Mode coupling at an imperfect Fresnel surface in a fluorine-trench dual-mode fiber

Mode coupling, often overlooked at an imperfect Fresnel surface, is now examined in a fluorine-trench dual- mode fiber to avoid energy losses and signal degradation. For invisible defects on the reflecting surface, the orthogonal forward LP01 (LP11) mode with group velocity v gLP 01 (vgLP11) partially converts to the backward LP11 (LP01) mode with v gLP 11 (vgLP01) through a transfer matrix, respectively. Consequently, this interaction generates a unique hybrid backward mode, which results in an average round-trip time delay and the mean of the velocities, ( v g LP 01 + v g LP 11 )/2. Upon harvesting and analyzing the backward reflections using a high-resolution coherent optical frequency domain reflectometry, a Fresnel reflection peak corresponding to the hybrid mode is observed with a high signal-to-noise ratio precisely between the LP01 and LP11 peaks. Additionally, the frequency difference between the hybrid and LP01 (or LP11) modes is calculated to be 20.625 Hz exactly half of the 41.250 Hz difference between the LP01 and LP11 modes. Further testing on five additional fiber segments ranging from 8.812 m to 10.812 m corroborates this theory, as their v ghybrid values align closely with ( v g LP 01 + v g LP 11 )/2. Our analytical insights detail the dynamic mode coupling at an imperfect Fresnel surface, promising a flexible method for dynamic mode observation and regulation for mode division multiplexing optical fiber communications, particularly in enhancing the detection and mitigation of defects at fiber lasing end faces.