Angular Spectrum Research Articles

All-dielectric metasurface for polarization-multiplexed single-pixel imaging

Integration and miniaturization of multi-channel single-pixel imaging systems have become a developing trend. However, it is challenging to meet such development needs solely relying on traditional optical devices. One feasible solution is the utilization of metasurfaces with multiplexing functionality. Here, we propose and validate an all-dielectric, anisotropic metasurface that provides a random mask with polarization multiplexing for single pixel imaging. The design ensures each mask contains 50% target information, allowing adaptive correlated imaging of different targets without needing to redesign the masks. By optimizing the metasurface, we enhance computational efficiency by preventing correlation between different polarization channels and mask patterns. We also adjust the parameters of the compressed sensing algorithm to accommodate various sampling rates, ensuring high-quality image reconstruction. Additionally, the whole system is simulated by the angular spectrum transmission and compressed sensing reconstruction algorithm, providing image reconstruction results for metasurfaces of different sizes, demonstrating the feasibility of the proposed approach. It is noteworthy that the designed metasurface works for single-wavelength operation and could be extended to multispectral imaging by introducing achromatic metasurface technology. The proposed method could miniaturize the optical devices and reduce light loss.

Constraining holographic dark energy and analyzing cosmological tensions

We investigate cosmological constraints on the holographic dark energy (HDE) using the state-of-the-art cosmological datasets: Planck CMB angular power spectra and weak lensing power spectra, Atacama Cosmology Telescope (ACT) temperature power spectra, baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) measurements from six-degree-field galaxy survey and Sloan Digital Sky Survey (DR12 & DR16) and the Cepheids-Supernovae measurement from SH0ES team (R22). We also examine the HDE model and ΛCDM with and without Neff (effective number of relativistic species) being treated as a free parameter. We find that the HDE model can relieve the tensions of H0 and S8 to certain degrees. With “Planck+ACT+BAO+RSD” datasets, the constraints are H0=69.70±1.39km s−1Mpc−1 and S8=0.823±0.011 in HDE model, which brings down the Hubble tension down to 1.92σ confidence level (C.L.) and the S8 tension to (1−2)σ C.L. By adding the R22 data, their values are improved as H0=71.86±0.93km s−1Mpc−1 and S8=0.813±0.010, which further brings the Hubble tension down to 0.85σ C.L. and relieves the S8 tension. We also quantify the goodness-of-fit of different models with Akaike information criterion (AIC) and Bayesian information criterion (BIC), and find that the HDE agrees with the observational data better than the ΛCDM and other extended models (treating Neff as free for fitting).

Modelling and simulation for the investigation on the ultrasonic propagation mechanism in advanced microelectronic packages

The miniaturisation, ultra-thinness and high-density multi-layer structure of advanced microelectronic packages complicate the propagation mechanism of ultrasonic waves. In this paper, a finite element model is used to simulate ultrasonic wave propagation in flip chip packages, investigating the laws of transmission and reflection at the lamination boundaries. The acoustic field of ultrasonic transducers is simulated using MATLAB and Abaqus software. The angular spectrum method (ASM) based on the Fourier transform is adopted to more precisely reveal the distribution characteristics and attenuation relationship of near‐field ultrasonic waves. The influence of the frequency and size of the ultrasonic transducer on the propagation characteristics of ultrasonic waves is analysed. Based on an acoustic field map generated by the detection model, the waveform conversions of acoustic waves in a multi-layer structure are analysed. The results show that ultrasonic waves are mainly presented in the form of reflected and transmitted waves at the layered interface and the model with a perfectly matched layer (PML) has higher accuracy. Therefore, this method is applied to ultrasonic testing in a flip chip package, which cannot only effectively exclude interference from boundary reflection but also greatly improve the reliability of waveform conversions analysis.

Single-beam digital holographic reconstruction: a phase-support enhanced complex wavefront on phase-only function for twin-image elimination.

In in-line digital holographic microscopy (DHM), twin-image artifacts pose a significant challenge, and reduction or complete elimination is essential for object reconstruction. To facilitate object reconstruction using a single hologram, significantly reduce inaccuracies, and avoid iterative processing, a digital holographic reconstruction algorithm called phase-support constraint on phase-only function (PCOF) is presented. In-line DHM simulations and tabletop experiments employing the sliding-window approach are used to compute the arithmetic mean and variance of the phase values in the reconstructed image. A support constraint mask, through variance thresholding, effectively enabled twin-image artifacts. Quantitative evaluations using metrics such as mean squared error, peak signal-to-noise ratio, and mean structural similarity index show PCOF's superior capability in eliminating twin-image artifacts and achieving high-fidelity reconstructions compared with conventional methods such as angular spectrum and iterative phase retrieval methods. PCOF stands as a promising approach to in-line digital holographic reconstruction, offering a robust solution to mitigate twin-image artifacts and enhance the fidelity of reconstructed objects.

Inflationary initial conditions for the cosmological gravitational wave background

The initial conditions on the anisotropies of the stochastic gravitational-wave background of cosmological origin (CGWB) largely depend on the mechanism that generates the gravitational waves. Since the CGWB is expected to be non-thermal, the computation of the initial conditions could be more challenging w.r.t. the Cosmic Microwave Background (CMB), whose interactions with other particles in the early Universe lead to a blackbody spectrum. In this paper, we show that the initial conditions for the cosmological background generated by quantum fluctuations of the metric during inflation deviate from adiabaticity. These primordial gravitational waves are indeed generated by quantum fluctuations of two independent degrees of freedom (the two polarization states of the gravitons). Furthermore, the CGWB plays a negligible role in the Einstein's equations, because its energy density is subdominant w.r.t. ordinary matter. Therefore, the only possible way to compute the initial conditions for inflationary gravitons is to perturb the energy-momentum tensor of the gravitational field defined in term of the small-scale tensor perturbation of the metric. This new and self-consistent approach shows that a large, non-adiabatic initial condition is present even during the single-field inflation. Such a contribution enhances the total angular power spectrum of the CGWB compared to the standard adiabatic case, increasing also the sensitivity of the anisotropies to the presence of relativistic and decoupled particles in the early Universe. In this work we have also proved that our findings are quite general and apply to both single-field inflation and other scenarios in which the CGWB is generated by the quantum fluctuations of the metric, like the curvaton.

Model-based navigation of transcranial focused ultrasound neuromodulation in humans: Application to targeting the amygdala and thalamus

BackgroundTranscranial focused ultrasound (tFUS) neuromodulation has shown promise in animals but is challenging to translate to humans because of the thicker skull that heavily scatters ultrasound waves. ObjectiveWe develop and disseminate a model-based navigation (MBN) tool for acoustic dose delivery in the presence of skull aberrations that is easy to use by non-specialists. MethodsWe pre-compute acoustic beams for thousands of virtual transducer locations on the scalp of the subject under study. We use the hybrid angular spectrum solver mSOUND, which runs in ∼4 s per solve per CPU yielding pre-computation times under 1 h for scalp meshes with up to 4000 faces and a parallelization factor of 5. We combine this pre-computed set of beam solutions with optical tracking, thus allowing real-time display of the tFUS beam as the operator freely navigates the transducer around the subject’ scalp. We assess the impact of MBN versus line-of-sight targeting (LOST) positioning in simulations of 13 subjects. ResultsOur navigation tool has a display refresh rate of ∼10 Hz. In our simulations, MBN increased the acoustic dose in the thalamus and amygdala by 8–67 % compared to LOST and avoided complete target misses that affected 10–20 % of LOST cases. MBN also yielded a lower variability of the deposited dose across subjects than LOST. ConclusionsMBN may yield greater and more consistent (less variable) ultrasound dose deposition than transducer placement with line-of-sight targeting, and thus could become a helpful tool to improve the efficacy of tFUS neuromodulation.

Velocity inversion of a relativistic electron incident by a vortex beam in a magnetic field

A method is proposed to invert the velocity of a relativistic electron incident by a vector Bessel vortex beam in a magnetic field by analyzing the spectra of the backward scattered echoes. The scattering power and spectra are investigated based on the vector plane wave angular spectrum theory and the Thomson scattering theory. The results indicate that the high velocity of an electron causes the distribution of the scattered power on the xoy plane to shift in the direction of the velocity. Additionally, the spectra of the scattered echoes display periodic bimodality due to the cyclotron motion of the electrons. The velocity of a relativistic electron parallel to the applied magnetic field can be obtained from the spectrum of the scattered echoes and the parameters of the vortex beam. The conclusions suggest that both the magnitude and the direction of the velocity of a relativistic electron can be determined using a set of orthogonal magnetic fields. This work is significant for studying the scattering of vortex beams by plasmas and developing diagnostic techniques of plasmas.

Real-time intelligent 3D holographic photography for real-world scenarios

Three-dimensional (3D) display can provide more information than two-dimensional display, and real-time 3D reconstruction of the real-world environment has broad application prospects as a key technology in the field of meta-universe and Internet of Things. 3D holographic display is considered to be an ideal 3D display scheme, thus enhancing the computational speed and reconstruction quality of 3D holograms can offer substantial support for real-time 3D reconstruction. Here, we proposed a real-time 3D holographic photography for real-world scenarios driven by both physical model and artificial intelligence. The 3D information of the real scene was acquired by a depth camera and then divided into 30 layers using the layer-based method. Convolutional neural networks (CNN) were used to build the mapping of intensity and depth maps to computer-generated holograms (CGH). The differentiability of the angular spectrum algorithm was used to realize the self-supervised training of the network, while the composite loss function was employed to optimize network parameters by calculating the loss between reconstructed and target images. The trained network can generate a CGH with a resolution of 1024×1024 in 14.5 ms. The proposed system operates at 22 frames per second and successfully reconstructs 3D video of dynamic scene. The system exhibits significant potential for application in intelligent manufacturing, remote office work, distance education and other fields.

Object azimuth measurement based on optical orbital angular momentum phase spectrum under tilted irradiation condition

In optical remote sensing, a beam carrying orbital angular momentum can be used to identify the azimuth of an object. However, most of the studies reported currently require the beam to be illuminated vertically to the surface of the object, and the general case of tilted irradiation for the beam has not been fully discussed. In this paper, an object azimuth measurement method based on orbital angular momentum phase spectrum under tilted irradiation condition is proposed. We analyze the relationship between the measurement error caused by the beam oblique irradiation and the angle of tilt and propose an error compensation method. In the experiment, the orbital angular momentum phase spectrum of the Laguerre-Gaussian beam is obtained by a four-step phase-shifting method, and the error caused by tilt modulation is measured. After implementing the error compensation scheme, the maximum absolute error in azimuth measurement under tilted irradiation conditions is maintained within 2.15°. Across all tilt angles, the average absolute error remains below 0.73°. The method proposed in this paper has a certain reference value for expanding the practical application of orbital angular momentum beams in the field of remote sensing.

Reflectionless propagation of beams through a stratified medium

Reflectionless potentials following the prescription of Kay and Moses allow for total transmission of incoming waves of any kinetic energy. The optical analogue of such potentials occur as dielectric stratified media that can offer null reflectivity and near total transmission over a large range of incidence angles and wavelengths. In a previous work (Gupta and Agarwal, 2007), this was demonstrated for linearly polarized plane waves. We extend the earlier work valid for plane waves to structured beams to show near-total transmission of beams across the reflectionless dielectric profile. The analysis is based on the angular spectrum decomposition treating the beam as a collection of plane waves. Gaussian and Laguerre–Gaussian beams are shown to be transmitted through the film with <1% reflection in most scenarios. We also discuss the superlative performance of our proposed profile in preserving the beam shape during transmission comparing these results to a conventional λ/2 antireflection coating.

Topography reconstruction of high aspect ratio silicon trench array via near-infrared coherence scanning interferometry

Topography measurement of high aspect ratio trench array using coherence scanning interferometry presents significant challenges because the numerical aperture of detection light is constrained by the trenches. Altering the detection light to penetrate the sample like near-infrared light for silicon could overcome this obstacle, but the trench array spreads the detection light. This study introduces a coherence scanning interferometry model based on three-dimensional point spread function and assuming sample is transparent to detection light, which is realized by integrating rigorous numerical electromagnetic field solution to quantify the modulation aberrations of detection light by transparent trench arrays, and theoretical angular spectrum diffraction utilized for far-field interference imaging. This model facilitates a thorough analysis of the aberrations introduced by trench arrays, encompassing comparisons between trench arrays and a single trench, as well as between the symmetric region of the array and the asymmetric region at the edge. Additionally, an investigation into the impact of unified compensation for low-order aberrations on the topography reconstruction is presented, and we find the sample-induced aberration compensation method utilizing a deformable mirror that we previously proposed for a single trench is still effective confronting trench array. Experimental measurements are performed on silicon trench arrays with the aspect ratio of up to 20:1 and the period of approximately 10 µm to validate the effectiveness of our model and measurement methods, thus providing valuable insights for enhancing high aspect ratio manufacturing.

Angular spectrum of quantum fluctuations in causal structure

Angular spectrum of quantum fluctuations in causal structure

Complete analysis of the background and anisotropies of scalar-induced gravitational waves: primordial non-Gaussianity f NL and g NL considered

Investigation of primordial non-Gaussianity holds immense importance in testing the inflation paradigm and shedding light on the physics of the early Universe. In this study, we conduct the complete analysis of scalar-induced gravitational waves (SIGWs) by incorporating the local-type non-Gaussianity f NL and g NL. We develop Feynman-like diagrammatic technique and derive semi-analytic formulas for both the energy-density fraction spectrum and the angular power spectrum. For the energy-density fraction spectrum, we analyze all the relevant Feynman-like diagrams, determining their contributions to the spectrum in an order-by-order fashion. As for the angular power spectrum, our focus lies on the initial inhomogeneities, giving rise to anisotropies in SIGWs, that arise from the coupling between short- and long-wavelength modes due to primordial non-Gaussianity. Our analysis reveals that this spectrum exhibits a typical multipole dependence, characterized by C̃ ℓ ∝ [ℓ(ℓ + 1)]-1, which plays a crucial role in distinguishing between different sources of gravitational waves. Depending on model parameters, significant anisotropies can be achieved. We also show that the degeneracies in model parameters can be broken. The findings of our study underscore the angular power spectrum as a robust probe for investigating primordial non-Gaussianity and the physics of the early Universe. Moreover, our theoretical predictions can be tested using space-borne gravitational-wave detectors and pulsar timing arrays.

LiteBIRD science goals and forecasts. A case study of the origin of primordial gravitational waves using large-scale CMB polarization

We study the possibility of using the LiteBIRD satellite B-mode survey to constrain models of inflation producing specific features in CMB angular power spectra. We explore a particular model example, i.e. spectator axion-SU(2) gauge field inflation. This model can source parity-violating gravitational waves from the amplification of gauge field fluctuations driven by a pseudoscalar “axionlike” field, rolling for a few e-folds during inflation. The sourced gravitational waves can exceed the vacuum contribution at reionization bump scales by about an order of magnitude and can be comparable to the vacuum contribution at recombination bump scales. We argue that a satellite mission with full sky coverage and access to the reionization bump scales is necessary to understand the origin of the primordial gravitational wave signal and distinguish among two production mechanisms: quantum vacuum fluctuations of spacetime and matter sources during inflation. We present the expected constraints on model parameters from LiteBIRD satellite simulations, which complement and expand previous studies in the literature. We find that LiteBIRD will be able to exclude with high significance standard single-field slow-roll models, such as the Starobinsky model, if the true model is the axion-SU(2) model with a feature at CMB scales. We further investigate the possibility of using the parity-violating signature of the model, such as the TB and EB angular power spectra, to disentangle it from the standard single-field slow-roll scenario. We find that most of the discriminating power of LiteBIRD will reside in BB angular power spectra rather than in TB and EB correlations.

P‐50: Multi‐depth‐SGD Based Tilted Plane Diffraction Propagation for Holographic Near‐eye Displays

To facilitate the practical application of wearable holographic near‐eye displays, the propagation between non‐parallel planes is essential for the hologram generation of off‐axis projection onto the holographic‐optical‐element (HOE) based combiners. However, existing methods, particularly the angular spectrum rotation‐based approach for generating tilted plane holograms, encounter challenges such as gradient loss when integrated with the stochastic gradient descent (SGD) algorithm. In this paper, we present a novel method for generating a tilted plane hologram using multi‐depth‐SGD, effectively mitigating the gradient loss issue.

Finding origins of CMB anomalies in the inflationary quantum fluctuations

In this paper, we present compelling evidence for the parity asymmetry (a discrete symmetry separate from isotropy) in the Cosmic Microwave Background (CMB) map, measured through two-point temperature correlations. Any asymmetry associated with discrete symmetries, such as parity, challenges our understanding of quantum physics associated with primordial physics rather than LCDM (Λ Cold-Dark-Matter) itself. We commence by conducting a comprehensive analysis of the Planck CMB, focusing on the distribution of power in low-multipoles and temperature anticorrelations at parity conjugate points in position space. We find tension with the near scale-invariant power-law power spectrum of Standard Inflation (SI), with p-values of the order 𝒪(10-4 - 10-3). Alternatively, we explore the framework of direct-sum inflation (DSI), where a quantum fluctuation arises as a direct sum of two components evolving forward and backward in time at parity conjugate points in physical space. This mechanism results in a parity-asymmetric scale-dependent power spectrum, particularly prominent at low-multipoles, without any additional free model parameters. Our findings indicate that DSI is consistent with data on parity asymmetry, the absence of power at θ > 60°, and power suppression at low-even-multipoles which are major data anomalies in the SI model. Furthermore, we discover that the parameters characterizing the hemispherical power asymmetry anomaly become statistically insignificant when the large SI quadrupole amplitude is reduced to align with the data. DSI explains this low quadrupole with a p-value of 3.5%, 39 times higher than SI. Combining statistics from parameters measuring parity and low-ℓ angular power spectrum, we find that DSI is 50-650 times more probable than SI. In summary, our investigation suggests that while CMB temperature fluctuations exhibit homogeneity and isotropy, they also display parity-asymmetric behavior consistent with predictions of DSI. This observation provides a tantalizing evidence for the quantum mechanical nature of gravity.

Improvement of optical wave propagation simulations: the scaled angular spectrum method for far-field and focal analysis

In the field of optics, accurately simulating wave propagation is essential for both theoretical insights and practical applications. This study introduces the scaled angular spectrum method (Sc-ASM) for simulating far-field and focal patterns, overcoming the limitations inherent in the standard angular spectrum method (ASM) by allowing variable sampling intervals between source and observation planes. Comparative analysis with the Rayleigh–Sommerfeld integral demonstrates Sc-ASM's superior accuracy in estimating the far-field patterns of beams with complex phase structures. Our results underscore Sc-ASM’s potential to set a new benchmark in optical simulations, significantly advancing optical system design and the study of wave propagation.

Soft Contact Lens Engraving Characterization by Wavefront Holoscopy.

Permanent engravings on contact lenses provide information about the manufacturing process and lens positioning when they are placed on the eye. The inspection of their morphological characteristics is important, since they can affect the user's comfort and deposit adhesion. Therefore, an inverted wavefront holoscope (a lensless microscope based on Gabor's principle of in-line digital holography) is explored for the characterization of the permanent marks of soft contact lenses. The device, based on an in-line transmission configuration, uses a partially coherent laser source to illuminate the soft contact lens placed in a cuvette filled with a saline solution for lens preservation. Holograms were recorded on a digital sensor and reconstructed by back propagation to the image plane based on the angular spectrum method. In addition, a phase-retrieval algorithm was used to enhance the quality of the recovered images. The instrument was experimentally validated through a calibration process in terms of spatial resolution and thickness estimation, showing values that perfectly agree with those that were theoretically expected. Finally, phase maps of different engravings for three commercial soft contact lenses were successfully reconstructed, validating the inverted wavefront holoscope as a potential instrument for the characterization of the permanent marks of soft contact lenses. To improve the final image quality of reconstructions, the geometry of lenses should be considered to avoid induced aberration effects.

Propagation of elliptical Gaussian vortex beam based on angular spectrum representation

Vortex beams with hollow elliptical ring structure have attracted broad interest in applications such as micro-particle trapping and manipulation. The paper investigates the dependence of the hollow elliptic ring structure of vortex beams on the beam order and the topological charge, while propagating in the near- and far-field zones. The electric field of the beam is formulated by using the angular spectrum method, which satisfies rigorously Maxwell's equation. The electric field, linear momentum and orbital angular momentum are calculated. Numerical results show that the hollow elliptical ring structure approximately remains unchanged over a finite propagation distance, accompanied by a rotation whose angle depends on the topological charge. In the far-field zone, the ring structure is broken, leading to two bright spots and several dark islands. It is found that the beam profile in the near-field zone is mainly related to the beam order but in the far-field zone is primarily affected by the topological charge. The results presented in the paper may be useful in predicting and explaining the interaction between the elliptic hollow Gaussian vortex beam and the micro-particles, such as the movement of micro-particles along the orbit and the rolling rotation.

Broadband angular spectrum analog processors based on all-dielectric metasurfaces

Broadband angular spectrum analog processors based on all-dielectric metasurfaces