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.

Propagation dynamics of multi-Gaussian Schell model beams in strongly nonlocal nonlinear media

The analytical propagation formulae of a single multi-Gaussian Schell model (MGSM) beam and two MGSM beams in strongly nonlocal nonlinear media (SNNM) are derived, and the optical breather characteristics of a single MGSM beam and two MGSM beams in SNNM are studied, respectively. It is found that a MGSM soliton is never formed because of the self-shaping feature of MGSM beams, but a MGSM breather can be formed. Furthermore, for a MGSM breather, the Gaussian-like profile and the flat-top profile alternate periodically during propagation. On the other hand, even if the separation distance is large enough, two MGSM breathers can be combined into a single breather due to nonlinearity when the threshold critical power arrives. Furthermore, the relationship between the threshold critical power and the MGSM beam parameters is also investigated.

Exploring the effects of urban network topologies on entropy trajectories of segregation

Segregation is a threat to the aspirations of producing a cohesive society and modelling its dynamics can be done in order to help design preventative measures. This work explores the question of whether the network topologies of urban spaces can affect the pace at which populations can become segregated. The simulation dynamics employed augment the canonical Schelling model in such a way that it also captures the affinity for agents to prefer denser regions which also offer sufficient local homogeneity. It is shown that different networks synthetically generated and from real city maps can alter the rate of segregation. The results also show that using the entropy trace on the distribution of agent edge degree across all agents correlates with the segregation reinforcing the relevance of physics inspired modeling of social systems. This investigation shows that it is possible to explore and select network arrangements which can be less conducive towards segregation movements during the stages of urban planning so that the rate is reduced. An additional finding is that the entropic measure is closely associated with the common statistic for such modeling efforts.

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.

Impact of joint turbulence of jet engine and marine environment on the propagation quality of partially coherent generalized Laguerre–Gaussian correlated Schell model beams

Impact of joint turbulence of jet engine and marine environment on the propagation quality of partially coherent generalized Laguerre–Gaussian correlated Schell model beams

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.

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.

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.

Hydrodynamic limit of the Schelling model with spontaneous Glauber and Kawasaki dynamics

Hydrodynamic limit of the Schelling model with spontaneous Glauber and Kawasaki dynamics

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.

Geovisualization of Temporal Change in Urban Racial Geography: A Step towards Explaining Persistent Segregation

To better understand the persistence of residential racial segregation in U.S. cities, it is essential to develop testable, spatially explicit models of racial dynamics. However, the original census data are not formatted in a way that facilitates the testing of such models. In this study, we propose a novel geoprocessing pipeline that transforms census data into image-like geovisualization of urban segregation. The process consists of converting original data to a grid format, transforming subpopulation shares in each grid cell into a CMYK color, and multiyear clustering of CMYK values followed by classification and smoothing of images. When applied to data from multiple censuses, our methodology generates a time series of snapshots that depict the spatio-temporal dynamics of racial change. As a demonstration, we have utilized our methodology to generate racial images for a period spanning from 1990 to 2020 in seven major cities. Detailed results are shown for Chicago and Atlanta. By visually examining these time series, we have identified patterns that challenge the conventional Schelling model of racial change. Instead, our findings point towards a model that incorporates the interplay of preferential growth and diffusion as significant factors that shape the complex dynamics of racial composition in these urban areas.

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.

Mobility constraints in segregation models

Since the development of the original Schelling model of urban segregation, several enhancements have been proposed, but none have considered the impact of mobility constraints on model dynamics. Recent studies have shown that human mobility follows specific patterns, such as a preference for short distances and dense locations. This paper proposes a segregation model incorporating mobility constraints to make agents select their location based on distance and location relevance. Our findings indicate that the mobility-constrained model produces lower segregation levels but takes longer to converge than the original Schelling model. We identified a few persistently unhappy agents from the minority group who cause this prolonged convergence time and lower segregation level as they move around the grid centre. Our study presents a more realistic representation of how agents move in urban areas and provides a novel and insightful approach to analyzing the impact of mobility constraints on segregation models. We highlight the significance of incorporating mobility constraints when policymakers design interventions to address urban segregation.

Not all strangers are the same: The impact of tolerance in Schelling games

Schelling's famous model of segregation assumes agents of different types, who would like to be located in neighborhoods having at least a certain fraction of agents of the same type. We consider natural generalizations that allow for the possibility of agents being tolerant towards other agents, even if they are not of the same type. In particular, we consider an ordering of the types, and make the realistic assumption that the agents are in principle more tolerant towards agents of types that are closer to their own according to the ordering. Based on this, we study the strategic games induced when the agents aim to maximize their utility for a variety of tolerance levels. We provide a collection of results about the existence of equilibria, and their quality in terms of social welfare.

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.

Beam Properties of a Partially Coherent Beam Propagating Horizontally in Atmospheric Turbulence

This study explored the impact of atmospheric turbulence on partially coherent light propagation. Atmospheric turbulence causes random modulation of the intensity and phase of light, resulting in a speckle pattern in the far field. This study focused on partially coherent Gaussian Schell model beams and derived an analytical expression of the cross-spectral density function for their transmission through atmospheric turbulence, based on the generalized Huygens–Fresnel principle and the Tatarski spectrum model. Numerical simulations were used to investigate the effects of the source parameters and turbulence strength on the intensity distribution, beam width, and coherence length of partially coherent light in horizontal atmospheric transmission. The results demonstrate that diffraction-induced broadening primarily affects the intensity distribution of light in free-space transmission. Short transmission distances in atmospheric turbulence have comparable characteristics to those in a vacuum; however, as the turbulence intensity and transmission distance increase, the beam broadening effect amplifies, and the coherence length is reduced. The findings are relevant to the design of acquisition, pointing, and tracking systems for wireless laser communication systems and offer insights into the optimization of optical systems for atmospheric conditions.

Reliability analysis of optical IRS-enabled FSO system with multiple detectors and PCB under composite turbulence fading channels considering the impact of GML

Free space optical (FSO) communication with optical intelligent reflecting surface (IRS) assistance is one promising and evolving technology that can relax the line-of-sight requirement and enable more efficient and reliable link performance in obstacles areas. In this work, an optical IRS-enabled FSO system is proposed with partially coherent beam (PCB) and multiple detectors. Specifically, for an end-to-end (e2e) IRS-assisted FSO link, the statistical model of optical signal fluctuations due to atmospheric turbulence is assumed to follow Fisher–Snedecor F-distribution, and the random movements of IRS, transmitter (Tx), and receiver (Rx) due to building sway is modeled by geometric and misalignment losses. Considering the Gaussian–Schell model and intensity modulation/direct detection, the analytical average bit error rate (ABER) expressions of the studied system are obtained for a single detector and multiple detectors, respectively, with selected combining (SC), equal gain combining (EGC) and maximum ratio combining (MRC) aperture diversity schemes over independent identically distributed composite fading channels. And the correctness of the analytical results is verified through the Monte-Carlo based statistical simulation method. Results show that the ABER and outage probability performance of IRS-assisted FSO link degrades with the increase in the strength of atmospheric turbulence and building sway. And even the position fluctuations variances of Tx, IRS, and Rx are the same, their impacts on the e2e IRS-assisted FSO link are not the same. Interestingly, aperture diversity techniques can significantly mitigate these adverse effects, especially in the case of MRC scheme. Besides, the studied system with PCB can achieve better system performance compared to that using coherent beam, and the performance gap would become more obvious as the spatial coherence radius decreases. This work could serve as a guide for the design and research of IRS-enabled FSO communication systems.