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Related Concept Videos

Elasticity01:12

Elasticity

Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
The elasticity of an object can be described by a stress-strain curve, which represents the relationship between stress...
Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
Transformation of Plane Strain01:12

Transformation of Plane Strain

When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...
Hooke's Law01:26

Hooke's Law

Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.
Transformations of Functions III01:20

Transformations of Functions III

Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...

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Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
09:43

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

Extreme non-linear elasticity and transformation optics.

Allan R Gersborg1, Ole Sigmund

  • 1Technical University of Denmark, Department of Mechanical Engineering, Solid Mechanics, Nils Koppels Allé, Bld. 404, DK-2800 Kgs. Lyngby, Denmark. agersborg.hansen@gmail.com

Optics Express
|October 14, 2010
PubMed
Summary

Transformation optics designs novel devices by minimizing elastic energy potentials. Ideal transformations for TE light use an incompressible Poisson

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Area of Science:

  • Optics and Photonics
  • Materials Science
  • Solid Mechanics

Background:

  • Transformation optics enables the design of advanced optical components like cloaking devices and waveguides.
  • Selecting optimal transformations for broadband, all-dielectric devices is a complex, non-unique problem.
  • Existing methods often lack a systematic approach for identifying ideal transformation parameters.

Purpose of the Study:

  • To establish a direct link between transformation optics and solid mechanics principles.
  • To identify specific mechanical properties that lead to ideal optical transformations.
  • To develop a more automated and broadened approach to designing optical devices using transformation optics.

Main Methods:

  • Investigated the relationship between transformation parameters and elastic energy potentials.
  • Analyzed the role of the mechanical Poisson's ratio (ν) in optical transformations.
  • Correlated ideal optical transformations with minimizers of elastic energy for extreme Poisson's ratio values.

Main Results:

  • Transformations minimizing elastic energy potentials correspond to ideal optical designs.
  • For Transverse Electric (TE) polarized light, an incompressible transformation (ν = 1/2) is optimal.
  • For Transverse Magnetic (TM) polarized light, a compressible transformation with a negative Poisson's ratio (ν = -1) is optimal, analogous to a modified Liao functional.

Conclusions:

  • The mechanical Poisson's ratio is a critical parameter for realizing broadband, all-dielectric optical devices.
  • The analogy to solid mechanics provides a powerful tool for automating and expanding transformation optics.
  • This approach unifies the design principles for diverse optical components through mechanical material models.