Highly-efficient mode calculations for novel optical fiber designs

• Applicant: Professor Dr. Thomas Weiss
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 449609999

Optical fibers build a key element in our modern information society. Conventional fibers guide light through total internal reflection. Such fibers are easy to fabricate and yield sufficiently low loss for most applications. However, they provide limited tuning capabilities, since the only degrees of freedom are the material decomposition and the core radius, and they require core materials with a higher refractive index than in the surrounding in order to enable total internal reflection. Several alternative fiber concepts have emerged recently that overcome these limitations such as bandgap photonic crystal fibers and antiresonant fibers. For understanding the physical mechanisms in such fibers and for designing fibers for particular applications, numerical modeling is of utmost importance. However, numerical calculations for these novel fibers are extremely challenging. One reason is that their structured cladding has to be resolved accurately, and it includes not only sub-wavelength elements, but spans over areas that can exceed more than ten wavelengths in diameter. Another reason is that the optical response of these fibers is dominated by so-called leaky modes, which radiate part of their energy perpendicularly to the direction of propagation. This contribution is often orders of magnitude smaller than the axial energy density, which needs to be resolved properly for the prediction of the radiative loss. Hence, conventional numerical calculations are often inaccurate or time-consuming.In this project, we aim for establishing a novel type of numerical method for such geometries with leaky modes. Particularly, we plan to extend the so-called resonant-state expansion for these structures by geometry-adapted longitudinal modes. The resonant-state expansion uses modes of a trivial geometry as basis to set up an eigenvalue problem for calculating the modes in a complex geometry. It is well-established for resonant states and permittivity eigenmodes in three-dimensional resonators, where it has been shown that longitudinal modes need to be implemented for changes of material interfaces between the trivial and the target geometry. We will not only extend this concept to guiding geometries, but also develop first- and second-order perturbation theories for frequency changes. This will allow us to directly obtain the most relevant properties for mode propagation including the group velocity and its dispersion from calculations at a single frequency. Furthermore, we will consider coupled-mode theory for longitudinal changes in guiding geometries in order to build up a universal tool for complex fiber designs. We will use this approach to study the impact of transverse and longitudinal perturbations, so that we can develop design rules for robust and stable light guiding.

• DFG Programme: Research Grants
• International Connection: Austria, Israel
• International Co-Applicant: Professor Yonatan Sivan, Ph.D.