Continuous Wavefront Research Articles

Formation of local heterogeneity under energy collection in neural networks

Static distribution of intracellular and extracellular ions can induce the spatial distribution of electric field in the cell, while stochastic diffusion and propagation of ions can generate channel current accompanied by the magnetic field. In fact, the field energy (including magnetic and electric fields) in each cell or neuron can be changed under external stimuli or the deformation of shape. Furthermore, energy pumping occurs, and the synaptic connection is created adaptively to keep energy balance when more neurons are clustered in the same region because of electromagnetic field superposition. For a synchronous and homogeneous network, all neurons keep energy balance with the adjacent neurons, and the network becomes uniform and identical. For cardiac tissue and biological media, local heterogeneity such as sinoatrial node can emit continuous wave front, and target waves are propagated to regulate the neural activities and heartbeat rhythm. In this paper, the Hamilton energy in a simple neuron model is calculated according to the Helmholtz theorem, and more neurons are clustered to build a regular network (chain network and square array). The creation and growth of synapse connection are controlled to pump energy, and local heterogeneity is formed by taming one intrinsic parameter when more energy is accumulated in a few neurons in the network. These results indicate that asymmetrical energy transport will induce the occurrence of heterogeneity in the network, and adaptive synaptic regulation on neurons is activated to keep local energy balance before reaching perfect synchronization. When external stimuli with diversity in intensity are applied, neurons are excited with energy diversity, and possible shape deformation is induced to keep local energy balance. As a result, heterogeneity is developed in a local area.

Coronagraphic detection of Earth-like planets with large, actively controlled space telescopes

We explore the capabilities of large segmented telescopes with active and adaptive optics, with a particular focus on a system view, which includes use of approaches that are routine for current large ground-based telescopes. Using a physically motivated order-of-magnitude model, we show that continuous control of telescope misalignments using adjustable optics in an exoplanet imaging instrument significantly relaxes stability requirements for the entire observatory. We start with the recent analysis by Nemati et al., (2020, JATIS 6, id. 039002), which asserts that small monolithic mirrors have an engineering advantage over larger segmented mirrors when it comes to obtaining images stable enough for direct exoplanet imaging and characterization, i.e., picometer stability. When we fold these results into our model of closed-loop operations and properly partition engineering challenges by optimizing error budget allocations, we find that even for the most sensitive modes, allowable drifts are actually of the order of nanometer over an hour, well within easily engineered tolerances. While this order-of-magnitude analysis does not include full end-to-end modeling or proper engineering margins, it showcases the importance of considering continuous wavefront sensing and control when discussing the feasibility of future exoplanet missions. We also quantify how large segmented architectures, in spite of appearing more complex at the observatory level, facilitate closed-loop operations due to their large photon collection abilities. We place our work in the context of larger discussions on aperture size that highlight a more fundamental challenge: the deeper uncertainties in performance of an exo-earth characterizing telescope primarily reside in our knowledge of the frequency of exo-earths; the effects of geological age on the resulting atmospheres; and, most importantly, on the likelihood of detectable life arising on such planets. A mission that sets out to establish whether we are alone among the nearby stars must adopt a mission architecture that is resilient against such intrinsic uncertainties: uncertainties that only direct observations can resolve. Large apertures enabled by segmented telescope designs historically have demonstrated such resilience.

Broadband and high-efficiency accelerating beam generation by dielectric catenary metasurfaces

Abstract Self-accelerating beams show considerable captivating phenomena and applications owing to their transverse acceleration, diffraction-free and self-healing properties in free space. Metasurfaces consisting of dielectric or metallic subwavelength structures attract enormous attention to acquire self-accelerating beams, owing to their extraordinary capabilities in the arbitrary control of electromagnetic waves. However, because the self-accelerating beam generator possesses a large phase gradient, traditional discrete metasurfaces suffer from insufficient phase sampling, leading to a low efficiency and narrow spectral band. To overcome this limitation, a versatile platform of catenary-inspired dielectric metasurfaces is proposed to endow arbitrary continuous wavefronts. A high diffraction efficiency approaching 100% is obtained in a wide spectral range from 9 to 13 μm. As a proof-of-concept demonstration, the broadband, high-efficiency and high-quality self-accelerating beam generation is experimentally verified in the infrared band. Furthermore, the chiral response of the proposed metasurfaces enables the spin-controlled beam acceleration. Considering these superior performances, this design methodology may find wide applications in particle manipulation, high-resolution imaging, optical vortex generation, and so forth.

Terahertz shifted optical sideband generation in graphene

Exploration of optical non-linear response of graphene predominantly relies on ultra-short time domain measurements. Here we propose an alternate technique that uses frequency modulated continuous wavefront optical fields, thereby probing graphene's steady state non-linear response. We predict frequency sideband generation in the reflected field that originates from coherent electron dynamics of the photo-excited carriers. The corresponding threshold in input intensity for optimal sideband generation provides a direct measure of the third order optical non-linearity in graphene. Our formulation yields analytic forms for the generated sideband intensity, is applicable to generic two-band systems and suggests a range of applications that include switching of frequency sidebands using non-linear phase shifts and generation of frequency combs.

Non-hogel-based computer generated hologram from light field using complex field recovery technique from Wigner distribution function.

We propose a novel method that synthesizes computer-generated holograms from light field data. Light field, or ray space, is the spatio-angular distribution of light rays coming from three-dimensional scene, and it can also be represented using a large number of views from different observation directions. The proposed method synthesizes a hologram by applying the complex field recovery technique from its Wigner distribution function to the light field data. Unlike conventional approaches, the proposed method synthesizes holograms without hogel configuration, generating a converging parabolic wave for each object point with continuous wavefront. The proposed method does not trade the spatial resolution with angular resolution like conventional hogel-based approaches. Moreover, the proposed method works not only for random phase light field like conventional approaches, but also for arbitrary phase distribution with corresponding carrier waves. Therefore, the proposed method is useful in synthesizing holographic contents for a wide range of applications. The proposed method is verified by simulations and optical experiments, showing successful reconstruction of three-dimensional objects.

Patchy spread patterns in three-species bistable systems with facultative mutualism

A three-species population system under a facultative mutualistic relationship of one of the species is studied. The considered interactions are as follows: facultative between the first species and the second species, obligatory mutualism between the second species and the first one, and the third species is a predator of the first species. For this purpose, we extend the model proposed by Morozov et al., originally used to describe obligatory mutualism, to consider obligatory and facultative mutualism and prove that under adequately selected parameters this system produces a spatial patchy spread of populations or continuous wave fronts. Since the analytical treatment of a three-species model is often prohibitive, we first analyze the interaction between two mutualist species without diffusion and without the presence of the predator. Some parameters are fixed in the bistable regime of the mutualistic species to further consider the influence of the third species. The remaining parameters are then selected to produce patchy patterns under different mortality rates. Finally, the equations of the final three-species system are numerically solved to test the influence of different initial conditions in the formation of patchy populations. It is confirmed that the velocity and the profile of a traveling front are independent on the initial conditions. Our approach opens the way to study more general biological situations.

Complex exponential reconstruction algorithm accelerated by cascadic multigrid method

When laser beam propagates through the turbulent atmosphere, there are branch points in wavefront, which are caused by deep turbulence or long propagation distance. Conventional least-square reconstruction algorithms cannot restore the discontinuous wavefront, which severely limits correction performance of an adaptive optics system. If the incoming wavefront contains a branch cut, there is <inline-formula><tex-math id="M1">\begin{document}$ {\rm{2}}n{\text{π}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20182137_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20182137_M1.png"/></alternatives></inline-formula> difference between the measured phase difference and the principle phase difference, which is the reason why conventional least-square reconstruction algorithms cannot reconstruct wavefront with branch points. The complex exponential reconstructor is developed to restore the discontinuous wavefront with phase difference replaced by complex exponents. However, thousands of iterations are required by the complex exponential reconstructor before converging to an acceptable solution. In order to speed up the iterative calculation, the cascadic multigrid method (CMG) is introduced in the process of wavefront reconstruction. The proposed method can be used to restore discontinuous wavefront with lower residual error similar to those reconstructed by the direct iteration. The number of float point multiplications required by the CMG method is nearly 2 orders of magnitude lower than that required by the direct iteration. The acceleration of the CMG method increases with the number of subapertures increasing. The performance of CMG method to recover continuous wavefront is also investigated and compared with conventional wavefront reconstruction algorithm based on successive over-relaxation. It is shown that the CMG method has good capability for wavefront reconstruction with high precision and low computation cost no matter whether it is applied to discontinuous or continuous wavefront. Furthermore, the CMG method is used in the adaptive optics for correcting the turbulence aberration. The direct slope wavefront reconstruction algorithm based on the assumption that the measured slope and the control voltage satisfy the linear relationship cannot restore the wavefront with branch points. As a result, the adaptive optics system with the CMG method doubles the correction quality evaluated by the Strehl ratio compared with that with the direct slope wavefront reconstruction algorithm.

Focusing light through dynamical samples using fast continuous wavefront optimization.

We describe a fast continuous optimization wavefront shaping system able to focus light through dynamic scattering media. A micro-electro-mechanical system-based spatial light modulator, a fast photodetector, and field programmable gate array electronics are combined to implement a continuous optimization of a wavefront with a single-mode optimization rate of 4.1kHz. The system performances are demonstrated by focusing light through colloidal solutions of TiO2 particles in glycerol with tunable temporal stability.

A comparative analysis of two-dimensional multi-valued ray tracing techniques

Seismic wavefront self-intersection (or multi-valued seismic rays) is a natural phenomenon when a seismic wave propagates through a complex medium, which is commonly ignored in most previous studies. The later arrivals not only contain useful information regarding low velocity anomalous zones and/or irregular reflecting interfaces, but also have the potential to improve the ray coverage in subsequent seismic imaging. Due to the relative immaturity of this field of research, it is instructive to compare different algorithms and therefore develop more advanced, efficient, and practical schemes for tracing multi-valued arrivals between the source and the receivers when the medium is heterogeneous and incorporates irregular or curved interfaces. For these reasons, we first modify the so-called reduced phase space method, in which a continuous wavefront mapping method is implemented for efficient and accurate consideration, and then compare it with two newly developed grid-based algorithms for tracing multi-valued direct arrivals in heterogeneous media and multi-valued reflected arrivals when undulating interfaces are present. The results show that the modified reduced phase space method is a potent and useful algorithm for tracking both multi-valued direct and reflected arrivals. The first-order “raylet” method is simple in principle but is unable to trace all possible later arrivals. Under such circumstances, the extremal solution method is a good choice to trace the multi-valued reflected arrivals; it is comparable to the modified reduced phase space method in practical application.

Transmission of blocked electric pulses in a cable neuron model by using an electric field

Signal propagation can be blocked when the axon is injured or ion channels are blocked by certain drug, and thus signal communication between neurons can be interrupted. It is found that defects could be induced in the injured area of the axon, and the local heterogeneity can emit continuous pulses or wave fronts. In this paper, a weak electric field is imposed on the neuron to suppress the blocking of the defects on signal propagation. It is found that appropriate electric field can help signal propagate along the axon even the electric field is imposed on a local area. Its potential mechanism could be that the local electric field can suppress the wave emitting from the defects and thus the injured area can be bridged to transmit the blocked signals by adding gradient forcing along the axon.

Accelerating and Abruptly-Autofocusing Beam Waves in the Fresnel Zone of Antenna Arrays

We introduce the concept of spatially accelerating (curved) beam waves in the Fresnel region of properly designed antenna arrays. These are transversely localized EM waves that propagate in free space in a diffraction-resisting manner, while at the same time laterally shifting their amplitude pattern along a curved trajectory. The proposed beams are the radiowave analogue of Airy and related accelerating optical waves, which, in contrast to their optical counterparts, are produced by the interference of discrete radiating elements rather than by the evolution of a continuous wavefront. Two dyadic array configurations are proposed comprising 2D line antennas: linear phased arrays with a power-law phase variation and curved power-law arrays with in-phase radiating elements. Through analysis and numerical simulations, the formation of broadside accelerating beams with power-law trajectories is studied versus the array parameters. Furthermore, the abrupt autofocusing effect, that occurs when beams of this kind interfere with opposite acceleration, is investigated. The concept and the related antenna setups can be of use in radar and wireless communications applications.

Discreteness of the set of radiant point sources: a physical feature of the second-order wave-fronts

The non-paraxial phase-space representation of diffraction of optical fields in any state of spatial coherence has been successfully modeled by assuming a discrete set of radiant point sources at the aperture plane instead of a continuous wave-front. More than a mere calculation strategy, this discreteness seems to be a physical feature of the field, independent from the sampling procedure of the modeling.

Limitations of adaptive control efficiency due to singular points in the wavefront of a laser beam

Optical vortices occur at light propagation in an inhomogeneous medium, disturbing the operation of adaptive optical systems and assuring a priori continuity of the phase fluctuation function. It is clear that the physical process of the light wave propagation has a threshold of complexity relative to the description and measurement of this process, after which the light wave contains points with zero intensity and there is no continuous wavefront. The appearance of zeros indicates the transition of phenomenon in a new condition. The results of numerous studies of phase fluctuations of optical waves in the atmosphere, first of all, provide a basis for estimating the efficiency of operation of adaptive optical systems, second, make it possible to determine the requirements on the wavefront sensors and adaptive mirrors, and, finally, make it possible to determine the structure and properties of phase-conjugated adaptive optical systems.

Changes in aberrations and retinal image quality due to tear film dynamics

A reliable and objective method to measure aberration changes due to the tear film is essential in improving clinical assessment of the tear film and in vivo retinal imaging. The tear film of 11 subjects are studied by acquiring continuous wavefront measurements in real-time with a customized Shack-Hartmann wavefront sensor. The device has a high resolution lenslet array (190 mum) and a topographer unit with an infrared pupil illuminator (940 nm). A Fourier transform reconstructor algorithm [1] was used to estimate the eyes' wavefront aberrations from slope measurements. Increasing irregularities in the tear film produced observable wavefront variations. The temporal behavior of tear induced aberrations and retinal image quality was evaluated by the root mean squared (RMS) error of the residual wavefront and the volume modulation transfer function (MTF). Similar trends were observed from both metrics. Our analysis demonstrates the applicability of the SH wavefront sensor to assessing the dynamics of the human tear film.

Discrete continuous-phase superresolving filters

A new type of phase-only superresolving pupil filter with a discrete continuous-phase profile is presented that is a combination of discrete multilevel-phase modulation and continuous-phase modulation. This type of filter can achieve better superresolution performance than the continuous-phase filters reported in Opt. Lett. 28, 607 (2003). Therefore, with regard to the superresolution effect, this type of filter deserves study for practical applications. More importantly, the diffraction performance of this type of filter can explain the effect of a discrete-phase filter illuminated with a continuous wave front, whose superresolving performance cannot be analyzed with previous superresolution methods.

Traveling waves in time periodic lattice differential equations

The current paper concerns with traveling wave solutions to time periodic two-dimensional lattice differential equations of bistable type. Employing the so-called ‘vanishing viscosity’ approach, we obtain the existence of monotone traveling wave solutions connecting the two spatially homogeneous periodic solutions. Uniqueness of the wave speed and uniqueness of continuous wave front are shown by repeatedly utilizing comparison arguments. The existence and uniqueness results of the current paper together with the stability results proved in an author's earlier paper generalize those in the time-independent case.

THE STOCHASTIC NATURE OF CARDIAC PROPAGATION DUE TO THE DISCRETE CELLULAR STRUCTURE OF THE MYOCARDIUM

The object of this paper is to describe cardiac conduction phenomena caused by the discrete nature of cardiac cellular structure. Recent results show that the myocardial architecture creates inhomogeneities of electrical load at the microscopic level that cause cardiac propagation to be stochastic in nature. That is, the excitatory events during propagation are constantly changing and disorderly in the sense of varying intracellular events and delays between cells. A unique feature of the stochastic nature of cardiac propagation is that electrical boundaries produced by cellular myocardial architecture create inhomogeneities of electrical load that affect conduction inside individual cells and influence conduction delays across gap junctions, as well as at muscle bundle junctions. This process produces discontinuous propagation as a primary reflection of the nonuniformities of electrical load due to the irregular arrangement of the cellular borders and the associated nonuniform distribution of their electrical interconnections. A fundamental consequence of the stochastic nature of normal propagation at a microscopic level is that it provides a major protective effect against arrhythmias by re-establishing the general trend of wave front movement after small variations in excitation events occur. When the diversity at a very small size scale decreases throughout the tissue, such as occurs when there are regularly repeating relatively isolated groups of cells, larger fluctuations of load can develop and be distributed over more cells than occurs normally. The myocardial architecture may then fail to re-establish a smoothed wave front and re-entry can develop. These relatively new discontinuous conduction phenomena provide important theoretical and experimental challenges to synthesize a complete theory linking continuous and discontinuous media as applied to cardiac conduction. The results show that it will be important to distinguish differences in wave front movement and conduction block caused by mechanisms of continuous media versus wave front movement and block imposed by directional or localized changes in cellular connectivity; i.e., the topology of the electrical connections between cells (gap junctions).

Path-independent phase unwrapping of subsampled phase maps

A technique for unwrapping subsampled phase maps is presented. The subsampled phase map is obtained by standard phase-shifting methods that use subsampled interferograms. The technique then estimates the wrapped local curvature of the subsampled phase map. This local curvature is then low-pass filtered with a free-boundary low-pass filter to reduce phase noise. Finally the estimated local curvature of the wave front is integrated by the use of a least-squares technique to obtain the searched continuous wave front.

Qualitative analysis of response caused by growing plane waves by underdetermined system theory

A qualitative analysis of the mechanical response of rate-dependent media caused by one-dimensional plane smooth- and continuous-wave fronts with the growing peaks of strain, particle velocity, and stress is performed by an underdetermined system of nonlinear partial differential equations. The response found by the analysis reveals that strain, particle velocity, and stress profiles in the smooth-wave front are not similar and that the front is composed of five partial waves having different properties. The property is represented by the set of strain rate, acceleration, and stress rate as in a previous study. The front of the wave front is necessarily a contraction wave in which strain, particle velocity, and stress increase with time. The second partial wave is another contraction wave. We call the wave a vice-contraction wave. The rear is assumed to be a rarefaction wave where they all decrease with time. Between these two partial waves there are two remaining partial waves. We call these waves mesorarefaction waves I and II. Wave II is a wave in which particle velocity and stress increase, notwithstanding the decrease in strain with time. It is followed by wave I in which the increase in stress with time occurs in spite of the decrease in strain and particle velocity. The continuous-wave front, which has discontinuous-movement velocities at the continuous, but nonsmooth, positions in the profiles of strain, particle velocity, and stress, is composed of five independent waves. These waves are a contraction wave, a vice-contraction wave, evolutional rarefaction waves II and I, and a rarefaction wave which possess the same properties as the corresponding partial waves in the smooth-wave front mentioned above. Both in the smooth-growing-wave front and in the continuous one the peak precedence is in the order of the strain, particle velocity, and stress peaks. The stress-strain path and stress-particle velocity path at a position in a rate-dependent medium which is passed by the continuous-wave front are schematically shown.

Qualitative analysis of degradation processes of attenuating plane waves by underdetermined system theory

A qualitative analysis of the mechanical response caused by smooth attenuating wave fronts and by continuous attenuating wave fronts degrading in rate-dependent media is performed by an underdetermined system of equations, that is, by equations of conservation of mass and momentum only. Degradation is defined as the decrease of the number of partial waves in a smooth wave front or of independent waves in a continuous wave front. For the smooth wave front the inceptive wave front with which the degradation commences is a wave that is composed of four partial waves found previously and named a contraction wave, mesocontraction waves I and II, and a rear rarefaction wave. The analysis reveals one possible degradation process that is caused by another rarefaction wave which first follows the rear wave and then outruns the rear wave, mesocontraction waves II and I in sequence. The continuous wave degrades from the inceptive continuous wave front which is composed of four independent waves found previously and named a contraction wave, degenerate contraction waves I and II, and a rear rarefaction wave. The analysis indicates that degradation from the inceptive wave front to the contraction wave is possible to progress in six different patterns. In short, the degradation can occur through six different processes. Each process gives rise to four different sets of strain, particle velocity, and stress profiles, and accordingly four different types of stress-strain paths and four different types of stress-particle velocity paths. The stress-strain paths induced during some of the processes are similar to the paths in sandstone computed by Seaman using the Lagrangian analysis. The stress-particle velocity paths induced during some of the processes are also similar to the paths in LASL graphite computed by Seaman.