Topic
Elliptic coordinate system
About: Elliptic coordinate system is a research topic. Over the lifetime, 670 publications have been published within this topic receiving 11135 citations. The topic is also known as: elliptical coordinate system & elliptic coordinates.
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TL;DR: In this article, an elliptic-symmetry vector optical field was proposed, which is more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields.
Abstract: We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.
21 citations
TL;DR: In this paper, a two-dimensional analytical model is developed to describe the free extensional vibrations of thin elastic plates of elliptical planform with or without a confocal cutout under general elastically restrained edge conditions, based on the Navier displacement equation of motion for a state of plane stress.
20 citations
TL;DR: In this article, a finite-embedded coordinate transformation method is applied to the design of EM beam-modulating devices both in Cartesian coordinates and in cylindrical coordinates.
Abstract: The transformation media concept based on the form-invariant Maxwell's equations under coordinate transformations has opened up new possibilities of manipulating electromagnetic (EM) fields. In this paper, we report on application of the finite-embedded coordinate transformation method to the design of EM beam-modulating devices both in Cartesian coordinates and in cylindrical coordinates. By designing the material constitutive tensors of the transformation optical structures through different kinds of coordinate transformations, either the beamwidth of an incident Gaussian plane wave could be modulated by a slab or the wave-propagating direction of an omnidirectional source could be modulated through a cylindrical shell. We present the design procedures and the full-wave EM simulations that clearly confirm the good performance of the proposed beam-modulating devices.
20 citations
20 citations
TL;DR: In this article, the authors presented numerical solutions for stresses around an elliptical hole in a long, thin, circular cylindrical shell subjected to axial tension for both the symmetric orientations of the hole with respect to the shell.
20 citations