42.00.00 Optics (for optical properties of gases, see 51.70.+f; for optical properties of bulk materials and thin films, see 78.20.-e; for x-ray optics, see 41.50.+h)
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There are a lot of photonic micro- and nano-structures in nature that consist of materials with a low refractive index and that can keep up with artificial structures concerning optical properties like scattering or coloration. This work aims to understand the photonic structures in the silver ant Cataglyphis bombycina, the blue butterfly of genus Morpho, the beetle Entimus imperialis, which shows polarization-dependent reflection, and the white beetle Cyphochilus insulanus. Furthermore, corresponding micro- and nano-structures are fabricated.
Bioinspired models with the same optical properties as the investigated structures are developed and analyzed using geometric optics and finite-difference time-domain calculations. These models are qualitatively and quantitatively compared regarding their optical properties with the original structures and fabricated by direct laser writing. To mimic potential effects of material-based disorder of the natural photonic structures, a cellulose-based resist for direct laser writing is developed and examined.
Conventional resists in direct laser writing can be replaced by a resist containing cellulose derivatives. Here, different combinations of cellulose derivatives, initiators, and solvents are examined. The best performance is observed for a combination of methacrylated cellulose acetate (MACA500), 2-Isopropyl-9H-thioxanthen-9-one (ITX), and dimethyl sulfoxide (DMSO). These resists allow for direction is attained. The achieved cross-linking enables stable three-dimensional structures and, together with the possible resolution, allows to fabricate the model inspired by the white beetle Cyphochilus insulanus in the cellulose-based resist.
The silver appearance of the Cataglyphis bombycina can be completely explained with geometric optics in the prism-shaped hairs that cover its body. The more complex structures of the other three insects use photonic crystal-like material arrangements with a varying amount of disorder. The polarization dependence of the Entimus imperialis arises from a diamond structure inside the scales of the beetle and can be mimicked with a photonic woodpile crystal. The blue butterfly of the genus Morpho and the white beetle Cyphochilus insulanus both can be reduced to disordered Bragg stacks, in which the exact properties are achieved by introducing different amounts of disorder. For Cataglyphis bombycina, Entimus imperialis, and Cyphochilus insulanus, the developed bioinspired models are fabricated using conventional resists in direct laser writing. All models show a qualitative correspondence to the optical properties of the original structures.
The cellulose-based resists enable the use of polysaccharides in direct laser writing and the concepts can be transferred to other polysaccharides, like chitin. The analysis of the different natural photonic structures and the developed bioinspired models reveal a material independence of the structures that allows the fabrication of these models in different transparent materials.
Topological insulators (TI) are a fascinating new state of matter. Like usual insulators, their band structure possesses a band gap, such that they cannot conduct current in their bulk. However, they are able to conduct current along their edges and surfaces, due to edge states that cross the band gap. What makes TIs so interesting and potentially useful are these robust unidirectional edge currents. They are immune to significant defects and disorder, which means that they provide scattering-free transport.
In photonics, using topological protection has a huge potential for applications, e.g. for robust optical data transfer [1-3] – even on the quantum level [4, 5] – or to make devices more stable and robust [6, 7]. Therefore, the field of topological insulators has spread to optics to create the new and active research field of topological photonics [8-10].
Well-defined and controllable model systems can help to provide deeper insight into the mechanisms of topologically protected transport. These model systems provide a vast control over parameters. For example, arbitrary lattice types without defects can be examined, and single lattice sites can be manipulated. Furthermore, they allow for the observation of effects that usually happen at extremely short time-scales in solids. Model systems based on photonic waveguides are ideal candidates for this.
They consist of optical waveguides arranged on a lattice. Due to evanescent coupling, light that is inserted into one waveguide spreads along the lattice. This coupling of light between waveguides can be seen as an analogue to electrons hopping/tunneling between atomic lattice sites in a solid.
The theoretical basis for this analogy is given by the mathematical equivalence between Schrödinger and paraxial Helmholtz equation. This means that in these waveguide systems, the role of time is assigned to a spatial axis. The field evolution along the waveguides' propagation axis z thus models the temporal evolution of an electron's wave-function in solid states. Electric and magnetic fields acting on electrons in solids need to be incorporated into the photonic platform by introducing artificial fields. These artificial gauge fields need to act on photons in the same way that their electro-magnetic counterparts act on electrons. E.g., to create a photonic analogue of a topological insulator the waveguides are bent helically along their propagation axis to model the effect of a magnetic field [3]. This means that the fabrication of these waveguide arrays needs to be done in 3D.
In this thesis, a new method to 3D micro-print waveguides is introduced. The inverse structure is fabricated via direct laser writing, and subsequently infiltrated with a material with higher refractive index contrast. We will use these model systems of evanescently coupled waveguides to look at different effects in topological systems, in particular at Floquet topological systems.
We will start with a topologically trivial system, consisting of two waveguide arrays with different artificial gauge fields. There, we observe that an interface between these trivial gauge fields has a profound impact on the wave vector of the light traveling across it. We deduce an analog to Snell's law and verify it experimentally.
Then we will move on to Floquet topological systems, consisting of helical waveguides. At the interface between two Floquet topological insulators with opposite helicity of the waveguides, we find additional trivial interface modes that trap the light. This allows to investigate the interaction between trivial and topological modes in the lattice.
Furthermore, we address the question if topological edge states are robust under the influence of time-dependent defects. In a one-dimensional topological model (the Su-Schrieffer-Heeger model [11]) we apply periodic temporal modulations to an edge wave-guide. We find Floquet copies of the edge state, that couple to the bulk in a certain frequency window and thus depopulate the edge state.
In the two-dimensional Floquet topological insulator, we introduce single defects at the edge. When these defects share the temporal periodicity of the helical bulk waveguides, they have no influence on a topological edge mode. Then, the light moves around/through the defect without being scattered into the bulk. Defects with different periodicity, however, can – likewise to the defects in the SSH model – induce scattering of the edge state into the bulk.
In the end we will briefly highlight a newly emerging method for the fabrication of waveguides with low refractive index contrast. Moreover, we will introduce new ways to create artificial gauge fields by the use of orbital angular momentum states in waveguides.