In this paper, the Geometric Optics (GO) method using the approximate ray paths coupled with the Computer Aided Tri-dimensional Interface Application (CATIA) meshing modeling are implemented to analyze the performance...In this paper, the Geometric Optics (GO) method using the approximate ray paths coupled with the Computer Aided Tri-dimensional Interface Application (CATIA) meshing modeling are implemented to analyze the performance of electric large three-dimensional dielectric radome-enclosed antenna of arbitrary contour shape. The surfaces of the radome are approximated by planar triangular patches, the influences of various number of patches on power transmission coefficient and Insertion Phase Delay (IPD) via an ogive and a conical radome are discussed by the hybrid method. The simulation results indicate that computational error from planar triangular patches can limit in one percent, meeting the engineering application requirements.展开更多
The perturbed Riemann problem for a hyperbolic system of conservation laws arising in geometrical optics with three constant initial states is solved.By studying the interactions among of the delta-shock,vacuum,and co...The perturbed Riemann problem for a hyperbolic system of conservation laws arising in geometrical optics with three constant initial states is solved.By studying the interactions among of the delta-shock,vacuum,and contact discontinuity,fourteen kinds of structures of Riemann solutions are obtained.The compound wave solutions consisting of delta-shocks,vacuums,and contact discontinuities are found.The single and double closed vacuum cavitations develop in solutions.Furthermore,it is shown that the solutions of the Riemann problem for the geometrical optics system are stable under certain perturbation of the initial data.Finally,the numerical results completely coinciding with theoretical analysis are presented.展开更多
Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface;however, there is a need for simulating surface scattering losses for devices having many surface interactions ...Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface;however, there is a need for simulating surface scattering losses for devices having many surface interactions such as light pipes. Light pipes are often simulated with geometric optics (GO) using ray tracing, where surface scattering is driven by the surface slope distribution. In the DO case, surface scattering analyses depend on the spatial frequency distribution and amplitude as well as wavelength, with the sinusoidal grating as a fundamental basis. A better understanding of the link, or transition, between DO and GO scattering domains would be helpful for efficiently incorporating scattering loss analyses into ray trace simulations. A formula for the root-mean-square (rms) scattered angle width of a sinusoidal reflection grating that depends only on the surface rms slope is derived from the nonparaxial scalar diffraction theory, thereby linking it to GO. The scatter angle’s mean and rms width are evaluated over a range of grating amplitudes and periods using scalar theory and full vector simulations from the COMSOL® wave optic module for a sinusoidal reflection grating. The conditions under which the diffraction-based solution closely approximates the GO solution, as predicted by the rms slope, are identified. Close agreement is shown between the DO and GO solutions for the same surface rms slope scattering loss due to angular filtering near the critical angle of a total internal reflection (TIR) glass-to-air interface.展开更多
We investigate a novel spatial geometric phase of hybrid-polarized vector fields consisting of linear, elliptical and circular polarizations by Young's two-slit interferometer instead of the widely used Mach-Zehnd...We investigate a novel spatial geometric phase of hybrid-polarized vector fields consisting of linear, elliptical and circular polarizations by Young's two-slit interferometer instead of the widely used Mach-Zehnder interferometer.This spatial geometric phase can be manipulated by engineering the spatial configuration of hybrid polarizations,and is directly related to the topological charge, the local states of polarization and the rotational symmetry of hybrid-polarized vector optical fields. The unique feature of geometric phase has implications in quantum information science as well as other physical systems such as electron vortex beams.展开更多
Researchers have recently attempted to monitor pool oscillations using the three-dimensional laser vision method.However,the deficiency of simulation software will result in significant capital expenditure.Both simula...Researchers have recently attempted to monitor pool oscillations using the three-dimensional laser vision method.However,the deficiency of simulation software will result in significant capital expenditure.Both simulations and experiments are performed in this study,and the Bessel equation is used to analyze the oscillation mode of a weld pool.The laser dot matrix images of(0,1),(1,1),(2,1),and(0,2)oscillation modes at different times are obtained via structured laser optical measurement simulation.The oscillation mode of a stationary gas tungsten arc weld pool is analyzed based on laser dot matrix images obtained from a structure laser experiment.Results show that the simulated laser dot matrix images are consistent with the experiment results.The oscillation mode of the weld pool can be recognized based on the laser dot matrix image.This study not only provides conditions for assessing the penetrating state of a weld pool,but also enable a further understanding of the oscillation mode of a weld pool and the development of more effective observation methods and measurement tools to effectively control and improve welding quality.展开更多
We consider the scattering of light in participating media composed of sparsely and randomly distributed discrete particles.The particle size is expected to range from the scale of the wavelength to several orders of ...We consider the scattering of light in participating media composed of sparsely and randomly distributed discrete particles.The particle size is expected to range from the scale of the wavelength to several orders of magnitude greater,resulting in an appearance with distinct graininess as opposed to the smooth appearance of continuous media.One fundamental issue in the physically-based synthesis of such appearance is to determine the necessary optical properties in every local region.Since these properties vary spatially,we resort to geometrical optics approximation(GOA),a highly efficient alternative to rigorous Lorenz–Mie theory,to quantitatively represent the scattering of a single particle.This enables us to quickly compute bulk optical properties for any particle size distribution.We then use a practical Monte Carlo rendering solution to solve energy transfer in the discrete participating media.Our proposed framework is the first to simulate a wide range of discrete participating media with different levels of graininess,converging to the continuous media case as the particle concentration increases.展开更多
In this paper,we revisit the simple problem of reflection from a dielectric sphere for light rays and define a form of optical inverse problem in the sense of geometrical optics(GO).A general analytic formula is deriv...In this paper,we revisit the simple problem of reflection from a dielectric sphere for light rays and define a form of optical inverse problem in the sense of geometrical optics(GO).A general analytic formula is derived to obtain the refraction index of the sphere for any incidence light to emerge in a deflected angle.Numerical wave simulation and ray tracing are performed to verify the inverse formulae derived.展开更多
The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical...The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical tool for the characterization and construction of images in Geometrical Optics. The Sympletic Map constitutes a Lie Group, with an algebra associated: the Lie Algebra. In general, the SM can be expressed as an infinite series, where each term corresponds to different contributions produced by the optical devices that constitute the optical system (lenses, apertures, bandwidth cutoff, etc.). The level of correction to be performed on the image to recover the original object is clear and controllable by SM. This formalism can be extended easily to physical optics to describe diffraction and interference phenomena.展开更多
We study the controversy about the proper determination of the electromagnetic energy-flux field in anisotropic materials, which has been revived due to the relatively recent experiments on negative refraction in meta...We study the controversy about the proper determination of the electromagnetic energy-flux field in anisotropic materials, which has been revived due to the relatively recent experiments on negative refraction in metamaterials. Rather than analyzing energy-balance arguments, we use a pragmatic approach inspired by geometrical optics, and compare the predictions on angles of refraction at a flat interface of two possible choices on the energy flux: and . We carry out this comparison for a monochromatic Gaussian beam propagating in an anisotropic non-dissipative anisotropic metamaterial, in which the spatial localization of the electromagnetic field allows a more natural assignment of directions, in contrast to the usual study of plane waves. We compare our approach with the formalism of geometrical optics, which we generalize and analyze numerically the consequences of either choice.展开更多
We construct a numerical scheme based on the Liouville equation of geometric optics coupled with the Geometric Theory of Diffraction(GTD)to simulate the high frequency linear waves diffracted by a half plane.We first ...We construct a numerical scheme based on the Liouville equation of geometric optics coupled with the Geometric Theory of Diffraction(GTD)to simulate the high frequency linear waves diffracted by a half plane.We first introduce a condition,based on the GTD theory,at the vertex of the half plane to account for the diffractions,and then build in this condition as well as the reflection boundary condition into the numerical flux of the geometrical optics Liouville equation.Numerical experiments are used to verify the validity and accuracy of this new Eulerian numerical method which is able to capture the moments of high frequency and diffracted waves without fully resolving the high frequency numerically.展开更多
In this Letter,a Gabor superlens with variable focus is presen ted.This configuration uses tunable liquid lenses in the third microlens array of the Gabor superlens.By applying voltage,the radius of curvature of the m...In this Letter,a Gabor superlens with variable focus is presen ted.This configuration uses tunable liquid lenses in the third microlens array of the Gabor superlens.By applying voltage,the radius of curvature of the microtunable doublet arrays changes,and the Gabor conditions are fulfilled at different focal planes.As a consequence,the magnification of the image at the focal planes changes,and a zoom effect is observed.The marginal depth plane for this system goes from 0.86 to 0.89 mm.The optical simulation,calculations,and results of the simulated optical system performance are presented.展开更多
The numerical approximation of high frequency wave propagation is important in many applications.Examples include the simulation of seismic,acoustic,optical waves and microwaves.When the frequency of the waves is high...The numerical approximation of high frequency wave propagation is important in many applications.Examples include the simulation of seismic,acoustic,optical waves and microwaves.When the frequency of the waves is high,this is a difficult multiscale problem.The wavelength is short compared to the overall size of the computational domain and direct simulation using the standard wave equations is very expensive.Fortunately,there are computationally much less costly models,that are good approximations of many wave equations precisely for very high frequencies.Even for linear wave equations these models are often nonlinear.The goal of this paper is to review such mathematical models for high frequency waves,and to survey numerical methods used in simulations.We focus on the geometrical optics approximation which describes the infinite frequency limit of wave equations.We will also discuss finite frequency corrections and some other models.展开更多
基金Supported by the National Natural Science Foundation of China (No. 61172024)
文摘In this paper, the Geometric Optics (GO) method using the approximate ray paths coupled with the Computer Aided Tri-dimensional Interface Application (CATIA) meshing modeling are implemented to analyze the performance of electric large three-dimensional dielectric radome-enclosed antenna of arbitrary contour shape. The surfaces of the radome are approximated by planar triangular patches, the influences of various number of patches on power transmission coefficient and Insertion Phase Delay (IPD) via an ogive and a conical radome are discussed by the hybrid method. The simulation results indicate that computational error from planar triangular patches can limit in one percent, meeting the engineering application requirements.
基金supported by the National Natural Science Foundation of China(12061084)the Natural Science Foundation of Yunnan Province(2019FY003007).
文摘The perturbed Riemann problem for a hyperbolic system of conservation laws arising in geometrical optics with three constant initial states is solved.By studying the interactions among of the delta-shock,vacuum,and contact discontinuity,fourteen kinds of structures of Riemann solutions are obtained.The compound wave solutions consisting of delta-shocks,vacuums,and contact discontinuities are found.The single and double closed vacuum cavitations develop in solutions.Furthermore,it is shown that the solutions of the Riemann problem for the geometrical optics system are stable under certain perturbation of the initial data.Finally,the numerical results completely coinciding with theoretical analysis are presented.
文摘Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface;however, there is a need for simulating surface scattering losses for devices having many surface interactions such as light pipes. Light pipes are often simulated with geometric optics (GO) using ray tracing, where surface scattering is driven by the surface slope distribution. In the DO case, surface scattering analyses depend on the spatial frequency distribution and amplitude as well as wavelength, with the sinusoidal grating as a fundamental basis. A better understanding of the link, or transition, between DO and GO scattering domains would be helpful for efficiently incorporating scattering loss analyses into ray trace simulations. A formula for the root-mean-square (rms) scattered angle width of a sinusoidal reflection grating that depends only on the surface rms slope is derived from the nonparaxial scalar diffraction theory, thereby linking it to GO. The scatter angle’s mean and rms width are evaluated over a range of grating amplitudes and periods using scalar theory and full vector simulations from the COMSOL® wave optic module for a sinusoidal reflection grating. The conditions under which the diffraction-based solution closely approximates the GO solution, as predicted by the rms slope, are identified. Close agreement is shown between the DO and GO solutions for the same surface rms slope scattering loss due to angular filtering near the critical angle of a total internal reflection (TIR) glass-to-air interface.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11534006,11674184 and 11374166the Natural Science Foundation of Tianjin under Grant No 16JC2DJC31300Collaborative Innovation Center of Extreme Optics
文摘We investigate a novel spatial geometric phase of hybrid-polarized vector fields consisting of linear, elliptical and circular polarizations by Young's two-slit interferometer instead of the widely used Mach-Zehnder interferometer.This spatial geometric phase can be manipulated by engineering the spatial configuration of hybrid polarizations,and is directly related to the topological charge, the local states of polarization and the rotational symmetry of hybrid-polarized vector optical fields. The unique feature of geometric phase has implications in quantum information science as well as other physical systems such as electron vortex beams.
基金Supported by National Natural Science Foundation of China(Grant No.51205197).
文摘Researchers have recently attempted to monitor pool oscillations using the three-dimensional laser vision method.However,the deficiency of simulation software will result in significant capital expenditure.Both simulations and experiments are performed in this study,and the Bessel equation is used to analyze the oscillation mode of a weld pool.The laser dot matrix images of(0,1),(1,1),(2,1),and(0,2)oscillation modes at different times are obtained via structured laser optical measurement simulation.The oscillation mode of a stationary gas tungsten arc weld pool is analyzed based on laser dot matrix images obtained from a structure laser experiment.Results show that the simulated laser dot matrix images are consistent with the experiment results.The oscillation mode of the weld pool can be recognized based on the laser dot matrix image.This study not only provides conditions for assessing the penetrating state of a weld pool,but also enable a further understanding of the oscillation mode of a weld pool and the development of more effective observation methods and measurement tools to effectively control and improve welding quality.
基金National Natural Science Foundation of China(Grant Nos.61972194 and 62032011)。
文摘We consider the scattering of light in participating media composed of sparsely and randomly distributed discrete particles.The particle size is expected to range from the scale of the wavelength to several orders of magnitude greater,resulting in an appearance with distinct graininess as opposed to the smooth appearance of continuous media.One fundamental issue in the physically-based synthesis of such appearance is to determine the necessary optical properties in every local region.Since these properties vary spatially,we resort to geometrical optics approximation(GOA),a highly efficient alternative to rigorous Lorenz–Mie theory,to quantitatively represent the scattering of a single particle.This enables us to quickly compute bulk optical properties for any particle size distribution.We then use a practical Monte Carlo rendering solution to solve energy transfer in the discrete participating media.Our proposed framework is the first to simulate a wide range of discrete participating media with different levels of graininess,converging to the continuous media case as the particle concentration increases.
基金the Hangdian University(ZX150204307002/023,KYZ043714070)Natural National Science Foundation(NSFC11174074,11804087)+1 种基金Hubei University(A201508)Science and Technology Department of Hubei Province(2018CFB148)and Ms.Shi N.’s Grant.
文摘In this paper,we revisit the simple problem of reflection from a dielectric sphere for light rays and define a form of optical inverse problem in the sense of geometrical optics(GO).A general analytic formula is derived to obtain the refraction index of the sphere for any incidence light to emerge in a deflected angle.Numerical wave simulation and ray tracing are performed to verify the inverse formulae derived.
文摘The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical tool for the characterization and construction of images in Geometrical Optics. The Sympletic Map constitutes a Lie Group, with an algebra associated: the Lie Algebra. In general, the SM can be expressed as an infinite series, where each term corresponds to different contributions produced by the optical devices that constitute the optical system (lenses, apertures, bandwidth cutoff, etc.). The level of correction to be performed on the image to recover the original object is clear and controllable by SM. This formalism can be extended easily to physical optics to describe diffraction and interference phenomena.
文摘We study the controversy about the proper determination of the electromagnetic energy-flux field in anisotropic materials, which has been revived due to the relatively recent experiments on negative refraction in metamaterials. Rather than analyzing energy-balance arguments, we use a pragmatic approach inspired by geometrical optics, and compare the predictions on angles of refraction at a flat interface of two possible choices on the energy flux: and . We carry out this comparison for a monochromatic Gaussian beam propagating in an anisotropic non-dissipative anisotropic metamaterial, in which the spatial localization of the electromagnetic field allows a more natural assignment of directions, in contrast to the usual study of plane waves. We compare our approach with the formalism of geometrical optics, which we generalize and analyze numerically the consequences of either choice.
文摘We construct a numerical scheme based on the Liouville equation of geometric optics coupled with the Geometric Theory of Diffraction(GTD)to simulate the high frequency linear waves diffracted by a half plane.We first introduce a condition,based on the GTD theory,at the vertex of the half plane to account for the diffractions,and then build in this condition as well as the reflection boundary condition into the numerical flux of the geometrical optics Liouville equation.Numerical experiments are used to verify the validity and accuracy of this new Eulerian numerical method which is able to capture the moments of high frequency and diffracted waves without fully resolving the high frequency numerically.
文摘In this Letter,a Gabor superlens with variable focus is presen ted.This configuration uses tunable liquid lenses in the third microlens array of the Gabor superlens.By applying voltage,the radius of curvature of the microtunable doublet arrays changes,and the Gabor conditions are fulfilled at different focal planes.As a consequence,the magnification of the image at the focal planes changes,and a zoom effect is observed.The marginal depth plane for this system goes from 0.86 to 0.89 mm.The optical simulation,calculations,and results of the simulated optical system performance are presented.
文摘The numerical approximation of high frequency wave propagation is important in many applications.Examples include the simulation of seismic,acoustic,optical waves and microwaves.When the frequency of the waves is high,this is a difficult multiscale problem.The wavelength is short compared to the overall size of the computational domain and direct simulation using the standard wave equations is very expensive.Fortunately,there are computationally much less costly models,that are good approximations of many wave equations precisely for very high frequencies.Even for linear wave equations these models are often nonlinear.The goal of this paper is to review such mathematical models for high frequency waves,and to survey numerical methods used in simulations.We focus on the geometrical optics approximation which describes the infinite frequency limit of wave equations.We will also discuss finite frequency corrections and some other models.
