Schell-model Sources Research Articles

Rectangular Multi-Gaussian Schell-Model beams in atmospheric turbulence

Optical beams radiated by a recently introduced class of Rectangular Multi-Gaussian Schell-Model (RMGSM) source are examined on propagation in free space and in atmospheric turbulence, with both classic and non-classic power spectra of the refractive-index fluctuations. The expression for the cross-spectral density function of such beams has been derived and used for the analysis of their spectral density (average intensity). The RMGSM beams are shown to preserve the square/rectangular shape of the transverse intensity distribution and the maximum intensity level in the flat part for relatively large distances from the source on propagation in classic turbulence. This makes the novel beams attractive for free-space optical communications and surface processing in the presence of the atmosphere.

Experimental generation of cosine-Gaussian-correlated Schell-model beams with rectangular symmetry

Cosine-Gaussian-correlated Schell-model sources whose degree of coherence (DOC) is of circular symmetry have been introduced just recently [Opt. Lett. 38, 2578 (2013)]. In this Letter, we propose a model for a source whose DOC is the superposition of two 1D cosine-Gaussian-correlated Schell-model sources, i.e., possesses rectangular symmetry. The novel model sources and beams they generate are termed rectangular cosine-Gaussian Schell-model (RCGSM). The RCGSM beam exhibits unique features on propagation, e.g., its intensity in the far field (or in the focal plane) displays a four-beamlet array profile, being qualitatively different from the ring-shaped profile of the CGSM beam whose DOC is of circular symmetry. Furthermore, we have carried out experimental generation of the proposed beam and measured its focusing properties. Our experimental results are consistent with the theoretical predictions.

Optical binding of cylinder photonic molecules in the near field of partially coherent fluctuating Gaussian Schell model sources: a coherent mode representation

We present a theory and computation method of radiation pressure from partially coherent light by establishing a coherent mode representation of the radiation forces. This is illustrated with the near field emitted from a Gaussian Schell model source, mechanically acting on a single cylinder with magnetodielectric behavior, or on a photonic molecule constituted by a pair of such cylinders. Thus after studying the force produced by a single particle, we address the effects of the spatial coherence on the bonding and antibonding states of two particles. The coherence length manifests the critical limitation of the contribution of evanescent modes to the scattered fields, and hence to the nature and strength of the electromagnetic forces, even when electric and/or magnetic partial wave resonances are excited.

Ghost imaging with shaped incoherent sources

We show that the image quality of ghost imaging (GI) can be controlled by the use of shaped incoherent sources. The formula for the point-spread function in the GI system has been derived and is determined by the Fourier transform of the source intensity distribution. Compared with the widely used Gaussian Schell-model source, we find that using a cosine-Gaussian Schell-model source can lead to the degradation of GI quality, while the quality of GI can be increased with a cosh-Gaussian Schell-model source. Even under atmospheric turbulence, the image resolution of GI still can be improved by means of the cosh-Gaussian Schell-model source.

Spectral Gaussian Schell-model beams

A generalization of the classic Gaussian Schell-model source is considered for which the rms width of the beam σ and the rms width of the spectral degree of coherence δ are assumed to depend on wavelength. It is shown that the functional form σ(λ) and δ(λ) of such a source can affect the behavior of the spectral density, the degree of coherence, and the degree of polarization of the propagating beam.

Tuning the spectral composition of random beams propagating in free space and in a turbulent atmosphere

We employ the spectral dependence of several parameters of Gaussian Schell-model sources for efficient manipulation of the spectral composition of the beams they generate on propagation in free space as well as in turbulent atmospheres of Kolmogorov and non-Kolmogorov type. We show that different combinations of spectral dependences of the source parameters might lead to controllable spectral shifts of both types, blue and red, either on- or off-axis of the beam. Moreover, depending on the parameter combinations the spectral shifts caused by source correlations at relatively short distances may or may not be suppressed by the effects of turbulence at large distances.

Propagation properties of multi-Gaussian Schell-model beams through ABCD optical systems and in atmospheric turbulence

The propagation behavior of the multi-Gaussian Schell-model source through ABCD optical systems and its spreading in the turbulent atmosphere are investigated. We obtain the analytic expressions for the cross spectral density and spectral degree of coherence of such beams in misaligned ABCD optical systems and beam width in atmospheric turbulence. Numerical results show that when the beam is focused, it still has the flattened intensity profile around the optical axis. However, the degree of coherence of field in the focal plane assumes Gaussian-like profile. The turbulence inner scale and correlation width and index M of the source have some effects on beam spreading through atmospheric turbulence.

Examining the validity of using a Gaussian Schell-model source to model the scattering of a fully coherent Gaussian beam from a rough impedance surface

Military applications that use adaptive optics (AO) often require a point source beacon at the target to measure and correct for wavefront aberrations introduced by atmospheric turbulence. However, turbulence prevents the formation of such a point beacon. The extended beacons that are created instead have finite spatial extents and exhibit varying degrees of spatial coherence. Modeling these extended beacons using a Gaussian Schell-model (GSM) form for the autocorrelation function would be a convenient approach due to the analytical tractability of Gaussian functions. We examine the validity of using such a model by evaluating the field scattered from a rough impedance surface using a full-wave computational technique called the method of moments (MoM). The MoM improves the fidelity of the analysis since it captures all the physics of the laser-target interaction, such as masking, shadowing, multiple reflections, etc. Two rough-surface targets with different roughness statistics are analyzed. The simulation results are verified with experimental bidirectional reflectance distribution function measurements. It is seen that for rough surfaces, in general, the scattered-field autocorrelation function is not of a GSM form. However, under certain conditions, modeling an extended beacon as a GSM source is legitimate. This analysis will aid in understanding the behavior of extended beacons and how they affect the overall performance of an AO system.

Factored form descent: a practical algorithm for coherence retrieval

We formulate coherence retrieval, the process of recovering via intensity measurements the two-point correlation function of a partially coherent field, as a convex weighted least-squares problem and show that it can be solved with a novel iterated descent algorithm using a coherent-modes factorization of the mutual intensity. This algorithm is more memory-efficient than the standard interior point methods used to solve convex problems, and we verify its feasibility by reconstructing the mutual intensity of a Schell-model source from both simulated data and experimental measurements.

Random sources generating ring-shaped beams

Two classes of scalar, stochastic sources are introduced, each capable of producing far fields with intensities forming rings. Although the Bessel-Gaussian and the Laguerre-Gaussian Schell-model sources are described by two different math models, the behavior of their degrees of coherence and, hence, the shapes of their far fields are qualitatively similar. The new beams are of importance for optical methods of particle manipulation.

Light sources generating far fields with tunable flat profiles

Planar, scalar, optical Schell-model, and quasi-homogeneous sources with correlations that are Fourier transforms of multi-Gaussian functions are introduced. It is demonstrated that far fields produced by these families of sources carry interesting characteristics, being flatlike with adjustable steepness of the edge. Beam conditions for such sources are also derived.

Experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model source

We report the experimental measurement of the beam parameters of an electromagnetic Gaussian Schell-model (EGSM) source based on the technique for measuring the fourth-order correlation function (i.e., intensity correlation function). Furthermore, we carry out experimental measurement of the intensity distribution of a focused EGSM beam, and we carry out theoretical simulation using the measured beam parameters. Our experimental results agree reasonably well with the theoretical predictions.

Propagation of a General Gaussian Beam by Paraxial Ray Tracing in an Arbitrary Optical System

The propagation of a partially coherent Gaussian beam in a homogeneous medium can be explained with various methods. One of them is Gaussian shell model beams [1–8]. It uses the Gaussian Schell-model source whose irradiance distribution and degree of coherence are both Gaussian. We will describe Gaussian beams as the ray distribution L as functions of linear and angular coordinates. Of course, since the Gaussian Shell model beam can be produced by a superposition of independent coherent Gaussian beams, our concept is similar to the Gaussian Shell model concept. However, the goal of the present paper is to describe the propagation of general Gaussian beams through an arbitrary optical system by using the geometrical paraxial ray tracing method. In other words, many rays propagate through a reference plane, these rays distribute with the Gaussian profile in linear and angular direction cosine coordinates, and every ray propagates according to the laws of geometrical optics. At first, we introduce the ray distribution density of a circular symmetric Gaussian beam and investigate how that Gaussian beam propagates through an arbitrary axially symmetric optical system or in a homogeneous medium under the paraxial approximation, and we determine the physical meanings of the parameters. Also, we introduce the complex parameter q and the Lagrange invariant L for this general Gaussian beam and discover that this Gaussian beam also follows the Kogelnik ABCD law, just as a classical coherent Gaussian beam does.

Coherence and polarization properties of a three-dimensional, primary, quasi-homogeneous, and isotropic source and its far field

We study the spatial coherence properties of a three-dimensional, primary, quasi-homogeneous, and isotropic source and the far field that it generates. We assess the spectrum, degree of polarization, electromagnetic degree of coherence, and effective degree of coherence of the source and of the far field. We also demonstrate the formalism for a spherical Gaussian Schell-model current source. The polarization properties of light are fully accounted for in the analysis, and it is found that certain results pertaining to scalar coherence theory are reproduced also within the electromagnetic treatment.

Generation of a secondary electromagnetic source with desired statistical properties

Two known alternative techniques for generating a secondary electromagnetic Schell-model source with the prescribed statistical properties are analyzed and compared from the point of view of their capability to provide the given degree of polarization and the desired transverse coherence length.

Partially coherent fundamental Gaussian wave generated by a fluctuating planar current source

The propagation characteristics of a spatially localized electromagnetic wave produced by a planar current source of different states of spatial coherence are analyzed by the use of a Gaussian Schell-model source. A linearly polarized fundamental electromagnetic Gaussian wave with the electric field perpendicular to the direction of propagation is treated. The effects of the degree of coherence of the source distribution on the radiation intensity distribution and the total radiated power are determined.

Second-order statistics of stochastic electromagnetic beams propagating through non-Kolmogorov turbulence

We present a detailed investigation, qualitative and quantitative, on how the atmospheric turbulence with a non-Kolmogorov power spectrum affects the major statistics of stochastic electromagnetic beams, such as the spectral composition and the states of coherence and polarization. We suggest a detailed survey on how these properties evolve on propagation of beams generated by electromagnetic Gaussian Schell-model sources, depending on the fractal constant alpha of the atmospheric power spectrum.

Coherence properties of hard x-ray synchrotron sources and x-ray free-electron lasers

A general theoretical approach based on the results of statistical optics is used for the analysis of the transverse coherence properties of third generation hard x-ray synchrotron sources and x-ray free-electron lasers (XFEL). Correlation properties of the wavefields are calculated at different distances from an equivalent Gaussian Schell-model source. This model is used to describe coherence properties of the 5 m undulator source at the synchrotron storage ring PETRA III. In the case of XFEL sources the decomposition of the statistical fields into a sum of independently propagating transverse modes is used for the analysis of the coherence properties of these new sources. A detailed calculation is performed for the parameters of the SASE1 undulator at the European XFEL. It is demonstrated that only a few modes contribute significantly to the total radiation field of that source.

Interference of a pair of symmetric partially coherent beams

We study theoretically and experimentally the interference of light produced by a pair of mutually correlated Schell-model sources. The spatial distributions of the fields produced by the two sources are inverted with respect to each other through their common center in the source plane. When the beams are in phase, a bright spot appears in the center of the spatial distribution of the beam intensity. When the beams have a phase shift phi= pi, a dark spot appears in the center of the spatial distribution of the beam intensity. Experimental results that illustrate these results are included. Both bright and dark spots diverge more slowly with the increasing distance from the sources than the beam itself.

Parametric study of uniformly polarized stochastic electromagnetic beam and its imaging

A parametric study is performed in investigating the stochastic electromagnetic beam generated by a uniformly polarized electromagnetic Gaussian Schell-model source and passing through ABCD optical systems. Through theoretical analysis, the requirement is derived that the uniformly polarized electromagnetic field can be obtained at the output plane of the imaging optical system. Furthermore, the general imaging formula of the stochastic electromagnetic beam is derived. Numerical examples are also presented to illustrate the application.