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Cloaking of structures with convex or concave geometry using higher order parameterised function verified using ray tracing

Sidhwa, H. H ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ijleo.2019.06.011
  3. Publisher: Elsevier GmbH , 2019
  4. Abstract:
  5. The accomplishment of design for devices and applications such as cloaking has been feasible using transformation optics. This feasibility has been extended to the design of cloaks for concave bodies. Even though the process of cloaking in concave shaped bodies has been addressed in literature, the problem of poor accuracy and poor quality of cloaking remains. In accordance with the aim to outmanoeuvre the problem, the surface of interest which could be of convex or concave nature is modelled using a piecewise higher order parametric function. This function is expressed using Lagrange's interpolation. The calculation of piecewise model involves the inversion of the Lagrangian polynomial. But the inverse is numerically unstable because it is a Vandermonde matrix. Here, a method which is more stable than one that involves the direct inversion of the Vandermonde matrix, has been suggested using a recurrence relation. As the order of the function increases, it is observed that the efficiency of the cloaking improves further. It can be inferred that usage of the piecewise higher order parametric function along with a recurrence relation leads to an improvement in the quality and accuracy of cloaking. © 2019 Elsevier GmbH
  6. Keywords:
  7. Cloaking ; Concave geometry ; Higher order parametric function ; Transformation optics ; Lagrange multipliers ; Matrix algebra ; Lagrange's interpolation ; Parametric functions ; Piece-wise models ; Recurrence relations ; Vandermonde matrix ; Inverse problems
  8. Source: Optik ; Volume 194 , 2019 ; 00304026 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0030402619307740