1,721,034 research outputs found
Analysis and design of a planarly layered slot antenna with minimal influence of surface waves
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Antennas for silicon-based mm-wave FMCW radars:antenna integration and MIMO system design
Full text linkChallenges in electromagnetic field computation for neurostimulation:the road to patient-specific modeling
No full textMethods and apparatus for modeling electromagnetic scattering properties of microscopic structures and methods and apparatus for reconstruction of microscopic structures
Full text linkImproved convergence in the volume-integral method (VIM) of calculating electromagnetic scattering properties of a structure is achieved by numerically solving a volume integral equation for a vector field, F, rather than the electric field, E. The vector field, F, may be related to the electric field, E, by a change of basis, and may be continuous at material boundaries where the electric field, E, has discontinuities. Convolutions of the vector field, F, are performed using convolution operators according the finite Laurent rule (that operate according to a finite discrete convolution), which allow for efficient matrix-vector products via ID and/or 2D FFTs (Fast Fourier Transforms). An invertible convolution-and-change-of-basis operator, C, is configured to transform the vector field, F, to the electric field, E, by performing a change of basis according to material and geometric properties of the periodic structure. After solving the volume integral for the vector field, F, an additional post-processing step may be used to obtain the electric field, E, from the vector field, F. The vector field, F, may be constructed from a combination of field components of the electric field, E, and the electric flux density, D, by using a normal-vector field, n, to filter out continuous components. The improved volume-integral method may be incorporated into a forward diffraction model in metrology tools for reconstructing an approximate structure of an object, for example to assess critical dimensions (CD) performance of a lithographic apparatus
Integro-differential equations for electromagnetic scattering : analysis and computation for objects with electric contrast
Full text linkMethods and apparatus for calculating electromagnetic scattering properties of a structure and for reconstruction of approximate structures
Full text linkAlgorithm for reconstructing grating profile in a metrology application is disclosed to numerically solve a volume integral equation for a current density. It employs implicit construction of a vector field that is related to electric field and a current density by a selection of continuous components of vector field being continuous at one or more material boundaries, so as to determine an approximate solution of a current density. The vector field is represented by a finite Fourier series with respect to at least one direction, x, y. Numerically solving volume integral equation comprises determining a component of a current density by convolution of the vector field with a convolution operator, which comprises material and geometric properties of structure in the x, y directions. The current density is represented by a finite Fourier series with respect to x, y directions. Continuous components are extracted using convolution operators acting on electric field and current density
Methods and apparatus for modeling electromagnetic scattering properties of microscopic structures and methods and apparatus for reconstruction of microscopic structures
Full text linkImproved convergence in the volume-integral method (VIM) of calculating electromagnetic scattering properties of a structure is achieved by numerically solving a volume integral equation for a vector field, F, rather than the electric field, E. The vector field, F, may be related to the electric field, E, by a change of basis, and may be continuous at material boundaries where the electric field, E, has discontinuities. Convolutions of the vector field, F, are performed using convolution operators according the finite Laurent rule (that operate according to a finite discrete convolution), which allow for efficient matrix-vector products via ID and/or 2D FFTs (Fast Fourier Transforms). An invertible convolution-and-change-of-basis operator, C, is configured to transform the vector field, F, to the electric field, E, by performing a change of basis according to material and geometric properties of the periodic structure. After solving the volume integral for the vector field, F, an additional post-processing step may be used to obtain the electric field, E, from the vector field, F. The vector field, F, may be constructed from a combination of field components of the electric field, E, and the electric flux density, D, by using a normal-vector field, n, to filter out continuous components. The improved volume-integral method may be incorporated into a forward diffraction model in metrology tools for reconstructing an approximate structure of an object, for example to assess critical dimensions (CD) performance of a lithographic apparatus
Methods and apparatus for calculating electromagnetic scattering properties of a structure and for reconstruction of approximate structures
Full text linkA CSI algorithm for reconstructing grating profiles is disclosed. Solving a volume integral equation for current density, J, employs the implicit construction of vector field, FS related to the electric field, ES, and current density, J, by selection of continuous components of E and J, F being continuous at one or more material boundaries, so as to determine an approximate solution of J. F is represented by at least one finite Fourier series with respect to at least one direction, x, y, and the step of numerically solving the volume integral equation comprises determining a component of J, by convolution of F, with a convolution operator, M comprising material and geometric structure properties in both directions. J may be represented by at least one finite Fourier series with respect to both directions. The continuous components can be extracted using convolution operators, PT and PN, acting on E and J
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