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Theory of transformation optics and invisibility cloak design
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Research on metamaterials has been growing ever since the first experimental realization of double negative media. The theory of transformation optics provides people with a perfect tool to make use of vast possibilities of the constitutive parameters for metamaterials. A lot of fascinating designs have been brought to us by transformation optics, with invisibility cloaks being the most intensely studied. The present thesis aims to develop the basic theory of transformation optics, and utilize it to design invisibility cloaks for various applications.

After the background description of this field, the theory of transformation optics is first introduced. Formulas of transformation medium parameters and transformed fields are derived with every detail explained, so that the working knowledge of transformation optics can be grasped with minimal prerequisite mathematics. Proof of form invariance of full Maxwell’s equations with sources is presented. Design procedure of transformation optics is then demonstrated by creating perfect invisibility cloaks. The introduction to basic theory is followed by discussions on our works included in our published papers.

As our first application, a method of designing two-dimensional reduced cloaks of complex shapes is proposed to relieve the difficulty of singularity occurring in perfect cloaks. The simple and intuitive method is the first way to design two-dimensional reduced cloaks of shapes other than cylindrical. Elliptical and bowtie shaped reduced cloaks are presented to verify the effectiveness of the method. Prominent scattering reduction is observed for both examples.

Considering the practical realization, transformations continuous in the whole space must be the identity operation outside certain volume, and thus they can only manipulate fields locally. Discontinuous transformations are naturally considered to break the limitation. We study the possible reflections from such a transformation medium due to a discontinuous transformation by a new concept of inverse transformation. This way, the reflection falls into the framework of transformation optics as well. A necessary and sufficient condition for no reflection is derived as a special case.

Unlike the invisibility realized by perfect cloaks, cloaking an object over a dielectric half-space has advantages in some particular applications. Starting from a perfect cloak, a half-space cloak is designed to achieve this. In our design, two matching strips embedded in the dielectric ground are used to induce proper reflection in the upper air space, so that the reflected field is the same as that from the bare dielectric ground.

Cloaks obtained from singular transformations and even reduced models all have null principal value in their material parameters, making invisibility inherently very narrowband. In contrast, a carpet cloak designed by only coordinate deformation does not have the narrowband issue, and can perform well in a broad spectrum. The invisibility accomplished by the carpet cloak is also for the half-space case as our previous design. In this part, we extend the original version of a carpet cloak above a PEC sheet to a general dielectric ground.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology , 2011. , xii, 55 p.
Series
Trita-EE, ISSN 1653-5146 ; 2011:028
Keyword [en]
Transformation optics, Maxwell’s equations, invisibility cloak, half-space cloak, reduced cloak, inverse transformation, carpet cloak
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-31673ISBN: 978-91-7415-947-9OAI: oai:DiVA.org:kth-31673DiVA: diva2:405390
Public defence
2011-05-06, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20110415Available from: 2011-04-15 Created: 2011-03-22 Last updated: 2011-04-18Bibliographically approved
List of papers
1. Cloaking an object on a dielectric half-space
Open this publication in new window or tab >>Cloaking an object on a dielectric half-space
2008 (English)In: Optics Express, ISSN 1094-4087, Vol. 16, no 5, 3161-3166 p.Article in journal (Refereed) Published
Abstract [en]

Cloaking an object on a dielectric half-space for an observer in air is studied. The proposed cloaking configuration has two vertical matching strips of isotropic and homogeneous material under the two bottom surfaces of a semi-cylindrical cloaking cover. Simple expression for the material parameters of the matching strips is derived. The theoretical results of cloaking are verified numerically for the incidence of plane wave and line current source. The vertical matching strips can be terminated with a finite depth by introducing some loss to the matching material.

Keyword
Electromagnetic optics, Anisotropic optical materials, Reflection
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-17385 (URN)000254121300034 ()2-s2.0-40349108558 (ScopusID)
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2013-11-19Bibliographically approved
2. Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak
Open this publication in new window or tab >>Obtaining a nonsingular two-dimensional cloak of complex shape from a perfect three-dimensional cloak
2008 (English)In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 93, no 24, 243502- p.Article in journal (Refereed) Published
Abstract [en]

A general method is proposed to construct an approximate nonsingular two-dimensional (2D) cloak by taking constitutive parameter tensors (CPTs) of a three-dimensional perfect cloak on a mirror-symmetric cross section in order to avoid any singularity at the inner boundary of a perfect 2D cloak. As two examples, reduced 2D models for an elliptic cloak and a bow-tie cloak are derived. The reduced 2D models are characterized explicitly with CPT of finite values and good cloaking effects are verified numerically.

Keyword
Metamaterials, mirrors
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-32574 (URN)10.1063/1.3021067 (DOI)000261896400079 ()2-s2.0-57849156263 (ScopusID)
Funder
Swedish Research Council
Note
QC 20110415Available from: 2011-04-15 Created: 2011-04-15 Last updated: 2013-11-19Bibliographically approved
3. Inverse Transformation Optics and Reflection Analysis for Two-Dimensional Finite-Embedded Coordinate Transformation
Open this publication in new window or tab >>Inverse Transformation Optics and Reflection Analysis for Two-Dimensional Finite-Embedded Coordinate Transformation
2010 (English)In: IEEE Journal of Selected Topics in Quantum Electronics, ISSN 1077-260X, E-ISSN 1558-4542, Vol. 16, no 2, 427-432 p.Article in journal (Refereed) Published
Abstract [en]

Inverse transformation optics is introduced, and used to calculate the reflection at the boundary of a transformation medium under consideration. The transformation medium for a practical device is obtained from a 2-D finite-embedded coordinate transformation (FECT), which is discontinuous at the boundary. For an electromagnetic excitation of particular polarization, many pairs of original medium (in a virtual space V') and inverse transformation can give exactly the same anisotropic medium through the conventional procedure of transformation optics. Nonuniqueness of these pairs is then exploited for the analysis and calculation of the boundary reflection. The reflection at the boundary of the anisotropic FECT medium (associated with the corresponding vacuum virtual space V) is converted to the simple reflection between two isotropic media in virtual space V' by a selected inverse transformation continuous at the boundary. A reflectionless condition for the boundary of the FECT medium is found as a special case. The theory is verified numerically with the finite element method.

Keyword
Finite-embedded coordinate transformation, inverse transformation, optics, reflection, reflectionless condition, design, metamaterials, cloaking, bends
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-19379 (URN)10.1109/jstqe.2009.2031163 (DOI)000276418100010 ()
Funder
Swedish Research Council
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2013-11-19Bibliographically approved
4. Carpet cloaking on a dielectric half-space
Open this publication in new window or tab >>Carpet cloaking on a dielectric half-space
2010 (English)In: Optics Express, ISSN 1094-4087, Vol. 18, no 17, 18158-18163 p.Article in journal (Refereed) Published
Abstract [en]

Carpet cloaking is proposed to hide an object on a dielectric half-space from electromagnetic (EM) detection. A two-dimensional conformal transformation specified by an analytic function is utilized for the design. Only one nonsingular material parameter distribution suffices for the characterization. The cloaking cover situates on the dielectric half-space, and consists of a lossless upper part for EM wave redirection and an absorbing bottom layer for inducing correct reflection coefficient and absorbing transmission. Numerical simulations with Gaussian beam incidence are performed for verification. The broadband behavior of the carpet cloaking is also illustrated.

Keyword
Physical optics, Electromagnetic optics, Metamaterials, Invisibility cloaks
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-26843 (URN)10.1364/OE.18.018158 (DOI)000281054400061 ()2-s2.0-77956380822 (ScopusID)
Note
QC 20101206Available from: 2010-12-06 Created: 2010-11-29 Last updated: 2013-11-19Bibliographically approved

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