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Determination of the mode reflection coefficient in air-core photonic bandgap fibers.

Using an eigenmode decomposition technique, we numerically determine the backreflection coefficient of the modes of air-core photonic bandgap fibers for flat terminations. This coefficient is found to be very small for the fundamental air-guided mode, of the order of 10(-5) to 10(-6), in contrast with the surface and bulk modes, which exhibit significantly higher reflections, by about three to four orders of magnitude. For the Crystal Fibre HC-1550-2 fiber, we find a reflection coefficient of 1.9x10(-6) for an air termination, and approximately 3.3% for a silica termination. We also find that the Fresnel approximation is ill suited for the determination of the modal reflection coefficient, and instead propose a more accurate new formula based on an averaged modal index.