Bennet, Francis Herbert

### Description

The action of light in periodic structures can be quite different to that in a homogenous medium. For example, while a nonlinear beam will spread out in a medium with a negative nonlinearity, in a periodic structure the beam is focused and a localised state is formed. In this thesis I will show my work on light propagation in tuneable nonlinear periodic photonic structures. Nature provides us with dazzling displays of periodic photonic structures in the form of butterfly wings, peacock...[Show more] feathers, and opals. How these magnificent natural spectacles work has been a source of great scientific interest since we mastered the modern scientific method. With new technologies we can utilise periodic photonic structures to control how light propagates, which wavelengths are transmitted or reflected, and how light moves between waveguiding structures. Coupled waveguides provide a platform in which to study the linear and nonlinear light propagation and interaction in periodic photonic structures. Nonlinearity in optics provides a feedback mechanism which allows one beam of light to influence the propagation of another, or even itself. Advancements in our understanding of how light propagates and interacts in nonlinear periodic photonic structures is leading us to new and interesting areas of Physics. It is hoped that one day photons and photonic components can be used in place of electrons in electronic components widely used today. This will propel our computing power and further advance our understanding of the physical universe. In order to fully understand how light behaves in photonic structures and to make use of nonlinear features to allow light to control light, we first must understand the fundamental interactions of light in linear and nonlinear periodic photonic structures. We must be able to tune the properties of the system to investigate the fundamental behaviour of nonlinear beam propagation. In this thesis I investigate light propagation in tuneable nonlinear periodic photonic structures. I begin by introducing relevant concepts and ideas necessary to understand my work (Chapter 1). Included in this introduction is theoretical and experimental work I conducted with two interacting beams in a bulk nonlinear liquid (Sec. 1.4.6). I discover that a high power pump beam influences the nonlinear medium in a way which locally alters its refractive index. This alteration occurs due to a change in temperature of the medium caused by absorption of the pump beam and results in the reflection of a probe beam from the pump beam. I then present my research on the development of two platforms in which liquid is used to guide light in a one-dimensional (1D) periodic array. The first platform is made from photolithographically defined air-filled channels in SU8 polymer (Sec. 2.1). These channels are infiltrated with an index matching oil and the linear diffraction is observed as the temperature of the platform is changed. I find that the discrete diffraction observed matches very well with an accompanying theoretical model of the system, and I am able to estimate the temperature of the liquid in the channels. The second platform for light propagation in a 1D periodic array is developed using selectively infiltrated Photonic Crystal Fibres (Sec. 2.2). I use a simple method of blocking an inverse pattern with oil on one side of the fibre. The other end of the fibre is then submersed in a reservoir of the infiltrating liquid to fill any unblocked holes. I produce a 1D periodic array in a of coupled waveguides and demonstrate temperature tuneable linear diffraction, and nonlinear defocusing. I then move on to present my observation of truncated nonlinear Bloch waves in Lithium Niobate waveguide arrays (Sec. 2.3). Such states are excited with a broad Gaussian input beam in a 1D array of coupled nonlinear waveguides. This state is different from well known solitons and nonlinear Bloch modes because it contains features of both: a constant phase across all guiding waveguides characteristic of a nonlinear Bloch wave, with sharp edges otherwise seen in gap solitons. This work is supported by theoretical modelling, and I am able to show that the width of the soliton is dependant only on the width of the input beam, in contrast to discrete or gap solitons who's width depends on the nonlinearity. Chapter 3 then exhibits my work with liquid infiltrated Photonic Crystal Fibres as a two-dimensional (2D) periodic array of nonlinear waveguides. Firstly I show the existence and excitation conditions of nonlocal gap solitons (Sec. 3.1), where the properties of the system far from the light field influence soliton formation. I find that below a certain refractive index contrast these solitons are no longer excitable and the beam only defocuses. I then present my work on this crossover from focusing to defocusing in nonlinear periodic systems (Sec. 3.2). I show that the bandgap closes before the index contrast reaches zero, and that the system crosses from focusing to defocusing before the bandgap is fully closed. I will finally discuss my theoretical and experimental work on vortex beams propagating around a surface in a nonlinear hexagonal array (Sec. 3.3). I use liquid infiltrated Photonic Crystal Fibres and propagate a vortex beam around the core defect of the fibre. I find that nonlinear vortex modes of charge one are unstable and will focus to occupy a single waveguide on the surface of the core using the discrete model. A continuous model shows that linear and nonlinear charge one vortex modes are unstable and result in an asymmetric output. Linear charge three vortex modes show greater stability due to the staggered phase profile of the input beam, while nonlinear charge three vortex modes lose symmetry at the output due to a loss of this phase profile. I will finish this thesis with conclusions about my work and ideas for future directions this work could take, including specific experimental ideas directly related to this work. I will include some ideas as to the future direction these ideas may provide.

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