Source In Free Space Research Articles

Asymmetric cosine-Gaussian Schell-model sources

We introduce a new class of Schell-model source whose spatial correlation function carries a finite series of nontrivial phases and is modulated by cosine function. The propagating formula for the cross-spectral density (CSD) function of the beams generated by this new source in free space is derived and used to investigate the characteristics of the light fields for different modulation parameters. The results show that the appearance of the modulating function and the nontrivial phase sequence cause the radiated fields with extraordinary characteristics during propagation, such as self-splitting and self-interfering in an asymmetric manner. This method of jointly controlling the magnitude and phase of the source complex coherence state provides a new approach for achieving beam shaping.

Reconstructing the Directivity Pattern of a Sound Source in Free Space by Measuring its Field in a Tank

The paper discusses reconstruction of the directivity pattern of a sound source in free space from measurements of the field excited by this source in a tank. The reconstruction procedure uses a reference acoustic monopole. The field of the calibrated source is compared with the fields emitted by the monopole from several specially selected points of the tank. The signals of the source and reference monopole are recorded by the same receivers. From these measurements, the field of the source in the tank is approximated by superposing the fields of the acoustic monopoles. Conditions are formulated under which the field of the source in free space can be represented as the superposed fields of the same monopoles. This makes it possible to calculate the directivity pattern of the calibrated source in free space. The efficiency of the method is confirmed by numerical simulation results.

Light of Two Atoms in Free Space: Bunching or Antibunching?

Photon statistics divides light sources into three different categories, characterized by bunched, antibunched, or uncorrelated photon arrival times. Single atoms, ions, molecules, or solid state emitters display antibunching of photons, while classical thermal sources exhibit photon bunching. Here we demonstrate a light source in free space, where the photon statistics depends on the direction of observation, undergoing a continuous crossover between photon bunching and antibunching. We employ two trapped ions, observe their fluorescence under continuous laser light excitation, and record spatially resolved the autocorrelation function g^{(2)}(τ) with a movable Hanbury Brown and Twiss detector. Varying the detector position we find a minimum value for antibunching, g^{(2)}(0)=0.60(5) and a maximum of g^{(2)}(0)=1.46(8) for bunching, demonstrating that this source radiates fundamentally different types of light alike. The observed variation of the autocorrelation function is understood in the Dicke model from which the observed maximum and minimum values can be modeled, taking independently measured experimental parameters into account.

Locating Transient Directional Sources in Free Space Based on the Electromagnetic Time Reversal Technique

Traditional location methods such as time of arrival and direction of arrival have been widely used to locate transient radiation sources. However, these approaches neglect the directional radiation pattern of the sources. Locating directional sources is a complicated task because the waveform and the amplitude of radiated signals in the time domain vary for different directions. In this article, the ability of the electromagnetic time reversal (EMTR) technique to locate directional sources is investigated. As a typical directional source, the impulse radiation antenna (IRA) is used to validate the method. A radiation model is first established, and the time reversal procedure is carried out in the frequency domain. The amplitude of the signals is kept constant in the reverse phase in order to eliminate the distance attenuation. After analyzing the characteristics of directionality, we choose the energy criterion to estimate the position of the source since the time reversed signals would add up in phase only at the position of the source. It is shown that the point with the maximum energy of the synthesized signal corresponds to the position of the source. Numerical validations are presented and the relationship between the spatial resolution and the influencing factors such as the central frequency and the bandwidth of the excitation, the background noise level, the baseline length, and the number of sensors, are discussed in this article. Experimental results in an anechoic chamber with an impulse radiation antenna as the radiator and multiple horn antennas as the receivers are presented which confirm the ability of the EMTR-based method to locate directional radiation sources. Furthermore, we show that the location accuracy obtained with the energy criterion is better than that obtained with the ∞-norm criterion in the considered scenarios.

Processing seismic source transients to quantify ecosystem impact

Modeling of acoustic field metrics for transient seismic signals in ocean environments is required for the regulatory and resource management purposes. The validation by calibrated measurements is a critical step to assess model’s accuracy. The talk discusses acoustic metrics derived from the field data collected in the Northern Gulf of Mexico. The purpose of the experiment was to characterize 3-dimemsional field of the industrial seismic exploration array. Received Sound Pressure Levels of direct arrivals showed a large variability (up to 50 dB re 1 μPa) for a fixed distance between source and receiver indicating that the distance cannot be used as a single parameter to derive meaningful exposure thresholds. However, the far-field primary acoustic field variations with distance along the true acoustic path for a narrow angular bin are accurately predicted using a simplified model of the theoretical monopole source in free space. The source level of a monopole depends on radiation direction. The different acoustic metrics show robust relationships. As distance between source and receiver increases, the direct arrival may not be present (shadow zone). In this case more comprehensive propagation modeling is required. [Research funded by the Sound and Marine Life Joint Industry Programme.]

Computational sound field in a virtual environment via field data in an arbitrary real environment

It is useful to compute sound field of a source in a virtual environment which is different from the measurement environment. For example, some properties of sound source, such as directivity index and frequency response curve, are required to be measured in an anechoic room or free space, but both of them cannot be always accessible. Consequently, it will be useful to compute sound field of a source in free space when sound field of the source is not measured in the free space. In the aforementioned example, the free space is a virtual environment. Based on reciprocity theorem and modal expansion, a method to predict sound field of a source in a virtual environment is given in this paper when the scattering effect of the source can be neglected. Reciprocity theorem builds the relationship between measured sound field and predicted sound field, which plays an important role in the method. Green’s function in the virtual environment is needed in the method. To restrict measurement points on an enclosed surface, the Green’s function is expanded by a set of modes. A simulation is given to examine the validity of the method.

Deterministic Free-Space Source of Single Photons Using Rydberg Atoms.

We propose an efficient free-space scheme to create single photons in a well-defined spatiotemporal mode. To that end, we first prepare a single source atom in an excited Rydberg state. The source atom interacts with a large ensemble of ground-state atoms via a laser-mediated dipole-dipole exchange interaction. Using an adiabatic passage with a chirped laser pulse, we produce a spatially extended spin wave of a single Rydberg excitation in the ensemble, accompanied by the transition of the source atom to another Rydberg state. The collective atomic excitation can then be converted to a propagating optical photon via a coherent coupling field. In contrast to previous approaches, our single-photon source does not rely on the strong coupling of a single emitter to a resonant cavity, nor does it require the heralding of collective excitation or complete Rydberg blockade of multiple excitations in the atomic ensemble.

Directional Dicke Subradiance with Nonclassical and Classical Light Sources.

We investigate Dicke subradiance of N≥2 distant quantum sources in free space, i.e., the spatial emission patterns of spontaneously radiating noninteracting multilevel atoms or multiphoton sources, prepared in totally antisymmetric states. We find that the radiated intensity is marked by a full suppression of spontaneous emission in particular directions. In resemblance to the analogous, yet inverted, superradiant emission profiles of N distant two-level atoms prepared in symmetric Dicke states, we call the corresponding emission patterns directional Dicke subradiance. We further derive that higher-order intensity correlations of the light emitted by statistically independent thermal light sources display the same directional Dicke subradiant behavior and show that it stems from the same interference phenomenon as in the case of quantum sources. We finally present measurements of directional Dicke subradiance for N=2,…,5 distant thermal light sources corroborating the theoretical findings.

Prediction of sound fields radiated by finite-size sources in room environments by using equivalent source models: three-dimensional simulation and validation

The use of equivalent source models (ESM) has recently been extended, with appropriate modifications, from its original application in acoustical holography to room acoustics simulations. This approach can serve as an alternative that is less computationally intense than the boundary element method and which is more flexible than traditional ray-tracing models in terms of dealing with non-compact sources and lower frequencies where the ray approximation is no longer accurate. Such room acoustics ESMs are based on the assumption that the room component of the total sound field can be represented by a number of equivalent sources of certain types, and that the total sound field can be predicted, with given free-space source information, by estimating the strengths of these equivalent sources based on a least-square match of the impedance boundary conditions on both the source and the room surfaces. However, to-date, the room acoustics ESMs have only been formulated and validated for two-dimensional cases. In the current work, the ESM formulation has been extended to three dimensions by replacing the two-dimensional equivalent sources with their three-dimensional counterparts, and its applications in a realistic three-dimensional room environment has been validated by successfully comparing the ESM and boundary element predictions.

Self-focusing of a partially coherent beam with circular coherence

In a recent publication [Opt. Lett.42, 1512 (2017)OPLEDP0146-959210.1364/OL.42.001512], a novel class of partially coherent sources with circular coherence was introduced. In this paper, we examine the propagation behavior of the spectral density and the spectral degree of spatial coherence of a beam generated by such a source in free space and in oceanic turbulent media. It is found that the beam exhibits self-focusing, which is dependent on the initial coherence and the parameters of oceanic turbulence. The self-focusing phenomenon disappears when the initial coherence is high enough or the oceanic turbulence is strong. The area of high coherence appears in the center and along two diagonal lines. With increasing turbulence, the coherence area reduces gradually along one diagonal line and is retained along the other one. A physical interpretation of the self-focusing phenomenon is presented, and potential applications in optical underwater communication and beam shaping are considered.

Active control of a finite line source using multiple directional sources

The active control of a finite line source in free space is studied using different types of secondary control sources to create a particular quiet zone. The simulations based on analytical formulation indicate that the active control improves significantly with the usage of directional secondary sources, such as axially oscillating baffled circular pistons. The comparison between directional sources of different directivity patterns shows that the directivity property has a determinant effect on the control results. A multi-part directional source, then, is introduced as the novel secondary control sources with its simplest two-part type. It consists of an inner-piston and an outer-concentric-annulus both oscillating axially with optimized amplitudes and relative phase. This novel secondary source helps to achieve excellent control results within a realistic physical size. The control performance regarding the novel sources with more outer annuluses are also studied.

Propagation of Gaussian Schell-model Array beams in free space and atmospheric turbulence

Based on the extended Huygens-Fresnel principle, the evolution behavior of the spectral density and the spectral degree of coherence of the beam produced by a recently introduced novel class of Gaussian Schell-model Arrays (GSMA) source in free space and turbulence atmospheric are explored and comparatively analyzed. And the influence of the fractal constant of the atmospheric power spectrum and refractive-index structure constant on the spectral density and the spectral degree of coherence of beams are analyzed. It is shown that the optical lattice profile is stable when beams propagate in free space, but the spectral density eventually is suppressed and transformed into a Gaussian profiles when it passes at sufficiently large distances through the turbulent atmosphere. The distributions of the spectral degree of coherence in far field eventually transformed into a shrink Gaussian profile relative to free space which means that the degree of spatial coherence turns worse.

Quantum limits to optical point-source localization

Motivated by the importance of optical microscopes to science and engineering, scientists have pondered for centuries how to improve their resolution and the existence of fundamental resolution limits. In recent years, a new class of microscopes that overcome a long-held belief about the resolution have revolutionized biological imaging. Termed "superresolution" microscopy, these techniques work by accurately locating optical point sources from far field. To investigate the fundamental localization limits, here I derive quantum lower bounds on the error of locating point sources in free space, taking full account of the quantum, nonparaxial, and vectoral nature of photons. These bounds are valid for any measurement technique, as long as it obeys quantum mechanics, and serve as general no-go theorems for the resolution of microscopes. To arrive at analytic results, I focus mainly on the cases of one and two classical monochromatic sources with an initial vacuum optical state. For one source, a lower bound on the root-mean-square position estimation error is on the order of $\lambda_0/\sqrt{N}$, where $\lambda_0$ is the free-space wavelength and $N$ is the average number of radiated photons. For two sources, owing to the statistical effect of nuisance parameters, the error bound diverges when their radiated fields overlap significantly. The use of squeezed light to enhance further the accuracy of locating one classical point source and the localization limits for partially coherent sources and single-photon sources are also discussed. The presented theory establishes a rigorous quantum statiscal inference framework for the study of superresolution microscopy and points to the possibility of using quantum techniques for true resolution enhancement.

A spectral domain approach for the calculation of the scattering of the stratified uniaxial electric anisotropic media under point source excitation with arbitrary orientation

A method for the calculation of the scattering of the stratified uniaxial electric anisotropic media (UEAM) under point source excitation with arbitrary orientation is presented. In this method, the total field is decomposed into three parts, the radiated field of the point source in free space, th e reflected field from the top interface of the UEAM and the transmitted field after multiple reflections in the anisotropic layer. The three parts are derived in spectral domain respectively and can be expressed by using Fourier transform. Then the saddle point technique (SPT) is introduced to obtain an asymptotic solution of the scattered field. Results from the asymptotic solution are compared with the results calculated by the method of moments (MOM) and the comparison shows good agreement.

Two types of sinc Schell-model beams and their propagation characteristics.

Two types of partially coherent beams with sinc Schell-model-correlated function are introduced. The evolution behaviors of scalar beams generated by these two types of sources in free space are investigated with the help of the weighted superposition method and numerical examples. It is illustrated that the far field produced by these two novel sources carry tunable flat and dark hollow profiles, respectively. Our results suggest two new kinds of modal structure of the correlation source and of the optical field that such sources produce.

Light sources generating self-splitting beams and their propagation in non-Kolmogorov turbulence

A class of random sources producing far fields self-splitting intensity profiles with variable spacing between the x and y directions is introduced. The beam conditions for ensuring the sources to generate a beam are derived. Based on the derived analytical expression, the evolution behavior of the beams produced by these families of sources in free space and turbulence atmospheric are explored and comparatively analyzed. By changing the modulation parameters n and m, the degree of coherence of Gaussian Schell-model source in the x and y directions are modulated respectively, and then the number of splitting beams and the spacing between splitting beams can be adjusted. It is illustrated that the self-splitting intensity profile is stable when beams propagate in free space, but they eventually transformed into a Gaussian profiles when it passes at sufficiently large distances from its source through the turbulent atmosphere.

Light sources generating self-focusing beams of variable focal length

A class of partially coherent beams with a nonuniformly cosine-Gaussian (NUCG) correlated function is introduced. The evolution behavior of scalar beams produced by these families of sources in free space and isotropic random media are investigated. It is shown that such light fields with NUCG correlated function propagating in free space and turbulent atmosphere have self-focusing effects and laterally shifted intensity maxima. The new source employs cosine function for modeling of the source degree of coherence, which can adjust the self-focusing focal length, the shift of intensity center, and the intensity profile.

A Convolutional Perfect Matched Layer (CPML) for One-Step Leapfrog ADI-FDTD Method and Its Applications to EMC Problems

A new convolutional perfectly matched layer (CPML) is proposed and implemented in one-step leapfrog alternately direction-implicit finite-difference time-domain (ADI-FDTD) method. Different from the previous developed perfectly matched layers (PMLs) used in the ADI-FDTD methods, the proposed PML has the same form as that used for the conventional FDTD method, requiring only one-step computations of the CPML auxiliary quantities. Stability of the proposed CPML is verified semianalytically and its high absorption efficiency is proven numerically. The proposed CPML is then applied to a number of applications; they include radiation generated by a current source in free space, propagating and evanescent modes in a rectangular waveguide, and transient current prediction on an aircraft that is modeled with a numerical grid of 402 × 48 × 262. Accurate results have been obtained in comparison with the results obtained with the other methods.

Blind extraction and localization of sound sources using point sources based approaches

This paper presents theoretical models for blind sound source localization and separation of the signals emitted by arbitrary point sources in free space. Source localizations are achieved by a model based approach that accounts for the spherical spreading of an acoustic wave and utilizes an iterative triangulation, based on the signals measured by a three-dimensional microphone array. Once source locations are determined, the source signals are separated by using the point source separation (PSS) method, which is valid for all types of signals, including harmonic, continuous, transient, random, narrowband and broadband. General solutions for signals separation are presented. Theoretically, PSS can reconstruct the individual source signals exactly. This is because it employs the free-space Green's function, which defines the exact correlation among individual sources and measurement microphones. To validate PSS, numerical simulations are carried out and results are compared with those obtained by FastICA (Independent Component Analysis) code. The impacts of various parameters such as the microphone configuration, type of source signals, signal to noise ratio, number of microphones and source localization errors on the quality of signals separation by using PSS and FastICA are examined. The advantages and disadvantages of PSS and FastICA are compared and discussed.

On Acoustic Radiation by Rotating Body Sources in Frequency Domain

For the complexity of the sound generated mechanism of rotating body source, this paper describes a frequency-domain numerical method for predicting sound radiation of rotating body sources based on the Kirchhoff integral equation with analytical Green's function of rotating monopole and dipole source in free space. The sound radiation model is established in free space and the relationship between characteristics of sound field and acoustic nature frequency of source, angular frequency and its harmonics can be revealed by the mathematical solution. Numerical simulation shows that sound field has a strong directivity, fundamental frequency transmitting in the rotary shaft direction and harmonics spreading along radial direction and frequency shift phenomena appearing clearly in higher rotating speed of source. The method has a theoretical significance for exploring the low-noise rotating machinery. Research about sound radiation of moving source originates from Lighthill. The first integral approach for acoustic propagation is the acoustic analogy. In the acoustic analogy, the governing Navier-Stokes equations are rearranged to be in wave-type form. There is some question as to which terms should be identified as part of the sound source and retained in the right-hand side of the equation and which terms should be in the left-hand side as part of the operator. The far-field sound pressure is then given in terms of a volume integral over the domain containing the sound source. However the major difficulty with the acoustic analogy is that the sound source is not compact in supersonic flows. Several modifications to Lighthill's original theory have been proposed to account for the moving sound source or other effects. The Ffowcs Williams and Hawkings (FW-H) equation was introduced to extend acoustic analogy in the case of solid surfaces. However, when acoustic sources are present in the flowfield a volume integration is needed. This volume integration of the quadrupole source term is difficult to compute and is usually neglected in most acoustic analogy codes. Errors could be encountered in calculating the sound field. Another alternative is the Kirchhoff method which assumes that the sound transmission is governed by the simple wave equation. Kirchhoff's method consists of the calculation of the nonlinear near- and mid-field, usually numerically, with the far-field solutions found from a linear Kirchhoff formulation evaluated on a control surface surrounding the nonlinear-field. The control surface is assumed to enclose all the nonlinear flow effects and noise sources. The sound pressure can be obtained in terms of a surface integral of the surface pressure and its normal and time derivatives. This approach has the potential to overcome some of the difficulties associated with the traditional acoustic analogy approach. The method is simple and accurate and accounts for the nonlinear quadrupole noise in the far-field. Full diffraction and focusing effects are included while eliminating the propagation of the reactive near-field. Kirchhoff's formula, published in 1882, is used in the theory of diffraction of light and in other electromaqnetic problems. It also has many applications to problems of wave in acoustics. One of the novel uses of this formula was proposed by Hawkinqs for predicting