Gaussian Schell-model Research Articles

Influence of astigmatic aberration on partially coherent Gaussian-Schell vortex beam focused by lensacon

Based on the mathematical framework of the partially coherent Gaussian Schell model vortex (PCGSMV) beam and the Huygens-Fresnel integral, we conducted a study to analyze the intensity distribution and depth of focus (DOF) of the PCGSMV beam as it propagates through a classical axicon. Our numerical results indicate the influence of factors such as the beam width, spatial degree of coherence, topological charge, and axicon base angle on the intensity distribution and DOF. In addition, we investigated the relationship between the beam spot size and propagation distance, as well as the effects of the spatial degree of coherence and propagation distance on the intensity profile. Our findings highlight the importance of the intensity values along the DOF for various applications, including the optical trapping and manipulation of micro particles.

The quantum Gaussian-Schell model: a link between classical and quantum optics.

The quantum theory of the electromagnetic field uncovered that classical forms of light were indeed produced by distinct superpositions of nonclassical multiphoton wave packets. This situation prevails for partially coherent light, the most common kind of classical light. Here, for the first time, to our knowledge, we demonstrate the extraction of the constituent multiphoton quantum systems of a partially coherent light field. We shift from the realm of classical optics to the domain of quantum optics via a quantum representation of partially coherent light using its complex-Gaussian statistical properties. Our formulation of the quantum Gaussian-Schell model (GSM) unveils the possibility of performing photon-number-resolving (PNR) detection to isolate the constituent quantum multiphoton wave packets of a classical light field. We experimentally verified the coherence properties of isolated vacuum systems and wave packets with up to 16 photons. Our findings not only demonstrate the possibility of observing quantum properties of classical macroscopic objects but also establish a fundamental bridge between the classical and quantum worlds.

Intensity distribution of the partially coherent Gaussian Schell vortex beam diffracted by classical axicon

Based on the mathematical framework of the partially coherent Gaussian Schell model vortex (PCGSMV) beam and the Huygens-Fresnel integral, we conducted a study to analyze the intensity distribution and depth of focus (DOF) of the PCGSMV beam as it propagates through a classical axicon. Our numerical results indicate the influence of factors such as the beam width, spatial degree of coherence, topological charge, and axicon base angle on the intensity distribution and DOF. In addition, we investigated the relationship between the beam spot size and propagation distance, as well as the effects of the spatial degree of coherence and propagation distance on the intensity profile. Our findings highlight the importance of the intensity values along the DOF for various applications, including the optical trapping and manipulation of micro-particles.

Modeling and characterization of deeply etched multilayer resonators under partial coherent excitation via multimode optical fibers

Recently, there has been a resurgence of interest in multimode optical fibers illuminated by a white light source. Largely, in anticipation of many integrated applications in the biomedical domain and spectral sensing benefiting from the broad spectral range and high numerical aperture (NA). Along these lines, the output light from these fibers can be captured by the physics of partially coherent sources. While the Gaussian Schell model has provided a framework for studying partial coherence, to our knowledge, its impact on microstructures remains unexplored. As the sheer complexity arising from the interplay between partial coherence and microstructures transfer function has posed fundamental challenges in deciphering their response. In this work, we introduce a comprehensive numerical model paired with experimental validation to assess the performance of multilayer optical resonators, which are meticulously crafted through high aspect ratio silicon etching under the influence of a partially coherent optical source. The model studies the effects of optical fiber NA, Bragg mirror order, cavity length, and surface roughness of the microstructures on the output of the resonator. The results show that the response under standard multimode fiber (MMF, partial coherent source) has lower insertion loss, more asymmetry versus wavelength, and larger full width at half maximum than the standard single mode fiber (full coherent source). A silicon-on-insulator chip is fabricated using 130 µm deep etching of silicon for Bragg mirrors with 2.25, 3, and 3.25 µm silicon layer widths and a different number of layers. The structures are characterized using a MMF of 62.5 µm core diameter illuminated by an infrared white light source. The theoretical results have been compared with the experimental results and a good agreement has been obtained.

Depth of focus and intensity distribution of a lensacon illuminated by a partially coherent Gaussian Schell vortex beam

Using the extended Huygens–Fresnel principle, a cross-spectral density formula was developed for a Gaussian Schell model vortex (PCGSMV) beam diffracted through a lensacon (lens with an axicon). The intensity and depth of focus (DOF) shaped by the lensacon were calculated. Our numerical results show the relationship between the intensity distribution and depth of focus with the beam waist width as well as the spatial correlation of the coherence length. Furthermore, the relationship between the beam spot size and propagation distance was investigated. In the case of the lensacon tandem, the maximum intensity was greater than that attained by the axicon alone for the same beam parameters, and the DOF was smaller than that of the axicon alone. The vortex structure canceled out the low value of the spatial degree of coherence length. Our numerical model exhibited high-intensity values and high-quality Bessel rings along the DOF, which are critical for various applications.

Propagation of the COAM matrix of a twisted Gaussian Schell-model beam

The Coherence-Orbital Angular Momentum (COAM) matrix elements of an optical beam describe its mode-to-mode radial correlations. An analytic expression for the COAM matrix of a Twisted Gaussian Schell-Model (TGSM) beam propagating in a vacuum is derived and analyzed in detail, with the help of the Huygens–Fresnel integral. Additionally, we show how to recover the cross-spectral density of the TGSM beam from its COAM matrix, expressing the result in an elegant symmetric form. Due to the unique properties of the TGSM beam, the analysis of its individual OAM correlations will deliver further insight for their applications to imaging, laser communication, optical tweezers, and other modalities.

Robustness of partially coherent vortex beams to the impact of dynamic Kolmogorov kind of turbulence

The wave propagation characteristics of Gaussian-Schell model vortex beams passing through a dynamic Kolmogorov type of turbulence are analyzed at the laboratory level. The effect of a rotating pseudo-random phase plate, which simulates Kolmogorov-type atmospheric turbulence, on the Gaussian-Schell model beams carrying twist phase is characterized by calculating the scintillation index and intensity line profiles. Our analysis proves the resilience of Gaussian-Schell model vortex beams to the impact of dynamic turbulence. Simulation studies are further used to validate the experimental results. Because of the resemblance between our investigation conditions and real-world atmospheric turbulence, these findings have potential applications in free-space communication systems.

Operation model of a skew-symmetric split-crystal neutron interferometer.

The observation of neutron interference using a triple Laue interferometer formed by two separate crystals opens the way to the construction and operation of skew-symmetric interferometers with extended arm separation and length. The specifications necessary for their successful operation are investigated here: most importantly, how the manufacturing tolerance and crystal alignments impact the interference visibility. In contrast with previous studies, both incoherent sources and the three-dimensional operation of the interferometer are considered. It is found that, with a Gaussian Schell model of an incoherent source, the integrated density of the particles leaving the interferometer is the same as that yielded by a coherent Gaussian source having a radius equal to the coherence length.

Study on the construction of twisted cosine partially coherent beams and their propagation characteristics

We propose a novel Schell model source for generating twisted partially coherent beams with an initial radius of curvature, which is called a twisted flat-topped cosine Gaussian Schell-model (TFCGSM) source. The TFCGSM beam comprises a wavefront phase and a flat-top structure, with the source degree of coherence determined by two cosine functions. Based on the Huygens–Fresnel principle, the general analytical expression of the cross-spectral density function of the TFCGSM beam propagating through the paraxial ABCD optical system is derived, and then its propagation properties are studied. The results show that the conversion of the array of the beam and the non-uniform structure can be realized by adjusting the parameters in the source plane. As the propagation distance of the TFCGSM beam increases, it rotates around the axis and increases the intensity of the array distribution. Surprisingly, the initial radius of curvature can cause the beam to rotate. The unique shape and properties of the TFCGSM beam create new possibilities for optical communication and enhanced optical functions.

Fourth-order moments analysis for partially coherent electromagnetic beams in random media

A theory for the characterization of the fourth-order moment of electromagnetic wave beams is presented in the case when the source is partially coherent. A Gaussian–Schell model is used for the partially coherent random source. The white-noise paraxial regime is considered, which holds when the wavelength is much smaller than the correlation radius of the source, the beam radius of the source, and the correlation length of the medium, which are themselves much smaller than the propagation distance. The complex wave amplitude field can then be described by the Itô-Schrödinger equation. This equation gives closed evolution equations for the wave field moments at all orders and here the fourth-order moment equations are considered. The general fourth-order moment equations are solved explicitly in the scintillation regime (when the correlation radius of the source is of the same order as the correlation radius of the medium, but the beam radius is much larger) and the result gives a characterization of the intensity covariance function. The form of the intensity covariance function derives from the solution of the transport equation for the Wigner distribution associated with the second-order wave moment. The fourth-order moment results for polarized waves are used in an application for imaging of partially coherent sources.

Two-dimensional spatial coherence measurement of X-ray sources using aperture array mask.

Fourth-generation synchrotron radiation delivers x-ray sources with unprecedented coherence and brilliance, which enables the development of many advanced coherent techniques taking advantage of the inherent high coherence of the x-ray beams. Simple and accurate measurement of two-dimensional (2D) coherence is of utmost importance for the applications of these coherent experimental techniques. Here, we propose a novel approach based on diffraction of aperture array mask (AAM) to obtain accurate 2D spatial coherence with a single-shot measurement. We utilize a coherent mode decomposition algorithm to simulate the diffraction of AAM illuminated by Gaussian-Schell model beam and demonstrate that spatial coherence function of the incident light beam can be accurately and robustly retrieved. We expect that this new approach will be applied into transverse coherence measurements for the new-generation synchrotron radiation source and relevant coherent experimental techniques.

OAM-resolved source correlation-induced spectral changes in random light beams.

The phenomenon of the correlation-induced spectral changes (CISC) in the spectral density of a wide-stationary light beam is shown to occur for each component in its single-radius coherence-OAM (COAM) matrix, with the magnitude quantitatively depending on the OAM indices. As the diagonal elements of the COAM matrix are also radially resolved OAM spectrum components, the new effect may be viewed as the CISC in the OAM spectrum. Using the Gaussian Schell-model beam with the Gaussian spectral line, we then demonstrate the spectral shifts appearing on propagation in vacuum in its radially resolved OAM spectrum. We also prove the spectral invariance of the spatially integrated OAM spectrum.

Coherence-OAM matrix properties of a twisted Gaussian Schell model beam.

Based on the cross-spectral density (CSD) function, the coherence-orbital angular momentum (COAM) matrix of twisted Gaussian Schell-model (TGSM) beam is proposed, and the COAM matrix is used to describe the correlation between OAM modes in TGSM optical field. The COAM matrix characteristics of TGSM beam are analyzed by numerical simulation. The results show that the COAM matrix characteristics of TGSM beam depend on the initial parameters of the beam. In addition, a method of generating TGSM beam by superposition of COAM matrix element modes is described, and the influence of different initial parameters on the superposition characteristics is studied. The results reveal the internal relationship between the coherent structure of the optical field, the twist phase and the OAM modes. Our work helps to explore new expressions of partially coherent beams and promote the practical application of optimizing partially coherent beams.

Evolution properties of a complex coherent square Gaussian-Schell-model beam in a uniaxial crystal orthogonal to the optical axis.

The analytical formulas for spectral density, degree of coherence, and effective beam widths of complex coherent square Gaussian-Schell-model (GSM) beams in a uniaxial crystal orthogonal to the optical axis are derived. Based on these analytical formulas, the evolution properties are investigated by a set of numerical examples. It is demonstrated that the complex coherent square GSM beams spread at different rates in the directions parallel and orthogonal to the optical axis due to the anisotropic crystal, but the self-shift effect of the light field is almost unaffected by the fact that the uniaxial crystal is anisotropic. The effect of anisotropy of the uniaxial crystal on the effective width of the beam in the x direction and that in the y direction is completely opposite. The results provide a way for the modulation of the complex coherent square GSM beams and enrich the propagation theory of uniaxial crystal.

Scintillation mitigation via the cross phase of the Gaussian Schell-model beam in a turbulent atmosphere.

Scintillation is an important problem for laser beams in free space optical (FSO) communications. We derived the analytical expressions for the scintillation index of a Gaussian Schell-model beam with cross phase propagation in a turbulent atmosphere. The numerical results show that the quadratic phase can be used to mitigate turbulence-induced scintillation, and the effects of the turbulent strength and beam parameters at the source plane on the scintillation index are analyzed. The variation trend of the experimentally measured scintillation index is consistent with the numerical results. Our results are expected to be useful for FSO communications.

Nonparaxial Focusing of Partially Coherent Gaussian Schell-Model and Bessel-Correlated Beams in Free Space

The nonparaxial focusing of partially coherent beams in free space has been studied using the coherent-state and coherent-mode decomposition methods. Analytical expressions for the width and angular divergence of partially coherent Gaussian Schell-model (GSM) beams have been obtained using the coherent-state method. It has been shown that the focusing plane is shifted in the opposite axial direction compared to the geometric focusing plane. The influence of the nonparaxiality and spatial coherence of Bessel-correlated vortex beams on the intensity distribution and displacement of the focus plane has been analyzed. It has been shown that the shift of the focus plane increases with a decrease in the coherence radius of the source. A smaller diffraction spread has been shown for partially coherent Bessel-correlated beams compared to GSM beams.

Virtual sources for structured partially coherent light fields.

A virtual source (VS) is a hypothetical source instead of an actual physical entity, but provides a distinctive perspective to understand physical fields in a source-free area. In this work, we generalize the VS theory to structured partially coherent light fields (PCLFs) by establishing the partially coherent inhomogeneous Helmholtz equation, then demonstrate that PCLFs can be generated from the incoherent extended VS in imaginary space. Especially, we put forward an understanding of the Gaussian Schell-model beam, which consists of a group of partially coherent paraxial complex rays. The mutual coherence between these rays depends on the included angle between them. In previous studies, the analytical solution of the partially coherent Airy beam was obtained with difficulty by the Huygens-Fresnel integral; however, by applying the VS, we put forward, to our knowledge, an unprecedented analytical solution for a partially coherent Airy beam. We believe this example will qualify the VS as an important perspective to understand structured PCLFs.

Experimental generation and characterization of partially spatially coherent qubits

Partially spatially coherent qubits are more immune to turbulent atmospheric conditions than coherent qubits, which makes them excellent candidates for free-space quantum communication. In this article, we report the generation of partially spatially coherent qubits in a spontaneous parametric down-conversion (SPDC) process using a Gaussian Schell model (GSM) pump beam. For this non-linear process, we demonstrate experimentally for the first time, the transfer of spatial coherence features of the pump (classical) to the biphotons (quantum) field. Also, the spatial profiles of partially coherent qubits generated in type-I and type-II non-collinear SPDC process are experimentally observed and multi-mode nature of partially coherent photons (qubit) is ascertained. These investigations pave the way toward the efficient generation of partially spatially coherent qubits with a tunable degree of spatial coherence, which lead to wide range of applications in frontier areas such as quantum cryptography, teleportation, imaging, and lithography.

Stable 3D particle manipulation using rotating elliptical Gauss–Schell model vortex partially coherent light sources

The Partially coherent light source can be applied to the noninvasive capture of particles, and increasing the freedom of capturing different types of particles simultaneously is of great significance. This paper studies the optical field distribution of a rotating elliptical Gaussian-Schell model vortex beam focused by a lens and the radiation force acting on Rayleigh particles. The beam’s rotation parameter, the vortex’s topological charge, and the spatial coherence length have different effects on the light intensity, which will determine the optical capture ability of Rayleigh particles with other refractive indices and generate equilibrium points at different positions. The longitudinal equilibrium points of high-refractive-index particles and the transverse equilibrium points of low-refractive-index particles are increased by adjusting the value of the rotation parameter and the topological charge. Finally, the appropriate size range for trapping Rayleigh particles is analyzed according to the comparison of Brownian force and radiant force. The results show that this partially coherent light source has a high degree of freedom in capturing particles with different refractive indices, which provides a new way for optical capture technology and three-dimensional (3D) particle manipulation.

Light field analysis for modeling and transmission characteristics of partially coherent light-emitting diodes

When analyzing the transmission characteristics of LEDs for long-distance lighting and communication applications, the light field is commonly assumed to be fully incoherent. However, in reality, the LED light source emits partially coherent light with a spatial coherence length on the order of microns. This paper is based on the generalized higher-order Lambert model of LEDs and aims to construct a Gaussian-Schell model for the LED beam (LED-GSM) on the near-field source plane, with a half-power angle of no more than 10o. Utilizing the cross-spectral density function transmission theory for partially coherent light, this paper provides the LED-GSM model’s spatial coherence length and beam radius at different distances and designs an experiment for measuring the spatial coherence length of LED beams. Experimental measurements of the spatial coherence length and beam spot size of LED beams at different distances are carried out using a Thorlabs LED528EHP light source. The experimental results match well with the theoretical simulations of the LED-GSM model, thus validating its effectiveness. Then, the proposed LED-GSM model is utilized to investigate the long-distance transmission characteristics of partially coherent narrow-beam LED light. Simulation results indicate that the spatial coherence length of the LED light field can reach tens to hundreds of millimeters over transmission distances of several kilometers. The beam radius is much smaller than that of the beam radius based on the fully incoherent model, and the beam intensity distribution also displays distinct differences.