### Abstract

Left-handed materials are a new class of photonic materials that are characterised by a negative index of refraction. Their properties are very promising: light refracts negatively, evanescent waves can be restored to their original amplitude, etc. In this thesis, we will perform a theoretical study of photonic devices with layers of left-handed materials and we will try to improve the properties of these devices.First, a Bragg structure will be studied. Its unit cell contains a right- and a left-handed material layer. An analytic study of the structure will be conducted in order to find the dispersion relation of such an infinite Bragg structure. The transmission through a finite Bragg structure will also be investigated. Next, a qualitative analysis about the competition between the Bragg and Fabry-Perot conditions will be given. The left-handed material layer will bring substantial changes into this competition. For example, a new region of transmission will be found in some cases. This region has a very narrow transmission peak, making it possible to make very selective filters.

Next, a waveguide consisting of two layers, one left- and one right-handed material, in the core will be studied. As we can compensate the optical path length of optical rays, one could expect to reduce the thickness of the core, or even to reduce it to zero. From the dispersion relation, we find, however, that this is not true and that it is impossible to reduce the thickness of a waveguide. To get more insight into the reason for this, a geometric approach is used and we observe that the phase shifts, occurring during the process of reflection on the cladding, are responsible for the opposite results. Subsequently, we add a left-handed material to the cladding in order to influence the phase shifts due to reflection. Once again, an analytical study to find the dispersion relation and a geometrical study will be performed. We show that this geometry allows the phases of reflection to compensate themselves, thus removing the need for a core. To have confined modes, we will still need a core, but the total thickness of the waveguide can be reduced with at least one order of magnitude.

In the last part of this master thesis, we will investigate the energy of electromagnetic waves in left-handed materials. We rewrite Poynting's theorem such that it can be used for dispersive, magnetic media. Then, we consider a few simplified cases to show that the terms of this Poynting's theorem make sense for optical propagation.

Date of Award | 6 Sep 2007 |
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Original language | English |

Supervisor | Irina Veretennicoff (Promotor), Ronald Van Loon (Jury), Jan Danckaert (Jury), Philippe Tassin (Jury), Guy Van Der Sande (Jury), Roger Vounckx (Jury) & Philippe Tassin (Advisor) |

### Keywords

- optics
- photonics
- metamaterial
- left-handed material
- Bragg
- waveguide
- electromagnetic energy