Automated numerical calculation of Sagnac correction for photonic paths

Abstract

Relativistic effects must be taken into account for highly accurate time and frequency transfers. The most important is the Sagnac correction which is also source of non-reciprocity in various directions of any transfer in relation with the Earth rotation. In this case, not all important parameters as exact trajectory of the optical fibre path (leased fibres) are known with sufficient precision thus it is necessary to estimate lower and upper bounds of computed corrections. The presented approach deals with uncertainty in knowledge of detailed fibre paths, and also with complex paths with loops. We made the whole process of calculation of the Sagnac correction fully automated.