Modeling loss and backscattering in a photonic-bandgap fiber using strong perturbation

We use coupled-mode theory with strong perturbation to model the loss and backscattering coefficients of a commercial hollow-core fiber (NKT Photonics’ HC-1550-02 fiber) induced by the frozen-in longitudinal perturbations of the fiber cross section. Strong perturbation is used, for the first time to the best of our knowledge, because the large difference between the refractive indices of the two fiber materials (silica and air) makes conventional weak-perturbation less accurate. We first study the loss and backscattering using the mathematical description of conventional surface-capillary waves (SCWs). This model implicitly assumes that the mechanical waves on the core wall of a PBF have the same power spectral density (PSD) as the waves that develop on an infinitely thick cylindrical tube with the same diameter as the PBF core. The loss and backscattering coefficients predicted with this thick-wall SCW roughness are 0.5 dB/km and 1.1×10^-10 mm^-1, respectively. These values are more than one order of magnitude smaller than the measured values (20−30 dB/km and ~1.5×10^-9 mm^-1, respectively). This result suggests that the thick-wall SCW PSD is not representative of the roughness of our fiber. We found that this discrepancy occurs at least in part because the effect of the finite thickness of the silica membranes (only ~120 nm) is neglected. We present a new expression for the PSD that takes into account this finite thickness and demonstrates that the finite thickness substantially increases the roughness. The predicted loss and backscattering coefficients predicted with this thin-film SCW PSD are 30 dB/km and 1.3×10^-9 mm^-1, which are both close to the measured values. We also show that the thin-film SCW PSD accurately predicts the roughness PSD measured by others in a solid-core photonic-crystal fiber.