Wave Propagation In Free Space Research Articles

Efficient light propagation algorithm using quantum computers

Quantum algorithms can potentially overcome the boundary of computationally hard problems. One of the cornerstones in modern optics is the beam propagation algorithm, facilitating the calculation of how waves with a particular dispersion relation propagate in time and space. This algorithm solves the wave propagation equation by Fourier transformation, multiplication with a transfer function, and subsequent back transformation. This transfer function is determined from the respective dispersion relation, which can often be expanded as a polynomial. In the case of paraxial wave propagation in free space or picosecond pulse propagation, this expansion can be truncated after the quadratic term. The classical solution to the wave propagation requires O(NlogN) computation steps, where N is the number of points into which the wave function is discretized. Here, we show that the propagation can be performed as a quantum algorithm with OlogN2 single-controlled phase gates, indicating exponentially reduced computational complexity. We herein demonstrate this quantum beam propagation method (QBPM) and perform such propagation in both one- and two-dimensional systems for the double-slit experiment and Gaussian beam propagation. We highlight the importance of the selection of suitable observables to retain the quantum advantage in the face of the statistical nature of the quantum measurement process, which leads to sampling errors that do not exist in classical solutions.

Close link between Fabry–Pérot resonance and natural-resonance frequencies

Mathematical and numerical analyses have been performed to examine the close link between Fabry–Pérot resonance and natural-resonance frequencies. For the mathematical analysis, the conditions resulting in minimum magnitudes of reflection coefficients in frequency-domain are derived for air-backed and metal-backed low-loss non-dispersive (or weakly dispersive) dielectric samples with relative complex permittivity and thickness L for free-space wave propagation at normal incidence. The close relation between Fabry–Pérot resonance and natural-resonance frequencies is demonstrated for three different sample scenarios as (i) no-dispersion and lossless case ( and L = 50 mm), (ii) no-dispersion and low-loss case ( and L = 50 mm), and (iii) weak-dispersion and low-loss case ( and L = 50 mm where σ is the conductivity of the sample and ω is the angular frequency). It is noted that operating frequency should be increased to observe late-time natural-resonance frequencies for a sample with smaller length or vice versa.

High-resolution ghost imaging through complex scattering media via a temporal correction

In this Letter, we propose high-resolution ghost imaging (GI) through complex scattering media using temporal correction. We provide evidence that the theoretical description about GI based on spatially correlated beams is still incomplete and cannot work in complex scenarios. We complete the description of temporal correction of beam correlations in GI. The optical experiments demonstrate that high-resolution ghost images can always be retrieved by using the rectified temporally corrected beam correlation algorithm even in complex, dynamic, and highly strong scattering environments where conventional GI cannot work. By using the proposed method, the quality of the retrieved ghost images through complex scattering media can be enhanced effectively as the number of realizations increases, which cannot be achieved by conventional GI. The established general framework provides optical insights beyond the current understanding of GI, and the rectified theory and experimental results would represent a key step toward applications of GI over a wide range of free-space wave propagation environments.

Physically-secured high-fidelity free-space optical data transmission through scattering media using dynamic scaling factors.

In this paper, we propose a method of physically-secured high-fidelity free-space optical data transmission through scattering media using physically- and dynamically-generated scaling factors. Optical channel characteristics are explored, and scaling factors are physically and dynamically generated to serve as security keys in the developed free-space optical data transmission system. The generated dynamic scaling factors provide a security layer for free-space optical data transmission. To the best of our knowledge, it is the first time to physically and dynamically generate scaling factors in free-space optical data transmission system to realize data encryption. The scaling factors existing in free-space optical data transmission channel are physically and dynamically controlled by using two optical devices, i.e., variable beam attenuator (VBA) and amplitude-only spatial light modulator (SLM). Nonlinear and dynamic variation of scaling factors is realized in different free-space wave propagation environments. It is experimentally demonstrated that high security can be guaranteed in the developed physically-secured high-fidelity free-space optical data transmission system, since one random scaling factor is physically and dynamically generated for the transmission of each signal pixel value. In addition, the proposed physically-secured free-space optical data transmission scheme is robust to noise and scattering, and high-fidelity signals are retrieved at the receiving end. The proposed method could open up a new research perspective for the secured free-space optical data transmission.

Finite-difference wave-propagation models for dispersive media: impact of space-time discretization

PurposeThe computational accuracy and performance of finite-difference time-domain (FDTD) methods are affected by the implementation of approximating derivative formulae in diverse ways. This study aims to focus on FDTD models featuring material dispersion with negligible losses and investigates two specific aspects that, until today, are usually examined in the context of non-dispersive media only. These aspects pertain to certain abnormal characteristics of coarsely resolved electromagnetic waves and the selection of the proper time-step size, in the case of a high-order discretization scheme.Design/methodology/approachConsidering a Lorentz medium with negligible losses, the propagation characteristics of coarsely resolved waves is examined first, by investigating thoroughly the numerical dispersion relation of a typical discretization scheme. The second part of the study is related to the unbalanced space-time errors in FDTD schemes with dissimilar space-time approximation orders. The authors propose a remedy via the suitable choice of the time-step size, based on the single-frequency minimization of an error expression extracted, again, from the scheme’s numerical dispersion formula.FindingsUnlike wave propagation in free space, there exist two parts of the frequency spectrum where waves in a Lorentz medium experience non-physical attenuation and display non-changing propagation constants, due to coarse discretization. The authors also show that an optimum time-step size can be determined, in the case of the (2,4) FDTD scheme, which minimizes the selected error formula at a specific frequency point, promoting more efficient implementations.Originality/valueUnique characteristics displayed by discretized waves, which have been known for non-dispersive media, are examined and verified for the first time in the case of dispersive materials, thus completing the comprehension of the space-time discretization impact on simulated quantities. In addition, the closed-form formula of the optimum time-step enables the efficient implementation of the (2,4) FDTD method, minimizing the detrimental influence of the low-order temporal integration.

Physically-enhanced ghost encoding.

In this Letter, we propose a physically enhanced ghost encoding scheme that is realized by exploring optical channel characteristics, i.e., physically and dynamically generated scaling factors. It is found that scaling factors can be physically and dynamically generated to serve as security keys in a ghost encoding scheme, dramatically enlarging the key space and enhancing the security of optical ghost encoding schemes. To the best of our knowledge, this is the first time that dynamic scaling factors have been controlled in the optical path to realize physically enhanced ghost encoding. In addition to the illumination patterns used in optical ghost encoding schemes, the proposed method applies a variable beam attenuator and an amplitude-only spatial light modulator (SLM) to physically generate dynamic scaling factors as keys. Nonlinear variation of scaling factors is achieved in different free-space wave-propagation environments in the proposed method. A series of optical experiments are conducted to verify the feasibility and effectiveness of the proposed physically enhanced ghost encoding scheme. The proposed method could open up new research perspectives in optical ghost encoding.

Photonic extreme learning machine by free-space optical propagation

Photonic brain-inspired platforms are emerging as novel analog computing devices, enabling fast and energy-efficient operations for machine learning. These artificial neural networks generally require tailored optical elements, such as integrated photonic circuits, engineered diffractive layers, nanophotonic materials, or time-delay schemes, which are challenging to train or stabilize. Here, we present a neuromorphic photonic scheme, i.e., the photonic extreme learning machine, which can be implemented simply by using an optical encoder and coherent wave propagation in free space. We realize the concept through spatial light modulation of a laser beam, with the far field acting as a feature mapping space. We experimentally demonstrate learning from data on various classification and regression tasks, achieving accuracies comparable with digital kernel machines and deep photonic networks. Our findings point out an optical machine learning device that is easy to train, energetically efficient, scalable, and fabrication-constraint free. The scheme can be generalized to a plethora of photonic systems, opening the route to real-time neuromorphic processing of optical data.

Предельная точность решения двумерного параболического уравнения методом дискретного преобразования Фурье

Numerical solution of the wave parabolic equation on a rectangular grid is analyzed, when the method of discrete split-step Fourier transform (FT) is used to calculate the values of the field in an inhomogeneous medium at the next step in the range. The goal was to identify the limiting possibilities of the FT method itself, so studies were carried out for the case of radio wave propagation in free space. Two related problems were solved: what is the minimum value of the root-mean-square error (RMSE) of the field calculation and what should be the values of the transfer coefficients of the Fourier series harmonics and the values of the coefficients of the artificial absorbing layer (AL) both depending on the parameters of the computational scheme. It is shown that the dependence of the RMSE on the distance to the source always has the maximum. The forms of the optimal AL differ from those traditionally used primarily due to the presence of a significant imaginary component.

Boreal Forest Properties From TanDEM-X Data Using Interferometric Water Cloud Model and Implications for a Bistatic C-Band Mission

Data from TanDEM-X in single-pass and bistatic interferometric mode together with the interferometric water cloud model (IWCM) can provide estimates of forest height and stem volume (or the related above-ground biomass) of boreal forests with high accuracy. We summarize results from two boreal test sites using two approaches, i.e., 1) based on model calibration using reference insitu stands, and 2) based on minimization of a cost function. Both approaches are based on inversion of IWCM, which models the complex coherence and backscattering coefficient of a homogeneous forest layer, which includes gaps where free-space wave propagation is assumed. A digital terrain model of the ground is also needed. IWCM is used to estimate forest height or stem volume, since the two variables are assumed to be related through an allometric equation. A relationship between the fractional area of gaps, the area-fill, and stem volume is also required to enable model inversion. The accuracy of the stem volume estimate in the two sites varies between 16% and 21% for height of ambiguity <100 m. The results clearly show the importance of using summer-time acquisitions. Based on the TanDEM-X results at X-band, C-band data from the ERS-1/ERS-2 tandem mission are revisited to investigate the potential of a future bistatic C-band interferometric mission. Out of nine ERS-1/ERS-2 pairs, only one pair was found to be acquired at summer temperatures, without precipitation and with high coherence. A simulated bistatic phase height is shown to give approximately the same sensitivity to stem volume as TanDEM-X.

МАТЕМАТИЧНА МОДЕЛЬ ПОШУКУ ТА ВИЯВЛЕННЯ ВИБУХОВИХ ПРИСТРОЇВ З НЕКОНТАКТНИМИ ДАТЧИКАМИ ЦІЛІ МЕТОДОМ НЕЛІНІЙНОЇ РАДІОЛОКАЦІЇ

Radical changes in the nature and significant increase in the dynamics of mine warfare in modern military conflicts are the result of shifting priorities towards the use of the latest models of minesweepers and improvised explosive devices with mostly non-contact target sensors. This state of affairs has exacerbated the problem of countering explosive threats, and with it the need to ensure the required level of efficiency, safety and cost of search and detection of explosive devices with non-contact (electronic) target sensors. Existing technical means of search and detection of explosive objects, as a rule, in most cases are based on the use of active electromagnetic methods. The approach of such search devices to explosive devices with magnetic (non-contact) target sensors or those controlled by radio, often led to an unauthorized explosion and as a consequence to losses among the sappers.It is established that almost all non-contact sensors of the target are united by a common feature - the presence of semiconductor elements in their composition, or transitions such as metal-oxide-metal. These features are the basis of modern means of detecting explosive devices with non-contact target sensors by nonlinear radar. However, the requirements for the safety of using search engines of this type in the manual version or on land vehicles are still problematic. One way to resolve this contradiction is to install search engines on a remote-controlled platform. Moreover, there is an urgent need to substantiate the tactical and technical requirements for this type of equipment when changing the conditions and methods of their application.Based on the analysis of previous studies, both domestic and foreign experts, on the use of electromagnetic methods of search and detection of man-made objects in sheltered environments (soil, snow, water, etc.), proposed an improved mathematical model of search and detection of explosive devices with non-contact target sensors nonlinear radar. This model, in contrast to the existing ones, takes into account the probabilistic nature of the search process and the plane indicators of the guaranteed detection zone of devices with non-contact target sensors by nonlinear radar, functional indicators of electromagnetic wave propagation in free space and shelter. In the field of nonlinear radar, the concept of "zone of guaranteed detection of explosive devices with non-contact target sensors" was introduced for the first time, the essence of which is to ensure the implementation of the requirements for equivalent probability of detection at a level not lower than specified. In addition, the proposed mathematical model, among other technical characteristics, allows to set the performance parameters of the remote-controlled radar complex search and detection of explosive devices with non-contact target sensors by nonlinear radar. The proposed improvements of the mathematical model and the sequence of calculations will increase the accuracy of the results of modeling the search and detection of explosive devices with non-contact target sensors in sheltered environments when substantiating the requirements for demining of this type.

Large Surface LC -Resonant Metamaterials: From Circuit Model to Modal Theory and Efficient Numerical Methods

We studied the harmonic magnetodynamic behavior (without free space wave propagation) of a resonant surface metamaterial, made of many identical and regularly arranged LC cells. The circuit model gives the exact solution, but it is not numerically efficient for simulating very large structures (e.g., 1000 × 1000 cells giving 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> unknowns with a full 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> matrix). For the first time, we highlight the modal characteristics of the spatial solutions, which make it possible to explain their frequency- and spatial-related properties. From these results, we show under what assumptions it is possible to significantly lighten the system of equations, which opens up the way to develop more efficient numerical methods.

Measuring the shielding properties of flexible or rigid enclosures for portable electronics.

Heaviside, in volume 1 of Electromagnetic theory, considered shielding of conducting materials in the form of attenuation. This treatment is still significant in the understanding of shielding effectiveness. He also considered propagation of electromagnetic waves in free-space. What Heaviside (1850-1925) could never have imagined is that 125 years later, there would be devices we know as mobile phones (or cell phones, handies, etc.) with capabilities beyond the dreams of the great science fiction writers of the day like H. G. Wells (1866-1949) or Jules Verne (1828-1905). More than this, that there would be a need for law enforcement agencies, among others, to use electromagnetically shielded enclosures to protect electronic equipment from communicating with the 'outside world'. Nevertheless, Heaviside's work is still fundamental to the developments discussed here. This paper provides a review of Heaviside's view of shielding and propagation provided in volume 1 of Electromagnetic theory and develops that to the design of new experiments to test the shielding of these portable enclosures in a mode-stirred reverberation chamber, a test environment that relies entirely on reflections from conducting surfaces for its operation.This article is part of the theme issue 'Celebrating 125 years of Oliver Heaviside's 'Electromagnetic Theory''.

Bounds and Conditions for Compressive Digital Holography Using Wavelet Sparsifying Bases

Numerous experiments have been conducted with success in the field of compressive digital holography, but the theory to determine optimal measurement conditions is lagging behind. In contrast to a prior study that expects object wavefields to be sparse in the spatial domain, we investigate how the configuration of the interferometer influences the reconstruction of wavefields that are sparse in a multiresolution orthogonal wavelet basis. In particular, we derive expressions for the coherence between the free-space wave propagation operator and the basis functions of a Shannon multiresolution representation as a function of the wavelength, the propagation distance, the image sensor's pixel pitch, and the scale of the basis functions. These expressions reveal that the coherence as a function of the Fresnel number is subject to specific scaling and translating rules as the scale of the basis functions changes. For a multiresolution orthogonal wavelet representation and digital holograms that are recorded in the near field, we deduce subsequently the optimal configuration of the interferometer and we show by means of hypothesis testing that the associated phase transition bound coincides with the weak threshold for block-sparse compressive sensing with a block length of 2, which is an optimal bound for the class of complex-valued compressive sensing problems. By means of experiments with a USAF 1951 resolution target and an angle grid, we validate our findings and demonstrate that the reconstructed object wavefields are resilient to sparsity defects and additive noise.

A Novel Method Based on Two Different Thicknesses of The Sample for Determining Complex Permittivity of Materials Using Electromagnetic Wave Propagation in Free Space at X-Band

In this paper, we present a method for determining complex permittivity of materials using two different thicknesses of the sample placed in free space. The proposed method is based on the use of transmission having the same geometry with different thicknesses with the aim to determine the complex propagation constant (γ). The reflection and transmission coefficients (S11 and S21) of material samples are determined using a free-space measurement system. The system consists of transmit and receive horn antennas operating at X-band. The complex permittivity of materials is calculated from the values of γ, in turns received from S11 and S21. The proposed method is tested with different material samples in the frequency range of 8.0 – 12.0 GHz. The results show that the dielectric loss tangent of low-loss material samples, the more accuracy of complex permittivity. However, the complex permittivity is slightly effected by the dielectric loss tangent of high-loss of material samples.

Multiple-Image Hiding Based on Cascaded Free-Space Wave Propagation Using the Structured Phase Mask for Lensless Optical Security System

A novel optical multiple-image hiding method is proposed based on two cascaded free-space propagation transforms in this paper. With the use of the structured phase mask in the phase retrieval algorithm, a plain image is encoded to only one statistically independent phase-only mask. All retrieved phase masks are integrated into the noise-like ciphertext by using the phase mask multiplexing technique. When reconstructing an original plain image, the architecture of double random phase encoding system is directly adopted, where the structured phase mask and the corresponding decryption key mask are located at determined positions along the axis of propagation. Besides the propagation distances, the optical parameters such as wavelength, focal length, and topological charge of the structured mask are considered as the security keys to expand the key space. To the best of our knowledge, it is the first report on employing the structured phase mask in the process of phase retrieval algorithm, which can enhance the level of security greatly. Simulation results have been given to verify the feasibility and robustness of the proposed scheme.

Three-dimensional single-cell imaging with X-ray waveguides in the holographic regime.

X-ray tomography at the level of single biological cells is possible in a low-dose regime, based on full-field holographic recordings, with phase contrast originating from free-space wave propagation. Building upon recent progress in cellular imaging based on the illumination by quasi-point sources provided by X-ray waveguides, here this approach is extended in several ways. First, the phase-retrieval algorithms are extended by an optimized deterministic inversion, based on a multi-distance recording. Second, different advanced forms of iterative phase retrieval are used, operational for single-distance and multi-distance recordings. Results are compared for several different preparations of macrophage cells, for different staining and labelling. As a result, it is shown that phase retrieval is no longer a bottleneck for holographic imaging of cells, and how advanced schemes can be implemented to cope also with high noise and inconsistencies in the data.

Off-axis angular spectrum method with variable sampling interval

We proposed a novel off-axis angular spectrum method (ASM) for simulating free space wave propagation with a large shifted destination plane. The off-axis numerical simulation took wave propagation between a parallel source and a destination plane, but a destination plane was shifted from a source plane. The shifted angular spectrum method was proposed for diffraction simulation with a shifted destination plane and satisfied the Nyquist condition for sampling by limiting a bandwidth of a propagation field to avoid an aliasing error due to under sampling. However, the effective sampling number of the shifted ASM decreased when the shifted distance of the destination plane was large which caused a numerical error in the diffraction simulation. To compensate for the decrease of an effective sampling number for the large shifted destination plane, we used a variable sampling interval in a Fourier space to maintain the same effective sampling number independent of the shifted distance of the destination plane. As a result, our proposed off-axis ASM with a variable sampling interval can produce simulation results with high accuracy for nearly every shifted distance of a destination plane when an off-axis angle is less than 75°. We compared the performances of the off-axis ASM using the Chirp Z transform and non-uniform FFT for implementing a variable spatial frequency in a Fourier space.

Gradual time reversal in thermo- and photo-acoustic tomography within a resonant cavity

Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods (including the popular time reversal algorithm) cannot be used. The inverse problem involving reflecting walls can be solved by the gradual time reversal method we propose here. It consists in solving back in time on the interval the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.

Outstanding Outcomes from a Recent Theory of Gravity

This article intends to fathom a development by M. Tailherer which introduces a second gravitational equation devised to complete General Relativity (TGR), based on the ansatz of equating the curvature tensor opportunely contracted to the 4-vorticity by a new constant S as measure of the intrinsic inertia of the curved Space-Time. After justifying the need to deal with the 2nd fundamental tensor in Relativity in discussing the dynamics of Space-Time structure, it has been shown how the model exhibits unforeseen analogies with the electromagnetic theory. As direct continuation of the analysis of the gravitational wave propagation in free space, it has been seen that on asymptotic conditions the polarization state can be retrieved as mixture of two independent modes likewise TGR as from harmonic constraints on the homogeneous solution of wave equation. Actually, in this gravitational framework, at least for one polarization state, transverse waves propagate causing equal in-phase deformation displacement, not counter-phase as expected in gravitational interferometry experiments at present status. Computation of gravitational power losses for the keplerian system B 1913+16 in the solution by approximations of the inhomogeneous problem has been carried out to the 1st order, which has allowed the assessment of a new universal gravitational constant for the first time ever.

Plane Wave Discontinuous Galerkin Method with Lagrange Multipliers for Solving Time-Harmonic Maxwell's Equations in Three Dimensions

A discontinuous Galerkin method is formulated with plane wave basis functions and Lagrange multipliers, and it is investigated for solving vector curl-curl equations derived from Maxwell's equations. This method was previously developed for solving the scalar Helmholtz equation in both two and three dimensions. By defining vector plane waves and vector Lagrange multipliers within tetrahedral elements and on element boundaries, this algorithm is extended to solve three-dimensional vector problems for electromagnetic analysis. Numerical results for wave propagation in free space and scattering by a perfectly electrically conducting sphere are presented to validate the proposed method and evaluate its potential capability.