Optics of polyhedra: from invisibility cloaks to curved spaces

Bělín, Jakub (2020) Optics of polyhedra: from invisibility cloaks to curved spaces. PhD thesis, University of Glasgow.

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Abstract

Transformation optics is a new and highly active field of research, which employs the mathematics of differential geometry to design optical materials and devices with unusual properties.Probably the most exciting device proposed by transformation optics is the invisibility cloak. However, transformation optics can be employed in many other cases, for example when designing a setup mimicking a curved space-time phenomena in a lab. The purpose of this thesis is to establish a new concept of transformation optics: instead of designing complicated materials, we will design our devices using standard optical elements such as lenses or optical wedges. We will stretch the possibilities of geometrical optics by providing a novel description of imaging due to combinations of tilted lenses and the theory of invisibility with ideal thin lenses. This theory will be then applied to design novel transformation optics devices, namely the omnidirectional lens and a number of ideal lens invisibility cloaks.

We also present a new approach of building optical systems that simulate light-field propagation in both 2D and 3D curved spaces. Instead of building the actual curved space, the light field is regarded to travel in the respective unfolded net, whose edges are optically identified, using the so-called space-cancelling wedges. By deriving a full analytical solution of the Schrodinger equation, we will also investigate a quantum motion in a number of two dimensional compact surfaces including the Klein bottle, Mobius strip and projective plane. We will show that the wavefunction exhibits perfect revivals on these surfaces and that quantum mechanics on many seemingly unphysical surfaces can be realised as simple diffraction experiments. Our work therefore offers a new concept of optical simulation of curved spaces, and potentially represents a new avenue for research of physics in curved spaces and simulating otherwise inaccessible phenomena in non-Euclidean geometries.

We conclude with a summary of potential future projects which lead naturally from the results of this thesis.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Keywords: Ray optics, physical optics, transformation optics, imaging systems, ideal lenses, invisibility, curved spaces.
Subjects: Q Science > QC Physics
Colleges/Schools: College of Science and Engineering > School of Physics and Astronomy
Supervisor's Name: Courtial, Dr. Johannes and Christoph, Dr. Englert
Date of Award: 2020
Depositing User: Mr Jakub Belin
Unique ID: glathesis:2020-81559
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 05 Aug 2020 13:14
Last Modified: 05 Aug 2020 13:26
URI: http://theses.gla.ac.uk/id/eprint/81559
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