Angular Spectrum Research Articles

Universal analyzer for measuring orbital angular momentum spectrum of randomly fluctuated beam

Universal analyzer for measuring orbital angular momentum spectrum of randomly fluctuated beam

P‐Hologen: An End‐to‐End Generative Framework for Phase‐Only Holograms

AbstractHolography stands at the forefront of visual technology, offering immersive, three‐dimensional visualizations through the manipulation of light wave amplitude and phase. Although generative models have been extensively explored in the image domain, their application to holograms remains relatively underexplored due to the inherent complexity of phase learning. Exploiting generative models for holograms offers exciting opportunities for advancing innovation and creativity, such as semantic‐aware hologram generation and editing. Currently, the most viable approach for utilizing generative models in the hologram domain involves integrating an image‐based generative model with an image‐to‐hologram conversion model, which comes at the cost of increased computational complexity and inefficiency. To tackle this problem, we introduce P‐Hologen, the first end‐to‐end generative framework designed for phase‐only holograms (POHs). P‐Hologen employs vector quantized variational autoencoders to capture the complex distributions of POHs. It also integrates the angular spectrum method into the training process, constructing latent spaces for complex phase data using strategies from the image processing domain. Extensive experiments demonstrate that P‐Hologen achieves superior quality and computational efficiency compared to the existing methods. Furthermore, our model generates high‐quality unseen, diverse holographic content from its learned latent space without requiring pre‐existing images. Our work paves the way for new applications and methodologies in holographic content creation, opening a new era in the exploration of generative holographic content. The code for our paper is publicly available on https://github.com/james0223/P-Hologen.

Phase Space Formulation of Light Propagation on Tilted Planes

The solution of the Helmholtz equation describing the propagation of light in free space from a plane to another can be described by the angular spectrum operator, which acts in the frequency domain. Many applications require this operator to be generalized to handle tilted source and target planes, which has led to research investigating the implications of these adaptations. However, the frequency domain representation intrinsically limits the understanding the way the signal is transformed through propagation. Instead, studying how the operator maps the space–frequency components of the wavefield provides essential information that is not available in the frequency domain. In this work, we highlight and exploit the deep relation between wave optics and quantum mechanics to explicitly describe the symplectic action of the tilted angular spectrum in phase space, using mathematical tools that have proven their efficiency for quantum particle physics. These derivations lead to new algorithms that open unprecedented perspectives in various domains involving the propagation of coherent light.

Large-scale Cosmic-ray Anisotropies with 19 yr of Data from the Pierre Auger Observatory

Results are presented for the measurement of large-scale anisotropies in the arrival directions of ultra–high-energy cosmic rays detected at the Pierre Auger Observatory during 19 yr of operation, prior to AugerPrime, the upgrade of the observatory. The 3D dipole amplitude and direction are reconstructed above 4 EeV in four energy bins. Besides the established dipolar anisotropy in R.A. above 8 EeV, the Fourier amplitude of the 8–16 EeV energy bin is now also above the 5σ discovery level. No time variation of the dipole moment above 8 EeV is found, setting an upper limit to the rate of change of such variations of 0.3% yr−1 at the 95% confidence level. Additionally, the results for the angular power spectrum are shown, demonstrating no other statistically significant multipoles. The results for the equatorial dipole component down to 0.03 EeV are presented, using for the first time a data set obtained with a trigger that has been optimized for lower energies. Finally, model predictions are discussed and compared with observations, based on two source emission scenarios obtained in the combined fit of spectrum and composition above 0.6 EeV.

Ultrasound-assisted aberration correction of transcranial photoacoustic imaging based on angular spectrum theory

To correct the refraction aberration induced by the skull in photoacoustic imaging, a method for phase distortion compensation is proposed based on the angular spectrum theory with the aid of ultrasonic signals. This method first updates the speed of sound distribution by iteratively performing aberration correction in the ultrasonic reconstruction. Then the speed of sound distribution obtained with ultrasound-assisted serves as prior knowledge to address phase distortion compensation by adjusting the phase shift factor of the wavefront in different media. Finally, the aberration-corrected ultrasonic-photoacoustic dual-modality image can be obtained. Numerical simulations and phantom experiments confirm the effectiveness of this method. Specifically, in simulations, the position error of the proposed method is reduced from −13.61% to 1.27% in depth compared to the method based on the reconstruction with constant speed. Moreover, a real ex-vivo rabbit skull experiment illustrates the potential biological application of the proposed method in transcranial photoacoustic imaging.

Loss-less passive polarization rectifier design with minimal etendue and size increase

We describe an approach allowing the passive rectification of the polarization of light with approximately the same beam size, minimal increase of the etendue of the beam and with negligible reduction of its power. This is done for arbitrary (including chaotic) input polarization states and without their prior identification. The tradeoff is the partial increase of the angular spectrum of light. Theoretical estimations are provided along with some preliminary experimental results describing the possible use of this approach with large diameter beams as well as in optical fibers.

Measurement Verification of a Developed Strategy of Inrush Current Reduction for a Non-Loaded Three-Phase Dy Transformer

This article presents the measurement verification of a novel strategy for inrush current reduction in an unloaded three-phase Dy transformer. The strategy combines appropriate pre-magnetization of transformer cores with an original control switching system using initial phase values of the supply voltage as control variables. Measurements were recorded for primary voltages and currents as well as secondary voltages during transient states at start-up under no-load conditions. Various inrush scenarios were examined across the full angular spectrum of initial phase angles, both polarities, and in regard to different pre-magnetization current values. A detailed analysis of the inrush currents was performed using proprietary automated software based on the recorded data. A comparative study with a nonlinear mathematical model of the transformer was also conducted. Additionally, key technical aspects of the designed system for implementing the proposed pre-magnetization strategy with controlled voltage energization are discussed.

Analyzing the spectrum characteristics of a double-grating transmission scheme

In this paper, the spectral characteristics formed by a double-grating transmission scheme are discussed based on the scalar diffraction theory. First, considering two different grating periods, the angular spectrum at the back of the second grating is obtained. Then, the spectral characteristics are discussed with three different periodic conditions, while it is proved that the spatial distribution and spacing of the spectrum are absolutely determined by the grating constants and angles. The theoretical results manifest that the spatial distribution range of the spectrum becomes larger as the angle increases, unlike the spectral points, which are distributed on a single line when the grating lines of the two gratings are parallel. Finally, for the sake of proving that our theoretical analysis is correct and reasonable, three sets of experiments are conducted with three different combinations of Ronchi gratings. As expected, the experimental and theoretical results are in perfect agreement. In a word, the involved results could be useful for expanding the application of moiré deflectometry.

Harnessing physics-guided neural networks for tailoring the orbital angular momentum spectrum in second harmonic generation

The management of orbital angular momentum (OAM) in frequency conversion processes is essential for numerous applications such as quantum and classical optical communications. This paper presents a wavefront modulation approach for the fundamental beam in second harmonic generation (SHG) to efficiently control the OAM spectrum. We employ an inverse design method to derive the necessary wavefront shape of the fundamental beam for achieving a desired SHG OAM spectrum. Specifically, we introduce an efficient inverse design technique based on physics-guided neural networks (PGNNs) that incorporates the coupled equations governing SHG, aimed at tailoring the OAM spectrum of SHG. Utilizing the proposed PGNN, we design the phase pattern for a spatial light modulator (SLM) to shape the wavefront of the fundamental beam. Furthermore, we present a novel loss function, to our knowledge, that effectively links the OAM of the SHG spectrum and efficiency to the SLM phase pattern and crystal temperature, independent of empirical weight coefficients. The proposed PGNN facilitates the purification of the SHG OAM spectrum, even when the fundamental beam comprises mixed Laguerre–Gaussian (LG) modes. Additionally, we demonstrate the generation of desired SHG spectra using the proposed PGNN framework. This study introduces what we believe to be a groundbreaking inverse design method for developing photonic devices with customized functionalities, addressing challenges associated with traditional data-driven deep learning techniques.

Characterization of weakly nonlinear effects in relationship to transducer parameters in focused ultrasound therapy.

Focused ultrasound therapy has been widely used for the treatment of various diseases, employing different types of transducers. The focused ultrasound pressure fields inevitably exhibit nonlinear effects, which can influence the ablation region. However, the nonlinear effects exhibit noticeable variations across different applications. The characterization of the nonlinear pressure fields of ultrasound is important for the effective implementation of focused ultrasound therapy. The traditional angular spectrum method (ASM) was extended to accurately and efficiently simulate the propagation of weakly nonlinear ultrasound in heterogeneous mediums of clinical model. The nonlinear effects were further analyzed in relationship to the transducer parameters that are different in various applications. The pressure fields were simulated using the extended ASM, incorporating calculations for phase aberration in the frequency domain and magnitude compensation in the spatial domain to account for heterogeneous acoustic impedance mismatch. Validation was performed by comparison to k-Wave simulation results using two simplified clinical models, an abdominal soft tissue and a transcranial skull model. The nonlinear effects were then analyzed in relation to the transducer parameters of f-number and effective source area based on the same acoustic output power. The analysis of nonlinear effects was conducted under both homogeneous medium and the clinical models. The simulation results demonstrated a maximum error of 3.93% in the calculated harmonic pressure of the abdominal model, and a maximum error of 4.89% within the transcranial model when comparing the extended ASM simulation results to those obtained from k-Wave simulations. The characterization of the nonlinear effects reveals a strong correlation with the transducer parameters. Specifically, the results indicate that the nonlinear effects intensify with an increase in the effective source area and f-number, under the same acoustic output power of the transducer. However, the clinical model also showed an influence on the nonlinear effects in relation to the f-number. The extended ASM was demonstrated as an accurate and efficient simulation tool, and the simulation results provide a reference for evaluating the intensity of nonlinear effects in various transducer designs.

Vector angular spectrum model for light traveling in scattering media

Strongly scattering media disrupt both the wavefront distribution and the polarization state of the incident light field. Controlling and effectively utilizing depolarization effects are crucial for optical applications in highly scattering environments, such as imaging through dense fog. However, current simulation models have difficulty simulating the evolution of vector light fields within scattering media, posing challenges for studying vector light fields in strongly scattering environments. Here, we propose the Vector Angular Spectrum (VAS) model for simulating the propagation of vector light fields within scattering media. By introducing the angular spectrum distribution of vector light scattering and polarization conversion mechanisms, this model can simulate the depolarization effects of vector light propagating through strongly scattering media. The VAS model has also been used to investigate the focusing of vector scattered light through scattering media. Furthermore, the simulation results of the model have been validated through experiments. The proposed VAS model is expected to play a role in the theoretical research of vector scattered light and optical applications in strongly scattering environments.

Gravitational wave luminosity distance-weighted anisotropies

Measurements of the luminosity distance of propagating gravitational waves can provide invaluable information on the geometry and content of our Universe. Due to the clustering of cosmic structures, in realistic situations we need to average the luminosity distance of events coming from patches inside a volume. In this work we evaluate, in a gauge-invariant and fully-relativistic treatment, the impact of cosmological perturbations on such averaging process. We find that clustering, lensing and peculiar velocity effects impact estimates for future detectors such as Einstein Telescope, Cosmic Explorer, the Big Bang Observer and DECIGO. The signal-to-noise ratio of the angular power spectrum of the average luminosity distance over all the redshift bins is 17 in the case of binary black holes detected by Einstein Telescope and Cosmic Explorer. We also provide fitting formulas for the corrections to the average luminosity distance due to general relativistic effects.

Cosmological forecasts from the combination of Stage-IV photometric galaxy surveys and the magnification from forthcoming GW observatories

In this work we have investigated the synergy between Stage-IV galaxy surveys and future GW observatories for constraining the underlying cosmological model of the Universe, focussing on photometric galaxy clustering, cosmic shear and GW magnification as cosmological probes. We have implemented a Fisher matrix approach for the evaluation of the full 6×2pt statistics composed by the angular power spectra of the single probes together with their combination. For our analysis, we have in particular considered dynamical dark energy and massive neutrino scenarios. We have found that the improvement to galaxy survey performance is below 1%, in the case of ℓ GW max=100 and a luminosity distance error of σ dL /dL =10%. However, when extending the analysis to ℓ GW max=1000, we find that the GW magnification improves the galaxy survey performance on all the cosmological parameters, reducing their errors by 3%-5%, when σ dL /dL =10%, and by 10%-18% when σ dL /dL =1%, especially for Mν , w 0 and wa . However, here our analysis is unavoidably optimistic: a much more detailed and realistic approach will be needed, especially by including systematic effects. But we can conclude that, in the case of future gravitational wave observatories, the inclusion of the gravitational wave magnification can improve Stage-IV galaxy surveys performance on constraining the underlying cosmological model of the Universe.

Baryonification extended to thermal Sunyaev Zel’dovich

Baryonification algorithms model the impact of galaxy formation and feedback on the matter field in gravity-only simulations by adopting physically motivated parametric prescriptions. In this paper, we extend these models to describe gas temperature and pressure, allowing for a self-consistent modelling of the thermal Sunyaev-Zel’dovich effect, weak gravitational lensing, and their cross-correlation, down to small scales. We validate our approach by showing that it can simultaneously reproduce the electron pressure, gas, stellar, and dark matter power spectra as measured in all BAHAMAS hydrodynamical simulations. Specifically, with only two additional free parameters, we can fit the electron pressure auto- and cross-power spectra at 10% while reproducing the suppression in the matter power spectrum induced by baryons at the per cent level, for different active galactic nuclei (AGN) feedback strengths in BAHAMAS. Furthermore, we reproduce BAHAMAS convergence and thermal Sunyaev Zel’dovich angular power spectra within 1% and 10% accuracy, respectively, down to ℓ = 5000. When used jointly with cosmological rescaling algorithms, the baryonification presented here allows for a fast and accurate exploration of cosmological and astrophysical scenarios. Therefore, it can be employed to create mock catalogues, lightcones, and large training sets for emulators aimed at interpreting forthcoming multi-wavelength observations of the large-scale structure of the Universe.

Realization and optimization of the gold-mesoporous silica based bimodal surface plasmon resonance sensor with digital Gaussian filter

Abstract This work presented a novel biomdal surface plasmon resonance (BSPR) sensor with mesoporous silica film (MSF) and digital Gaussian filter. A modified Stöber solution growth approach was applied to prepare MSF film on the gold film. The conventional SPR sensor was coupled with a digital Gaussian filter to realize the BSPR sensor. After that, the Gaussian parameters were modified and the BSPR angular spectrum was obtained for further sensing experiments. Porosity and thickness of the MSF film were measured and calculated by means of a combination of simulation and measurement. The simulation results indicate that the refractive index (RI) sensitivity of the BSPR sensor could reach 75.11 deg/RIU which is 66.91% higher than the 45 deg/RIU of the conventional gold-MSF SPR sensor. Based on the experiments, the RI resolution of BSPR sensor was improved by 37.1% to 6.61 × 10−6 RIU, the limit of detection (LOD) for glucose was raised from 320 mg l−1 to 131 mg l−1, and the LOD for CTAB molecule was raised from 124.98 nM to 63.78 nM when compared to the gold-MSF SPR sensor.

Decimeter-depth and polarization addressable color 3D meta-holography

Fueled by the rapid advancement of nanofabrication, metasurface has provided unprecedented opportunities for 3D holography. Large depth 3D meta-holography not only greatly increases information storage capacity, but also enables distinguishing of the relative spatial relationship of 3D objects, which has important applications in fields like optical information storage and medical diagnosis. Although the methods based on Fresnel diffraction theory can reconstruct the real depth information of 3D objects, the maximum depth is only 2 mm. Here, we develop a 3D meta-holography based on angular spectrum diffraction theory to break through the depth limit. By developing the angular spectrum diffraction theory into meta-holography, the metasurface structure with independent polarization control is used to create a polarization multiplexing 3D meta-hologram. The fabricated amorphous silicon metasurface increases the depth range by 47.5 times and realizes 0.95 dm depth reconstruction for polarization independent and different color 3D meta-hologram in visible. Such polarization controlled large-depth color meta-holography is expected to open avenue for data storage, display, information security and virtual reality.

Rapid hologram generation through backward ray tracing and adaptive-resolution wavefront recording plane

Abstract An advanced method for rapidly computing holograms of large three-dimensional (3D) objects combines backward ray tracing with adaptive resolution wavefront recording plane (WRP) and adaptive angular spectrum propagation. In the initial phase, a WRP with adjustable resolution and sampling interval based on the object’s size is defined to capture detailed information from large 3D objects. The second phase employs an adaptive angular spectrum method (ASM) to efficiently compute the propagation from the large-sized WRP to the small-sized computer-generated hologram (CGH). The computation process is accelerated using CUDA and OptiX. Optical experiments confirm that the algorithm can generate high-quality holograms with shadow and occlusion effects at a resolution of 1024 × 1024 in 29 ms.

Effect of evanescent wave on vector vortex beams on higher-order Poincaré sphere

Abstract Based on the vector angular spectrum representation, the contributions of the propagating and evanescent waves to the vector vortex Laguerre–Gaussian beams on the higher-order Poincaré sphere are investigated in the nonparaxial regime. The evolution properties of the propagating and evanescent waves are closely related to the topological charge, the radial order, the ellipticity angle, and the waist width. The influences of the evanescent waves on the intensity, the spin and orbital angular momenta of the vector vortex beams are discussed in detail.

Cosmic variance of the Hellings and Downs correlation for ensembles of universes having nonzero angular power spectra

Cosmic variance of the Hellings and Downs correlation for ensembles of universes having nonzero angular power spectra

Three-dimensional computer holography based on two hybrid constraint iterative angular spectrum algorithms

A method for three-dimensional holographic image calculation based on angular spectrum layering is presented, which significantly reduces the noise resulting from image overlap during hologram reconstruction. In order to enhance the reconstruction quality, we proposed a two-hybrid constraint algorithm, which employs two parallel processing frameworks to allocate multiple plane images effectively. Additionally, by applying two different hybrid constraint factors, spatial resource allocation is utilized efficiently to mitigate the impact of axial inter-layer crosstalk noise. The numerical simulations and optical experiment results demonstrated that our method has successfully improved the reconstruction quality of holograms and proved its effectiveness and feasibility.