Cumulative Polarization Rotation Angle in Fiber-Optic Communication Lines Under Lightning Electromagnetic Impact

Abstract

The problem of quantitative description of the total effect of electromagnetic fields of lightning discharges on the polarization state (SOP) of light in fiber-optic communication lines (FOCL) of the ITU-T G. 652 standard is considered. The cumulative angle parameter is proposed, which is defined as the integral of the norm of the local Stokes rotation vector along the line length, taking into account random birefringence, magnetooptical Faraday effect and electro-optical Kerr effect. Using the Jones matrix formalism, analytical expressions for cumulative polarization rotation angle are obtained in terms of the Verde constant, the induction of the lightning magnetic field, and the correlation length of the polarization-mode dispersion (PMD). It is established that the cumulative angle is related to the dynamic differential group delay (DGD), as well as to the quantum error coefficient QBER for the BB84 quantum key distribution (QKD) protocol. Based on the obtained dependences, a classification of exposure modes (I-IV) is formed according to the lightning current amplitude and the distance to the discharge channel. Numerical estimates are derived for SSMF (G. 652), DSF (G. 653), and NZ-DSF (G. 655) fibers with line lengths up to 50 km and lightning currents of$\mathbf{1 0 - 1 0 5 ~ k A}$. It is shown that at Category I currents (over 105 kA) at a distance of 100 m, the rate of SOP change reaches$17.5 \text{Mrad} / \mathrm{s}$, which leads to a critical increase in QBER and termination the QKD session. The results allow us to use the cumulative angle as a single integral criterion for lightning resistance of high-speed and quantum fiber-optic lines in the design of routes and justification of lightning protection parameters.