Light propagation in free-form dielectric waveguides: a modal perspective

Light propagation in curved waveguides has recently attracted increasing attention due to their numerous applications and advancements in fabrication technologies. For instance, emerging three-dimensional nano-printing techniques enable the production of photonic wire bonds that connect different photonic integrated circuits to form complete chips. Curved waveguides and ring resonators can also be employed to generate nonclassical states of light on a chip, provided that nonlinear effects occur in these structures. The nonclassical states of light are crucial for on-chip quantum photonic technologies such as quantum communication and computation.

While numerical solvers for Maxwell’s equations facilitate the study of light propagation in free-form waveguides, the large spatial extent of the waveguides often excludes these approaches. This limitation necessitates the development of approximate methods to describe light propagation in curved waveguides, exploiting the fact that light is guided through propagating modes. An understanding of the modal properties of curved photonic structures such as waveguides and disk-shaped resonators is essential for their effective design.
... mehr

This thesis investigates light propagation and mode interactions in curved waveguides from various perspectives. We present a modal approach to analyse light propagation and losses in free-form waveguides. Changing the curvature of a waveguide may lead to excitement of multiple-modes in this waveguide. The number of supported modes depends on the size and refractive index contrast between the waveguide's core and the cladding. We introduce a multi-mode approximation method for calculating transmission through free-form waveguides. The obtained transmission is used as an objective function to identify the optimal waveguide trajectory in just a few minutes. These trajectories are optimised to minimise propagation losses caused by bends, while adhering to various constraints.

Additionally, we explore the enhancement of nonlinearity in bent waveguides, while considering propagation losses. We demonstrate that bending a waveguide may reduce the effective mode area, which in turn locally increases the intensity of the guided light. This enhances nonlinear interactions and boosts photon pair generation rates, significantly improving the efficiency of signal-processing devices in integrated photonic circuits.

Finally, we analyse mode interactions in disk-shaped whispering gallery resonators. Similarly to the bent waveguides, where the electromagnetic field localises near the outer side of the bend, in disk-shaped resonators, the field localises at the rim, creating resonances through the formation of standing waves. These resonators can be viewed as extreme cases of bent waveguides with a constant radius of curvature. The radiation modes emitted from these structures pose challenges in capturing their properties. We utilise a cross-energy scalar product to analyse these radiation modes, determining the resonator's dimensions at which the orthogonality between resonant modes is disrupted, leading to interactions between them.