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

• Dynamics of mode coupling at imperfect Fresnel reflecting surfaces explored by Optical Frequency Domain Reflectometry . • A unique hybrid backward mode with a group velocity closely approximating the average of the LP 01 and LP 11 modes. • The hybrid mode peak consistently appears at half the frequency spacing between the LP 01 and LP 11 peaks. • The linear relationship between beat frequency differences and fiber length , confirming theoretical predictions. • Implications for mode division multiplexing optical fiber communications , particularly in defect mitigation at end faces. 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 LP 01 (LP 11 ) mode with group velocity v g LP 01 ( v g LP 11 ) partially converts to the backward LP 11 (LP 01 ) mode with v g LP 11 ( v g LP 01 ) 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 LP 01 and LP 11 peaks. Additionally, the frequency difference between the hybrid and LP 01 (or LP 11 ) modes is calculated to be 20.625 Hz exactly half of the 41.250 Hz difference between the LP 01 and LP 11 modes. Further testing on five additional fiber segments ranging from 8.812 m to 10.812 m corroborates this theory, as their v g hybrid 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.