displays. This paper proposes an optimized iterative algorithm based on the angular spectrum method (ASM) to achieve high-quality holographic imaging across multiple planes. To effectively utilize spatial resources for multi-image reconstruction and mitigate the speckle noise caused by the overlapping of target images, constraint factors are introduced between different layers within the same region. The seeking rule of the constraint factor is also analyzed. By utilizing both constraint factors and variable factors, the presented method is able to calculate phase holograms for target figure imaging at four different planes. Simulation and experimental results demonstrate that the proposed method effectively improves the overall quality of the different planes, thus holding great potential for wide-ranging applications in the field of holography.

Independent wavefront manipulation of broadband spin-decoupled metasurfaces based on equivalent circuit model

Various functional meta-devices have exhibited powerful manipulation of orbital angular momentum spectrums, but they are still faced with the issue of inherent spin-correlated characteristic and lack of effective method to design metasurface. In this work, a broadband spin-decoupled metasurface is presented to realize independent regulation of dual circularly polarized waves. Based on the transmission line theory, an equivalent circuit model of meta-atom is proposed to establish the relationship between reflection coefficients and structural parameters. By utilizing the model, a group of meta-atoms has been designed with a step phase difference of 45°, which can form a 3-bit coding metasurface. The proposed meta-atoms have a broad frequency band covering 11.56 − 18.17 GHz (44.5%). Moreover, the bifunctional reflection-type metasurfaces are constructed for producing the vortex waves along the +z axis, the off-axis pencil beams, and their synthetic beams. Based on the Fourier transform analysis, the mode purity and the electric field distribution of the generated beams are discussed in detail. The experimental measurements have good agreement with the simulation results, thus revealing the effectiveness of the proposed methodology to design metasurface.

Measurement of the cross-correlation angular power spectrum between the stochastic gravitational wave background and galaxy overdensity

Measurement of the cross-correlation angular power spectrum between the stochastic gravitational wave background and galaxy overdensity

Towards 21-cm intensity mapping at z = 2.28 with uGMRT using the tapered gridded estimator – III. Foreground removal

ABSTRACT Neutral hydrogen (${\rm H\, \small {I}}$) 21-cm intensity mapping (IM) is a promising probe of the large-scale structures in the Universe. However, a few orders of magnitude brighter foregrounds obscure the IM signal. Here, we use the tapered gridded estimator to estimate the multifrequency angular power spectrum Cℓ(Δν) from a $24.4\hbox{-} \rm {MHz}$ bandwidth upgraded Giant Metrewave Radio Telescope Band 3 data at $432.8\ \rm {MHz}$. In Cℓ(Δν) foregrounds remain correlated across the entire Δν range, whereas the 21-cm signal is localized within Δν ≤ [Δν] (typically, 0.5–1 MHz). Assuming the range Δν > [Δν] to have minimal 21-cm signal, we use Cℓ(Δν) in this range to model the foregrounds. This foreground model is extrapolated to Δν ≤ [Δν], and subtracted from the measured Cℓ(Δν). The residual [Cℓ(Δν)]res in the range Δν ≤ [Δν] is used to constrain the 21-cm signal, compensating for the signal loss from foreground subtraction. [Cℓ(Δν)]res is found to be noise-dominated without any trace of foregrounds. Using [Cℓ(Δν)]res, we constrain the 21-cm brightness temperature fluctuations Δ2(k), and obtain the 2σ upper limit $\Delta _{\rm UL}^2(k)\le (18.07)^2\ \rm {mK^2}$ at $k=0.247\ \rm {Mpc}^{-1}$. We further obtain the 2σ upper limit $[\Omega _{{\rm H\, \small {I}}}b_{{\rm H\, \small {I}}}]_{\rm UL}\le 0.022$, where $\Omega _{{\rm H\, \small {I}}}$ and $b_{{\rm H\, \small {I}}}$ are the comoving ${\rm H\, \small {I}}$ density and bias parameters, respectively. Although the upper limit is nearly 10 times larger than the expected 21-cm signal, it is 3 times tighter over previous works using foreground avoidance on the same data.

Multiclustering needlet ILC for CMB B-mode component separation

ABSTRACT The Cosmic Microwave Background (CMB) primordial B-mode signal is predicted to be much lower than the polarized Galactic emission (foregrounds) in any region of the sky pointing to the need for sophisticated component separation methods. Among them, the blind Needlet Internal Linear Combination (NILC) has great relevance given our current poor knowledge of the B-mode foregrounds. However, the expected level of spatial variability of the foreground spectral properties complicates the NILC subtraction of the Galactic contamination. We therefore propose a novel extension of the NILC approach, the Multiclustering NILC (MC-NILC), which performs NILC variance minimization on separate regions of the sky (clusters) properly chosen to have similar spectral properties of the B-mode Galactic emission within them. Clusters are identified thresholding either the ratio of simulated foregrounds-only B modes (ideal case) or the one of cleaned templates of Galactic emission obtained from realistic simulations. In this work we present an application of MC-NILC to the future LiteBIRD satellite, which targets the observation of both reionization and recombination peaks of the primordial B-mode angular power spectrum with a total error on the tensor-to-scalar ratio δr < 0.001. We show that MC-NILC provides a CMB solution with residual foreground and noise contamination that is significantly lower than the NILC one and the primordial signal targeted by LiteBIRD at all angular scales for the ideal case and at the reionization peak for a realistic ratio. Thus, MC-NILC will represent a powerful method to mitigate B-mode foregrounds for future CMB polarization experiments.

Diffraction Impact onto Regularized Plasma Channel Formation by Femtosecond Laser Filamentation

Focused femtosecond beam filamentation after amplitude masks has been studied experimentally and numerically. We deduced conditions (energy per hole, diameter and geometrical composition of holes, focal length) providing for the formation of the regularized bundle of filaments or single on-axis filament at the given pulse duration and beam diameter. We showed that a light channel with small diameter (∼200 μm) and overcritical peak power may be formed well before both the focal distance and the Marburger length, and this channel collapses due to self-focusing and forms the filament. The start position of such a filament can be predicted based on the linear propagation equation, while a more sophisticated non-linear approach that takes into account the Kerr nonlinearity, plasma effects, etc., helps to describe the temporal structure of a filament, its frequency, and its angular spectrum.

CONCERTO: Extracting the power spectrum of the [CII] emission line

Context. CONCERTO is the first experiment to perform a [CII] line intensity mapping (LIM) survey on the COSMOS field to target z > 5.2. Measuring the [CII] angular power spectrum allows us to study the role of dusty star-forming galaxies in the star formation history during the epochs of Reionization and post-Reionization. The main obstacle to this measurement is the contamination by bright foregrounds: the dust continuum emission and atomic and molecular lines from foreground galaxies at z ≲ 3. Aims. We evaluate our ability to retrieve the [CII] signal in mock observations of the sky using the Simulated Infrared Dusty Extragalactic Sky (SIDES), which covers the mid-infrared to millimetre range. We also measure the impact of field-to-field variance on the residual foreground contamination. Methods. We compared two methods for dealing with the dust continuum emission from galaxies (i.e. the cosmic infrared background fluctuations): the standard principal component analysis (PCA) and the asymmetric re-weighted penalized least-squares (arPLS) method. For line interlopers, the strategy relies on masking low-redshift galaxies using the instrumental beam profile and external catalogues. As we do not have observations of CO or deep-enough classical CO proxies (such as LIR), we relied on the COSMOS stellar mass catalogue, which we demonstrate to be a reliable CO proxy for masking. To measure the angular power spectrum of masked data, we adapted the P of K EstimatoR (POKER) from cosmic infrared background studies and discuss its use on LIM data. Results. The arPLS method achieves a reduction in the cosmic infrared background fluctuations to a sub-dominant level of the [CII] power at z ∼ 7, a factor of > 70 below our fiducial [CII] model. When using the standard PCA, this factor is only 0.7 at this redshift. The masking lowers the power amplitude of line contamination down to 2 × 10−2 Jy2 sr−1. This residual level is dominated by faint undetected sources that are not clustered around the detected (and masked) sources. For our [CII] model, this results in a detection at z = 5.2 with a power ratio [CII]/(residual interlopers) = 62 ± 32 for a 22% area survey loss. However, at z = 7, [CII]/(residual interlopers) = 2.0 ± 1.4, due to the weak contrast between [CII] and the residual line contamination. Thanks to the large area covered by SIDES-Uchuu, we show that the power amplitude of line residuals varies by 12–15% for z = 5.2 − 7, which is less than the field-to-field variance affecting [CII] power spectra. Conclusions. We present an end-to-end simulation of the extragalactic foreground removal that we ran to detect the [CII] at high redshift via its angular power spectrum. We show that cosmic infrared background fluctuations are not a limiting foreground for [CII] LIM. On the contrary, the CO and [CI] line contamination severely limits our ability to accurately measure the [CII] angular power spectrum at z ≳ 7.

The observed number counts in luminosity distance space

Next generation surveys will provide us with an unprecedented number of detections of supernovae Type Ia and gravitational wave merger events. Cross-correlations of such objects offer novel and powerful insights into the large-scale distribution of matter in the universe. Both of these sources carry information on their luminosity distance, but remain uninformative about their redshifts; hence their clustering analyses and cross-correlations need to be carried out in luminosity distance space, as opposed to redshift space. In this paper, we calculate the full expression for the number count fluctuation in terms of a perturbation to the observed luminosity distance. We find the expression to differ significantly from the one commonly used in redshift space. Furthermore, we present a comparison of the number count angular power spectra between luminosity distance and redshift spaces. We see a wide divergence between the two at large scales, and we note that lensing is the main contribution to such differences. On such scales and at higher redshifts the difference between the angular power spectra in luminosity distance and redshift spaces can be roughly 50%. We also investigate cross-correlating different redshift bins using different tracers, i.e. one in luminosity distance space and one in redshift, simulating the cross-correlation angular power spectrum between background gravitational waves/supernovae and foreground galaxies. Finally, we show that in a cosmic variance limited survey, the relativistic corrections to the density-only term ought to be included.

Spin angular momentum and angular harmonics spectrum of two-order polarization vortices at the tight focus

We investigate the spin angular momentum (SAM) of two-order cylindrical vector beams at the tight focus. Such beams are a generalization of the conventional cylindrical vector beams since the transverse field components on the Cartesian axes have different polarization orders. Using the Richards-Wolf approximation, we derive an expression for the longitudinal component of the SAM density distribution. We show that if the polarization indices are of different parity then, an optical spin Hall effect arises at the tight focus, meaning that alternating areas with positive and negative SAM are originated although the initial light field is linearly polarized. We study the angular harmonics spectrum of all the components of the focused light field and determine the predominant angular harmonics. Then, neglecting the insignificant harmonics, we define the shape of the longitudinal component of the SAM density distribution and demonstrate the possibility of generating a focal SAM distribution where the areas with positive and negative SAM reside on a circle as alternating pairs or separated into different half-circles.

Downlink massive full dimension-multiple input multiple output downlink beamforming analysis at 3.5 GHz using coordinated ON-OFF switching

<p><span lang="EN-US">The long-term evolution and advancement (LTE-A) of the 5G wireless network depends critically on energy consumption. Many existing solutions focus on limiting power constraints and consequently system coverage. So, improving the antenna array elements of the base station (BS) can solve this issue. In this paper, introduce a coordinated ON-OFF switching method in the massive full dimensional multiple input multiple output (massive-FD-MIMO) system. It enhances the radiation pattern of the antenna array element by adjusting the angular power spectra at the BS. By the way, it allows to select the minimum number of antennas for effective beamforming toward specific user equipment’s (UEs). In this context, part of antenna element should be active mode and remining should be sleep mode at the time of signal beamforming. The multipath spatial profiles are decided the beamforming frequency band with minimize energy consumption. As part of the method, we used a conjugated beamforming with power optimization scheme to determine the individual antenna potential and fading channel condition, power optimization is performed. This method quality of service, reliability, energy consumption and data rate can all be evaluated by experimenting with different-sized antenna arrays such as 16×16, 32×32, 64×64 and 128×128.</span></p>

The Hawking energy in a perturbed Friedmann-Lemaître universe

Hawking's quasi-local energy definition quantifies the energy enclosed by a spacelike 2-sphere in terms of the amount of lightbending on the sphere caused by the energy distribution inside the sphere. This paper establishes for the first time a direct connection between the formal mathematical definition of a quasi-local energy and observations, in the context of cosmological perturbation theory. This is achieved by studying the Hawking Energy of spherical sections of the past lightcone of a cosmic observer in a perturbed Friedmann-Lemaître spacetime. We express the Hawking Energy in terms of gauge-invariant perturbation variables and comment on the cosmic observables needed to in principle measure it. We then calculate its angular power spectrum and interpret its contributions.

Relativistic matter bispectrum of cosmic structures on the light cone

Upcoming surveys of cosmic structures will probe scales close to the cosmological horizon, which opens up new opportunities for testing the cosmological concordance model to high accuracy. In particular, constraints on the squeezed bispectrum could rule out the single-field hypothesis during inflation. However, the squeezed bispectrum is also sensitive to dynamical effects of general relativity as well as interactions of matter with residual radiation from the early Universe. In this paper, we present a relativistic simulation pipeline that includes these relativistic effects consistently. We produce light cones and calculate the observed number counts of cold dark matter for five redshift bins between z = 0.55-2.25. We compare the relativistic results against reference Newtonian simulations by means of angular power- and bispectra. We find that the dynamical relativistic effects scale roughly inversely proportional to the multipole in the angular power spectrum, with a maximum amplitude of 10% for ℓ ≲ 5. By using a smoothing method applied to the binned bispectrum we detect the Newtonian bispectrum with very high significance. The purely relativistic part of the matter bispectrum, obtained by subtracting the Newtonian bispectrum from the relativistic one, is detected with a significance of ∼ 3σ, mostly limited by cosmic variance. We find that the pure dynamical relativistic effects accounts for up to 3% and 10% of the total amplitude, respectively in the squeezed and equilateral limits. Our relativistic pipeline for modelling ultra-large scales yields gauge-independent results as we compute observables consistently on the past light cone, while the Newtonian treatment employs approximations that leave some residual gauge dependence. A gauge-invariant approach is required in order to meet the expected level of precision of forthcoming probes of cosmic structures on ultra-large scales.

Inference of the optical depth to reionization τ from Planck CMB maps with convolutional neural networks

The optical depth to reionization, τ, is the least constrained parameter of the cosmological Λ cold dark matter (ΛCDM) model. To date, its most precise value is inferred from large-scale polarized cosmic microwave background (CMB) power spectra from the High Frequency Instrument (HFI) aboard the Planck satellite. These maps are known to contain significant contamination by residual non-Gaussian systematic effects, which are hard to model analytically. Therefore, robust constraints on τ are currently obtained through an empirical cross-spectrum likelihood built from simulations. In this paper, we present a likelihood-free inference of τ from polarized Planck HFI maps which, for the first time, is fully based on neural networks (NNs). NNs have the advantage of not requiring an analytical description of the data and can be trained on state-of-the-art simulations, combining the information from multiple channels. By using Gaussian sky simulations and Planck SRoll2 simulations, including CMB, noise, and residual instrumental systematic effects, we trained, tested, and validated NN models considering different setups. We inferred the value of τ directly from Stokes Q and U maps at ∼4° pixel resolution, without computing angular power spectra. On Planck data, we obtained τNN = 0.0579 ± 0.0082, which is compatible with current EE cross-spectrum results but with a ∼30% larger uncertainty, which can be assigned to the inherent nonoptimality of our estimator and to the retraining procedure applied to avoid biases. While this paper does not improve on current cosmological constraints on τ, our analysis represents a first robust application of NN-based inference on real data, and highlights its potential as a promising tool for complementary analysis of near-future CMB experiments, also in view of the ongoing challenge to achieve the first detection of primordial gravitational waves.

Towards a full wCDM map-based analysis for weak lensing surveys

ABSTRACT The next generation of weak lensing surveys will measure the matter distribution of the local universe with unprecedented precision, allowing the resolution of non-Gaussian features of the convergence field. This encourages the use of higher-order mass-map statistics for cosmological parameter inference. We extend the forward-modelling based methodology introduced in a previous forecast paper to match these new requirements. We provide multiple forecasts for the $w$CDM parameter constraints that can be expected from stage 3 and 4 weak lensing surveys. We consider different survey setups, summary statistics and mass map filters including wavelets. We take into account the shear bias, photometric redshift uncertainties, and intrinsic alignment. The impact of baryons is investigated and the necessary scale cuts are applied. We compare the angular power spectrum analysis to peak and minima counts as well as Minkowski functionals of the mass maps. We find a preference for Starlet over Gaussian filters. Our results suggest that using a survey setup with 10 instead of 5 tomographic redshift bins is beneficial. Adding cross-tomographic information improves the constraints on cosmology and especially on galaxy intrinsic alignment for all statistics. In terms of constraining power, we find the angular power spectrum and the peak counts to be equally matched for stage 4 surveys, followed by minima counts and the Minkowski functionals. Combining different summary statistics significantly improves the constraints and compensates the stringent scale cuts. We identify the most ‘cost-effective’ combination to be the angular power spectrum, peak counts and Minkowski functionals following Starlet filtering.

Off‐Resonance Spin‐Locked Metasurfaces Empowered by Quasi‐Bound States in the Continuum for Optical Analog Computing

AbstractMetasurfaces with engineered phase discontinuity offer extra degrees of freedom to control the angular spectrum characteristics of light and can be used to construct planar metalenses with a variety of anomalous functionalities. Here, off‐resonance spin‐locked metasurfaces empowered by quasi‐bound states in the continuum are reported, in order to achieve a concept of hybridized analog computing over both frequency and angular spectrum domains. By introducing two types of asymmetric degrees, high‐quality resonance empowered by the symmetry‐protected bound states in the continuum emerges in an image‐coupled resonance system. Such high‐quality resonance can be excited in a broadband spin‐locked scattering spectrum, promising required functions for scalar multiplication and convolution operations. Off‐resonance meta‐splitter and meta‐deflector are experimentally implemented to verify the concept of hybridized analog computing in two domains, as well as providing an advantage of high robustness against scattering interference from environment. Optical spatial‐frequency processing by engineering the off‐resonance metasurfaces is also discussed. The findings provide an alternative approach toward optical analog computing over multi‐domains.

Analytical Model of Three-Dimensional Ultrasonic Beam Interaction with an Immersed Plate

This paper proposes an analytical model to describe the interaction of a bounded ultrasonic beam with an immersed plate. This model, based on the Gaussian beams decomposition, takes into account multiple reflections into the plate. It allows predicting three-dimensional spatial distributions of both transmitted and reflected fields. Thereby, it makes it easy to calculate the average pressure over the receiver’s area taking into account diffraction losses. So the acoustical parameters of the plate can be determined more accurately. A Green’s function for the interaction of an ultrasonic beam with the plate is derived. The obtained results are compared to those given by the angular spectrum approach. A good agreement is seen showing the validity of the proposed model.

Angular correlations on causally-coherent inflationary horizons

We develop a model for correlations of cosmic microwave background (CMB) anisotropy on the largest angular scales, based on standard causal geometrical relationships in slow-roll inflation. Unlike standard models based on quantized field modes, it describes perturbations with nonlocal directional coherence on spherical boundaries of causal diamonds. Causal constraints reduce the number of independent degrees of freedom, impose new angular symmetries, and eliminate cosmic variance for purely angular 2-point correlations. Distortions of causal structure from vacuum fluctuations are modeled as gravitational memory from randomly oriented outgoing and incoming gravitational null shocks, with nonlocally coherent directional displacements on curved surfaces of causal diamonds formed by standard inflationary horizons. The angular distribution is determined by axially symmetric shock displacements on circular intersections of the comoving sphere that represents the CMB photosphere with other inflationary horizons—those centered on it, and those that pass through an observer’s world line. Displacements on thin spheres at the end of inflation have a unique angular power spectrum that approximates the standard expectation on small angular scales, but differs substantially at large angular scales due to horizon curvature. For a thin sphere, the model predicts a universal angular correlation function with an exact ‘causal shadow’ symmetry, , and significant large-angle parity violation. We apply a rank statistic to compare models with WMAP and Planck satellite data, and find that a causally-coherent model with no shape parameters or cosmic variance agrees with the measured better than a large fraction () of standard model realizations. Model-independent tests of holographic causal symmetries are proposed.

Enhanced beam shifts mediated by bound states in continuum

The interaction of light beams with resonant structures has led to the development of various optical platforms for sensing, particle manipulation, and strong light–matter interaction. In the current study, we investigate the manifestations of the bound states in continuum (BIC) on the in plane and out of plane shifts (referred to as Goos–Hänchen (GH) and Imbert–Fedorov (IF) shifts, respectively) of a finite beam with specific polarization incident at an arbitrary angle. Based on the angular spectrum decomposition, we develop a generic formalism for understanding the interaction of the finite beam with an arbitrary stratified medium with isotropic and homogeneous components. It is applied to the case of a Gaussian beam with p and circularly polarized light incident on a symmetric structure containing two polar dielectric layers separated by a spacer layer. For p-polarized plane wave incidence one of the coupled Berreman modes of the structure was recently shown to evolve to the bound state with infinite localization and diverging quality factor coexisting with the other mode with large radiation leakage (Remesh et al 2021 Opt. Commun. 498 127223). A small deviation from the ideal BIC resonance still offers resonances with very high quality factors and these are exploited in this study to report giant GH shifts. A notable enhancement in the IF shift for circularly polarized light is also shown. Moreover, the reflected beam is shown to undergo distortion leading to a satellite spot. The origin of such a splitting of the reflected beam is traced to a destructive interference due to the left and right halves of the corresponding spectra.

CMB polarization by the asymmetric template of scalar perturbations

Inspired by a dipole asymmetric template for the CMB temperature map in the primordial scalar fluctuations observed by Planck at a large scale, we examine the contribution of a similar template for power asymmetry in modifying the linear polarization pattern of CMB. Replacing un-modulated temperature fluctuation with dipolar modulated one in time evolution equations somehow breaks linear perturbation in the various components of the CMB map. This non-linearity allows deflecting CMB polarization in patterns that contain divergence-free components. The explicit expressions for the angular power spectra of the electric and magnetic-type parities of linear polarization are derived in the form of the line of sight integral solutions. Our results demonstrate that the electric-type polarization is modified and the magnetic-type polarization would be produced. Such imprints depend on the linear and square of the asymmetric amplitude for E- and B-modes power spectra, respectively. For the observed dipole template, the value of B polarization spectrum at the large scale (ell lesssim 10) is almost equivalent to the power spectrum obtained from Compton scattering in the presence of tensor perturbation with tensor to scalar ratio about rsimeq 0.005.

An Analytical Model for Understanding Active Directivity Noise Control with Near-Field Error Sensing

Recent research shows that a directional quiet zone from near to far field can be created with a near-field microphone array. However, there is no systematic theoretical analysis of this error-sensing strategy. In this paper, an analytical model of the angular spectrum of point sources in the free field is proposed, based on which the near-field error-sensing strategy for active directivity noise control can be quantitively analyzed. It is found that the noise reduction in the far field is determined by the angular spectrum estimation error of both the primary and secondary sources. The impacts of the error microphone array configuration, sound source position, and target direction on the estimation error of angular spectrum are investigated. Finally, experiments were conducted in the anechoic chamber to validate the impact of the location of the secondary source.