Coupling between two collinear air-core Bragg fibers

We characterize coupling between two identical collinear hollow core Bragg fibers, assuming TE01 launching condition. Using multipole method and finite element method we investigate dependence of the beat length between supermodes of the coupled fibers and supermode radiation losses as a function of the inter-fiber separation, fiber core radius and index of the cladding. We established that coupling is maximal when fibers are touching each other decreasing dramatically during the first tens of nanometers of separation. However, residual coupling with the strength proportional to the fiber radiation loss is very long range decreasing as an inverse square root of the inter-fiber separation, and exhibiting periodic variation with inter-fiber separation. Finally, coupling between the TE01 modes is considered in a view of designing a directional coupler. We find that for fibers with large enough core radii one can identify broad frequency ranges where inter-modal coupling strength exceeds super-mode radiation losses by an order of magnitude, thus opening a possibility of building a directional coupler. We attribute such unusually strong inter-mode coupling both to the resonant effects in the inter-mirror cavity as well as a proximity interaction between the leaky modes localized in the mirror.