Scalar Phase Research Articles

The Correction Method for Wavefront Aberration Caused by Spectrum-Splitting Filters in Multi-Modal Optical Imaging System

In current biomedical and environmental detection, multi-modal optical imaging technology is playing an increasingly important role. By utilizing information from dimensions such as spectra and polarization, it reflects the detailed characteristics and material properties of the targets. However, as detection system performance becomes more complex, issues such as aberrations introduced by multilayered lenses, signal attenuation, decreased polarization sensitivity, and latency can no longer be ignored. These factors directly affect the assessment of image details, influencing subsequent analyses. In this paper, we propose a method for designing and optimizing spectrum-splitting filters that considers the wavefront aberration and transmittance of the multi-modal optical imaging system. The method of optimizing coating phases to minimize scalar phase aberrations while maximizing system transmission leads to substantially improved imaging performance. Simulation and experimental results demonstrate that the method can improve the imaging performance. The proposed approach has potential applications in fields such as biomedical field, multi-spectral, remote sensing and microscopy.

Toroidal phase topologies within paraxial laser beams

Control of topologies in structured light fields with multi-degrees of freedom integrates fundamental optical physics and topological invariance. Beyond the simple phase vortex, three-dimensional (3D) topological singularities and related nonsingular textures have recently gained significant interest. Here, we experimentally demonstrate the creation of a family of toroidal phase topologies within paraxial laser beams. By employing single two-dimensional (2D) phase control, we generate propagating 3D topological textures, effectively embodying the topological configuration of a four-dimensional (4D) parameter space. The resulting light fields exhibit amplitude isosurfaces of toroidal vortices and hopfionic phase textures, both controlled by topological charges. The ability to prepare scalar phase textures of light offers new insights into the high-dimensional control of complex structured textures and may find significant applications in light-matter interactions, optical manipulation, and optical information encoding.

Benefits of adding radial phase dimples on scalar coronagraph phase masks

Benefits of adding radial phase dimples on scalar coronagraph phase masks

Binary boson stars: Merger dynamics and formation of rotating remnant stars

Scalar boson stars have attracted attention as simple models for exploring the nonlinear dynamics of a large class of ultra compact and black hole mimicking objects. Here, we study the impact of interactions in the scalar matter making up these stars. In particular, we show the pivotal role the scalar phase and vortex structure play during the late inspiral, merger, and post-merger oscillations of a binary boson star, as well as their impact on the properties of the merger remnant. To that end, we construct constraint satisfying binary boson star initial data and numerically evolve the nonlinear set of Einstein-Klein-Gordon equations. We demonstrate that the scalar interactions can significantly affect the inspiral gravitational wave amplitude and phase, and the length of a potential hypermassive phase shortly after merger. If a black hole is formed after merger, we find its spin angular momentum to be consistent with similar binary black hole and binary neutron star merger remnants. Furthermore, we formulate a mapping that approximately predicts the remnant properties of any given binary boson star merger. Guided by this mapping, we use numerical evolutions to explicitly demonstrate, for the first time, that rotating boson stars can form as remnants from the merger of two non-spinning boson stars. We characterize this new formation mechanism and discuss its robustness. Finally, we comment on the implications for rotating Proca stars.

Optical response of Higgs mode in superconductors at clean limit

The phenomenological Ginzburg–Landau theory and the charge conservation directly lead to the finite Higgs-mode generation and vanishing charge-density fluctuation in the second-order optical response of superconductors at clean limit. Nevertheless, recent microscopic theoretical studies of the second-order optical response, apart from the one through the gauge-invariant kinetic equation (Yang and Wu, 2019), have derived a vanishing Higgs-mode generation but finite charge-density fluctuation at clean limit. We resolve this controversy by re-examining the previous derivations with the vector potential alone within the path-integral and Eilenberger-equation approaches, and show that both previous derivations contain flaws. After fixing these flaws, a finite Higgs-mode generation through the drive effect of vector potential is derived at clean limit, exactly recovering the previous result from the gauge-invariant kinetic equation as well as Ginzburg–Landau theory. By further extending the path-integral approach to include electromagnetic effects from the scalar potential and phase mode, in the second-order response, a finite contribution from the drive effect of scalar potential to the Higgs-mode generation at clean limit as well as the vanishing charge-density fluctuation are derived, also recovering the results from the gauge-invariant kinetic equation. Particularly, we show that the phase mode is excited in the second-order response, and exactly cancels the previously reported unphysical excitation of the charge-density fluctuation, guaranteeing the charge conservation.

Adjoint-based phase reduction analysis of incompressible periodic flows

We establish the theoretical framework for adjoint-based phase reduction analysis for incompressible periodic flows. Through this adjoint-based method, we obtain spatiotemporal phase sensitivity fields through a single pair of forward and backward direct numerical simulations, as opposed to the impulse-based method that requires a very large number of simulations. Phase-based analysis involves perturbation analysis about a periodically varying base state and hence is tailored for the analysis of periodic flows. We formulate the phase description of periodic flows with respect to the potential and vortical perturbations in the flow field. The current phase-reduction analysis can also be implemented consistently in the immersed boundary projection method, which facilitates the analysis over arbitrarily-shaped bodies. We demonstrate the strength of the phase-based analysis for periodic flows over circular cylinder and symmetric airfoils at high incidence angles. The critical regions for phase modification in the cylinder flow are investigated and the locations of flow separation are shown to be the most sensitive regions. Further, the results reveal the influence of the angle of attack and airfoil thickness on the phase-sensitivity distribution of flows over various airfoils. The phase for such flows is defined based on the lift coefficient, and hence is influenced by the vortical structures responsible for lift production. The present framework sheds light on the connection between phase-sensitivity and vortex formation dynamics.

Scalar Čerenkov radiation from high-energy cosmic rays

As first noted by Robert Wagoner in the 1970s, if a scalar field is nonminimally coupled to the Ricci scalar and propagates at subluminal speeds, then there exists the possibility of scalar $\check{\hbox{C}}$erenkov radiation from a moving particle. The mere observation of high-energy cosmic rays could in principle rule out the existence of such scalar fields since any particle moving faster than scalar perturbations would lose energy in the form of scalar waves until it moves slower than those. We compute in detail the energy loss to scalar waves and find that it scales with the square of the ultra-violet (UV) cutoff frequency of the effective field theory (EFT) of gravity. For dark-energy-motivated EFTs, the UV cutoff can be low, in which case that energy loss could always be negligible. In contrast, if viewed as a covariant theory valid at all scales or as an EFT valid at higher energies, perhaps even all the way up to the Planck scale, as may be the case if motivated by quantum-gravity perspectives, then the energy loss to scalar waves may diverge or become dramatically large. In this case, high-energy cosmic rays of extragalactic origin stringently constrain any conformally coupled scalar fields with non-canonical kinetic terms, although a minimum scalar phase velocity is required to trust the EFT.

Scalar Vector and Phase Characteristics of an Acoustic Field in an Arbitrary Regular Inhomogeneous Liquid Medium

Scalar Vector and Phase Characteristics of an Acoustic Field in an Arbitrary Regular Inhomogeneous Liquid Medium

Quantum backreaction on a classical universe

We study a first-order formulation for the coupled evolution of a quantum scalar field and a classical Friedmann universe. The model is defined by a state dependent Hamiltonian constraint and the time dependent Schr\"odinger equation for the scalar field. We solve the resulting nonlinear equations numerically for initial data consisting of a Gaussian scalar field state and gravity phase space variables. This gives a self-consistent semiclassical evolution that includes nonperturbative ``backreaction'' due to particle production. We compare the results with the evolution of a quantum scalar field on a fixed background, and find that the backreaction modifies both particle production and cosmological expansion, and that these effects remain bounded.

Vectorial Doppler metrology

The Doppler effect is a universal wave phenomenon that has spurred a myriad of applications. In early manifestations, it was implemented by interference with a reference wave to infer linear velocities along the direction of motion, and more recently lateral and angular velocities using scalar phase structured light. A consequence of the scalar wave approach is that it is technically challenging to directly deduce the motion direction of moving targets. Here we overcome this challenge using vectorially structured light with spatially variant polarization, allowing the velocity and motion direction of a moving particle to be fully determined. Using what we call a vectorial Doppler effect, we conduct a proof of principle experiment and successfully measure the rotational velocity (magnitude and direction) of a moving isotropic particle. The instantaneous position of the moving particle is also tracked under the conditions of knowing its starting position and continuous tracking. Additionally, we discuss its applicability to anisotropic particle detection, and show its potential to distinguish the rotation and spin of the anisotropic particle and measure its rotational velocity and spin speed (magnitude and direction). Our demonstration opens the path to vectorial Doppler metrology for detection of universal motion vectors with vectorially structured light.

Establishment of the fundamental phase-to-polarization link in classical optics

Vector polarization induced by a change in the scalar phase is far beyond our understanding of the relationship between polarization and phase in classical optics due to the entanglement of the inherent polarized modes of light beams. To overcome this limitation, we establish this miraculous relationship by the principle of phase vectorization, which can transform three particular phases into linear, circular and elliptical polarizations. A polarized-spatial light modulator based on the principle of phase vectorization can be achieved using a phase-only spatial light modulator, which not only enables pixel-level polarization manipulation of light beams in a real-time dynamic way but also simultaneously retains complete phase control. This work demonstrates the phase-to-polarization link and reports the creation of a polarized-spatial light modulator, which will transform our view of the natural properties of light beams and pave the way for the era of vector optics.

Self-imaging vectorial singularity networks in 3d structured light fields

We transfer on-demand structuring of three-dimensional scalar amplitude and phase patterns to polarization-structured, vectorial light fields and its singularities. Our approach allows inheriting non-diffracting as well as self-imaging propagation properties to tailored singular ellipse fields, including self-replicating amplitude, polarization, and singularity configurations. It is experimentally realized by amplitude, phase and polarization modulation of the angular spectrum of the light field. We demonstrate the customization of complex singularity formations embedded in three-dimensionally (3d) tailored vectorial field. Our findings show that embedded networks of polarization singularities can be customized to propagate in a robust way along curved trajectories, creating and annihilating during propagation. This 3d structuring of vectorial singular light fields opens new perspectives for in-depth singularity studies and for advancing applications as optical micro-manipulation and material machining.

Phase-field modeling of interactions between double cracks on brittle fracture of Zircaloy-4 cladding

The phase-field model was implemented in Abaqus via user-defined element (UEL) and user-defined material model (UMAT) subroutines for the brittle fracture analysis of a cladding tube. With this method, a scalar damage phase field was utilized to represent the diffuse crack topology, rather than numerical tracking of discontinuities in the cracking area. It was found that the burst hoop stress of the cladding was dependent on the competition of the interference effect and the damage field merging effect of double cracks. Moreover, there was a critical distance between the two cracks at which the burst hoop stress of the cladding reached a minimum. When the distance between two cracks was greater than the critical distance, the damage field merging effect was dominant, whereas when the distance was less than the critical distance, the interference effect was dominant. Furthermore, it was also observed that the burst hoop stress of the cladding was reduced due to the simultaneous initiation of two cracks.

Coupled diffusion and phase transition: Phase fields, constraints, and the Cahn\u2013Hilliard equation

We develop a constrained theory for constituent migration in bodies with microstructure described by a scalar phase field. The distinguishing features of the theory stem from a systematic treatment and characterization of the reactions needed to maintain the internal constraint given by the coincidence of the mass fraction and the phase field. We also develop boundary conditions for situations in which the interface between the body and its environment is structureless and cannot support constituent transport. In addition to yielding a new derivation of the Cahn–Hilliard equation, the theory affords an interpretation of that equation as a limiting variant of an Allen–Cahn type diffusion system arising from the unconstrained theory obtained by considering the mass fraction and the phase field as independent quantities. We corroborate that interpretation with three-dimensional numerical simulations of a recently proposed benchmark problem.

Revealing the phase diagram of Kitaev materials by machine learning: Cooperation and competition between spin liquids

Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-$\Gamma$ model in a magnetic field. Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic $S_3$ magnets, and two modulated $S_3 \times Z_3$ magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic order already occur in the large-$S$ limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level. Moreover, the two $S_3 \times Z_3$ orders are induced by competition between Kitaev and $\Gamma$ spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors. Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.

Real scalar phase transitions: a nonperturbative analysis

We study the thermal phase transitions of a generic real scalar field, without a Z2-symmetry, referred to variously as an inert, sterile or singlet scalar, or ϕ3 + ϕ4 theory. Such a scalar field arises in a wide range of models, including as the inflaton, or as a portal to the dark sector. At high temperatures, we perform dimensional reduction, matching to an effective theory in three dimensions, which we then study both perturbatively to three-loop order and on the lattice. For strong first-order transitions, with large tree-level cubic couplings, our lattice Monte-Carlo simulations agree with perturbation theory within error. However, as the size of the cubic coupling decreases, relative to the quartic coupling, perturbation theory becomes less and less reliable, breaking down completely in the approach to the Z2-symmetric limit, in which the transition is of second order. Notwithstanding, the renormalisation group is shown to significantly extend the validity of perturbation theory. Throughout, our calculations are made as explicit as possible so that this article may serve as a guide for similar calculations in other theories.

Phase-synchronization properties of laminar cylinder wake for periodic external forcings

Abstract

Ultralight scalar decay and the Hubble tension

We examine whether the Hubble tension, the mismatch between early and late measurements of H0, can be alleviated by ultralight scalar fields in the early universe, and we assess its plausibility within UV physics. Since their energy density needs to rapidly redshift away, we explore decays to massless fields around the era of matter-radiation equality. We highlight a concrete implementation of ultralight pseudo-scalars, axions, that decay to an abelian dark sector. This scenario circumvents major problems of other popular realizations of early universe scalar models in that it uses a regular scalar potential that is quadratic around the minimum, instead of the extreme fine-tuning of many existing models. The idea is that the scalar is initially frozen in its potential until H∼ m, then efficient energy transfer from the scalar to the massless field can occur shortly after the beginning of oscillations due to resonance. We introduce an effective fluid model which captures the transition from the frozen scalar phase to the radiation dark sector phase. We perform a fit to a combined Planck 2018, BAO, SH0ES and Pantheon supernovae dataset and find that the model gives H0=69.9−0.86+0.84 km/s/Mpc with Δχ2 ≈ −9 compared to ΛCDM; while inclusions of other data sets may worsen the fit. Importantly, we find that large values of the coupling between fields is required for sufficiently rapid decay: for axion-gauge field models ϕ FF̃/Λ it requires Λ≲ f/80, where 2π f is the field range. We find related conclusions for scalar-scalar models ∼ϕ χ2 and for models that utilize perturbative decays. We conclude that these sorts of ultralight scalar models that purport to alleviate the Hubble tension, while being reasonable effective field theories, require features that are difficult to embed within UV physics.

A Toolbox for Isophase-Curvature Guided Computation of Metrology Hologram.

We describe the algorithmic foundations of an open-source numerical toolbox, written in the Octave language, for the creation of computer-generated binary and multi-level holograms used in interferometric form error measurements of complex aspheric and free-form precision surfaces and wavefronts. In a typical measurement setup for this type of surface, a hologram is used to generate a test wavefront that has the design shape of the surface, which is then compared to a fabricated part using an imaging laser interferometer. The optical function of the hologram in the measurement is generally modeled with optical ray-tracing software and it can be encapsulated by a scalar optical phase function φ : R2 →R. The toolbox converts phase functions into equivalent binary holograms that generate the desired test wavefronts for an interferometric form error measurement. The algorithms in this toolbox take advantage of the relationship between the local properties of phase functions and the local geometry (curvature) of isophase lines. It forms the core of an effcient algorithm for the computation of optical holograms. Holograms are created in a format that can be processed by most laser-or e-beam lithography systems. While the toolbox is chiefy aimed at the creation of hologram layouts needed for measurements of precision surfaces and wavefronts, we show that the isophase-following algorithm is easily extended to phase functions with singularities and discontinuities. Such phase functions result in holograms with zone bifurcation and they can be used to generate helical wavefronts. Light beams with helical wavefronts have applications beyond surface and wavefront metrology. The toolbox also includes a family of functions for the effcient estimation and evaluation of Zernike polynomials, which are widely used in optical applications.

On failure mode transition: a phase field assisted non-equilibrium thermodynamics model for ductile and brittle fracture at finite strain

A non-equilibrium thermodynamics model of viscoplasticity coupled with damage is presented. Keeping in view the experimentally observed failure mode transitions, e.g. brittle to ductile, under dynamic loading condition, the emphasis of the present work has been to endow the formulation with capability of modelling such transitions in a physically consistent manner. Within a framework of internal variables, the current formulation tracks the effect of isotropic viscoplasticity with accumulated plastic strain, and a scalar phase field variable traces the degradation of the material caused by either tensile cracking or shear induced failure. An explicit-implicit strategy is adopted for numerical implementation of the nonlinear formulation. A series of numerical simulations has been carried out on notched metallic specimen to demonstrate the predictive ability of the proposed model and to investigate the influence of several parameters in governing failure mode transition.