99 results about "Maxwell's equations" patented technology

Method for determining time-dependent changes [73] in the earth vertical and horizontal electrical resistivity and fluid saturations from offshore electromagnetic survey measurements. The method requires both online and offline data, which should include at least one electromagnetic field component sensitive at least predominantly to vertical resistivity and another component sensitive at least predominately to horizontal resistivity [62]. Using a horizontal electric dipole source, online Ez and offline Hz measurements are preferred. For a horizontal magnetic dipole source, online H2 and offline E2 data are preferred. Magnetotelluric data may be substituted for controlled source data sensitive at least predominantly to horizontal resistivity. Maxwell's equations are solved by forward modeling [64,65] or by inversion [66,67], using resistivity models of the subsurface that are either isotropic contrast, and [64,66] or anisotropic [65,67]. Fluid saturation is determined from the vertical and horizontal resistivities using empirical relations or rock physics models [70].

Methods and apparatus to perform wavefront analysis, including phase and amplitude information, and 3D measurements in optical systems, and in particular those based on analyzing the output of an intermediate plane, such as an image plane, of an optical system. Measurement of surface topography in the presence of thin film coatings, or of the individual layers of a multilayered structure is described. Multi-wavelength analysis in combination with phase and amplitude mapping is utilized. Methods of improving phase and surface topography measurements by wavefront propagation and refocusing, using virtual wavefront propagation based on solutions of Maxwell's equations are described. Reduction of coherence noise in optical imaging systems is achieved by such phase manipulation methods, or by methods utilizing a combination of wideband and coherent sources. The methods are applied to Integrated Circuit inspection, to improve overlay measurement techniques, by improving contrast or by 3-D imaging, in single shot imaging. Data supplied from the esp@cenet database—Worldwide

An electronic device simulator includes a three-dimensional lumped device model, a three-dimensional visco-elastic process simulation model and a material design model that are interlinked with each other. The three-dimensional lumped device element model comprises a Poisson's equation model, an electron continuity equation model, a hole continuity equation model, a Maxwell's equations model, an eddy current equation model, and an Ohm's law equation model. The simulator accounts for the three dimensional characteristics of the circuit to determine circuit performance.

The present invention is a marine controlled source electromagnetic method finite element forward method of anisotropic media. The method comprises: firstly, setting a reference electrical conductivity, wherein three non-zero diagonal elements of the reference electrical conductivity are electrical conductivities in the direction of three main axes: x, y, z; next, setting three Euler rotation angles, and after three times of Euler rotation, obtaining an electrical conductivity tensor model in any direction; then starting from Maxwell equations, obtaining a finite element equation that is satisfied by magnetic vector potential and scalar potential under Coulomb regulations on a condition that the electrical conductivity presents anisotropy; then, performing discrete segmentation on a research region by using a non-structural grid, so that a complicated geoelectric model can be constructed; combining an incomplete LU discomposition pre-condition factor with an IDR(s) algorithm, so as to realize efficient and precise solution of a large sparse linear equation; and finally, deriving vector potential and scalar potential of a secondary field by using weighted moving least squares solution, to obtain each component of an electromagnetic field. The method provided by the present invention has excellent universality and can be promoted for electromagnetic method numerical value simulation with complicated electrical conductivity distribution and high precision.

A method and apparatus for converting electromagnetic surface waves from TE mode to TM mode or from TM mode to TE mode. The apparatus includes a dielectric surface having an anisotropic impedance tensor which is preferably obtained by a plurality of electrically conductive unit cells disposed on the dielectric surface and arranged in a two dimensional array of unit cells, a majority of the unit cells in said array being divided into at least two portions, with at least one gap separating the at least two portions from each other into two or more patches or plates, the array of unit cells having a surface wave input end and a surface wave output end, gaps in the unit cells disposed closest to the surface wave input end having a first orientation and gaps in said unit cells disposed closest to the surface wave output end having a second orientation different than said first orientation. The electromagnetic surface waves have a frequency greater than a TE cutoff frequency determined by a second solution of Maxwell's equations for said dielectric surface.

Method for completely specifying orientation of electromagnetic receivers dropped to the ocean bottom in an electromagnetic survey. Survey data are selected, rejecting noisy data with long offsets and data where the receiver has saturated with short offsets (61). A model is developed comprising three independent receiver orientation angles completely specifying the receiver orientation in three dimensions, and an earth resistivity model including a water layer and possibly an air layer (62). Maxwell's equations, applied to the model and the selected data, are then inverted to determine the receiver orientations (63).

A structure of interest is irradiated with radiation for example in the x-ray or EUV waveband, and scattered radiation is detected by a detector (306). A processor (308) calculates a property such as linewidth (CD) by simulating interaction of radiation with a structure and comparing the simulated interaction with the detected radiation. A layered structure model (600, 610) is used to represent the structure in a numerical method. The structure model defines for each layer of the structure a homogeneous background permittivity and for at least one layer a non-homogeneous contrast permittivity. The method uses Maxwell's equation in Born approximation, whereby a product of the contrast permittivity and the total field is approximated by a product of the contrast permittivity and the background field. A computation complexity is reduced by several orders of magnitude compared with known methods.

The invention belongs to the field of numerical simulation technology of ECR ion sources, and particularly relates to an MPM hybrid algorithm applied to numerical simulation of an ECR ion source. Thealgorithm is suitable for use in an ECR ion source structure. The MPM hybrid algorithm of simulation of the ECR ion source is established through combining an MAGY theory and PIC/MCC simulation algorithms, a time-varying electromagnetic field is described by the MAGY theory, self-consistent interaction of charged particles and the electromagnetic field is described by the PIC algorithm, and inter-particle collision processes are described by the MCC algorithm. A complex and complete solving process which originally needs to be carried out on Maxwell's equations is enabled to be simplified to solving on a set of coupled one-dimensional partial differential equations about mode amplitudes, relatively larger time step length can also be taken due to that compared with high-frequency cycles, changes of the mode amplitudes are slower, and computational complexity and a computational amount are greatly reduced. In addition, an electromagnetic model is adopted, and thus compared with adoptingan electrostatic model, the algorithm can more accurately describe an actual physical process.

A tetrahedralization and triangulation method used with the proximity based rounding method to satisfy topological consistency of tetrahedralization with the bounded precision of a digital computer is described. Tetrahedralization is applied to a VLSI design, and more specifically for solving Maxwell's equation to extract parasitic capacitances and 3-D optical proximity correction applications. The exactness of solving Maxwell's equation and finite element analysis depends on the correctness of the topological properties of the tetrahedralization. Among the important aspects of the correctness of the topological properties is the absence of spurious intersection of two or more tetrahedra. In a typical digital computer, numbers are represented using finite sized words. Round-off errors occur when a long number is represented using the finite word size. As a result, tetrahedralization loses its topological consistency. The proximity based rounding method finds potential locations of spurious intersections and pre-corrects these locations to avoid the generation of any topological inconsistencies.

The invention relates to a method for remodeling medium objects by electromagnetic inverse scattering. The method comprises following steps: utilizing Maxwell's equations and constitutive equations to deduce forward and reverse integral equations for electromagnetic scattering; guessing the shape of an object to be detected and discretizing integral equations with a method in order to obtain matrix equations; utilizing a Gauss-Newton minimization method to regularize ill-conditioned equations during the reverse scattering process following discretization, wherein used regularized parameters are obtained by a multiplicative regularization method; and adopting a born iterative method to carry out iteration and obtaining wave number of detected mediums at the needed precision in order to achieve the objective of remodeling mediums.The method helps to avoid the problem in the conventional method that parameters are obtained by a lot of experiment data so that solving efficiency is increased.

The diffraction of electromagnetic radiation from periodic grating profiles is determined using rigorous coupled-wave analysis, with intermediate calculations cached to reduce computation time. To implement the calculation, the periodic grating is divided into layers, cross-sections of the ridges of the grating are discretized into rectangular sections, and the permittivity, electric fields and magnetic fields are written as harmonic expansions along the direction of periodicity of the grating. Application of Maxwell's equations to each intermediate layer, i.e., each layer except the atmospheric layer and the substrate layer, provides a matrix wave equation with a wave-vector matrix A coupling the harmonic amplitudes of the electric field to their partial second derivatives in the direction perpendicular to the plane of the grating, where the wave-vector matrix A is a function of intra-layer parameters and incident-radiation parameters. W is the eigenvector matrix obtained from wave-vector matrix A, and Q is a diagonal matrix of square roots of the eigenvalues of the wave-vector matrix A. The requirement of continuity of the fields at boundaries between layers provides a matrix equation in terms of Wand Q for each layer boundary, and the solution of the series of matrix equations provides the diffraction reflectivity. Look-up of W and Q, which are precalculated and cached for a useful range of intra-layer parameters (i.e., permittivity harmonics, periodicity lengths, ridge widths, ridge offsets) and incident-radiation parameters (i.e., wavelengths and angles of incidence), provides a substantial reduction in computation time for calculating the diffraction reflectivity.

The invention relates to an electric dipole source three-dimensional time domain finite difference direct interpretation imaging method. The method includes the steps of loading Gaussian pulses on an electric dipole source, establishing Maxwell equations and constitutive equations for the ocean air space, the seawater space and the seabed ground space, conducting uniform mesh generation on prism object models of the three spaces, obtaining difference equations of seawater and the seabed ground through a time domain finite difference method according to meshes obtained through mesh generation by consuming that the conductivities and the magnetic conductivities of all the meshes obtained through mesh generation are unchanged, processing the Maxwell equations of ocean air through analysis solutions, calculating the electromagnetic field of the air above the sea surface, processing the boundary conditions of the generation space, setting stabilization conditions, solving the established difference equations through the combination with the processing results of the boundary conditions and the set stability conditions, and obtaining the distribution of the electromagnetic field of the seawater and the seabed ground at any moment.

The invention discloses a microwave passive circuit electromagnetic heat integral analysis method based on a spectrum element method. According to the method, firstly, a time domain spectrum element method is adopted for solving maxwell's equations, the instantaneous electric field and magnetic field distribution of a circuit under the effect of high-power pulses is worked out, and the electromagnetic loss at the current moment is obtained. If all of the electromagnetic loss inside a mold is converted into heat energy, the obtained heat energy is substituted into a heat conduction equation, and the temperature distribution conditions of each point at the current moment are obtained. Electricity characteristic parameters of materials at a next moment are obtained by utilizing a relational expression of dielectric parameters along with the temperature change, an electromagnetic field equation is calculated again, and the electromagnetic loss is obtained. The operation is repeatedly cycled in such a way until the preset heating time is completed. Through the electromagnetic heat integral analysis, the distribution condition of the temperature inside the mold along the time change when a filter receives the effect of different pulses can be clearly obtained, the modeling is flexible, the subdivision is convenient, formed matrixes have good sparsity, and the solving efficiency is higher.

Methods and apparatus for concentrating light into a specified focal volume and for collecting light from a specified volume. Incident light is coupled through a plurality of successive transmissive asymmetric microstructure elements. The succession of transmissive asymmetric microstructure elements may be designed by representing an electromagnetic field as a linear combination of eigenmodes of one of the succession of transmissive asymmetric microstructure elements. The asymmetric microstructure elements are represented as a plurality of mesh lattice units and eigenmode solutions to Maxwell's equations are obtained for each mesh lattice unit subject to consistent boundary conditions. S-matrix formalism is employed to calculate a field output and weighting coefficients for the eigenmodes are selected to achieve a specified set of field output characteristics.

The problem of modeling and designing a structure including a planar element(s) (e.g., antenna, RF circuit, etc.) arranged in association with a non-planar element(s) (e.g., non-planar packaging, a non-planar scattering element, a complex meta material, a periodic array element, etc.), in a computationally efficient and rigorous manner is solved by (1) modeling each of the planar elements using both conventional space-spectral analysis and complex space-spectral analysis to obtain an electro-magnetic (EM) signature matrix for each planar element, (2) determining (e.g., using a brute force modeling based on Maxwell's equations, by measuring experimentally, or by reading one from a stored library) an EM signature matrix (e.g., reflection and scattering matrices) compatible with those of the planar elements, for each of the non-planar elements, and (3) combining the EM signatures of the elements using matrix analysis to obtain a complete EM signature the structure.

A system and method for identification of conductor surface roughness model associated with a transmission line conductor is proposed. A network analyzer measures scattering parameters over a specified frequency band for at least two line segments of different length and substantially identical cross-section with investigated rough conductors. A first engine determines non-reflective (generalized) modal scattering parameters of the difference segment based on the measured scattering parameters of two line segments. A second engine computes generalized modal scattering parameters of the line difference segment by solving Maxwell's equations for geometry of the line cross-section with a given conductor surface roughness model. A third engine performs optimization by changing conductor surface roughness model parameters and model type until the computed and measured generalized modal scattering parameters match. The model that produces generalized modal S-parameters closest to the measured is the final conductor surface roughness model.

The present invention discloses a label reception power prediction method of UHF RFID ETC applications. The method comprises the steps of setting a reader antenna as a Cartesian coordinate origin, setting the Cartesian coordinate of a label as unknown, and solving a first-order reflection surface equation by the application scene geometrical parameters and the geometrical relationships, namely a plane equation of an automobile engine hood plane, a left temporary road vehicle right side surface and a right temporary road left side surface; by a free space radio wave propagation formula, calculating a visual range electric field intensity vector from the reader antenna to the label; separately calculating the coordinates of the reflection points on the above reflection surface; by a first-order reflection matrix equation of an electromagnetic wave, separately calculating the electric field intensity vectors of an incident wave and a reflection wave arriving at the label at the reflection surface; solving the label electric field vector sum, a label chip antenna port matching coefficient and a polarization matching coefficient, and finally obtaining a label reception power calculation result in the space. The label reception power prediction method of the present invention can obtain a higher prediction precision than the conventional lognormal model and Leslie Model, and obtain the prediction speed more convenient and faster than a commercial electromagnetic calculation software based on Maxwell's equations.