Spatial phase retrieval of vortex beam using convolutional neural network

Vortex beam (VB) possessing spatially helical phase–front has attracted widespread attention in free-space optical communication, etc. However, the spiral phase of VB is susceptible to atmospheric turbulence, and effective retrieval of the distorted conjugate phase is crucial for its practical applications. Herein, a convolutional neural network (CNN) approach to retrieve the phase distribution of VB is experimentally demonstrated. We adopt a spherical wave to interfere with VB for converting its phase information into intensity changes, and construct a CNN model with excellent image processing capabilities to directly extract phase–front features from the interferogram. Since the interference intensity is correlated with the phase–front, the CNN model can effectively reconstruct the wavefront of conjugate VB carrying different initial phases from a single interferogram. The results show that the CNN-based phase retrieval method has a loss of 0.1418 in the simulation and a loss of 0.2344 for the experimental data, and remains robust even in turbulence environments. This approach can improve the information acquisition capability for recovering the distorted wavefront and reducing the reliance on traditional inverse retrieval algorithms, which may provide a promising tool to retrieve the spatial phase distributions of VBs.

Spatial Property of Optical Wave Propagation through Anisotropic Atmospheric Turbulence

For the free-space optical (FSO) communication system, the spatial coherence of a laser beam is influenced obviously as it propagates through the atmosphere. This loss of spatial coherence limits the degree to which the laser beam is collimated or focused, resulting in a significant decrease in the power level of optical communication and radar systems. In this work, the analytic expressions of wave structure function for plane and spherical wave propagation through anisotropic non-Kolmogorov turbulence in a horizontal path are derived. Moreover, the new expressions for spatial coherence radius are obtained considering different scales of atmospheric turbulence. Using the newly obtained expressions for the spatial coherent radius, the effects of the inner scales and the outer scales of the turbulence, the power law exponent, and the anisotropic factor are analyzed. The analytical simulation results show that the wave structure functions are greatly influenced by the power law exponent α , the anisotropic factor ζ , the turbulence strength σ ~ R 2 , and the turbulence scales. Moreover, the spatial coherence radiuses are also significantly affected by the anisotropic factor ζ and the turbulence strength σ ~ R 2 , while they are gently influenced by the power law exponent α and the inner scales of the optical waves.

Equations of Electrodynamics

Maxwell’s equations are valid only for a stationary observation point, therefore, to adequately describe real processes so far we have had to move to a moving reference frame. This paper presents the equations of electrodynamics for the moving observation point, it is shown that plane and spherical electromagnetic waves are their solutions, while the spherical wave propagates only outward, which cannot be said about Maxwell’s equations. The fields of uniformly moving charges are also solutions of the equations. Now there is no need to move to a moving reference frame, to use four-dimensional space and covariant form of equations. The question of finding a universal form of the equations that allows a solution in the form of the field of an arbitrarily moving charge remains open. This raises the question of the existence of a two-parameter group of transformations of electromagnetic fields along with the known one-parameter group has been posed. The phenomena derived from the equations, which make an additional contribution to the phase overrun in the Aharonov-Bohm effect are considered. The equation of motion of a charged particle in an electromagnetic field without simplifying approximations is considered, which allows us to take into account the radiation effects. It is shown that the fields in a moving observation point depend on its velocity and acceleration. In particular, although in a constant uniform electric field a force qE acts on a motionless charged particle, but on the same motionless but not fixed particle the force 4/3qE acts already, because it has a nonzero acceleration and the electric field at this point is larger. As the speed increases, the field decreases, and when it reaches the speed of light, when the particle stops accelerating, the force again becomes equal to qE The principle of operation of an unconventional alternator in a constant electric field and its corresponding engine, as well as new types of direct and impulse current generators, predicted by the equations, are described.

Seismic inversion using complex spherical-wave reflection coefficient at different offsets and frequencies

Compared with the plane-wave reflection coefficient, the spherical-wave reflection coefficient (SRC) can more accurately describe the reflected wavefield excited by a point source, especially in the case of low seismic frequency and short travel distance. However, unlike the widely used plane-wave amplitude-variation-with-offset/frequency (AVO/AVF) inversion, the practical application of spherical-wave AVO/AVF inversion in multilayer elastic media is still in the exploratory stage. One of the difficulties is how to fully use the amplitude and phase information of the complex-valued SRC and the spherical-wave response property of each frequency component to obtain the spherical-wave synthetic seismogram in multilayer elastic media. In view of this, we have developed a complex convolution model considering the amplitude and phase information of a SRC to obtain the complex synthetic seismogram of a certain frequency component. A simple harmonic superposition method is further developed. By superposing the complex synthetic seismograms of different frequency components, the synthetic seismogram of the full-frequency band can be obtained. In addition, a novel three-parameter SRC in terms of P- and S-wave moduli and density is derived. Based on the SRC and complex seismic traces with different offsets (or incidence angles) and frequency components, an inversion approach of complex spherical-wave amplitude and phase variation with offset and frequency is proposed. A noisy synthetic data example verifies the robustness of our complex spherical-wave inversion approach. Field data examples indicate that the P- and S-wave moduli estimated by the complex spherical-wave inversion approach can reasonably match the filtered well-logging data. Considering spherical waves rather than plane waves can improve the accuracy of seismic inversion results.

Simulation of wave propagation using graph-theoretical algorithm

We simulate the wave propagation through various mediums using a graph-theoretical path-finding algorithm. The mediums are discretized to the square lattices, where each node is connected up to its 4th nearest neighbours. The edge connecting any 2 nodes is weighted by the time of flight of the wave between the nodes, which is calculated from the Euclidean distance between the nodes divided by the average velocity at the positions of those nodes. According to Fermat’s principle of least time, wave propagation between 2 nodes will follow the path with minimal weight. We thus use the path-finding algorithm to find such a path. We apply our method to simulate wave propagation from a point source through a homogeneous medium. By defining a wavefront as a contour of nodes with the same time of flight, we obtain a spherical wave as expected. We next investigate the wave propagation through a boundary of 2 mediums with different wave velocities. The result shows wave refraction that exactly follows Snell’s law. Finally, we apply the algorithm to determine the velocity model in a wood sample, where the wave velocity is determined by the angle between the propagation direction and the radial direction from its pith. By comparing the time of flight from our simulation with the measurements, the parameters in the velocity model can be obtained. The advantage of our method is its simplicity and straightforwardness. In all the above simulations, the same simple path-finding code is used, regardless of the complexity of the wave velocity model of the mediums. We expect that our method can be useful in practice when an investigation of wave propagation in a complex medium is needed.

Electromagnetic Insights Into Path Loss Modelling of IRS-Assisted SISO Links: Method-Of-Moment Based Analysis

In this paper, we demonstrate the usefulness of MoM (Method-of-Moments) based methods in efficient path-loss modelling for SISO (single-input single-output) communication links assisted by IRS (Intelligent Reflecting Surfaces). Being a full-wave computational electromagnetic tool, MoM is better equipped compared to high-frequency asymptotic methods like PO (Physical Optics), to handle the crucial electromagnetic (EM) effects like: mutual coupling between IRS unit-cells or interactions with spherical wave-front in antenna near-field. Furthermore, in terms of computational speed, accuracy and reproducibility, the MoM-based MATLAB Antenna Toolbox is significantly advantageous to emulate IRS-assisted wireless channels, as compared to the in-house FDTD (finite-difference time-domain) techniques. We consider a SISO system of two half-wavelength dipoles, and use a rectangular array of circular loops loaded with lumped circuit components as IRS. The lumped circuit loading enables us to control the reactance of individual unit-cells, resulting in alteration of IRS reflection coefficient and consequent changes in channel characteristics. Using numerous numerical simulations, we highlight the impacts of various IRS-parameters like: electrical size and number of unit-cells, distance of IRS from the transmitter/receiver as well as mutual coupling, on the path-loss models (both sub-6 GHz and mm-wave).

Equations of Electrodynamics

The equations of electrodynamics are presented, it is shown that plane and spherical electromagnetic waves are their solutions, while the spherical wave propagates only outward. Fields of uniformly moving charges are also solutions of equations. The question of finding a universal form of equations admitting a solution in the form of a field of an arbitrarily moving charge remains open. The question is raised about the existence of a two-parameter group of transformations of electromagnetic fields along with the well-known one-parameter group. The equation of motion of a charged particle in an electromagnetic field is considered without simplifying approximations. The principle of operation of an unconventional alternator in a constant electric field and a corresponding engine, as well as new types of generators of direct and impulse current, are described.