Design method for quasi-isotropic transformation materials based on inverse Laplace's equation with sliding boundaries

Abstract

The deformation method of transformation optics has been demonstrated to be a useful tool, especially in designing arbitrary and nonsingular transformation materials. Recently, there are emerging demands for isotropic material parameters, arising from the broadband requirement of the designed devices. In this work, the deformation method is further developed to design quasi-isotropic/isotropic transformation materials. The variational functional of the inverse Laplace's equation is investigated and found to involve the smooth and quasi-conformal nature of coordinate transformation. Together with the sliding boundary conditions, the inverse Laplace's equation can be utilized to give transformations which are conformal or quasi-conformal, depending on functionalities of interest. Examples of designing an arbitrary carpet cloak and a waveguide with arbitrary cross sections are given to validate the proposed idea. Compared with other quasi-conformal methods based on grid generation tools, the proposed method unifies the design and validation of transformation devices, and thus is much convenient.

8 pages, 4 figures

References in corpus (7)

• Hiding Under the Carpet: a New Strategy for Cloaking
• Illusion optics: The optical transformation of an object into another object
• Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell's Equations
• Silicon nanostructure cloak operating at optical frequencies
• Design Method for Electromagnetic Cloak with Arbitrary Shapes Based on Laplace's Equation
• Ground-Plane Quasi-Cloaking for Free Space
• Nonsingular two dimensional cloak of arbitrary shape

Cited by in corpus (13)

• Transformational Plasmon Optics
• Design and experimental demonstration of a high-directive emission with optical transformations
• Quasi isotropic underwater acoustic carpet cloak based on latticed pentamode metafuid
• Transformation Inverse Design
• Ultrasound Beam Steering with Flattened Acoustic Metamaterial Luneburg Lens
• Controlling elastic wave with isotropic transformation materials
• Carpet cloaking on a dielectric half-space
• Design of arbitrarily shaped acoustic cloaks through PDE-constrained optimization satisfying sonic-metamaterial design requirements
• Moulding the flow of surface plasmons using conformal and quasiconformal mapping
• Conformal Transformation Electromagnetics Based on Schwarz-Christoffel Mapping for the Synthesis of Doubly Connected Metalenses
• Direct manipulation of wave amplitude and phase through inverse design of isotropic media
• Longitudinal elastic wave control by pre-deforming semi-linear materials
• Theory and experiment of isotropic electromagnetic beam bender made of dielectric materials