Theoretical modelling of the Faraday effect within a gas-filled photonic bandgap fiber

Recently we have demonstrated that conventional (free-space) Faraday rotation spectroscopy (FRS) can be successfully
transitioned into optical fiber-based sensing architectures using paramagnetic gas-filled hollow-core photonic bandgap
fibers (HC-PCFs)1. Our measurements revealed that due to the birefringence properties of the HC-PCFs, behavior of the
fiber-optic FRS signals is substantially different compared to free-space FRS systems. Furthermore, magnetic circular
dichroism tends to have much higher influence on the FRS signals than in other systems. To explain this behavior we
have developed a theoretical model, and shown that close agreement with the experimental data can be achieved. In this
paper we focus attention on the detailed explanation and the in-depth discussion of the model and assumptions
incorporated within it. This approach can be easily extended to account for parasitic effects that take place in real-world
FRS sensor systems such as imperfect polarizers or birefringent gas cell windows.