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Off-axis twisted waveguides possess unique optical properties such ascircular and orbital angular momentum (OAM) birefringence, setting them apartfrom their straight counterparts. Analyzing mode formation in such helicalwaveguides relies on the use of specific coordinate frames that follow thetwist of the structure, making the waveguide invariant along one of the newcoordinates. In this study, the differences between modes forming inhigh-contrast off-axis twisted waveguides defined in the three most importantcoordinate systems - the Frenet-Serret, the helicoidal, or the Overfelt frame -are investigated through numerical simulations. We explore modalcharacteristics up to high twist rates (pitch: 50 $\mu$m) and clarify atransformation allowing to map the modal fields and the effective index back tothe laboratory frame.  In case the waveguide is single-mode, the fundamental modes of the threetypes of waveguides show significant differences in terms of birefringence,propagation loss, and polarization. Conversely, the modal characteristics ofthe investigated waveguides are comparable in the multimode domain.Furthermore, our study examines the impact of twisting on spatial modeproperties with the results suggesting a potential influence of the photonicspin Hall and orbital Hall effects. Additionally, modes of single-mode helicalwaveguides were found to exhibit superchiral fields on their surfaces.  Implementation approaches such as 3D-nanoprinting or fiber-preform twistingopen the doors to potential applications of such highly twisted waveguides,including chip-integrated devices for broadband spin- and OAM-preservingoptical signal transport, as well as applications in chiral spectroscopy ornonlinear frequency conversion.

Impact of coordinate frames on mode formation in twisted waveguides