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Manipulation of Light with Transformation Optics
KTH, School of Information and Communication Technology (ICT), Microelectronics and Applied Physics, MAP.
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Transformation optics, a recently booming area, provides people a new approach to design optical devices for manipulating light. With transformation optics, a lot of novel optical devices are proposed, such as invisibility cloaks, optical wormholes, optical black holes, illusion devices. The present thesis is devoted to investigate transformation optics for manipulating light.

Firstly, an introduction to transformation optics is given. This part includes: (1) introducing differential geometry as the mathematical preparation; (2) expressing Maxwell’s equations in an arbitrary coordinate system and introducing the concept of transformation media as the foundation stone of transformation optics; (3) discussing light from the geometry perspective as the essence of transformation optics; (4) showing how to use transformation optics to design optical devices.

For our works on invisibility cloaks, we analyze the properties of arbitrary shaped invisibility cloaks, and confirm their invisibility abilities. The geometrical perturbations to cylindrical and spherical shaped cloaks are analyzed in detail. We show that the cylindrical cloak is more sensitive to the perturbation than a spherical cloak. By imposing a PEC (PMC) layer at the interior boundary of the cylindrical cloak shell for TM (TE) wave, the sensitivity can be reduced dramatically. A simplified non-magnetic cylindrical cloak is also designed. We show that the dominant zeroth order scattering term can be eliminated by employing an air gap between the cloak and the cloaked region.

We propose a compensated bilayer by a folding coordinate transformation based on transformation optics. It is pointed out that complementary media, perfect negative index lens and perfect bilayer lens made of indefinite media are well unified under the scope of the transformed compensated bilayer. We demonstrate the applications of the compensated bilayer, such as perfect imaging and optical illusion. Arbitrary shaped compensated bilayers are also analyzed.

Nihility media known as the media with ε =μ= 0, are generalized from transformation optics as transformation media derived from volumeless geometrical elements. The practical constructions of nihility media by metamaterials are discussed. The eigen fields in the nihility media are derived. The interactions between an external incident wave and a slab of nihility media in the free space background are analyzed.

A new type of transformation media called α media is proposed for manipulating light. Light rays in the α media have a simple displacement or rotation relationship with those in another media (seed media). Such relationship is named α relationship. The α media can be designed and simplified to a certain class of diagonal anisotropic media, which are related to certain isotropic media by the α relationship. Several optical devices based on the α transformation media are designed. Invisibility cloaks obtained from the coordinate transformation approach are revisited from a different perspective.

Place, publisher, year, edition, pages
Stockholm: KTH , 2010. , xiii, 99 p.
Series
Trita-ICT/MAP AVH, ISSN 1653-7610 ; 2010:09
Keyword [en]
transformation optics, Maxwell’s equations, invisibility cloaks, compensated bilayer, perfect imaging, optical illusion, nihility media, α media
National Category
Atom and Molecular Physics and Optics
Identifiers
URN: urn:nbn:se:kth:diva-25849OAI: oai:DiVA.org:kth-25849DiVA: diva2:360237
Public defence
2010-11-22, Sal / Hall C1, KTH-Electrum, Isafjordsgatan 26, Kista, 10:00 (English)
Opponent
Supervisors
Note
QC 20101102Available from: 2010-11-02 Created: 2010-11-02 Last updated: 2012-03-28Bibliographically approved
List of papers
1. Coordinate transformations make perfect invisibility cloaks with arbitrary shape
Open this publication in new window or tab >>Coordinate transformations make perfect invisibility cloaks with arbitrary shape
2008 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 10Article in journal (Refereed) Published
Abstract [en]

By investigating wave properties at cloak boundaries, invisibility cloaks with arbitrary shape constructed by general coordinate transformations are confirmed to be perfectly invisible to the external incident wave. The differences between line transformed cloaks and point transformed cloaks are discussed. The fields in the cloak medium are found analytically to be related to the fields in the original space via coordinate transformation functions. At the exterior boundary of the cloak, it is shown that no reflection is excited even though the permittivity and permeability do not always have a perfectly matched layer form, whereas at the inner boundary, no reflection is excited either, and in particular no field can penetrate into the cloaked region. However, for the inner boundary of any line transformed cloak, the permittivity and permeability in a specific tangential direction are always required to be infinitely large. Furthermore, the field discontinuity at the inner boundary always exists; the surface current is induced to make this discontinuity self-consistent. A point transformed cloak does not experience such problems. The tangential fields at the inner boundary are all zero, implying that no field discontinuity exists.

Keyword
frequencies, devices
Identifiers
urn:nbn:se:kth:diva-17528 (URN)10.1088/1367-2630/10/4/043040 (DOI)000255793300001 ()2-s2.0-46449091497 (Scopus ID)
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
2. Influence of geometrical perturbation at inner boundaries of invisibility cloaks
Open this publication in new window or tab >>Influence of geometrical perturbation at inner boundaries of invisibility cloaks
2008 (English)In: Journal of the Optical Society of America A, ISSN 0740-3232, Vol. 25, no 4, 968-973 p.Article in journal (Refereed) Published
Abstract [en]

The influence of a geometrical perturbation (5 at the inner boundaries of both cylindrical and spherical invisibility cloaks on invisibility performance is presented. The analytic solutions for such influence in the case of the general coordinate transformation are given. We show that the cylindrical cloak is more sensitive than a spherical cloak to such a perturbation. The difference results from the different asymptotic properties of eigen-functions for the cylindrical and spherical wave equations. In particular, the zeroth-order scattering coefficient for a cylindrical cloak determined by -1/ln(delta) converges to zero very slowly. The noticeable scattering induced by the slow convergence speed can be decreased by choosing appropriate coordinate transformation functions. More interestingly, the slow convergence can be overcome dramatically by putting a PEC (PMC) layer at the interior boundary of the cloak shell for TM (TE) wave.

Identifiers
urn:nbn:se:kth:diva-17476 (URN)000255297100016 ()2-s2.0-57849166864 (Scopus ID)
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
3. Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering
Open this publication in new window or tab >>Non-magnetic simplified cylindrical cloak with suppressed zeroth order scattering
2008 (English)In: Applied Physics Letters, ISSN 0003-6951, E-ISSN 1077-3118, Vol. 93, no 2Article in journal (Refereed) Published
Abstract [en]

A type of simplified cloaks with matched exterior boundaries is proposed. The cloak uses nonmagnetic material for the TM polarization and can function with a relatively thin thickness. It is shown that the zeroth order scattering of such cloak is dominant among all cylindrical scattering terms. A gap is added at the cloak's inner surface to eliminate the zeroth order scattering through the mechanism of scattering resonance. The reduction in scattering is relatively smooth, indicating that the proposed scattering reduction method has good tolerance to perturbations. Numerical simulations also confirm that the proposed structure has very low scattering.

National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-17707 (URN)10.1063/1.2958344 (DOI)000257796100037 ()2-s2.0-47549101402 (Scopus ID)
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
4. Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens
Open this publication in new window or tab >>Achieving perfect imaging beyond passive and active obstacles by a transformed bilayer lens
2009 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 79, no 16Article in journal (Refereed) Published
Abstract [en]

A bilayer lens is proposed based on transformation optics. It is shown that Pendry's perfect lens, perfect bilayer lens made of indefinite media, and the concept of compensated media are well unified under the scope of the proposed bilayer lens. Using this concept, we also demonstrate how one is able to achieve perfect imaging beyond passive objects or active sources which are present in front of the lens.

Keyword
lenses, negative refraction
Identifiers
urn:nbn:se:kth:diva-18412 (URN)10.1103/PhysRevB.79.161101 (DOI)000265945200001 ()2-s2.0-65649106501 (Scopus ID)
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
5. Generalized compensated bilayer structure from the transformation optics perspective
Open this publication in new window or tab >>Generalized compensated bilayer structure from the transformation optics perspective
2009 (English)In: Journal of the Optical Society of America. B, Optical physics, ISSN 0740-3224, E-ISSN 1520-8540, Vol. 26, no 12, B39-B49 p.Article in journal (Refereed) Published
Abstract [en]

A systematic study on a generalized compensated bilayer structure is presented based on transformation optics. A compensated bilayer can be constructed through a general transformation plus a coordinate inversion based on a single layer in the electromagnetic (EM) space. Two outer boundaries of the obtained bilayer are mapped from the same surface. Such a bilayer has an optically zero volume (nihility) regardless of the material composition in the original single layer. This fact directly leads to the property of invariant scattering. A bilayer is also able to transfer the EM field from one side to the other with a scaling factor, which is determined by how the two side boundaries are mapped. For a properly chosen background, it is possible to achieve perfect optical imaging. Extensive numerical examples are given to demonstrate these identified properties and applications. Our study provides a more complete understanding of this class of transformation media by considering general geometries and arbitrary material properties.

Keyword
negative refractive-index, cloak, metamaterials, invisibility, frequencies, light
Identifiers
urn:nbn:se:kth:diva-19011 (URN)000272389800008 ()2-s2.0-73849084721 (Scopus ID)
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved
6. Generalized nihility media from transformation optics
Open this publication in new window or tab >>Generalized nihility media from transformation optics
2011 (English)In: Journal of optics, ISSN 0150-536X, Vol. 13, no 2Article in journal (Refereed) Published
Abstract [en]

Nihility media in the previous literature are usually understood as media with epsilon = mu = 0. Transformation optics opens a new perspective for capturing the essence of such media. From this perspective, we generalize the definition of nihility media as transformation media derived from volumeless geometrical elements. A volumeless geometrical elements can be either a point (P), a line (L), or a surface (S). Their corresponding transformation media are therefore called P-, L-, or S-type nihility media, respectively. The previous defined nihility media with epsilon = mu = 0 is a special case under the P-type nihility media. The constructions of nihility media by metamaterials are discussed. The eigenfields in different types of nihility media are derived. The interactions between an externally incident wave and a slab of nihility media in a free space background are analyzed. Furthermore, we discuss compensated bilayers composed of nihility media. It is shown that for a slab of P-type nihility media, a normally incident wave can perfectly transmit through, while all obliquely incident waves are completely blocked; for a slab made of L-type nihility media, both normally and obliquely incident waves can transmit with some reflections, which can be eliminated by adding a compensating L-type nihility media; for a slab of S-type nihility media, all field components can perfectly transmit through.

Keyword
transformation optics, metamaterials
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-25701 (URN)10.1088/2040-8978/13/2/024005 (DOI)000286457800007 ()2-s2.0-79551713079 (Scopus ID)
Funder
Swedish Research Council
Note
Uppdaterad från Accepted till Published (20110221) QC 20110221Available from: 2010-10-28 Created: 2010-10-28 Last updated: 2017-12-12Bibliographically approved
7. Manipulation of light with α transformation media
Open this publication in new window or tab >>Manipulation of light with α transformation media
2011 (English)In: Optical Society of America. Journal A: Optics, Image Science, and Vision, ISSN 1084-7529, E-ISSN 1520-8532, Vol. 28, no 6, 1058-1066 p.Article in journal (Refereed) Published
Abstract [en]

A type of transformation media called α media is proposed by performing a direct transformation to the metric tensor of another kind of media, called seed media. Light rays in an α medium correlate to those in its seed medium through a simple displacement or rotation relation. Three types of commonly encountered anisotropic media are covered by the concept of α media: (1) media of slab shape, having continuous translational symmetry with respect to two Cartesian coordinate components; (2) media of cylindrical shape, having cylindrical rotational symmetry and continuous translational symmetry along the longitudinal direction; (3) media of spherical shape, having spherical rotational symmetry, with two principal axes along the symmetry directions, and with the material parameters in the same sign. Optical properties of such media can be effectively interpreted through recalling the properties of certain isotropic media, i.e., their seed media. Conversely, from simple isotropic media in which light trajectories are well known, one can design α media for manipulating light. Based on this fact, several optical devices, including frequency demultiplexers, beam splitters, focusing lenses, and radiation controllers, are designed and numerically verified. The famed invisibility cloak derived from a conventional coordinate transformation is revisited from the α media perspective.

National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-25702 (URN)10.1364/JOSAA.28.001058 (DOI)2-s2.0-79958807353 (Scopus ID)
Note
QC 20120328. Updated from manuscript to article in journal.Available from: 2010-10-28 Created: 2010-10-28 Last updated: 2017-12-12Bibliographically approved

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