This thesis presents an investigation into some of the structural colours that are produced in nature. There are many animals and plants that produce structural colour, with a particularly high structural colour diversity in insects. Of the species that exhibit structural colours, three species are the subjects for investigation of this thesis. Those comprise a group of beetles from South-East Asia, Torynorrhina flammea, a buttery, Parides sesostris and a fruit, Margaritaria nobilis, both from South American rainforests. The structures that produce the vivid colours of these species were analysed using electron microscopy. This information aided the design and creation of three inorganic, synthetic replicas of the natural structures. The fruit of Margaritaria nobilis was structurally analysed, yielding the discovery of a novel multilayer fibre. These fibres were cylindrical in design and were found to be layered together producing the epidermis of the fruit. The multilayer structure produced a vivid blue colour appearance, which is believed to offer a selective advantage because the colour deceives birds into thinking that the fruit contains nutritious flesh. This selective advantage earns M. nobilis the label of mimetic fruit. The structure found within the M. nobilis fruit epidermis inspired the synthesis of a structure which comprises single cylindrical multilayer fibres. The synthetic fibres were manufactured from elastic materials which allow the structure to be deformed under strain and, therefore, a change in colour can be observed. As the structure was stretched, this made the layers get thinner and, therefore, the colour of the fibre blue-shifted. The fibre was able to be stretched to over twice its original length which yields a shift in peak reflected wavelength of over 200 nm. Four beetles from the Torynorrhina flammea species were investigated with the aim of replicating the nanostructures responsible for their colour appearance. The initial interest in the beetles came from their strikingly vivid colour appearances. The structure responsible for the vivid colours in all four of the subspecies is a multilayer with high structural order and over 100 laminae. Both of these attributes contribute to the saturation of the colours exhibited. The multilayer was found to be intersected by an array of rods, the long axis of which is orthogonal to the surface. The rods are believed to be the cause of an interesting diffraction phenomenon exhibited by the beetles. Using imaging scatterometry, the structure was found to diffract the colour produced by the multilayers into an annulus around a specularly reflected white spot. This inspired the synthesis of a multilayer permeated with an array of holes with the aim of replicating a system that could reproduce the annular pattern of colour reflection. The initial synthesised system comprised a quarter-wave stack with a perfectly ordered hexagonal array of holes permeating the surface orthogonally. The sample displayed the scattering characteristics of a hexagonal array, and the reflection spectra of the multilayer stack. When disordered hexagonal arrays were milled into the structure with a focussed ion beam, the scattering pattern started to show more of the green colour from the multilayer and less of the ordered scattering pattern. The highly disordered, synthesised structure displayed no hexagonal scattering pattern, but instead it showed a highly scattered bluish-green colouration. One sample was created by directly mapping out the array of holes using an image of the original array from one of the beetle samples. This sample was expected the same annular diffraction pattern as the beetles, however, the sample instead exhibited the same scattering pattern as the highly disordered array. Some structurally coloured systems in nature have more than one light scattering structure, all of which contribute to the overall colour of the system. For complicated systems such as this, it is necessary to devise a technique to characterise the individual scattering structures separately. One such species that displays a complex, multicomponent system is Parides sesostris. The male of the species displays bright green patches on the dorsal side of the forewings which are made up of thousands of green wing scales. These green scales contain a 3D gyroid poly-crystal at centre with a membrane layer surrounding the underside of each scale and a scattering structure on top. Using focussed ion beam milling techniques allowed the individual characterisation of each of these structures. The gyroid poly-crystal was found to reflect not green but blue wavelengths. This led to the discovery by another group [1] that the scales contain at least one type of fluorophore. The removal of the membrane structure and some of the gyroid poly-crystal from the base of the scale resulted in the change of the overall scale structure from green to cyan. This suggests that the membrane maybe a significant source of fluorescence. Computational modelling, without fluorescence, suggests that the addition of the membrane layer to the gyroid does not shift the band-gap wavelengths; however, the overall reflection intensity does increase. The scattering structure on the top side of each scale is comprised a bi-grating which sits on top of the 3D gyroid structure. The long periodicity of the bi-grating protrudes above the surface, resulting in the very top layer of the scale to be a mono-grating. This whole structure decreases the angular-dependence of the colour by efficiently scattering the incident light into the gyroid and also scattering the reflected light from the gyroid, resulting in a double-scattering. FIB-milling was used to isolate the scattering part of the structure. Analysis of this component of the structure revealed that it was not a source of the green colour itself; however, it did show the characteristic scattering pattern of a mono-grating. The small periodicity of the bi-grating did not produce a scattering pattern since the periodicity is too small to produce optical diffraction at normal incidence. To characterise the effect of the fluorophores, the whole scale structure was photo-bleached using ultra-violet radiation for two months with the aim of destroying the fluorophores contained within the structure. The expected result occurred which was the blue-shifting of the peak reflected wavelengths. However, it could not be confirmed whether or not the photo-bleaching reduced the physical size of the light scattering structures which would, in theory, result in a blue-shift of the peak reflected wavelengths. The male P. sesostris green wing scales were also the subject for investigation for trying to make inorganic replicas of the gyroid-polycrystal. A surface sol-gel coating process was utilised to coat the green wing scales with titania. This coating process was performed using a few different methods. Half of the samples were coated with TiO2 and the other half with tin-doped TiO2. Half of each of these samples had their surfaces dendritically amplified before the coating processes and the other half were left untreated. The samples were coated with 25 surface sol-gel (SSG) cycles of each treatment at a time. After each 25 cycle treatment the samples were optically characterised. The total number of cycles applied to the samples at the end was 150. The addition of layers of titania resulted in a general red-shift that was higher for the tin-doped titania samples than for the titania samples. Another general trend found was that the samples that had their surfaces dendritically amplified, produced a lower red-shift in peak wavelength. This was contrary to the hypothesis that the amplification process was supposed to aid the SSG coating process and, therefore, increases the red-shift in peak wavelength.

The field of nanophotonics is a major research topic, as it offers potential solutions to important challenges, such as the creation of low power, high bandwidth interconnects or optical sensors. Within this field, resonant structures and slow light waveguides are used to improve device performance further. Photonic crystals are of particular interest, as they allow the fabrication of a wide variety of structures, including high Q-factor cavities and slow light waveguides. The high scattering loss of photonic crystal waveguides, caused by fabrication disorder, however, has so far proven to be the limiting factor for device applications. In this thesis, I present a detailed study of propagation loss in slow light photonic crystal waveguides. I examine the dependence of propagation loss on the group index, and on disorder, in more depth than previous work by other authors. I present a detailed study of the relative importance of different components of the propagation loss, as well as a calculation method for the average device properties. A new calculation method is introduced to study different device designs and to show that photonic crystal waveguide propagation loss can be reduced by device design alone. These “loss engineered” waveguides have been used to demonstrate the lowest loss photonic crystal based delay line (35 dB/ns) with further improvements being predicted (< 20 dB/ns). Novel fabrication techniques were investigated, with the aim of reducing fabrication disorder. Initial results showed the feasibility of a silicon anneal in a nitrogen atmosphere, however poor process control led to repeatability issues. The use of a slow-fast-slow light interface allowed for the fabrication of waveguides spanning multiple writefields of the electron-beam lithography tool, overcoming the problem of stitching errors. The slow-fast-slow light interfaces were combined with loss engineering waveguide designs, to achieve an order of magnitude reduction in the propagation loss compared to a W1 waveguide, with values as low as 130 dB/cm being achieved for a group index around 60.

The presence of photonic band gap in an arbitrarily shaped photonic structure, particularly structures that are fabricated by exploiting rolled-up nanotechnology, can be understood from the density of optical states. In this thesis, the density of optical states and the local density of optical states in finite-sized photonic structures are calculated using the finite difference time domain method together with a parallelized message passing interface. With this approach, a software package suitable for high-performance computing on multi-platform was published under GNU GPL license. When light is guided to propagate along a rolled-up thin film, whispering gallery mode resonances can be formed in a microtubular structure. Dynamic probing and tuning via a plasmonic nanoparticle-coated glass tip are investigated to demonstrate the transition from dielectric-dielectric to dielectric-plasmonic coupling in the tubular microcavity. The competition of these two coupling mechanisms allow the tuning of the optical cavity modes towards lower and then higher energies in a single coupling system. Moreover, three dimensionally confined higher order axial modes can be selectively coupled and tuned by the glass tip due to their unique spatial distribution of the optical field along the tube axis. In addition, the interaction between sharp optical cavity modes and broad plasmonic modes supported by silver nanoparticles leads to the occurrence of Fano resonance. In particular, Fano resonances occurring at higher-order axial modes has been observed as well. The experimental results are supported by numerical simulations based on the finite difference time domain method. In photonic lattice structures, light propagation behavior can be influenced and defined by the photonic band structure. By designing the unit cell with glide mirror symmetry, topologically protected edge states operating in the visible spectral range have been proposed in two dimensional photonic crystals which can be made of feasible materials. Topological phenomena such as unidirectional waveguiding and/or effective zero refractive index are presented. In addition, a scheme to study topological phase transition in a single photonic crystal device is proposed and studied via unevenly stretching photonic lattice. Moreover, a new method is explored to distinguish the topological phase from the bulk modes. The research presented in this thesis concerns molding the flow of light in specially designed photonic devices for various potential applications. The software package can be used to design and investigate finite-sized photonic structures with an arbitrary shape, which is much faster in terms of computation than other reported techniques and software packages. The rolled-up microcavities can be employed to trap and store light in the way of whispering gallery mode resonances, and the resonant light can be tuned and modulated by a plasmonic nanoparticles-coated glass tip. This research is particularly interesting for optical signal processing, slowing light via Fano resonances, and high sensitive sensing. In addition, the topological photonic crystal design and examination scheme presented in this thesis provide a simplified yet more efficient way to obtain non-trivial topological phase from a tunable photonic crystal that can be verified not only by edge modes but also by bulk modes.:Bibliographic record 1 Abstract 1 LIST OF ABBREVIATIONS and Symbols 3 1 Introduction 9 1.1 Introduction and Motivation 9 1.2 Objectives 11 1.3 Organization of the thesis 12 2 Density of optical states in rolled-up photonic crystals and quasi crystals 15 2.1 Introduction 15 2.1.1 background 17 2.1.2 Infinitely extended ideal photonic crystal 17 2.2 Finite-sized photonic crystal, photonic quasicrystal, and arbitrary photonics structures 20 2.2.1 Numerical algorithm 25 2.2.2 Rolled-up photonic crystals and quasi crystals 30 2.3 Software package 33 2.3.1 Computational performance 33 2.3.2 FPS User interface 35 2.3.3 Detailed tutorial 37 2.3.4 Alternative rolled-up photonic crystals 47 2.3.5 Beyond 3D photonic crystals. 48 2.4 Conclusion 49 3 Rolled-up microesonator 51 3.1 Introduction 51 3.2 Rolled-up microresonators 52 4 Tip-assisted photon-plasmon coupling in three-dimensionally confined microtube cavities 57 4.1 Introduction 57 4.2 Tube and plasmonic particle preparation and characterization 60 4.3 Results and discussion 62 4.4 Axial mode tuning 64 4.5 Fano resonance 65 4.5.1 Background 65 4.5.2 Fano resonance in the tip assisted coupling setup 68 4.6 Conclusion 71 5 Topological photonics 73 5.1 Introduction and motivation 73 5.2 Topological phase transition point 77 5.2.1 Fundamental phase transition point 77 5.2.2 Zero refractive index material 79 5.3 Non-trivial topology in realistic materials 80 6 Topological phase transition in stretchable photonic crystals 85 6.1 Introduction and motivation 85 6.2 SSH model 88 6.3 Photonic crystal 91 6.4 Band structure and end modes of the photonic crystal 99 6.5 Conclusion 101 7 Summary and outlook 103 7.1 Summary 103 7.2 Outlook 104 Bibliography 111 List of figures 127 Publications 133 Acknowledgments 136 Selbständigkeitserklärung 137 Curriculum Vitae 138